%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW224+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 18:18:53 EDT 2024

% Result   : Theorem 29.97s 30.19s
% Output   : Proof 29.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.24  % Problem    : SWW224+1 : TPTP v8.2.0. Released v5.2.0.
% 0.25/0.25  % Command    : do_cvc5 %s %d
% 0.25/0.46  % Computer : n003.cluster.edu
% 0.25/0.46  % Model    : x86_64 x86_64
% 0.25/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.46  % Memory   : 8042.1875MB
% 0.25/0.46  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.25/0.46  % CPULimit   : 300
% 0.25/0.46  % WCLimit    : 300
% 0.25/0.46  % DateTime   : Sun May 26 04:29:39 EDT 2024
% 0.25/0.46  % CPUTime    : 
% 0.56/0.85  %----Proving TF0_NAR, FOF, or CNF
% 29.97/30.19  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 29.97/30.19  --- Run --no-e-matching --full-saturate-quant at 5...
% 29.97/30.19  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 29.97/30.19  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 29.97/30.19  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 29.97/30.19  % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.8f6EC8uEMZ/cvc5---1.0.5_7543.smt2
% 29.97/30.19  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.8f6EC8uEMZ/cvc5---1.0.5_7543.smt2
% 29.97/30.19  (assume a0 (forall ((V_ga_2 $$unsorted) (V_fa_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_fa_2 B_x) (tptp.hAPP V_ga_2 B_x))) (= V_fa_2 V_ga_2))))
% 29.97/30.19  (assume a1 (forall ((V_ra_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x_2 V_a_2)) V_ra_2) (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ra_2) V_x_2) (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_ra_2)))))))
% 29.97/30.19  (assume a2 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 29.97/30.19  (assume a3 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d)))))))
% 29.97/30.19  (assume a4 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 29.97/30.19  (assume a5 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 29.97/30.19  (assume a6 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 29.97/30.19  (assume a7 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 29.97/30.19  (assume a8 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 29.97/30.19  (assume a9 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 29.97/30.19  (assume a10 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))))
% 29.97/30.19  (assume a11 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_y)))))
% 29.97/30.19  (assume a12 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 29.97/30.19  (assume a13 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 29.97/30.19  (assume a14 (forall ((V_x_2 $$unsorted) (V_ga_2 $$unsorted) (V_fa_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_fa_2 V_ga_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_fa_2 V_x_2) (tptp.hAPP V_ga_2 V_x_2))))))
% 29.97/30.19  (assume a15 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x))))))
% 29.97/30.19  (assume a16 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= V_x V_y))))))
% 29.97/30.19  (assume a17 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))))
% 29.97/30.19  (assume a18 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= V_x V_y))))))
% 29.97/30.19  (assume a19 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))))
% 29.97/30.19  (assume a20 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))))
% 29.97/30.19  (assume a21 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))))
% 29.97/30.19  (assume a22 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))))
% 29.97/30.19  (assume a23 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 29.97/30.19  (assume a24 (forall ((V_x_2 $$unsorted) (V_ga_2 $$unsorted) (V_fa_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_fa_2 V_ga_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_fa_2 V_x_2) (tptp.hAPP V_ga_2 V_x_2))))))
% 29.97/30.19  (assume a25 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 29.97/30.19  (assume a26 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))
% 29.97/30.19  (assume a27 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 29.97/30.19  (assume a28 (forall ((V_ga_2 $$unsorted) (V_fa_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_fa_2 V_ga_2) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_fa_2 B_x) (tptp.hAPP V_ga_2 B_x)))))))
% 29.97/30.19  (assume a29 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 29.97/30.19  (assume a30 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 29.97/30.19  (assume a31 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 29.97/30.19  (assume a32 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 29.97/30.19  (assume a33 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))))
% 29.97/30.19  (assume a34 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))))
% 29.97/30.19  (assume a35 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))))
% 29.97/30.19  (assume a36 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))))
% 29.97/30.19  (assume a37 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 29.97/30.19  (assume a38 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (not (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 29.97/30.19  (assume a39 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_y V_x))))))
% 29.97/30.19  (assume a40 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))))
% 29.97/30.19  (assume a41 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 29.97/30.19  (assume a42 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 29.97/30.19  (assume a43 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))))
% 29.97/30.19  (assume a44 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 29.97/30.19  (assume a45 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))))
% 29.97/30.19  (assume a46 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 29.97/30.19  (assume a47 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2) (= V_x_2 V_y_2))))))
% 29.97/30.19  (assume a48 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))))
% 29.97/30.19  (assume a49 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_x)))))
% 29.97/30.19  (assume a50 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))))
% 29.97/30.19  (assume a51 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 29.97/30.19  (assume a52 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 29.97/30.19  (assume a53 (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2)) (= V_b_2 V_c_2)))))
% 29.97/30.19  (assume a54 (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2)) (= V_b_2 V_c_2)))))
% 29.97/30.19  (assume a55 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 29.97/30.19  (assume a56 (forall ((V_da_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_da_2)) (= (= V_a_2 V_b_2) (= V_c_2 V_da_2))))))
% 29.97/30.19  (assume a57 (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z) (= V_z V_w)))))
% 29.97/30.19  (assume a58 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_k)))))
% 29.97/30.19  (assume a59 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))))
% 29.97/30.19  (assume a60 (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_w)))
% 29.97/30.19  (assume a61 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 29.97/30.19  (assume a62 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 29.97/30.19  (assume a63 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 29.97/30.19  (assume a64 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 29.97/30.19  (assume a65 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 29.97/30.19  (assume a66 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 29.97/30.19  (assume a67 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 29.97/30.19  (assume a68 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y))))))
% 29.97/30.19  (assume a69 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))))
% 29.97/30.19  (assume a70 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 29.97/30.19  (assume a71 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))))
% 29.97/30.19  (assume a72 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 29.97/30.19  (assume a73 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 29.97/30.19  (assume a74 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 29.97/30.19  (assume a75 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))))
% 29.97/30.19  (assume a76 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 29.97/30.19  (assume a77 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 29.97/30.19  (assume a78 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))))
% 29.97/30.19  (assume a79 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (= V_x_2 V_y_2)))))))
% 29.97/30.19  (assume a80 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 29.97/30.19  (assume a81 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)))))
% 29.97/30.19  (assume a82 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))
% 29.97/30.19  (assume a83 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))))
% 29.97/30.19  (assume a84 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))))
% 29.97/30.19  (assume a85 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 29.97/30.19  (assume a86 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 29.97/30.19  (assume a87 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 29.97/30.19  (assume a88 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))))
% 29.97/30.19  (assume a89 (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))))
% 29.97/30.19  (assume a90 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))))
% 29.97/30.19  (assume a91 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))))
% 29.97/30.19  (assume a92 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 29.97/30.19  (assume a93 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 29.97/30.19  (assume a94 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 29.97/30.19  (assume a95 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))))
% 29.97/30.19  (assume a96 (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))))
% 29.97/30.19  (assume a97 (forall ((V_da_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_da_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_da_2))))))
% 29.97/30.19  (assume a98 (forall ((V_da_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_da_2)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_da_2))))))
% 29.97/30.19  (assume a99 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) V_a))))
% 29.97/30.19  (assume a100 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))))
% 29.97/30.19  (assume a101 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))))
% 29.97/30.19  (assume a102 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 29.97/30.19  (assume a103 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (= V_x_2 V_y_2)))))
% 29.97/30.19  (assume a104 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (not (= V_x_2 V_y_2))))))
% 29.97/30.19  (assume a105 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 29.97/30.19  (assume a106 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus T_a V_c V_d))))))
% 29.97/30.19  (assume a107 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_RealDef_Opositive (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_y_2 V_x_2)))))
% 29.97/30.19  (assume a108 (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))))
% 29.97/30.19  (assume a109 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a) V_A_2 V_B_2) V_x_2) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP V_A_2 V_x_2) (tptp.hAPP V_B_2 V_x_2))))))
% 29.97/30.19  (assume a110 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))))
% 29.97/30.19  (assume a111 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))))
% 29.97/30.19  (assume a112 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 29.97/30.19  (assume a113 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))))
% 29.97/30.19  (assume a114 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))))
% 29.97/30.19  (assume a115 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))
% 29.97/30.19  (assume a116 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 29.97/30.19  (assume a117 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a118 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_d____))
% 29.97/30.19  (assume a119 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_r))
% 29.97/30.19  (assume a120 (not (tptp.c_RealDef_Opositive (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 29.97/30.19  (assume a121 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 29.97/30.19  (assume a122 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a123 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a124 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 29.97/30.19  (assume a125 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 29.97/30.19  (assume a126 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oone T_a) (= (= (tptp.c_Groups_Oone__class_Oone T_a) V_x_2) (= V_x_2 (tptp.c_Groups_Oone__class_Oone T_a))))))
% 29.97/30.19  (assume a127 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a128 (forall ((V_ga_2 $$unsorted) (V_fa_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a T_b) V_fa_2 V_ga_2) (and (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_fa_2 V_ga_2) (not (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_ga_2 V_fa_2)))))))
% 29.97/30.19  (assume a129 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 29.97/30.19  (assume a130 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a131 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 29.97/30.19  (assume a132 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 29.97/30.19  (assume a133 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a134 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 29.97/30.19  (assume a135 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 29.97/30.19  (assume a136 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 29.97/30.19  (assume a137 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 29.97/30.19  (assume a138 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a139 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 29.97/30.19  (assume a140 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 29.97/30.19  (assume a141 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 29.97/30.19  (assume a142 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a143 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a144 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 V_b_2)))))
% 29.97/30.19  (assume a145 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a146 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a147 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))))))
% 29.97/30.19  (assume a148 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 29.97/30.19  (assume a149 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))))
% 29.97/30.19  (assume a150 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))))
% 29.97/30.19  (assume a151 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a152 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 29.97/30.19  (assume a153 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y_2) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 29.97/30.19  (assume a154 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 29.97/30.19  (assume a155 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 29.97/30.19  (assume a156 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a157 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_RealDef_Opositive V_x) (=> (tptp.c_RealDef_Opositive V_y) (tptp.c_RealDef_Opositive (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y))))))
% 29.97/30.19  (assume a158 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))))
% 29.97/30.19  (assume a159 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a160 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 29.97/30.19  (assume a161 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a162 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a163 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a164 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 29.97/30.19  (assume a165 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a166 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))))
% 29.97/30.19  (assume a167 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a168 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2)) (not (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a169 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))))
% 29.97/30.19  (assume a170 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a171 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 29.97/30.19  (assume a172 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 29.97/30.19  (assume a173 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 29.97/30.19  (assume a174 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 29.97/30.19  (assume a175 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a176 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a177 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a178 (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_b) (exists ((B_d $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (forall ((B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x B_y)) B_d) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_a B_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y V_b))))))))))
% 29.97/30.19  (assume a179 (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_u) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_v) V_y)) V_a)))))))))
% 29.97/30.19  (assume a180 (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_b) (exists ((B_d $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (forall ((B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x B_y)) B_d) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a B_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_y V_b))))))))))
% 29.97/30.19  (assume a181 (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__1 T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_u) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_v) V_y)) V_a)))))))))
% 29.97/30.19  (assume a182 (forall ((V_n $$unsorted) (V_r $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_m) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_m V_n)))))
% 29.97/30.19  (assume a183 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))))
% 29.97/30.19  (assume a184 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 29.97/30.19  (assume a185 (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_w)))
% 29.97/30.19  (assume a186 (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 29.97/30.19  (assume a187 (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 29.97/30.19  (assume a188 (forall ((V_k $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_k) (tptp.c_Groups_Osgn__class_Osgn T_a V_k))))))
% 29.97/30.19  (assume a189 (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2))))
% 29.97/30.19  (assume a190 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z))))
% 29.97/30.19  (assume a191 (forall ((V_wa_2 $$unsorted) (V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 V_wa_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_za_2 V_wa_2) (not (= V_za_2 V_wa_2))))))
% 29.97/30.19  (assume a192 (forall ((V_za_2 $$unsorted) (V_wa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_wa_2 V_za_2))))
% 29.97/30.19  (assume a193 (forall ((V_za_2 $$unsorted) (V_wa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_wa_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 V_za_2))))
% 29.97/30.19  (assume a194 (forall ((V_x_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a195 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Oabs__class_Oabs T_a V_x)) V_x))))
% 29.97/30.19  (assume a196 (forall ((V_za_2 $$unsorted) (V_wa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_wa_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 V_za_2))))
% 29.97/30.19  (assume a197 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_a_2) V_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_b_2) V_c_2)) (= V_a_2 V_b_2)))))
% 29.97/30.19  (assume a198 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c_2) V_b_2)) (= V_a_2 V_b_2)))))
% 29.97/30.19  (assume a199 (forall ((V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z)))))
% 29.97/30.19  (assume a200 (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z))))
% 29.97/30.19  (assume a201 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_i) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_j)))))
% 29.97/30.19  (assume a202 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_k)))))
% 29.97/30.19  (assume a203 (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z) (= V_z V_w)))))
% 29.97/30.19  (assume a204 (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_H V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_H V_z_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))))
% 29.97/30.19  (assume a205 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) V_ry))))))
% 29.97/30.19  (assume a206 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_ry))))))
% 29.97/30.19  (assume a207 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)))))))
% 29.97/30.19  (assume a208 (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) V_ly)))))
% 29.97/30.19  (assume a209 (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) V_rx))))))
% 29.97/30.19  (assume a210 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) V_ry)))))
% 29.97/30.19  (assume a211 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ry))))))
% 29.97/30.19  (assume a212 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))
% 29.97/30.19  (assume a213 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)))))
% 29.97/30.19  (assume a214 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) V_x))))
% 29.97/30.19  (assume a215 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a) V_a))))
% 29.97/30.19  (assume a216 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_a)) (tptp.c_Groups_Osgn__class_Osgn T_a V_b))))))
% 29.97/30.19  (assume a217 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a)) (tptp.c_Groups_Osgn__class_Osgn T_a V_a)))))
% 29.97/30.19  (assume a218 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 29.97/30.19  (assume a219 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x_2) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_y_2)) (= V_x_2 V_y_2))))
% 29.97/30.19  (assume a220 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x)) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_y)))))
% 29.97/30.19  (assume a221 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x_2) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2 V_y_2))))
% 29.97/30.19  (assume a222 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a223 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_n_2))))
% 29.97/30.19  (assume a224 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x_2) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 V_y_2))))
% 29.97/30.19  (assume a225 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a226 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_n_2))))
% 29.97/30.19  (assume a227 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_y)))))
% 29.97/30.19  (assume a228 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_y)))))
% 29.97/30.19  (assume a229 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a230 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a231 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a232 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a233 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a234 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 29.97/30.19  (assume a235 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a236 (forall ((V_x $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x)))))
% 29.97/30.19  (assume a237 (forall ((V_za_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (V_wa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_wa_2) V_y_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_za_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_wa_2) V_za_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_y_2))) (or (= V_wa_2 V_x_2) (= V_y_2 V_za_2))))))
% 29.97/30.19  (assume a238 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_e) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_e) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_e) V_c)))))
% 29.97/30.19  (assume a239 (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_m)))))
% 29.97/30.19  (assume a240 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 29.97/30.19  (assume a241 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 29.97/30.19  (assume a242 (forall ((V_da_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_a_2 V_b_2)) (not (= V_c_2 V_da_2))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_da_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_da_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_c_2))))))))
% 29.97/30.19  (assume a243 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Oplus__class_Oplus T_a V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_z))))))
% 29.97/30.19  (assume a244 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))))
% 29.97/30.19  (assume a245 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 29.97/30.19  (assume a246 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 29.97/30.19  (assume a247 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 29.97/30.19  (assume a248 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))))
% 29.97/30.19  (assume a249 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))))
% 29.97/30.19  (assume a250 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_za_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 29.97/30.19  (assume a251 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y))))))
% 29.97/30.19  (assume a252 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_y))))))
% 29.97/30.19  (assume a253 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))
% 29.97/30.19  (assume a254 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 29.97/30.19  (assume a255 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_z) V_z)))
% 29.97/30.19  (assume a256 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z1 V_z2)) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z2) V_w)))))
% 29.97/30.19  (assume a257 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a258 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a259 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Osgn__if T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a260 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_RealDef_Opositive V_x) (=> (tptp.c_RealDef_Opositive V_y) (tptp.c_RealDef_Opositive (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y))))))
% 29.97/30.19  (assume a261 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a262 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))
% 29.97/30.19  (assume a263 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 29.97/30.19  (assume a264 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 29.97/30.19  (assume a265 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 29.97/30.19  (assume a266 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 29.97/30.19  (assume a267 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__comm__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 29.97/30.19  (assume a268 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 29.97/30.19  (assume a269 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 29.97/30.19  (assume a270 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 29.97/30.19  (assume a271 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a272 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a273 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a274 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 29.97/30.19  (assume a275 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b_2)))))))
% 29.97/30.19  (assume a276 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 29.97/30.19  (assume a277 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))
% 29.97/30.19  (assume a278 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 29.97/30.19  (assume a279 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 29.97/30.19  (assume a280 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__comm__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 29.97/30.19  (assume a281 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 29.97/30.19  (assume a282 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 29.97/30.19  (assume a283 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 29.97/30.19  (assume a284 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a285 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2))))))
% 29.97/30.19  (assume a286 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 29.97/30.19  (assume a287 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 29.97/30.19  (assume a288 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a289 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a290 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 29.97/30.19  (assume a291 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2))))))
% 29.97/30.19  (assume a292 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2)))))))
% 29.97/30.19  (assume a293 (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_c_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2)))))))
% 29.97/30.19  (assume a294 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a295 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_d)))))))))
% 29.97/30.19  (assume a296 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_m) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) V_n)))))))
% 29.97/30.19  (assume a297 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) V_b))))))
% 29.97/30.19  (assume a298 (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_da_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2)) V_e_2) V_c_2) V_da_2)))))
% 29.97/30.19  (assume a299 (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_da_2)) (= V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_a_2)) V_e_2) V_da_2))))))
% 29.97/30.19  (assume a300 (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 29.97/30.19  (assume a301 (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 29.97/30.19  (assume a302 (forall ((V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 29.97/30.19  (assume a303 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_b) V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_d)))))))
% 29.97/30.19  (assume a304 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_za_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_za_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 29.97/30.19  (assume a305 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_za_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_za_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 29.97/30.19  (assume a306 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a307 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))))
% 29.97/30.19  (assume a308 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_m_2)))))
% 29.97/30.19  (assume a309 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_n V_x))))
% 29.97/30.19  (assume a310 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_m_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a311 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 29.97/30.19  (assume a312 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 29.97/30.19  (assume a313 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 29.97/30.19  (assume a314 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 29.97/30.19  (assume a315 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 29.97/30.19  (assume a316 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 29.97/30.19  (assume a317 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 29.97/30.19  (assume a318 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 29.97/30.19  (assume a319 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 29.97/30.19  (assume a320 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 29.97/30.19  (assume a321 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2))))))
% 29.97/30.19  (assume a322 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2))))))
% 29.97/30.19  (assume a323 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_x) V_x)))))))
% 29.97/30.19  (assume a324 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) V_x)))))))
% 29.97/30.19  (assume a325 (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_da_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2)) V_e_2) V_c_2) V_da_2)))))
% 29.97/30.19  (assume a326 (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_da_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_a_2)) V_e_2) V_da_2))))))
% 29.97/30.19  (assume a327 (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_da_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2)) V_e_2) V_c_2) V_da_2)))))
% 29.97/30.19  (assume a328 (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2) V_da_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_a_2)) V_e_2) V_da_2))))))
% 29.97/30.19  (assume a329 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Groups_Ominus__class_Ominus T_a V_x (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 29.97/30.19  (assume a330 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring__abs T_a) (=> (and (or (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))))))
% 29.97/30.19  (assume a331 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_y)) V_x) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_x)))))))
% 29.97/30.19  (assume a332 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_w____) tptp.v_r))
% 29.97/30.19  (assume a333 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2))) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 29.97/30.19  (assume a334 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a335 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a336 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y))))))
% 29.97/30.19  (assume a337 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y))) (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a338 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a339 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)))))))
% 29.97/30.19  (assume a340 (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.v_g____ B_n)) tptp.v_r)))
% 29.97/30.19  (assume a341 (forall ((V_z $$unsorted)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a342 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))
% 29.97/30.19  (assume a343 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) V_z)))
% 29.97/30.19  (assume a344 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)))
% 29.97/30.19  (assume a345 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a346 (forall ((V_za_2 $$unsorted) (V_wa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wa_2 V_za_2) (= V_wa_2 V_za_2)))))
% 29.97/30.19  (assume a347 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z2)))))
% 29.97/30.19  (assume a348 (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_za_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_za_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a349 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 29.97/30.19  (assume a350 (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) V_za_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a351 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m_2) V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 29.97/30.19  (assume a352 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_j))))))
% 29.97/30.19  (assume a353 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m) V_n)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_m) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a354 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)))
% 29.97/30.19  (assume a355 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z) V_z)))
% 29.97/30.19  (assume a356 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 29.97/30.19  (assume a357 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))))
% 29.97/30.19  (assume a358 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z))))
% 29.97/30.19  (assume a359 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_z3)))))
% 29.97/30.19  (assume a360 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j V_k)))))
% 29.97/30.19  (assume a361 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 29.97/30.19  (assume a362 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z2) V_z3)))))
% 29.97/30.19  (assume a363 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z2 V_z3)))))
% 29.97/30.19  (assume a364 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z2)))))
% 29.97/30.19  (assume a365 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))))
% 29.97/30.19  (assume a366 (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))))
% 29.97/30.19  (assume a367 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_w) V_z))))
% 29.97/30.19  (assume a368 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))
% 29.97/30.19  (assume a369 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)))))
% 29.97/30.19  (assume a370 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 29.97/30.19  (assume a371 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a372 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a373 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))))
% 29.97/30.19  (assume a374 (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_y) V_s) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) V_s)))))))
% 29.97/30.19  (assume a375 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)))))
% 29.97/30.19  (assume a376 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a377 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a378 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a379 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))) (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a380 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2)) (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a381 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))))
% 29.97/30.19  (assume a382 (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_y) V_s) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_r V_s)))))))
% 29.97/30.19  (assume a383 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))))))
% 29.97/30.19  (assume a384 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))
% 29.97/30.19  (assume a385 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 29.97/30.19  (assume a386 (forall ((V_z $$unsorted) (V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_w V_z)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z)))))
% 29.97/30.19  (assume a387 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d)))))))
% 29.97/30.19  (assume a388 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (and (=> (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 29.97/30.19  (assume a389 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 29.97/30.19  (assume a390 (forall ((V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a391 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a392 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a393 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a394 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 29.97/30.19  (assume a395 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 29.97/30.19  (assume a396 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 29.97/30.19  (assume a397 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_b_H)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 29.97/30.19  (assume a398 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) V_ya) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 29.97/30.19  (assume a399 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 29.97/30.19  (assume a400 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 29.97/30.19  (assume a401 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_b_H)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 29.97/30.19  (assume a402 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a403 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a404 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Osgn__class_Osgn T_a V_y))))))
% 29.97/30.19  (assume a405 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 29.97/30.19  (assume a406 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a407 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_d))))))
% 29.97/30.19  (assume a408 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_d)) V_z))))
% 29.97/30.19  (assume a409 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_q))))))
% 29.97/30.19  (assume a410 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 29.97/30.19  (assume a411 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q)))))))))
% 29.97/30.19  (assume a412 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q_H) V_r_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q V_q_H)))))))
% 29.97/30.19  (assume a413 (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))))
% 29.97/30.19  (assume a414 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_q_H))))))
% 29.97/30.19  (assume a415 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 29.97/30.19  (assume a416 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q_H) V_r_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H V_q)))))))
% 29.97/30.19  (assume a417 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q V_q_H)))))))))
% 29.97/30.19  (assume a418 (forall ((V_a $$unsorted) (V_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_b V_a)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_b)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_a))))
% 29.97/30.19  (assume a419 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y))))))
% 29.97/30.19  (assume a420 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y))))))
% 29.97/30.19  (assume a421 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))
% 29.97/30.19  (assume a422 (forall ((V_x_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_x_2))) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a423 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))
% 29.97/30.19  (assume a424 (forall ((V_r $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint B_n) V_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))))
% 29.97/30.19  (assume a425 (forall ((V_r $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint B_n) V_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))))
% 29.97/30.19  (assume a426 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 29.97/30.19  (assume a427 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 29.97/30.19  (assume a428 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K))))))))
% 29.97/30.19  (assume a429 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 29.97/30.19  (assume a430 (forall ((V_x $$unsorted) (V_y $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y V_x) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y))) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y V_x)) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a431 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_da_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_da_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint B_x V_da_2))))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_da_2)))))))))))
% 29.97/30.19  (assume a432 (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat tptp.v_N1____ B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.v_g____ (tptp.hAPP tptp.v_f____ B_n)) tptp.v_z____)) tptp.v_d____))))
% 29.97/30.19  (assume a433 (forall ((V_r $$unsorted)) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint B_n) V_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))))
% 29.97/30.19  (assume a434 (tptp.c_SEQ_Osubseq tptp.v_f____))
% 29.97/30.19  (assume a435 (forall ((B_e $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_e) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_N B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.v_g____ (tptp.hAPP tptp.v_f____ B_n)) tptp.v_z____)) B_e)))))))
% 29.97/30.19  (assume a436 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_l_2) (exists ((B_n $$unsorted)) (= V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 B_n))))))
% 29.97/30.19  (assume a437 (forall ((V_x_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x_2)) V_x_2) (exists ((B_n $$unsorted)) (= V_x_2 (tptp.c_RealDef_Oreal tptp.tc_Int_Oint B_n))))))
% 29.97/30.19  (assume a438 (forall ((V_n $$unsorted)) (= (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n)) V_n)))
% 29.97/30.19  (assume a439 (forall ((V_r $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_r)))))
% 29.97/30.19  (assume a440 (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_a_2)))))
% 29.97/30.19  (assume a441 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x) V_a))))
% 29.97/30.19  (assume a442 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x) V_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_a)))))
% 29.97/30.19  (assume a443 (forall ((V_x_2 $$unsorted) (V_a_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a_2 (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_a_2) V_x_2))))
% 29.97/30.19  (assume a444 (forall ((V_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x) V_a))))
% 29.97/30.19  (assume a445 (forall ((V_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x) V_a))))
% 29.97/30.19  (assume a446 (forall ((V_r $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_r)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_r (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a447 (forall ((V_r $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_r)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_r)))
% 29.97/30.19  (assume a448 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Nat__Transfer_Otsub V_x V_y))))))
% 29.97/30.19  (assume a449 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y V_x) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y)))))
% 29.97/30.19  (assume a450 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n)) (= (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x) V_n)))))
% 29.97/30.19  (assume a451 (forall ((V_x_2 $$unsorted) (V_a_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a_2 (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_a_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x_2))))
% 29.97/30.19  (assume a452 (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_a_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a453 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Archimedean__Field_Oceiling tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 29.97/30.19  (assume a454 (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_N B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.v_g____ (tptp.hAPP tptp.v_f____ B_n)) tptp.v_z____)) tptp.v_d____)))))
% 29.97/30.19  (assume a455 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Archimedean__Field_Oceiling T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling T_a V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a456 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Archimedean__Field_Oceiling T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling T_a V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a457 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) (tptp.c_Archimedean__Field_Oceiling T_a V_x_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_x_2)))))
% 29.97/30.19  (assume a458 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n)))))))
% 29.97/30.19  (assume a459 (forall ((T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Archimedean__Field_Oceiling T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a460 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling T_a V_y) (tptp.c_Archimedean__Field_Oceiling T_a V_x))))))
% 29.97/30.19  (assume a461 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling T_a V_x) (tptp.c_Archimedean__Field_Oceiling T_a V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))))
% 29.97/30.19  (assume a462 (forall ((T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Archimedean__Field_Oceiling T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a463 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a464 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Archimedean__Field_Oceiling T_a V_x_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2)))))
% 29.97/30.19  (assume a465 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) (tptp.c_Archimedean__Field_Oceiling T_a V_x_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2)))))
% 29.97/30.19  (assume a466 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling T_a V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.19  (assume a467 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Archimedean__Field_Oarchimedean__field T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Archimedean__Field_Oceiling T_a V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.c_Groups_Oone__class_Oone T_a))))))
% 29.97/30.19  (assume a468 (not (forall ((B_N1 $$unsorted)) (not (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_N1 B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.v_g____ (tptp.hAPP tptp.v_f____ B_n)) tptp.v_z____)) tptp.v_d____)))))))
% 29.97/30.19  (assume a469 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)))
% 29.97/30.19  (assume a470 (forall ((V_n_2 $$unsorted) (V_fa_2 $$unsorted)) (=> (tptp.c_SEQ_Osubseq V_fa_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 (tptp.hAPP V_fa_2 V_n_2)))))
% 29.97/30.19  (assume a471 (forall ((V_z $$unsorted)) (=> (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_z (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_z (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_z tptp.c_Complex_Oii)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_z tptp.c_Complex_Oii)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a472 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a473 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 29.97/30.19  (assume a474 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m))))
% 29.97/30.19  (assume a475 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 29.97/30.19  (assume a476 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) V_n)))
% 29.97/30.19  (assume a477 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a478 (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 29.97/30.19  (assume a479 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))
% 29.97/30.19  (assume a480 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a481 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a482 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a483 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a484 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (or (= V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a485 (forall ((V_n $$unsorted)) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n))))
% 29.97/30.19  (assume a486 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_j))))))
% 29.97/30.19  (assume a487 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_k))))))
% 29.97/30.19  (assume a488 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a489 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 29.97/30.19  (assume a490 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 29.97/30.19  (assume a491 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a492 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)))))
% 29.97/30.19  (assume a493 (forall ((V_n_2 $$unsorted)) (= (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2))))
% 29.97/30.19  (assume a494 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a495 (not (= tptp.c_Complex_Oii (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 29.97/30.19  (assume a496 (not (= tptp.c_Complex_Oii (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))))
% 29.97/30.19  (assume a497 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 29.97/30.19  (assume a498 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a499 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)))
% 29.97/30.19  (assume a500 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 29.97/30.19  (assume a501 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 29.97/30.19  (assume a502 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 29.97/30.19  (assume a503 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m)))))
% 29.97/30.19  (assume a504 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_n) V_k))))
% 29.97/30.19  (assume a505 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m))))))
% 29.97/30.19  (assume a506 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m V_n)))))
% 29.97/30.19  (assume a507 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_k) V_j))))
% 29.97/30.19  (assume a508 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) V_n)))
% 29.97/30.19  (assume a509 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)))))
% 29.97/30.19  (assume a510 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)))
% 29.97/30.19  (assume a511 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a512 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a513 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_k))))
% 29.97/30.19  (assume a514 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 29.97/30.19  (assume a515 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))))
% 29.97/30.19  (assume a516 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 29.97/30.19  (assume a517 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))))
% 29.97/30.19  (assume a518 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))))
% 29.97/30.19  (assume a519 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a520 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 29.97/30.19  (assume a521 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 29.97/30.19  (assume a522 (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_i))))
% 29.97/30.19  (assume a523 (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_i))))
% 29.97/30.19  (assume a524 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 29.97/30.19  (assume a525 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_z)))))
% 29.97/30.19  (assume a526 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)))))
% 29.97/30.19  (assume a527 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (= V_m_2 V_n_2))))
% 29.97/30.19  (assume a528 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))
% 29.97/30.19  (assume a529 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n) V_m)))
% 29.97/30.19  (assume a530 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_n) V_m)))
% 29.97/30.19  (assume a531 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 29.97/30.19  (assume a532 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a533 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a534 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 29.97/30.19  (assume a535 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2))))
% 29.97/30.19  (assume a536 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 29.97/30.19  (assume a537 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_d $$unsorted)) (=> (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))
% 29.97/30.19  (assume a538 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (not (or (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (exists ((B_d $$unsorted)) (and (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))))
% 29.97/30.19  (assume a539 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)))
% 29.97/30.19  (assume a540 (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m))))
% 29.97/30.19  (assume a541 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a542 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_k)))))
% 29.97/30.19  (assume a543 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))))
% 29.97/30.19  (assume a544 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a545 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))))
% 29.97/30.19  (assume a546 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))))
% 29.97/30.19  (assume a547 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_m) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))))
% 29.97/30.19  (assume a548 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))))
% 29.97/30.19  (assume a549 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_l))))))
% 29.97/30.19  (assume a550 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_c V_a) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a V_c) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_b V_c))))))
% 29.97/30.19  (assume a551 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (not (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 29.97/30.19  (assume a552 (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_i)) V_i))))
% 29.97/30.19  (assume a553 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_l)))))
% 29.97/30.19  (assume a554 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m)))))
% 29.97/30.19  (assume a555 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_j)))))
% 29.97/30.19  (assume a556 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_k)))))
% 29.97/30.19  (assume a557 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a558 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a559 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 29.97/30.19  (assume a560 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 29.97/30.19  (assume a561 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a562 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))))
% 29.97/30.19  (assume a563 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (not (= V_m_2 V_n_2))))))
% 29.97/30.19  (assume a564 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m)))
% 29.97/30.19  (assume a565 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a566 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)))
% 29.97/30.19  (assume a567 (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m)))))
% 29.97/30.19  (assume a568 (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m))))
% 29.97/30.19  (assume a569 (forall ((V_fa_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_fa_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_fa_2 B_m) (tptp.hAPP V_fa_2 B_n)))))))
% 29.97/30.19  (assume a570 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a571 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 29.97/30.19  (assume a572 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k))))))
% 29.97/30.19  (assume a573 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) V_j)))))
% 29.97/30.19  (assume a574 (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted) (V_j_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2) V_i_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2)))))
% 29.97/30.19  (assume a575 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a576 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))))
% 29.97/30.19  (assume a577 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))))
% 29.97/30.19  (assume a578 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_k)))))
% 29.97/30.19  (assume a579 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 29.97/30.19  (assume a580 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 29.97/30.19  (assume a581 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k)))))
% 29.97/30.19  (assume a582 (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2)))))
% 29.97/30.19  (assume a583 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n) V_m))))
% 29.97/30.19  (assume a584 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2) V_k_2) (= V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_i_2))))))
% 29.97/30.19  (assume a585 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))))))
% 29.97/30.19  (assume a586 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k)))))
% 29.97/30.19  (assume a587 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i)))))
% 29.97/30.19  (assume a588 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))))
% 29.97/30.19  (assume a589 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n))))
% 29.97/30.19  (assume a590 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a591 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n)))))))
% 29.97/30.19  (assume a592 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (= V_m_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2)) V_u_2) V_n_2))))))
% 29.97/30.19  (assume a593 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_u $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_i)) V_u) V_n))))))
% 29.97/30.19  (assume a594 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2)) V_u_2) V_n_2))))))
% 29.97/30.19  (assume a595 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2)) V_u_2) V_n_2))))))
% 29.97/30.19  (assume a596 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 29.97/30.19  (assume a597 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))))
% 29.97/30.19  (assume a598 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))))
% 29.97/30.19  (assume a599 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 29.97/30.19  (assume a600 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m) (not (= V_m V_n)))))
% 29.97/30.19  (assume a601 (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_s V_t) (not (= V_s V_t)))))
% 29.97/30.19  (assume a602 (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (=> (=> (= V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2)))))))
% 29.97/30.19  (assume a603 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (= V_m_2 V_n_2)))))
% 29.97/30.19  (assume a604 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 29.97/30.19  (assume a605 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m_2 V_n_2)))))
% 29.97/30.19  (assume a606 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j)) V_u) V_k))))
% 29.97/30.19  (assume a607 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 29.97/30.19  (assume a608 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 V_i_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_m_2) V_n_2)))))
% 29.97/30.19  (assume a609 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 V_i_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_m_2) V_n_2)))))
% 29.97/30.19  (assume a610 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_i) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j)) V_u) V_m) V_n)))))
% 29.97/30.19  (assume a611 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 V_i_2) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_n_2)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_m_2) V_n_2)))))
% 29.97/30.19  (assume a612 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a613 (forall ((V_X_2 $$unsorted) (V_M_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__vector T_b) (tptp.class_Orderings_Oord T_a)) (=> (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_M_2 B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.hAPP V_X_2 V_M_2) (tptp.hAPP V_X_2 B_n))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_M_2 B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 V_M_2))))))))))
% 29.97/30.19  (assume a614 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a615 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 29.97/30.19  (assume a616 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x))))
% 29.97/30.19  (assume a617 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) (tptp.c_RComplete_Onatfloor V_y)))))
% 29.97/30.19  (assume a618 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 29.97/30.19  (assume a619 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 29.97/30.19  (assume a620 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x))))
% 29.97/30.19  (assume a621 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_RComplete_Onatceiling V_y)))))
% 29.97/30.19  (assume a622 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 29.97/30.19  (assume a623 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a624 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a625 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2))))
% 29.97/30.19  (assume a626 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a627 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_a)) (tptp.c_RComplete_Onatfloor V_b)) (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_a) V_b)))))))
% 29.97/30.19  (assume a628 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 29.97/30.19  (assume a629 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 29.97/30.19  (assume a630 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y))))
% 29.97/30.19  (assume a631 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 29.97/30.19  (assume a632 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 29.97/30.19  (assume a633 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 29.97/30.19  (assume a634 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Odecseq T_a V_X_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 B_m))))))))
% 29.97/30.19  (assume a635 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_da_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_da_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x V_da_2))))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_da_2)))))))))))
% 29.97/30.19  (assume a636 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))
% 29.97/30.19  (assume a637 (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x))))
% 29.97/30.19  (assume a638 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (= V_n_2 V_m_2))))
% 29.97/30.19  (assume a639 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 29.97/30.19  (assume a640 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 29.97/30.19  (assume a641 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 29.97/30.19  (assume a642 (forall ((V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a643 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a644 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2))))
% 29.97/30.19  (assume a645 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))))
% 29.97/30.19  (assume a646 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 29.97/30.19  (assume a647 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 29.97/30.19  (assume a648 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 29.97/30.19  (assume a649 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)))))
% 29.97/30.19  (assume a650 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a651 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))))
% 29.97/30.19  (assume a652 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) V_x))))
% 29.97/30.19  (assume a653 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x) V_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_RComplete_Onatfloor V_a)))))
% 29.97/30.19  (assume a654 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a))))
% 29.97/30.19  (assume a655 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2))))
% 29.97/30.19  (assume a656 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)))))
% 29.97/30.19  (assume a657 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a658 (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_a_2 (tptp.c_RComplete_Onatfloor V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2) V_x_2)))))
% 29.97/30.19  (assume a659 (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2))))))
% 29.97/30.19  (assume a660 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a661 (forall ((V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a)))))
% 29.97/30.19  (assume a662 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)))))
% 29.97/30.19  (assume a663 (forall ((V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a) V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a)))))
% 29.97/30.19  (assume a664 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_n)))))
% 29.97/30.19  (assume a665 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a)))))
% 29.97/30.19  (assume a666 (forall ((V_n $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_z (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 29.97/30.19  (assume a667 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatfloor V_x) V_n)))))
% 29.97/30.19  (assume a668 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a)))))
% 29.97/30.19  (assume a669 (forall ((V_r $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat B_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)))))))
% 29.97/30.19  (assume a670 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2)) (exists ((B_k $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_k V_n_2) (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i B_k) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_k (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 29.97/30.19  (assume a671 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 29.97/30.19  (assume a672 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K))))))))
% 29.97/30.19  (assume a673 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 29.97/30.19  (assume a674 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) V_n)))))
% 29.97/30.19  (assume a675 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 29.97/30.19  (assume a676 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_p)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_p V_q))))))
% 29.97/30.19  (assume a677 (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n)))))
% 29.97/30.19  (assume a678 (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n)))))
% 29.97/30.19  (assume a679 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_p)) V_q) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) V_q))))))
% 29.97/30.19  (assume a680 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_x))))
% 29.97/30.19  (assume a681 (forall ((V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_q))))))
% 29.97/30.19  (assume a682 (forall ((V_x $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))))
% 29.97/30.19  (assume a683 (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 29.97/30.19  (assume a684 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n))))))))
% 29.97/30.19  (assume a685 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 29.97/30.19  (assume a686 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_i) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 29.97/30.19  (assume a687 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a688 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_y) V_z)))))
% 29.97/30.19  (assume a689 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n)))))
% 29.97/30.19  (assume a690 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_z)))))
% 29.97/30.19  (assume a691 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) V_n) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)))))
% 29.97/30.19  (assume a692 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) V_n))))
% 29.97/30.19  (assume a693 (forall ((V_n $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x)) V_n) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n)))))
% 29.97/30.19  (assume a694 (forall ((V_n $$unsorted) (V_x $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Int_Oint V_x)) V_n))))
% 29.97/30.19  (assume a695 (forall ((V_n $$unsorted) (V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x)) V_n))))
% 29.97/30.19  (assume a696 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (= V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x))) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) V_n)))))
% 29.97/30.19  (assume a697 (forall ((V_p $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) V_m) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))))
% 29.97/30.19  (assume a698 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x_2)) V_n_2)) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 29.97/30.19  (assume a699 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a700 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n))))))
% 29.97/30.19  (assume a701 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 29.97/30.19  (assume a702 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_n) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 29.97/30.19  (assume a703 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) V_n)))))
% 29.97/30.19  (assume a704 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) V_n)))))
% 29.97/30.19  (assume a705 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_a))))
% 29.97/30.19  (assume a706 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n)))))))
% 29.97/30.19  (assume a707 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 29.97/30.19  (assume a708 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 29.97/30.19  (assume a709 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 29.97/30.19  (assume a710 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_n_2)) (= V_m_2 V_n_2))))))
% 29.97/30.19  (assume a711 (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Omult__zero T_a) (tptp.class_Rings_Ono__zero__divisors T_a) (tptp.class_Rings_Ozero__neq__one T_a)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 29.97/30.19  (assume a712 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 29.97/30.19  (assume a713 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 29.97/30.19  (assume a714 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 29.97/30.19  (assume a715 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 29.97/30.19  (assume a716 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 29.97/30.19  (assume a717 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 29.97/30.19  (assume a718 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) V_n)))))
% 29.97/30.19  (assume a719 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2))))))
% 29.97/30.19  (assume a720 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))))
% 29.97/30.19  (assume a721 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)))))))
% 29.97/30.19  (assume a722 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)))))))
% 29.97/30.19  (assume a723 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 29.97/30.19  (assume a724 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))))
% 29.97/30.19  (assume a725 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_a V_b))))))))
% 29.97/30.19  (assume a726 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))))
% 29.97/30.19  (assume a727 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))))
% 29.97/30.19  (assume a728 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x_2 V_y_2))))))
% 29.97/30.19  (assume a729 (forall ((V_n $$unsorted) (V_b $$unsorted)) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (exists ((B_z $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) B_z) V_n)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 29.97/30.19  (assume a730 (forall ((T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Power_Opower_Opower T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Otimes__class_Otimes T_a))))))
% 29.97/30.19  (assume a731 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2)) (or (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2)))))
% 29.97/30.19  (assume a732 (forall ((V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_one_2)))
% 29.97/30.19  (assume a733 (forall ((V_n $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r V_a)) V_n) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_r) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_a)))))
% 29.97/30.19  (assume a734 (forall ((V_a $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (exists ((B_x $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_x) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_x) V_n) V_a) (forall ((B_y $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_y) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_y) V_n) V_a)) (= B_y B_x)))))))))
% 29.97/30.19  (assume a735 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Complex_Orcis V_r V_a)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))))
% 29.97/30.19  (assume a736 (forall ((V_a $$unsorted)) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 29.97/30.19  (assume a737 (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))))
% 29.97/30.19  (assume a738 (forall ((V_a $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (exists ((B_r $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_r) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_r) V_n) V_a)))))))
% 29.97/30.19  (assume a739 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Transcendental_Oln V_x))))))
% 29.97/30.19  (assume a740 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2))))))
% 29.97/30.19  (assume a741 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (= (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (= V_x_2 V_y_2))))))
% 29.97/30.19  (assume a742 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x) V_x))))
% 29.97/30.19  (assume a743 (= (tptp.c_Transcendental_Oln (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 29.97/30.19  (assume a744 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2))))))
% 29.97/30.19  (assume a745 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)))))
% 29.97/30.19  (assume a746 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)))))
% 29.97/30.19  (assume a747 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2)))))
% 29.97/30.19  (assume a748 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (= (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a749 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a750 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 29.97/30.19  (assume a751 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)))))
% 29.97/30.19  (assume a752 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2)))))
% 29.97/30.19  (assume a753 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)))))
% 29.97/30.19  (assume a754 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (= (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x) (tptp.c_Transcendental_Oln V_y)))))))
% 29.97/30.19  (assume a755 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)) V_x))))
% 29.97/30.19  (assume a756 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) B_K))))))))
% 29.97/30.19  (assume a757 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Oincseq T_a V_X_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m) (tptp.hAPP V_X_2 B_n))))))))
% 29.97/30.19  (assume a758 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) B_K))))))))
% 29.97/30.19  (assume a759 (forall ((V_X_2 $$unsorted) (V_K_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_K_2) (=> (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) V_K_2)) (tptp.c_SEQ_OBseq T_a V_X_2))))))
% 29.97/30.19  (assume a760 (= (tptp.c_Complex_Oexpi (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)))
% 29.97/30.19  (assume a761 (forall ((V_k_2 $$unsorted) (V_fa_2 $$unsorted) (V_n_2 $$unsorted)) (=> (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i V_n_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP V_fa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_i (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.hAPP V_fa_2 B_i))) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP V_fa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 (tptp.hAPP V_fa_2 V_n_2)) (exists ((B_i $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i V_n_2) (= (tptp.hAPP V_fa_2 B_i) V_k_2))))))))
% 29.97/30.19  (assume a762 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Complex_Oexpi (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Oexpi V_a)) (tptp.c_Complex_Oexpi V_b)))))
% 29.97/30.19  (assume a763 (forall ((V_k_2 $$unsorted) (V_fa_2 $$unsorted) (V_n_2 $$unsorted)) (=> (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i V_n_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP V_fa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_i (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.hAPP V_fa_2 B_i))) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP V_fa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 (tptp.hAPP V_fa_2 V_n_2)) (exists ((B_i $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i V_n_2) (= (tptp.hAPP V_fa_2 B_i) V_k_2))))))))
% 29.97/30.19  (assume a764 (forall ((V_K_2 $$unsorted) (V_X_2 $$unsorted) (V_N_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_N_2 B_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) V_K_2))) (tptp.c_SEQ_OBseq T_a V_X_2)))))
% 29.97/30.19  (assume a765 (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) B_K)))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))))
% 29.97/30.19  (assume a766 (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) B_K)))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))))
% 29.97/30.19  (assume a767 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)))))
% 29.97/30.19  (assume a768 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_n))))
% 29.97/30.19  (assume a769 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_n))))
% 29.97/30.19  (assume a770 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a771 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a772 (forall ((V_m_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_m_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_x_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 29.97/30.19  (assume a773 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q))))))
% 29.97/30.19  (assume a774 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q))))))
% 29.97/30.19  (assume a775 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q))))))
% 29.97/30.19  (assume a776 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 29.97/30.19  (assume a777 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) V_a)))))
% 29.97/30.19  (assume a778 (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.hAPP (tptp.hAPP V_times_2 V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2) V_n_2)))))
% 29.97/30.19  (assume a779 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (or (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_x (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 29.97/30.19  (assume a780 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_n_2)) (= V_m_2 V_n_2))))
% 29.97/30.19  (assume a781 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 29.97/30.19  (assume a782 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k)))))))
% 29.97/30.19  (assume a783 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_i)))))
% 29.97/30.19  (assume a784 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_m)))))
% 29.97/30.19  (assume a785 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a786 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))))
% 29.97/30.19  (assume a787 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n))))
% 29.97/30.19  (assume a788 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 29.97/30.19  (assume a789 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a790 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a791 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))))
% 29.97/30.19  (assume a792 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 29.97/30.19  (assume a793 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a794 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc V_m))))
% 29.97/30.19  (assume a795 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 29.97/30.19  (assume a796 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 29.97/30.19  (assume a797 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a798 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))))
% 29.97/30.19  (assume a799 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a800 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n))))
% 29.97/30.19  (assume a801 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))))
% 29.97/30.19  (assume a802 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))
% 29.97/30.19  (assume a803 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 29.97/30.19  (assume a804 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 29.97/30.19  (assume a805 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 29.97/30.19  (assume a806 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Nat_OSuc V_x) (tptp.c_Nat_OSuc V_y)) (= V_x V_y))))
% 29.97/30.19  (assume a807 (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc V_nat_2) (tptp.c_Nat_OSuc V_nat_H_2)) (= V_nat_2 V_nat_H_2))))
% 29.97/30.19  (assume a808 (forall ((V_n $$unsorted)) (not (= (tptp.c_Nat_OSuc V_n) V_n))))
% 29.97/30.19  (assume a809 (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Nat_OSuc V_n)))))
% 29.97/30.19  (assume a810 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_k))))
% 29.97/30.19  (assume a811 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a812 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a813 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n)) (= V_m (tptp.c_Nat_OSuc V_n))))))
% 29.97/30.19  (assume a814 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 29.97/30.19  (assume a815 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) (tptp.c_Nat_OSuc V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))))
% 29.97/30.19  (assume a816 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 (tptp.c_Nat_OSuc V_n_2))))))
% 29.97/30.19  (assume a817 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))))
% 29.97/30.19  (assume a818 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) V_n))))
% 29.97/30.19  (assume a819 (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a820 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))))
% 29.97/30.19  (assume a821 (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a822 (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a823 (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_nat_H)))))
% 29.97/30.19  (assume a824 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))))
% 29.97/30.19  (assume a825 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a826 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 29.97/30.19  (assume a827 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= V_m V_n)))))
% 29.97/30.19  (assume a828 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_i) V_k)))))
% 29.97/30.19  (assume a829 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (not (= (tptp.c_Nat_OSuc V_m) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n)))))
% 29.97/30.19  (assume a830 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 29.97/30.19  (assume a831 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_m)) (= V_m V_n)))))
% 29.97/30.19  (assume a832 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))))
% 29.97/30.19  (assume a833 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 29.97/30.19  (assume a834 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))))
% 29.97/30.19  (assume a835 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)))))
% 29.97/30.19  (assume a836 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 29.97/30.19  (assume a837 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 29.97/30.19  (assume a838 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (exists ((B_m $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc B_m))))))
% 29.97/30.19  (assume a839 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a840 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_j $$unsorted)) (and (= V_m_2 (tptp.c_Nat_OSuc B_j)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_n_2)))))))
% 29.97/30.19  (assume a841 (forall ((V_fa_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_fa_2) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_fa_2 B_n) (tptp.hAPP V_fa_2 (tptp.c_Nat_OSuc B_n)))))))
% 29.97/30.19  (assume a842 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) (tptp.c_Nat_OSuc V_n))) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (= V_a V_b)))))))
% 29.97/30.19  (assume a843 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) (tptp.c_Nat_OSuc V_n))) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 29.97/30.19  (assume a844 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)))))))
% 29.97/30.19  (assume a845 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n))))))
% 29.97/30.19  (assume a846 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m))))))
% 29.97/30.19  (assume a847 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n))))))
% 29.97/30.19  (assume a848 (forall ((V_i $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_i)) V_n))))
% 29.97/30.19  (assume a849 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) V_n))))
% 29.97/30.19  (assume a850 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n_2)))))
% 29.97/30.19  (assume a851 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)))))
% 29.97/30.19  (assume a852 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_j) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m))))))
% 29.97/30.19  (assume a853 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Nat_OSuc V_j))))))
% 29.97/30.19  (assume a854 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 29.97/30.19  (assume a855 (forall ((V_n $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 29.97/30.19  (assume a856 (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_i) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n)))))
% 29.97/30.19  (assume a857 (forall ((V_n $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_r) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_r (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_r) (tptp.c_Nat_OSuc V_n)) V_r))))))
% 29.97/30.19  (assume a858 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 29.97/30.19  (assume a859 (forall ((V_y $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_p V_n) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) V_p)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_p))) V_y))))))
% 29.97/30.19  (assume a860 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n))))
% 29.97/30.19  (assume a861 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_n (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 29.97/30.19  (assume a862 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n)) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))))))
% 29.97/30.19  (assume a863 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))))
% 29.97/30.19  (assume a864 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))))
% 29.97/30.19  (assume a865 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y))))))
% 29.97/30.19  (assume a866 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_y) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_n))) V_y))))))))
% 29.97/30.19  (assume a867 (forall ((V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))))
% 29.97/30.19  (assume a868 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_y))))))
% 29.97/30.19  (assume a869 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a870 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a_2)))))
% 29.97/30.19  (assume a871 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a872 (forall ((V_a $$unsorted)) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a873 (forall ((V_b $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 29.97/30.19  (assume a874 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a875 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a876 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 29.97/30.19  (assume a877 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 29.97/30.19  (assume a878 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))
% 29.97/30.19  (assume a879 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))
% 29.97/30.19  (assume a880 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) V_b) V_a)))))
% 29.97/30.19  (assume a881 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) V_a)))))
% 29.97/30.19  (assume a882 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (and (=> (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 29.97/30.19  (assume a883 (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_i_2 V_k_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_i_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i_2 V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_i_2))))))
% 29.97/30.19  (assume a884 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a_2)))))
% 29.97/30.19  (assume a885 (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_i_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_i_2)))))
% 29.97/30.19  (assume a886 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_2))))))
% 29.97/30.19  (assume a887 (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b_H)))))))
% 29.97/30.19  (assume a888 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a889 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a V_b) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a890 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a891 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a892 (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b_H) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)))))))
% 29.97/30.19  (assume a893 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_a) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 29.97/30.19  (assume a894 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a V_a_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_H V_b))))))
% 29.97/30.19  (assume a895 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a V_a_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_H V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b))))))
% 29.97/30.19  (assume a896 (forall ((V_k $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_k) V_x)))))
% 29.97/30.19  (assume a897 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c)))))
% 29.97/30.19  (assume a898 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 29.97/30.19  (assume a899 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 29.97/30.19  (assume a900 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 29.97/30.19  (assume a901 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 29.97/30.19  (assume a902 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_i $$unsorted)) (=> (exists ((B_j $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint B_j V_k_2) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j)))) (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (forall ((B_i $$unsorted)) (=> (exists ((B_j $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 B_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j)))) (tptp.hBOOL (tptp.hAPP V_P_2 B_i)))))))))
% 29.97/30.19  (assume a903 (forall ((V_r_1 $$unsorted) (V_y $$unsorted) (V_b_1 $$unsorted) (V_a_1 $$unsorted)) (=> (= V_a_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_1) V_y) V_r_1)) (=> (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_1) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_1 V_b_1))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_1)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_1 V_r_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))) (=> (not (= V_b_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_1 V_b_1) V_y))))))
% 29.97/30.19  (assume a904 (forall ((V_r $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n) V_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_n))))))))
% 29.97/30.19  (assume a905 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 B_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))))
% 29.97/30.19  (assume a906 (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m)))
% 29.97/30.19  (assume a907 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 29.97/30.19  (assume a908 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 29.97/30.19  (assume a909 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a910 (forall ((V_a $$unsorted)) (and (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a))))
% 29.97/30.19  (assume a911 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c)))))
% 29.97/30.19  (assume a912 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) V_m)))
% 29.97/30.19  (assume a913 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_k) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_n V_k)))))
% 29.97/30.19  (assume a914 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) V_a))))
% 29.97/30.19  (assume a915 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))))
% 29.97/30.19  (assume a916 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))))
% 29.97/30.19  (assume a917 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))
% 29.97/30.19  (assume a918 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))
% 29.97/30.19  (assume a919 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_b) V_c))))
% 29.97/30.19  (assume a920 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (and (=> (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n))))))
% 29.97/30.19  (assume a921 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_k V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_k V_m))))))
% 29.97/30.19  (assume a922 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) V_n) V_m))))
% 29.97/30.19  (assume a923 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m) V_n) V_m))))
% 29.97/30.19  (assume a924 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)))))
% 29.97/30.19  (assume a925 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) V_m)))))
% 29.97/30.19  (assume a926 (forall ((V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_m)) V_y) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y) V_m))))
% 29.97/30.19  (assume a927 (forall ((V_da_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m_2 V_da_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (exists ((B_q $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_da_2) B_q))))))
% 29.97/30.19  (assume a928 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b_H) V_c)))))))
% 29.97/30.19  (assume a929 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c)))))
% 29.97/30.19  (assume a930 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c))))
% 29.97/30.19  (assume a931 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c)))))
% 29.97/30.19  (assume a932 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))))))
% 29.97/30.19  (assume a933 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 29.97/30.19  (assume a934 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c)))))
% 29.97/30.19  (assume a935 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c))))
% 29.97/30.19  (assume a936 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 29.97/30.19  (assume a937 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 29.97/30.19  (assume a938 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 29.97/30.19  (assume a939 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a940 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a941 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a942 (forall ((V_m $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_y V_m)) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y) V_m))))
% 29.97/30.19  (assume a943 (forall ((V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_m) V_y) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y) V_m))))
% 29.97/30.19  (assume a944 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 29.97/30.19  (assume a945 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c)))))
% 29.97/30.19  (assume a946 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 29.97/30.19  (assume a947 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_H V_b_H) V_c)))))))
% 29.97/30.19  (assume a948 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 29.97/30.19  (assume a949 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_H V_b_H) V_c)))))))
% 29.97/30.19  (assume a950 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c)))))
% 29.97/30.19  (assume a951 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c)))))
% 29.97/30.19  (assume a952 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 29.97/30.19  (assume a953 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c)))))
% 29.97/30.19  (assume a954 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 29.97/30.19  (assume a955 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 29.97/30.19  (assume a956 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 29.97/30.19  (assume a957 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a958 (forall ((V_b $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 29.97/30.19  (assume a959 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 29.97/30.19  (assume a960 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 29.97/30.19  (assume a961 (forall ((V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 29.97/30.19  (assume a962 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b))))
% 29.97/30.19  (assume a963 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 29.97/30.19  (assume a964 (forall ((V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_k) V_m))))
% 29.97/30.19  (assume a965 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_y))))))
% 29.97/30.19  (assume a966 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_a) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_a)))))
% 29.97/30.19  (assume a967 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))))))
% 29.97/30.19  (assume a968 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 29.97/30.19  (assume a969 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a V_b) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_a)))))
% 29.97/30.19  (assume a970 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b)))))
% 29.97/30.19  (assume a971 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 29.97/30.19  (assume a972 (forall ((V_k $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_k))))
% 29.97/30.19  (assume a973 (forall ((V_k $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_k))))
% 29.97/30.19  (assume a974 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c)))))
% 29.97/30.19  (assume a975 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 29.97/30.19  (assume a976 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_m V_n)) V_n)))))
% 29.97/30.19  (assume a977 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_m (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_n)))))
% 29.97/30.19  (assume a978 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n))))))))
% 29.97/30.19  (assume a979 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n)))))))
% 29.97/30.19  (assume a980 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (not (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_k_2) (=> (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) B_i) B_j)) (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))))))))
% 29.97/30.19  (assume a981 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_b))))))
% 29.97/30.19  (assume a982 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m_2 V_n_2))) (or (and (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (exists ((B_q $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) B_q) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) (tptp.c_Nat_OSuc B_q))) (tptp.hBOOL (tptp.hAPP V_P_2 B_q))))))))
% 29.97/30.19  (assume a983 (forall ((V_m_2 $$unsorted) (V_q_2 $$unsorted) (V_n_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (= (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_q_2) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) (tptp.c_Nat_OSuc V_q_2)))) (= V_q_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m_2 V_n_2))))))
% 29.97/30.19  (assume a984 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n)))))))
% 29.97/30.19  (assume a985 (forall ((V_y $$unsorted) (V_q_1 $$unsorted) (V_b_1 $$unsorted) (V_a_1 $$unsorted)) (=> (= V_a_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_1) V_q_1) V_y)) (=> (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_1) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_b_1))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_1)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))) (=> (not (= V_b_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a_1 V_b_1) V_y))))))
% 29.97/30.19  (assume a986 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c)) V_r) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 29.97/30.20  (assume a987 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c)) V_r)))))))
% 29.97/30.20  (assume a988 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c)) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)))))))
% 29.97/30.20  (assume a989 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c)) V_r)))))))
% 29.97/30.20  (assume a990 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint B_j V_k_2) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP V_P_2 B_j))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 B_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP V_P_2 B_j)))))))))
% 29.97/30.20  (assume a991 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))))))
% 29.97/30.20  (assume a992 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint B_j V_k_2) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))))
% 29.97/30.20  (assume a993 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_y) (= (tptp.c_RComplete_Onatfloor (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_y))) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_y))))))
% 29.97/30.20  (assume a994 (forall ((V_a $$unsorted) (V_n $$unsorted)) (= (tptp.c_Complex_Ocis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n))) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocis V_a)) (tptp.c_Complex_Ocis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_a))))))
% 29.97/30.20  (assume a995 (forall ((V_c $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_a) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_c)) V_c)))))
% 29.97/30.20  (assume a996 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_b V_c)) V_c)))))
% 29.97/30.20  (assume a997 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))))
% 29.97/30.20  (assume a998 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))))
% 29.97/30.20  (assume a999 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))))
% 29.97/30.20  (assume a1000 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ominus T_1) (tptp.class_Groups_Ominus (tptp.tc_fun T_2 T_1)))))
% 29.97/30.20  (assume a1001 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1002 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1003 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1004 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1005 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1006 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1007 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1008 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1009 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1010 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1011 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1012 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1013 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1014 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1015 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1016 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1017 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1018 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1019 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1020 (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1021 (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1022 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1023 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1024 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1025 (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1026 (tptp.class_Rings_Oordered__ring__abs tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1027 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1028 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1029 (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1030 (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1031 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1032 (tptp.class_Divides_Osemiring__div tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1033 (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1034 (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1035 (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1036 (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1037 (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1038 (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1039 (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1040 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1041 (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1042 (tptp.class_Rings_Osemiring__0 tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1043 (tptp.class_Groups_Ogroup__add tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1044 (tptp.class_Divides_Oring__div tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1045 (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1046 (tptp.class_Orderings_Oorder tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1047 (tptp.class_Rings_Osemiring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1048 (tptp.class_Orderings_Oord tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1049 (tptp.class_Groups_Osgn__if tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1050 (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1051 (tptp.class_Groups_Ominus tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1052 (tptp.class_Power_Opower tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1053 (tptp.class_Groups_Ozero tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1054 (tptp.class_Rings_Oring tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1055 (tptp.class_Groups_Oone tptp.tc_Int_Oint))
% 29.97/30.20  (assume a1056 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1057 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1058 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1059 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1060 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1061 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1062 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1063 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1064 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1065 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1066 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1067 (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1068 (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1069 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1070 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1071 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1072 (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1073 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1074 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1075 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1076 (tptp.class_Divides_Osemiring__div tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1077 (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1078 (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1079 (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1080 (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1081 (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1082 (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1083 (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1084 (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1085 (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1086 (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1087 (tptp.class_Orderings_Oord tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1088 (tptp.class_Groups_Ominus tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1089 (tptp.class_Power_Opower tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1090 (tptp.class_Groups_Ozero tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1091 (tptp.class_Groups_Oone tptp.tc_Nat_Onat))
% 29.97/30.20  (assume a1092 (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool))
% 29.97/30.20  (assume a1093 (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool))
% 29.97/30.20  (assume a1094 (tptp.class_Orderings_Oord tptp.tc_HOL_Obool))
% 29.97/30.20  (assume a1095 (tptp.class_Groups_Ominus tptp.tc_HOL_Obool))
% 29.97/30.20  (assume a1096 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1097 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1098 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1099 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1100 (tptp.class_Archimedean__Field_Oarchimedean__field tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1101 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1102 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1103 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1104 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1105 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1106 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1107 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1108 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1109 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1110 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1111 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1112 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1113 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1114 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1115 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1116 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1117 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1118 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1119 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1120 (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1121 (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1122 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1123 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1124 (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1125 (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1126 (tptp.class_Rings_Oordered__ring__abs tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1127 (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1128 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1129 (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1130 (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1131 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1132 (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1133 (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1134 (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1135 (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1136 (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1137 (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1138 (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1139 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1140 (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1141 (tptp.class_Rings_Osemiring__0 tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1142 (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1143 (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1144 (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1145 (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1146 (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1147 (tptp.class_Groups_Osgn__if tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1148 (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1149 (tptp.class_Groups_Ominus tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1150 (tptp.class_Power_Opower tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1151 (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1152 (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1153 (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal))
% 29.97/30.20  (assume a1154 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1155 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1156 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1157 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1158 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1159 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1160 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1161 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1162 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1163 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1164 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1165 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1166 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1167 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1168 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1169 (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1170 (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1171 (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1172 (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1173 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1174 (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1175 (tptp.class_Rings_Osemiring__0 tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1176 (tptp.class_Groups_Ogroup__add tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1177 (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1178 (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1179 (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1180 (tptp.class_Groups_Ominus tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1181 (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1182 (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1183 (tptp.class_Rings_Oring tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1184 (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex))
% 29.97/30.20  (assume a1185 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))
% 29.97/30.20  (assume a1186 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))
% 29.97/30.20  (assume a1187 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e)))
% 29.97/30.20  (assume a1188 true)
% 29.97/30.20  (step t1 (cl (not (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) :rule or_pos)
% 29.97/30.20  (step t2 (cl (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule reordering :premises (t1))
% 29.97/30.20  (step t3 (cl (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule and_neg)
% 29.97/30.20  (step t4 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t5)
% 29.97/30.20  (assume t5.a0 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (assume t5.a1 (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (step t5.t1 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t5.t2)
% 29.97/30.20  (assume t5.t2.a0 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (assume t5.t2.a1 (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (step t5.t2.t1 (cl (= (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) true) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule equiv_simplify)
% 29.97/30.20  (step t5.t2.t2 (cl (not (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) true)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule equiv1 :premises (t5.t2.t1))
% 29.97/30.20  (step t5.t2.t3 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 29.97/30.20  (step t5.t2.t4 (cl (= tptp.v_e tptp.v_e)) :rule refl)
% 29.97/30.20  (step t5.t2.t5 (cl (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule symm :premises (t5.t2.a1))
% 29.97/30.20  (step t5.t2.t6 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule symm :premises (t5.t2.t5))
% 29.97/30.20  (step t5.t2.t7 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule cong :premises (t5.t2.t3 t5.t2.t4 t5.t2.t6))
% 29.97/30.20  (step t5.t2.t8 (cl (= (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) true) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule equiv_simplify)
% 29.97/30.20  (step t5.t2.t9 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) true) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule equiv2 :premises (t5.t2.t8))
% 29.97/30.20  (step t5.t2.t10 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) true)) :rule resolution :premises (t5.t2.t9 t5.t2.a0))
% 29.97/30.20  (step t5.t2.t11 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) true)) :rule trans :premises (t5.t2.t7 t5.t2.t10))
% 29.97/30.20  (step t5.t2.t12 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule resolution :premises (t5.t2.t2 t5.t2.t11))
% 29.97/30.20  (step t5.t2 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule subproof :discharge (t5.t2.a0 t5.t2.a1))
% 29.97/30.20  (step t5.t3 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t5.t4 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t5.t5 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t5.t2 t5.t3 t5.t4))
% 29.97/30.20  (step t5.t6 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule reordering :premises (t5.t5))
% 29.97/30.20  (step t5.t7 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule contraction :premises (t5.t6))
% 29.97/30.20  (step t5.t8 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule resolution :premises (t5.t1 t5.t7))
% 29.97/30.20  (step t5.t9 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule implies_neg2)
% 29.97/30.20  (step t5.t10 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t5.t8 t5.t9))
% 29.97/30.20  (step t5.t11 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule contraction :premises (t5.t10))
% 29.97/30.20  (step t5.t12 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule implies :premises (t5.t11))
% 29.97/30.20  (step t5.t13 (cl (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule and_neg)
% 29.97/30.20  (step t5.t14 (cl (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t5.t13 t5.a0 t5.a1))
% 29.97/30.20  (step t5.t15 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule resolution :premises (t5.t12 t5.t14))
% 29.97/30.20  (step t5 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule subproof :discharge (t5.a0 t5.a1))
% 29.97/30.20  (step t6 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t7 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t8 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t5 t6 t7))
% 29.97/30.20  (step t9 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule reordering :premises (t8))
% 29.97/30.20  (step t10 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule contraction :premises (t9))
% 29.97/30.20  (step t11 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule resolution :premises (t4 t10))
% 29.97/30.20  (step t12 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule implies_neg2)
% 29.97/30.20  (step t13 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t11 t12))
% 29.97/30.20  (step t14 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule contraction :premises (t13))
% 29.97/30.20  (step t15 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule implies :premises (t14))
% 29.97/30.20  (step t16 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule resolution :premises (t3 t15))
% 29.97/30.20  (step t17 (cl (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e)) :rule or_pos)
% 29.97/30.20  (step t18 (cl (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e)))) :rule reordering :premises (t17))
% 29.97/30.20  (step t19 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t20)
% 29.97/30.20  (assume t20.a0 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))
% 29.97/30.20  (step t20.t1 (cl (or (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e)))) :rule forall_inst :args ((:= V_x (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (:= V_y tptp.v_e) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t20.t2 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) :rule or :premises (t20.t1))
% 29.97/30.20  (step t20.t3 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) :rule resolution :premises (t20.t2 t20.a0))
% 29.97/30.20  (step t20 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) :rule subproof :discharge (t20.a0))
% 29.97/30.20  (step t21 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) :rule resolution :premises (t19 t20))
% 29.97/30.20  (step t22 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e)))) :rule implies_neg2)
% 29.97/30.20  (step t23 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e)))) :rule resolution :premises (t21 t22))
% 29.97/30.20  (step t24 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e)))) :rule contraction :premises (t23))
% 29.97/30.20  (step t25 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) :rule implies :premises (t24))
% 29.97/30.20  (step t26 (cl (not (= (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) :rule equiv_pos2)
% 29.97/30.20  (step t27 (cl (= (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) :rule all_simplify)
% 29.97/30.20  (step t28 (cl (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) :rule resolution :premises (t26 t27 a75))
% 29.97/30.20  (step t29 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e))) :rule resolution :premises (t25 t28))
% 29.97/30.20  (step t30 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t18 a1187 a1137 t29))
% 29.97/30.20  (step t31 (cl (not (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule or_pos)
% 29.97/30.20  (step t32 (cl (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule reordering :premises (t31))
% 29.97/30.20  (step t33 (cl (not (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule or_pos)
% 29.97/30.20  (step t34 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule reordering :premises (t33))
% 29.97/30.20  (step t35 (cl (not (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule equiv_pos1)
% 29.97/30.20  (step t36 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule reordering :premises (t35))
% 29.97/30.20  (step t37 (cl (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t38 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule reordering :premises (t37))
% 29.97/30.20  (step t39 (cl (not (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule equiv_pos2)
% 29.97/30.20  (step t40 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule reordering :premises (t39))
% 29.97/30.20  (step t41 (cl (not (= (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (not (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) :rule equiv_pos2)
% 29.97/30.20  (step t42 (cl (= (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))))) :rule refl)
% 29.97/30.20  (step t43 (cl (= (= tptp.v_m tptp.v_x) (= tptp.v_m tptp.v_x))) :rule refl)
% 29.97/30.20  (step t44 (cl (= (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) true) (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) :rule equiv_simplify)
% 29.97/30.20  (step t45 (cl (not (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) true)) (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) :rule equiv1 :premises (t44))
% 29.97/30.20  (step t46 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))))) :rule all_simplify)
% 29.97/30.20  (step t47 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) :rule refl)
% 29.97/30.20  (step t48 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) :rule all_simplify)
% 29.97/30.20  (step t49 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) :rule cong :premises (t47 t48))
% 29.97/30.20  (step t50 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) true)) :rule all_simplify)
% 29.97/30.20  (step t51 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) true)) :rule trans :premises (t49 t50))
% 29.97/30.20  (step t52 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) true)) :rule trans :premises (t46 t51))
% 29.97/30.20  (step t53 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) :rule resolution :premises (t45 t52))
% 29.97/30.20  (step t54 (cl (= (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) :rule cong :premises (t42 t43 t53))
% 29.97/30.20  (step t55 (cl (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) :rule equiv_pos1)
% 29.97/30.20  (step t56 (cl (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (not (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))))) :rule or_neg)
% 29.97/30.20  (step t57 (cl (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (not (= tptp.v_m tptp.v_x))) :rule or_neg)
% 29.97/30.20  (step t58 (cl (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (not (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) :rule or_neg)
% 29.97/30.20  (step t59 (cl (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) :rule resolution :premises (t55 t56 t57 t58))
% 29.97/30.20  (step t60 (cl (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) :rule contraction :premises (t59))
% 29.97/30.20  (step t61 (cl (or (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) :rule resolution :premises (t41 t54 t60))
% 29.97/30.20  (step t62 (cl (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) (= tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) :rule or :premises (t61))
% 29.97/30.20  (step t63 (cl (= tptp.v_m tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) :rule reordering :premises (t62))
% 29.97/30.20  (step t64 (cl (not (= (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) (not (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule equiv_pos2)
% 29.97/30.20  (step t65 (cl (= (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule refl)
% 29.97/30.20  (step t66 (cl (= (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) true) (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule equiv_simplify)
% 29.97/30.20  (step t67 (cl (not (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) true)) (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule equiv1 :premises (t66))
% 29.97/30.20  (step t68 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))) :rule all_simplify)
% 29.97/30.20  (step t69 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule refl)
% 29.97/30.20  (step t70 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule all_simplify)
% 29.97/30.20  (step t71 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule cong :premises (t69 t70))
% 29.97/30.20  (step t72 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) true)) :rule all_simplify)
% 29.97/30.20  (step t73 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) true)) :rule trans :premises (t71 t72))
% 29.97/30.20  (step t74 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) true)) :rule trans :premises (t68 t73))
% 29.97/30.20  (step t75 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule resolution :premises (t67 t74))
% 29.97/30.20  (step t76 (cl (= (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule refl)
% 29.97/30.20  (step t77 (cl (= (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule refl)
% 29.97/30.20  (step t78 (cl (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule refl)
% 29.97/30.20  (step t79 (cl (= (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) :rule cong :premises (t65 t75 t76 t77 t78))
% 29.97/30.20  (step t80 (cl (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule and_neg)
% 29.97/30.20  (step t81 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t82)
% 29.97/30.20  (assume t82.a0 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))
% 29.97/30.20  (assume t82.a1 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 29.97/30.20  (assume t82.a2 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 29.97/30.20  (assume t82.a3 (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (step t82.t1 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t82.t2)
% 29.97/30.20  (assume t82.t2.a0 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 29.97/30.20  (assume t82.t2.a1 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 29.97/30.20  (assume t82.t2.a2 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))
% 29.97/30.20  (assume t82.t2.a3 (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (step t82.t2.t1 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) false) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule equiv_simplify)
% 29.97/30.20  (step t82.t2.t2 (cl (not (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) false)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule equiv1 :premises (t82.t2.t1))
% 29.97/30.20  (step t82.t2.t3 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 29.97/30.20  (step t82.t2.t4 (cl (= tptp.v_e tptp.v_e)) :rule refl)
% 29.97/30.20  (step t82.t2.t5 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule symm :premises (t82.t2.a3))
% 29.97/30.20  (step t82.t2.t6 (cl (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule symm :premises (t82.t2.t5))
% 29.97/30.20  (step t82.t2.t7 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) :rule symm :premises (t82.t2.a2))
% 29.97/30.20  (step t82.t2.t8 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule cong :premises (t82.t2.t3 t82.t2.t7))
% 29.97/30.20  (step t82.t2.t9 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) :rule symm :premises (t82.t2.a1))
% 29.97/30.20  (step t82.t2.t10 (cl (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) :rule trans :premises (t82.t2.t6 t82.t2.t8 t82.t2.t9))
% 29.97/30.20  (step t82.t2.t11 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule cong :premises (t82.t2.t3 t82.t2.t4 t82.t2.t10))
% 29.97/30.20  (step t82.t2.t12 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) false) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule equiv_simplify)
% 29.97/30.20  (step t82.t2.t13 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) false) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule equiv2 :premises (t82.t2.t12))
% 29.97/30.20  (step t82.t2.t14 (cl (not (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) :rule not_not)
% 29.97/30.20  (step t82.t2.t15 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) false) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) :rule resolution :premises (t82.t2.t13 t82.t2.t14))
% 29.97/30.20  (step t82.t2.t16 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) false)) :rule resolution :premises (t82.t2.t15 t82.t2.a0))
% 29.97/30.20  (step t82.t2.t17 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) false)) :rule trans :premises (t82.t2.t11 t82.t2.t16))
% 29.97/30.20  (step t82.t2.t18 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t82.t2.t2 t82.t2.t17))
% 29.97/30.20  (step t82.t2 (cl (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule subproof :discharge (t82.t2.a0 t82.t2.a1 t82.t2.a2 t82.t2.a3))
% 29.97/30.20  (step t82.t3 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 29.97/30.20  (step t82.t4 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 29.97/30.20  (step t82.t5 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t82.t6 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t82.t7 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t82.t2 t82.t3 t82.t4 t82.t5 t82.t6))
% 29.97/30.20  (step t82.t8 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule reordering :premises (t82.t7))
% 29.97/30.20  (step t82.t9 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule contraction :premises (t82.t8))
% 29.97/30.20  (step t82.t10 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t82.t1 t82.t9))
% 29.97/30.20  (step t82.t11 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule implies_neg2)
% 29.97/30.20  (step t82.t12 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (=> (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t82.t10 t82.t11))
% 29.97/30.20  (step t82.t13 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule contraction :premises (t82.t12))
% 29.97/30.20  (step t82.t14 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies :premises (t82.t13))
% 29.97/30.20  (step t82.t15 (cl (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule and_neg)
% 29.97/30.20  (step t82.t16 (cl (and (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t82.t15 t82.a1 t82.a2 t82.a0 t82.a3))
% 29.97/30.20  (step t82.t17 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t82.t14 t82.t16))
% 29.97/30.20  (step t82 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule subproof :discharge (t82.a0 t82.a1 t82.a2 t82.a3))
% 29.97/30.20  (step t83 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t84 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 29.97/30.20  (step t85 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 29.97/30.20  (step t86 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t87 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t82 t83 t84 t85 t86))
% 29.97/30.20  (step t88 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule reordering :premises (t87))
% 29.97/30.20  (step t89 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule contraction :premises (t88))
% 29.97/30.20  (step t90 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t81 t89))
% 29.97/30.20  (step t91 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule implies_neg2)
% 29.97/30.20  (step t92 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t90 t91))
% 29.97/30.20  (step t93 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule contraction :premises (t92))
% 29.97/30.20  (step t94 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies :premises (t93))
% 29.97/30.20  (step t95 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t80 t94))
% 29.97/30.20  (step t96 (cl (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule or_neg)
% 29.97/30.20  (step t97 (cl (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule or_neg)
% 29.97/30.20  (step t98 (cl (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule or_neg)
% 29.97/30.20  (step t99 (cl (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule or_neg)
% 29.97/30.20  (step t100 (cl (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule or_neg)
% 29.97/30.20  (step t101 (cl (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t95 t96 t97 t98 t99 t100))
% 29.97/30.20  (step t102 (cl (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule contraction :premises (t101))
% 29.97/30.20  (step t103 (cl (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t64 t79 t102))
% 29.97/30.20  (step t104 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule or :premises (t103))
% 29.97/30.20  (step t105 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule reordering :premises (t104))
% 29.97/30.20  (step t106 (cl (not (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule or_pos)
% 29.97/30.20  (step t107 (cl (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule reordering :premises (t106))
% 29.97/30.20  (step t108 (cl (=> (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t109)
% 29.97/30.20  (assume t109.a0 (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.20  (step t109.t1 (cl (or (not (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule forall_inst :args ((:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t109.t2 (cl (not (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule or :premises (t109.t1))
% 29.97/30.20  (step t109.t3 (cl (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t109.t2 t109.a0))
% 29.97/30.20  (step t109 (cl (not (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule subproof :discharge (t109.a0))
% 29.97/30.20  (step t110 (cl (=> (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t108 t109))
% 29.97/30.20  (step t111 (cl (=> (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule implies_neg2)
% 29.97/30.20  (step t112 (cl (=> (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (=> (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule resolution :premises (t110 t111))
% 29.97/30.20  (step t113 (cl (=> (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule contraction :premises (t112))
% 29.97/30.20  (step t114 (cl (not (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule implies :premises (t113))
% 29.97/30.20  (step t115 (cl (not (= (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))) (not (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))) :rule equiv_pos2)
% 29.97/30.20  (anchor :step t116 :args ((T_a $$unsorted) (:= T_a T_a)))
% 29.97/30.20  (step t116.t1 (cl (= T_a T_a)) :rule refl)
% 29.97/30.20  (step t116.t2 (cl (= (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.class_RealVector_Oreal__normed__vector T_a))) :rule refl)
% 29.97/30.20  (step t116.t3 (cl (= (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) :rule all_simplify)
% 29.97/30.20  (step t116.t4 (cl (= (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))) :rule cong :premises (t116.t2 t116.t3))
% 29.97/30.20  (step t116 (cl (= (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))) :rule bind)
% 29.97/30.20  (step t117 (cl (= (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))) :rule all_simplify)
% 29.97/30.20  (step t118 (cl (= (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))) :rule trans :premises (t116 t117))
% 29.97/30.20  (step t119 (cl (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))) :rule resolution :premises (t115 t118 a371))
% 29.97/30.20  (step t120 (cl (or (not (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t114 t119))
% 29.97/30.20  (step t121 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule resolution :premises (t107 a1113 t120))
% 29.97/30.20  (step t122 (cl (not (= (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) (not (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule equiv_pos2)
% 29.97/30.20  (step t123 (cl (= (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))))) :rule refl)
% 29.97/30.20  (step t124 (cl (= (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule all_simplify)
% 29.97/30.20  (step t125 (cl (= (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule cong :premises (t123 t124))
% 29.97/30.20  (step t126 (cl (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r)))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t127)
% 29.97/30.20  (assume t127.a0 (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))))
% 29.97/30.20  (step t127.t1 (cl (or (not (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r)))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule forall_inst :args ((:= V_r (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (step t127.t2 (cl (not (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r)))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule or :premises (t127.t1))
% 29.97/30.20  (step t127.t3 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t127.t2 t127.a0))
% 29.97/30.20  (step t127 (cl (not (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r)))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule subproof :discharge (t127.a0))
% 29.97/30.20  (step t128 (cl (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t126 t127))
% 29.97/30.20  (step t129 (cl (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies_neg2)
% 29.97/30.20  (step t130 (cl (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t128 t129))
% 29.97/30.20  (step t131 (cl (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule contraction :premises (t130))
% 29.97/30.20  (step t132 (cl (=> (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t122 t125 t131))
% 29.97/30.20  (step t133 (cl (not (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r)))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule implies :premises (t132))
% 29.97/30.20  (step t134 (cl (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t133 a413))
% 29.97/30.20  (step t135 (cl (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule or_pos)
% 29.97/30.20  (step t136 (cl (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule reordering :premises (t135))
% 29.97/30.20  (step t137 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t138)
% 29.97/30.20  (assume t138.a0 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))
% 29.97/30.20  (step t138.t1 (cl (or (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule forall_inst :args ((:= V_y tptp.v_e) (:= V_x (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t138.t2 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule or :premises (t138.t1))
% 29.97/30.20  (step t138.t3 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t138.t2 t138.a0))
% 29.97/30.20  (step t138 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule subproof :discharge (t138.a0))
% 29.97/30.20  (step t139 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t137 t138))
% 29.97/30.20  (step t140 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule implies_neg2)
% 29.97/30.20  (step t141 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t139 t140))
% 29.97/30.20  (step t142 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule contraction :premises (t141))
% 29.97/30.20  (step t143 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies :premises (t142))
% 29.97/30.20  (step t144 (cl (not (= (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) :rule equiv_pos2)
% 29.97/30.20  (anchor :step t145 :args ((V_y $$unsorted) (:= V_y V_y) (V_x $$unsorted) (:= V_x V_x) (T_a $$unsorted) (:= T_a T_a)))
% 29.97/30.20  (step t145.t1 (cl (= V_y V_y)) :rule refl)
% 29.97/30.20  (step t145.t2 (cl (= V_x V_x)) :rule refl)
% 29.97/30.20  (step t145.t3 (cl (= T_a T_a)) :rule refl)
% 29.97/30.20  (step t145.t4 (cl (= (tptp.class_Orderings_Olinorder T_a) (tptp.class_Orderings_Olinorder T_a))) :rule refl)
% 29.97/30.20  (step t145.t5 (cl (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) :rule refl)
% 29.97/30.20  (step t145.t6 (cl (= (= V_x V_y) (= V_y V_x))) :rule all_simplify)
% 29.97/30.20  (step t145.t7 (cl (= (not (= V_x V_y)) (not (= V_y V_x)))) :rule cong :premises (t145.t6))
% 29.97/30.20  (step t145.t8 (cl (= (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))) :rule refl)
% 29.97/30.20  (step t145.t9 (cl (= (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)) (=> (not (= V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) :rule cong :premises (t145.t7 t145.t8))
% 29.97/30.20  (step t145.t10 (cl (= (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) :rule cong :premises (t145.t5 t145.t9))
% 29.97/30.20  (step t145.t11 (cl (= (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))) :rule cong :premises (t145.t4 t145.t10))
% 29.97/30.20  (step t145 (cl (= (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))) :rule bind)
% 29.97/30.20  (step t146 (cl (= (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) :rule all_simplify)
% 29.97/30.20  (step t147 (cl (= (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) :rule trans :premises (t145 t146))
% 29.97/30.20  (step t148 (cl (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_y V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) :rule resolution :premises (t144 t147 a29))
% 29.97/30.20  (step t149 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t143 t148))
% 29.97/30.20  (step t150 (cl (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule and_neg)
% 29.97/30.20  (step t151 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t152)
% 29.97/30.20  (assume t152.a0 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))
% 29.97/30.20  (assume t152.a1 (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (assume t152.a2 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 29.97/30.20  (assume t152.a3 (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (step t152.t1 (cl (=> (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t152.t2)
% 29.97/30.20  (assume t152.t2.a0 (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (assume t152.t2.a1 (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (assume t152.t2.a2 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))
% 29.97/30.20  (assume t152.t2.a3 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))
% 29.97/30.20  (step t152.t2.t1 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) :rule symm :premises (t152.t2.a3))
% 29.97/30.20  (step t152.t2.t2 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule symm :premises (t152.t2.t1))
% 29.97/30.20  (step t152.t2.t3 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 29.97/30.20  (step t152.t2.t4 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) :rule symm :premises (t152.t2.a2))
% 29.97/30.20  (step t152.t2.t5 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule symm :premises (t152.t2.t4))
% 29.97/30.20  (step t152.t2.t6 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule cong :premises (t152.t2.t3 t152.t2.t5))
% 29.97/30.20  (step t152.t2.t7 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule symm :premises (t152.t2.a1))
% 29.97/30.20  (step t152.t2.t8 (cl (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) tptp.v_e)) :rule symm :premises (t152.t2.a0))
% 29.97/30.20  (step t152.t2.t9 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule trans :premises (t152.t2.t2 t152.t2.t6 t152.t2.t7 t152.t2.t8))
% 29.97/30.20  (step t152.t2 (cl (not (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule subproof :discharge (t152.t2.a0 t152.t2.a1 t152.t2.a2 t152.t2.a3))
% 29.97/30.20  (step t152.t3 (cl (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t152.t4 (cl (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t152.t5 (cl (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t152.t6 (cl (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 29.97/30.20  (step t152.t7 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e) (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule resolution :premises (t152.t2 t152.t3 t152.t4 t152.t5 t152.t6))
% 29.97/30.20  (step t152.t8 (cl (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule reordering :premises (t152.t7))
% 29.97/30.20  (step t152.t9 (cl (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule contraction :premises (t152.t8))
% 29.97/30.20  (step t152.t10 (cl (=> (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule resolution :premises (t152.t1 t152.t9))
% 29.97/30.20  (step t152.t11 (cl (=> (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule implies_neg2)
% 29.97/30.20  (step t152.t12 (cl (=> (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (=> (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule resolution :premises (t152.t10 t152.t11))
% 29.97/30.20  (step t152.t13 (cl (=> (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule contraction :premises (t152.t12))
% 29.97/30.20  (step t152.t14 (cl (not (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule implies :premises (t152.t13))
% 29.97/30.20  (step t152.t15 (cl (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule and_neg)
% 29.97/30.20  (step t152.t16 (cl (and (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t152.t15 t152.a1 t152.a3 t152.a0 t152.a2))
% 29.97/30.20  (step t152.t17 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule resolution :premises (t152.t14 t152.t16))
% 29.97/30.20  (step t152 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule subproof :discharge (t152.a0 t152.a1 t152.a2 t152.a3))
% 29.97/30.20  (step t153 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t154 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t155 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 29.97/30.20  (step t156 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule and_pos)
% 29.97/30.20  (step t157 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t152 t153 t154 t155 t156))
% 29.97/30.20  (step t158 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule reordering :premises (t157))
% 29.97/30.20  (step t159 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule contraction :premises (t158))
% 29.97/30.20  (step t160 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule resolution :premises (t151 t159))
% 29.97/30.20  (step t161 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule implies_neg2)
% 29.97/30.20  (step t162 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule resolution :premises (t160 t161))
% 29.97/30.20  (step t163 (cl (=> (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule contraction :premises (t162))
% 29.97/30.20  (step t164 (cl (not (and (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule implies :premises (t163))
% 29.97/30.20  (step t165 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) :rule resolution :premises (t150 t164))
% 29.97/30.20  (step t166 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_e (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule reordering :premises (t165))
% 29.97/30.20  (step t167 (cl (not (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))) :rule or_pos)
% 29.97/30.20  (step t168 (cl (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)) (not (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule reordering :premises (t167))
% 29.97/30.20  (step t169 (cl (=> (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t170)
% 29.97/30.20  (assume t170.a0 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))
% 29.97/30.20  (step t170.t1 (cl (or (not (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule forall_inst :args ((:= V_d tptp.v_x) (:= V_c tptp.v_m) (:= V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (:= V_a tptp.v_e) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t170.t2 (cl (not (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule or :premises (t170.t1))
% 29.97/30.20  (step t170.t3 (cl (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule resolution :premises (t170.t2 t170.a0))
% 29.97/30.20  (step t170 (cl (not (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule subproof :discharge (t170.a0))
% 29.97/30.20  (step t171 (cl (=> (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule resolution :premises (t169 t170))
% 29.97/30.20  (step t172 (cl (=> (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule implies_neg2)
% 29.97/30.20  (step t173 (cl (=> (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (=> (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule resolution :premises (t171 t172))
% 29.97/30.20  (step t174 (cl (=> (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule contraction :premises (t173))
% 29.97/30.20  (step t175 (cl (not (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule implies :premises (t174))
% 29.97/30.20  (step t176 (cl (not (= (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (not (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) :rule equiv_pos2)
% 29.97/30.20  (step t177 (cl (= (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) :rule all_simplify)
% 29.97/30.20  (step t178 (cl (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) :rule resolution :premises (t176 t177 a8))
% 29.97/30.20  (step t179 (cl (or (not (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule resolution :premises (t175 t178))
% 29.97/30.20  (step t180 (cl (not (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule equiv_pos1)
% 29.97/30.20  (step t181 (cl (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (not (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)))) :rule reordering :premises (t180))
% 29.97/30.20  (step t182 (cl (not (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)))) (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule or_pos)
% 29.97/30.20  (step t183 (cl (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)) (not (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))))) :rule reordering :premises (t182))
% 29.97/30.20  (step t184 (cl (not (= (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)))))) (not (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))))) :rule equiv_pos2)
% 29.97/30.20  (step t185 (cl (= (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))) :rule refl)
% 29.97/30.20  (step t186 (cl (= (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)))) :rule refl)
% 29.97/30.20  (step t187 (cl (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule refl)
% 29.97/30.20  (step t188 (cl (= (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule all_simplify)
% 29.97/30.20  (step t189 (cl (= (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)))) :rule cong :premises (t187 t188))
% 29.97/30.20  (step t190 (cl (= (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))))) :rule cong :premises (t186 t189))
% 29.97/30.20  (step t191 (cl (= (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)))))) :rule cong :premises (t185 t190))
% 29.97/30.20  (step t192 (cl (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t193)
% 29.97/30.20  (assume t193.a0 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 29.97/30.20  (step t193.t1 (cl (or (not (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule forall_inst :args ((:= V_a_2 tptp.v_e) (:= V_b_2 tptp.v_m) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t193.t2 (cl (not (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule or :premises (t193.t1))
% 29.97/30.20  (step t193.t3 (cl (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t193.t2 t193.a0))
% 29.97/30.20  (step t193 (cl (not (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule subproof :discharge (t193.a0))
% 29.97/30.20  (step t194 (cl (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t192 t193))
% 29.97/30.20  (step t195 (cl (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (not (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule implies_neg2)
% 29.97/30.20  (step t196 (cl (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule resolution :premises (t194 t195))
% 29.97/30.20  (step t197 (cl (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_e (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) :rule contraction :premises (t196))
% 29.97/30.20  (step t198 (cl (=> (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))))) :rule resolution :premises (t184 t191 t197))
% 29.97/30.20  (step t199 (cl (not (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)))) :rule implies :premises (t198))
% 29.97/30.20  (step t200 (cl (not (= (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))) (not (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) :rule equiv_pos2)
% 29.97/30.20  (step t201 (cl (= (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))) :rule all_simplify)
% 29.97/30.20  (step t202 (cl (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a)) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) :rule resolution :premises (t200 t201 a133))
% 29.97/30.20  (step t203 (cl (or (not (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal)) (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e)))) :rule resolution :premises (t199 t202))
% 29.97/30.20  (step t204 (cl (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_e))) :rule resolution :premises (t183 a1096 t203))
% 29.97/30.20  (step t205 (cl (not (= (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))))) (not (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule equiv_pos2)
% 29.97/30.20  (step t206 (cl (= (not (= tptp.v_m tptp.v_x)) (not (= tptp.v_m tptp.v_x)))) :rule refl)
% 29.97/30.20  (step t207 (cl (= (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) true) (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule equiv_simplify)
% 29.97/30.20  (step t208 (cl (not (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) true)) (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule equiv1 :premises (t207))
% 29.97/30.20  (step t209 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))))) :rule all_simplify)
% 29.97/30.20  (step t210 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule refl)
% 29.97/30.20  (step t211 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule all_simplify)
% 29.97/30.20  (step t212 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule cong :premises (t210 t211))
% 29.97/30.20  (step t213 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) true)) :rule all_simplify)
% 29.97/30.20  (step t214 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) true)) :rule trans :premises (t212 t213))
% 29.97/30.20  (step t215 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) true)) :rule trans :premises (t209 t214))
% 29.97/30.20  (step t216 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule resolution :premises (t208 t215))
% 29.97/30.20  (step t217 (cl (= (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule refl)
% 29.97/30.20  (step t218 (cl (= (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule refl)
% 29.97/30.20  (step t219 (cl (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule refl)
% 29.97/30.20  (step t220 (cl (= (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))))) :rule cong :premises (t206 t65 t216 t217 t218 t219))
% 29.97/30.20  (step t221 (cl (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule and_neg)
% 29.97/30.20  (step t222 (cl (=> (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t223)
% 29.97/30.20  (assume t223.a0 (= tptp.v_m tptp.v_x))
% 29.97/30.20  (assume t223.a1 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))
% 29.97/30.20  (assume t223.a2 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))
% 29.97/30.20  (assume t223.a3 (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))
% 29.97/30.20  (assume t223.a4 (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))
% 29.97/30.20  (step t223.t1 (cl (=> (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t223.t2)
% 29.97/30.20  (assume t223.t2.a0 (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))
% 29.97/30.20  (assume t223.t2.a1 (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))
% 29.97/30.20  (assume t223.t2.a2 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))
% 29.97/30.20  (assume t223.t2.a3 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))
% 29.97/30.20  (assume t223.t2.a4 (= tptp.v_m tptp.v_x))
% 29.97/30.20  (step t223.t2.t1 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)) false) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule equiv_simplify)
% 29.97/30.20  (step t223.t2.t2 (cl (not (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)) false)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule equiv1 :premises (t223.t2.t1))
% 29.97/30.20  (step t223.t2.t3 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 29.97/30.20  (step t223.t2.t4 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) :rule symm :premises (t223.t2.a0))
% 29.97/30.20  (step t223.t2.t5 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) :rule symm :premises (t223.t2.a3))
% 29.97/30.20  (step t223.t2.t6 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule symm :premises (t223.t2.t5))
% 29.97/30.20  (step t223.t2.t7 (cl (= tptp.v_x tptp.v_m)) :rule symm :premises (t223.t2.a4))
% 29.97/30.20  (step t223.t2.t8 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) :rule cong :premises (t223.t2.t3 t223.t2.t6 t223.t2.t7))
% 29.97/30.20  (step t223.t2.t9 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m) tptp.v_x)) :rule symm :premises (t223.t2.a1))
% 29.97/30.20  (step t223.t2.t10 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x) tptp.v_x)) :rule trans :premises (t223.t2.t8 t223.t2.t9))
% 29.97/30.20  (step t223.t2.t11 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule cong :premises (t223.t2.t3 t223.t2.t4 t223.t2.t10))
% 29.97/30.20  (step t223.t2.t12 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) false) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule equiv_simplify)
% 29.97/30.20  (step t223.t2.t13 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) false) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule equiv2 :premises (t223.t2.t12))
% 29.97/30.20  (step t223.t2.t14 (cl (not (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) :rule not_not)
% 29.97/30.20  (step t223.t2.t15 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) false) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) :rule resolution :premises (t223.t2.t13 t223.t2.t14))
% 29.97/30.20  (step t223.t2.t16 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) false)) :rule resolution :premises (t223.t2.t15 t223.t2.a2))
% 29.97/30.20  (step t223.t2.t17 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)) false)) :rule trans :premises (t223.t2.t11 t223.t2.t16))
% 29.97/30.20  (step t223.t2.t18 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule resolution :premises (t223.t2.t2 t223.t2.t17))
% 29.97/30.20  (step t223.t2 (cl (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule subproof :discharge (t223.t2.a0 t223.t2.a1 t223.t2.a2 t223.t2.a3 t223.t2.a4))
% 29.97/30.20  (step t223.t3 (cl (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t223.t4 (cl (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t223.t5 (cl (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule and_pos)
% 29.97/30.20  (step t223.t6 (cl (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t223.t7 (cl (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (= tptp.v_m tptp.v_x)) :rule and_pos)
% 29.97/30.20  (step t223.t8 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)))) :rule resolution :premises (t223.t2 t223.t3 t223.t4 t223.t5 t223.t6 t223.t7))
% 29.97/30.20  (step t223.t9 (cl (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule reordering :premises (t223.t8))
% 29.97/30.20  (step t223.t10 (cl (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule contraction :premises (t223.t9))
% 29.97/30.20  (step t223.t11 (cl (=> (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule resolution :premises (t223.t1 t223.t10))
% 29.97/30.20  (step t223.t12 (cl (=> (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule implies_neg2)
% 29.97/30.20  (step t223.t13 (cl (=> (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (=> (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule resolution :premises (t223.t11 t223.t12))
% 29.97/30.20  (step t223.t14 (cl (=> (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule contraction :premises (t223.t13))
% 29.97/30.20  (step t223.t15 (cl (not (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule implies :premises (t223.t14))
% 29.97/30.20  (step t223.t16 (cl (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_m tptp.v_x))) :rule and_neg)
% 29.97/30.20  (step t223.t17 (cl (and (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x))) :rule resolution :premises (t223.t16 t223.a4 t223.a3 t223.a2 t223.a1 t223.a0))
% 29.97/30.20  (step t223.t18 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule resolution :premises (t223.t15 t223.t17))
% 29.97/30.20  (step t223 (cl (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule subproof :discharge (t223.a0 t223.a1 t223.a2 t223.a3 t223.a4))
% 29.97/30.20  (step t224 (cl (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (= tptp.v_m tptp.v_x)) :rule and_pos)
% 29.97/30.20  (step t225 (cl (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t226 (cl (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule and_pos)
% 29.97/30.20  (step t227 (cl (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t228 (cl (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t229 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule resolution :premises (t223 t224 t225 t226 t227 t228))
% 29.97/30.20  (step t230 (cl (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule reordering :premises (t229))
% 29.97/30.20  (step t231 (cl (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule contraction :premises (t230))
% 29.97/30.20  (step t232 (cl (=> (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule resolution :premises (t222 t231))
% 29.97/30.20  (step t233 (cl (=> (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule implies_neg2)
% 29.97/30.20  (step t234 (cl (=> (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (=> (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule resolution :premises (t232 t233))
% 29.97/30.20  (step t235 (cl (=> (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule contraction :premises (t234))
% 29.97/30.20  (step t236 (cl (not (and (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule implies :premises (t235))
% 29.97/30.20  (step t237 (cl (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule resolution :premises (t221 t236))
% 29.97/30.20  (step t238 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (not (= tptp.v_m tptp.v_x)))) :rule or_neg)
% 29.97/30.20  (step t239 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule or_neg)
% 29.97/30.20  (step t240 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule or_neg)
% 29.97/30.20  (step t241 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule or_neg)
% 29.97/30.20  (step t242 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule or_neg)
% 29.97/30.20  (step t243 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule or_neg)
% 29.97/30.20  (step t244 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule resolution :premises (t237 t238 t239 t240 t241 t242 t243))
% 29.97/30.20  (step t245 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule contraction :premises (t244))
% 29.97/30.20  (step t246 (cl (or (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x))))) :rule resolution :premises (t205 t220 t245))
% 29.97/30.20  (step t247 (cl (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_x)))) :rule or :premises (t246))
% 29.97/30.20  (step t248 (cl (not (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) :rule or_pos)
% 29.97/30.20  (step t249 (cl (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (not (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule reordering :premises (t248))
% 29.97/30.20  (step t250 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t251)
% 29.97/30.20  (assume t251.a0 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))
% 29.97/30.20  (step t251.t1 (cl (or (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule forall_inst :args ((:= V_c tptp.v_e) (:= V_a tptp.v_m) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t251.t2 (cl (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule or :premises (t251.t1))
% 29.97/30.20  (step t251.t3 (cl (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule resolution :premises (t251.t2 t251.a0))
% 29.97/30.20  (step t251 (cl (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule subproof :discharge (t251.a0))
% 29.97/30.20  (step t252 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule resolution :premises (t250 t251))
% 29.97/30.20  (step t253 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule implies_neg2)
% 29.97/30.20  (step t254 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule resolution :premises (t252 t253))
% 29.97/30.20  (step t255 (cl (=> (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule contraction :premises (t254))
% 29.97/30.20  (step t256 (cl (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule implies :premises (t255))
% 29.97/30.20  (step t257 (cl (not (= (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))) (not (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) :rule equiv_pos2)
% 29.97/30.20  (step t258 (cl (= (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))) :rule all_simplify)
% 29.97/30.20  (step t259 (cl (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Ocomm__semiring__1 T_a)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a))))) :rule resolution :premises (t257 t258 a115))
% 29.97/30.20  (step t260 (cl (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule resolution :premises (t256 t259))
% 29.97/30.20  (step t261 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) :rule resolution :premises (t249 a1131 t260))
% 29.97/30.20  (step t262 (cl (not (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) :rule or_pos)
% 29.97/30.20  (step t263 (cl (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (not (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule reordering :premises (t262))
% 29.97/30.20  (step t264 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t265)
% 29.97/30.20  (assume t265.a0 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))))
% 29.97/30.20  (step t265.t1 (cl (or (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b))))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule forall_inst :args ((:= V_b tptp.v_m) (:= V_a tptp.v_x) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t265.t2 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b))))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule or :premises (t265.t1))
% 29.97/30.20  (step t265.t3 (cl (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t265.t2 t265.a0))
% 29.97/30.20  (step t265 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b))))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule subproof :discharge (t265.a0))
% 29.97/30.20  (step t266 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t264 t265))
% 29.97/30.20  (step t267 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule implies_neg2)
% 29.97/30.20  (step t268 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule resolution :premises (t266 t267))
% 29.97/30.20  (step t269 (cl (=> (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule contraction :premises (t268))
% 29.97/30.20  (step t270 (cl (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b))))) (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule implies :premises (t269))
% 29.97/30.20  (step t271 (cl (not (= (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))))) (not (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b))))) :rule equiv_pos2)
% 29.97/30.20  (anchor :step t272 :args ((V_b $$unsorted) (:= V_b V_b) (V_a $$unsorted) (:= V_a V_a) (T_a $$unsorted) (:= T_a T_a)))
% 29.97/30.20  (step t272.t1 (cl (= V_b V_b)) :rule refl)
% 29.97/30.20  (step t272.t2 (cl (= V_a V_a)) :rule refl)
% 29.97/30.20  (step t272.t3 (cl (= T_a T_a)) :rule refl)
% 29.97/30.20  (step t272.t4 (cl (= (tptp.class_Groups_Ogroup__add T_a) (tptp.class_Groups_Ogroup__add T_a))) :rule refl)
% 29.97/30.20  (step t272.t5 (cl (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))) :rule all_simplify)
% 29.97/30.20  (step t272.t6 (cl (= (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a)) (=> (tptp.class_Groups_Ogroup__add T_a) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b))))) :rule cong :premises (t272.t4 t272.t5))
% 29.97/30.20  (step t272 (cl (= (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))))) :rule bind)
% 29.97/30.20  (step t273 (cl (= (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))))) :rule all_simplify)
% 29.97/30.20  (step t274 (cl (= (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b)))))) :rule trans :premises (t272 t273))
% 29.97/30.20  (step t275 (cl (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ogroup__add T_a)) (= V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b))))) :rule resolution :premises (t271 t274 a100))
% 29.97/30.20  (step t276 (cl (or (not (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t270 t275))
% 29.97/30.20  (step t277 (cl (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) :rule resolution :premises (t263 a1142 t276))
% 29.97/30.20  (step t278 (cl (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule or_pos)
% 29.97/30.20  (step t279 (cl (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule reordering :premises (t278))
% 29.97/30.20  (step t280 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t281)
% 29.97/30.20  (assume t281.a0 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 29.97/30.20  (step t281.t1 (cl (or (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule forall_inst :args ((:= V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (:= V_x tptp.v_x) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t281.t2 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule or :premises (t281.t1))
% 29.97/30.20  (step t281.t3 (cl (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule resolution :premises (t281.t2 t281.a0))
% 29.97/30.20  (step t281 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule subproof :discharge (t281.a0))
% 29.97/30.20  (step t282 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule resolution :premises (t280 t281))
% 29.97/30.20  (step t283 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule implies_neg2)
% 29.97/30.20  (step t284 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule resolution :premises (t282 t283))
% 29.97/30.20  (step t285 (cl (=> (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule contraction :premises (t284))
% 29.97/30.20  (step t286 (cl (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule implies :premises (t285))
% 29.97/30.20  (step t287 (cl (not (= (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))) (not (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) :rule equiv_pos2)
% 29.97/30.20  (step t288 (cl (= (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))) :rule all_simplify)
% 29.97/30.20  (step t289 (cl (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) :rule resolution :premises (t287 t288 a30))
% 29.97/30.20  (step t290 (cl (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule resolution :premises (t286 t289))
% 29.97/30.20  (step t291 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule resolution :premises (t279 a1136 a1186 t290))
% 29.97/30.20  (step t292 (cl (not (= (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (or (not (= tptp.v_m tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) (not (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (or (not (= tptp.v_m tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule equiv_pos2)
% 29.97/30.20  (step t293 (cl (= (= (= (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) true) (= (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule equiv_simplify)
% 29.97/30.20  (step t294 (cl (not (= (= (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) true)) (= (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule equiv1 :premises (t293))
% 29.97/30.20  (step t295 (cl (= (= (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))))) :rule all_simplify)
% 29.97/30.20  (step t296 (cl (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule refl)
% 29.97/30.20  (step t297 (cl (= (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule all_simplify)
% 29.97/30.20  (step t298 (cl (= (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule cong :premises (t296 t297))
% 29.97/30.20  (step t299 (cl (= (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) true)) :rule all_simplify)
% 29.97/30.20  (step t300 (cl (= (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) true)) :rule trans :premises (t298 t299))
% 29.97/30.20  (step t301 (cl (= (= (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) true)) :rule trans :premises (t295 t300))
% 29.97/30.20  (step t302 (cl (= (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule resolution :premises (t294 t301))
% 29.97/30.20  (step t303 (cl (= (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule refl)
% 29.97/30.20  (step t304 (cl (= (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (or (not (= tptp.v_m tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule cong :premises (t206 t302 t303))
% 29.97/30.20  (step t305 (cl (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule and_neg)
% 29.97/30.20  (step t306 (cl (=> (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t307)
% 29.97/30.20  (assume t307.a0 (= tptp.v_m tptp.v_x))
% 29.97/30.20  (assume t307.a1 (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))
% 29.97/30.20  (step t307.t1 (cl (=> (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t307.t2)
% 29.97/30.20  (assume t307.t2.a0 (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))
% 29.97/30.20  (assume t307.t2.a1 (= tptp.v_m tptp.v_x))
% 29.97/30.20  (step t307.t2.t1 (cl (= (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) false) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule equiv_simplify)
% 29.97/30.20  (step t307.t2.t2 (cl (not (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) false)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule equiv1 :premises (t307.t2.t1))
% 29.97/30.20  (step t307.t2.t3 (cl (= tptp.v_x tptp.v_m)) :rule symm :premises (t307.t2.a1))
% 29.97/30.20  (step t307.t2.t4 (cl (= tptp.v_m tptp.v_x)) :rule symm :premises (t307.t2.t3))
% 29.97/30.20  (step t307.t2.t5 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) :rule refl)
% 29.97/30.20  (step t307.t2.t6 (cl (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule cong :premises (t307.t2.t4 t307.t2.t5))
% 29.97/30.20  (step t307.t2.t7 (cl (= (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) false) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule equiv_simplify)
% 29.97/30.20  (step t307.t2.t8 (cl (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) false) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule equiv2 :premises (t307.t2.t7))
% 29.97/30.20  (step t307.t2.t9 (cl (not (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) :rule not_not)
% 29.97/30.20  (step t307.t2.t10 (cl (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) false) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) :rule resolution :premises (t307.t2.t8 t307.t2.t9))
% 29.97/30.20  (step t307.t2.t11 (cl (= (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) false)) :rule resolution :premises (t307.t2.t10 t307.t2.a0))
% 29.97/30.20  (step t307.t2.t12 (cl (= (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) false)) :rule trans :premises (t307.t2.t6 t307.t2.t11))
% 29.97/30.20  (step t307.t2.t13 (cl (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule resolution :premises (t307.t2.t2 t307.t2.t12))
% 29.97/30.20  (step t307.t2 (cl (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m tptp.v_x)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule subproof :discharge (t307.t2.a0 t307.t2.a1))
% 29.97/30.20  (step t307.t3 (cl (not (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule and_pos)
% 29.97/30.20  (step t307.t4 (cl (not (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) (= tptp.v_m tptp.v_x)) :rule and_pos)
% 29.97/30.20  (step t307.t5 (cl (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) (not (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x)))) :rule resolution :premises (t307.t2 t307.t3 t307.t4))
% 29.97/30.20  (step t307.t6 (cl (not (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) (not (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule reordering :premises (t307.t5))
% 29.97/30.20  (step t307.t7 (cl (not (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule contraction :premises (t307.t6))
% 29.97/30.20  (step t307.t8 (cl (=> (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule resolution :premises (t307.t1 t307.t7))
% 29.97/30.20  (step t307.t9 (cl (=> (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule implies_neg2)
% 29.97/30.20  (step t307.t10 (cl (=> (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (=> (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule resolution :premises (t307.t8 t307.t9))
% 29.97/30.20  (step t307.t11 (cl (=> (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule contraction :premises (t307.t10))
% 29.97/30.20  (step t307.t12 (cl (not (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule implies :premises (t307.t11))
% 29.97/30.20  (step t307.t13 (cl (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m tptp.v_x))) :rule and_neg)
% 29.97/30.20  (step t307.t14 (cl (and (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (= tptp.v_m tptp.v_x))) :rule resolution :premises (t307.t13 t307.a1 t307.a0))
% 29.97/30.20  (step t307.t15 (cl (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule resolution :premises (t307.t12 t307.t14))
% 29.97/30.20  (step t307 (cl (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule subproof :discharge (t307.a0 t307.a1))
% 29.97/30.20  (step t308 (cl (not (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (= tptp.v_m tptp.v_x)) :rule and_pos)
% 29.97/30.20  (step t309 (cl (not (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule and_pos)
% 29.97/30.20  (step t310 (cl (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule resolution :premises (t307 t308 t309))
% 29.97/30.20  (step t311 (cl (not (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule reordering :premises (t310))
% 29.97/30.20  (step t312 (cl (not (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule contraction :premises (t311))
% 29.97/30.20  (step t313 (cl (=> (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule resolution :premises (t306 t312))
% 29.97/30.20  (step t314 (cl (=> (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule implies_neg2)
% 29.97/30.20  (step t315 (cl (=> (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (=> (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule resolution :premises (t313 t314))
% 29.97/30.20  (step t316 (cl (=> (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule contraction :premises (t315))
% 29.97/30.20  (step t317 (cl (not (and (= tptp.v_m tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule implies :premises (t316))
% 29.97/30.20  (step t318 (cl (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule resolution :premises (t305 t317))
% 29.97/30.20  (step t319 (cl (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (not (= tptp.v_m tptp.v_x)))) :rule or_neg)
% 29.97/30.20  (step t320 (cl (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule or_neg)
% 29.97/30.20  (step t321 (cl (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule or_neg)
% 29.97/30.20  (step t322 (cl (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule resolution :premises (t318 t319 t320 t321))
% 29.97/30.20  (step t323 (cl (or (not (= tptp.v_m tptp.v_x)) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule contraction :premises (t322))
% 29.97/30.20  (step t324 (cl (or (not (= tptp.v_m tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule resolution :premises (t292 t304 t323))
% 29.97/30.20  (step t325 (cl (not (= tptp.v_m tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (not (= tptp.v_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule or :premises (t324))
% 29.97/30.20  (step t326 (cl (not (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule equiv_pos2)
% 29.97/30.20  (step t327 (cl (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule reordering :premises (t326))
% 29.97/30.20  (step t328 (cl (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule or_neg)
% 29.97/30.20  (step t329 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule reordering :premises (t328))
% 29.97/30.20  (step t330 (cl (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule resolution :premises (t329 a1186))
% 29.97/30.20  (step t331 (cl (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule or_pos)
% 29.97/30.20  (step t332 (cl (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))))) :rule reordering :premises (t331))
% 29.97/30.20  (step t333 (cl (not (= (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))))) (not (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))))) :rule equiv_pos2)
% 29.97/30.20  (step t334 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))))) :rule refl)
% 29.97/30.20  (step t335 (cl (= (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)))) :rule refl)
% 29.97/30.20  (step t336 (cl (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule refl)
% 29.97/30.20  (step t337 (cl (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule all_simplify)
% 29.97/30.20  (step t338 (cl (= (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule cong :premises (t337))
% 29.97/30.20  (step t339 (cl (= (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule cong :premises (t336 t338))
% 29.97/30.20  (step t340 (cl (= (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))))) :rule cong :premises (t335 t339))
% 29.97/30.20  (step t341 (cl (= (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))))) :rule cong :premises (t334 t340))
% 29.97/30.20  (step t342 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2)))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t343)
% 29.97/30.20  (assume t343.a0 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))))
% 29.97/30.20  (step t343.t1 (cl (or (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))))) :rule forall_inst :args ((:= V_y_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (:= V_x_2 tptp.v_x) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t343.t2 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule or :premises (t343.t1))
% 29.97/30.20  (step t343.t3 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule resolution :premises (t343.t2 t343.a0))
% 29.97/30.20  (step t343 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule subproof :discharge (t343.a0))
% 29.97/30.20  (step t344 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule resolution :premises (t342 t343))
% 29.97/30.20  (step t345 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))))) :rule implies_neg2)
% 29.97/30.20  (step t346 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))))) :rule resolution :premises (t344 t345))
% 29.97/30.20  (step t347 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))))) :rule contraction :premises (t346))
% 29.97/30.20  (step t348 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))))) :rule resolution :premises (t333 t341 t347))
% 29.97/30.20  (step t349 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule implies :premises (t348))
% 29.97/30.20  (step t350 (cl (not (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))))) (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2)))))) :rule equiv_pos2)
% 29.97/30.20  (anchor :step t351 :args ((V_y_2 $$unsorted) (:= V_y_2 V_y_2) (V_x_2 $$unsorted) (:= V_x_2 V_x_2) (T_a $$unsorted) (:= T_a T_a)))
% 29.97/30.20  (step t351.t1 (cl (= V_y_2 V_y_2)) :rule refl)
% 29.97/30.20  (step t351.t2 (cl (= V_x_2 V_x_2)) :rule refl)
% 29.97/30.20  (step t351.t3 (cl (= T_a T_a)) :rule refl)
% 29.97/30.20  (step t351.t4 (cl (= (tptp.class_Orderings_Olinorder T_a) (tptp.class_Orderings_Olinorder T_a))) :rule refl)
% 29.97/30.20  (step t351.t5 (cl (= (= V_x_2 V_y_2) (= V_y_2 V_x_2))) :rule all_simplify)
% 29.97/30.20  (step t351.t6 (cl (= (not (= V_x_2 V_y_2)) (not (= V_y_2 V_x_2)))) :rule cong :premises (t351.t5))
% 29.97/30.20  (step t351.t7 (cl (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)))) :rule refl)
% 29.97/30.20  (step t351.t8 (cl (= (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))) (= (not (= V_y_2 V_x_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))) :rule cong :premises (t351.t6 t351.t7))
% 29.97/30.20  (step t351.t9 (cl (= (= (not (= V_y_2 V_x_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) :rule all_simplify)
% 29.97/30.20  (step t351.t10 (cl (= (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) :rule trans :premises (t351.t8 t351.t9))
% 29.97/30.20  (step t351.t11 (cl (= (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)))) (=> (tptp.class_Orderings_Olinorder T_a) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2)))))) :rule cong :premises (t351.t4 t351.t10))
% 29.97/30.20  (step t351 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))))) :rule bind)
% 29.97/30.20  (step t352 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))))) :rule all_simplify)
% 29.97/30.20  (step t353 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2))))))) :rule trans :premises (t351 t352))
% 29.97/30.20  (step t354 (cl (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (not (= V_y_2 V_x_2)))))) :rule resolution :premises (t350 t353 a48))
% 29.97/30.20  (step t355 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule resolution :premises (t349 t354))
% 29.97/30.20  (step t356 (cl (= (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule resolution :premises (t332 a1137 t355))
% 29.97/30.20  (step t357 (cl (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule resolution :premises (t327 t330 t356))
% 29.97/30.20  (step t358 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_m tptp.v_x)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_m tptp.v_x))) :rule resolution :premises (t105 t121 t134 t136 t149 a1187 a1137 t166 t121 t134 t168 t179 a1185 a1097 t181 t204 t247 t261 t277 t291 t325 t357))
% 29.97/30.20  (step t359 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (= tptp.v_m tptp.v_x))) :rule contraction :premises (t358))
% 29.97/30.20  (step t360 (cl (not (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (= tptp.v_m tptp.v_x)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule equiv_pos2)
% 29.97/30.20  (step t361 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (not (= tptp.v_m tptp.v_x)) (not (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule reordering :premises (t360))
% 29.97/30.20  (step t362 (cl (not (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule or_pos)
% 29.97/30.20  (step t363 (cl (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (not (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule reordering :premises (t362))
% 29.97/30.20  (step t364 (cl (not (= (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) (not (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x))))) (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule equiv_pos2)
% 29.97/30.20  (step t365 (cl (= (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))))) :rule refl)
% 29.97/30.20  (step t366 (cl (= (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)))) :rule refl)
% 29.97/30.20  (step t367 (cl (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule all_simplify)
% 29.97/30.20  (step t368 (cl (= (= tptp.v_m tptp.v_x) (= tptp.v_m tptp.v_x))) :rule refl)
% 29.97/30.20  (step t369 (cl (= (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)))) :rule cong :premises (t367 t368))
% 29.97/30.20  (step t370 (cl (= (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (= tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule all_simplify)
% 29.97/30.20  (step t371 (cl (= (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule trans :premises (t369 t370))
% 29.97/30.20  (step t372 (cl (= (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule cong :premises (t366 t371))
% 29.97/30.20  (step t373 (cl (= (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) :rule cong :premises (t365 t372))
% 29.97/30.20  (step t374 (cl (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t375)
% 29.97/30.20  (assume t375.a0 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))))
% 29.97/30.20  (step t375.t1 (cl (or (not (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2))))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x))))) :rule forall_inst :args ((:= V_b_2 tptp.v_m) (:= V_a_2 tptp.v_x) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t375.t2 (cl (not (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2))))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) :rule or :premises (t375.t1))
% 29.97/30.20  (step t375.t3 (cl (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) :rule resolution :premises (t375.t2 t375.a0))
% 29.97/30.20  (step t375 (cl (not (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2))))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) :rule subproof :discharge (t375.a0))
% 29.97/30.20  (step t376 (cl (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) :rule resolution :premises (t374 t375))
% 29.97/30.20  (step t377 (cl (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) (not (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x))))) :rule implies_neg2)
% 29.97/30.20  (step t378 (cl (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x)))) (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x))))) :rule resolution :premises (t376 t377))
% 29.97/30.20  (step t379 (cl (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= tptp.v_m tptp.v_x))))) :rule contraction :premises (t378))
% 29.97/30.20  (step t380 (cl (=> (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t364 t373 t379))
% 29.97/30.20  (step t381 (cl (not (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2))))) (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies :premises (t380))
% 29.97/30.20  (step t382 (cl (not (= (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))))) (not (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2))))) :rule equiv_pos2)
% 29.97/30.20  (anchor :step t383 :args ((V_b_2 $$unsorted) (:= V_b_2 V_b_2) (V_a_2 $$unsorted) (:= V_a_2 V_a_2) (T_a $$unsorted) (:= T_a T_a)))
% 29.97/30.20  (step t383.t1 (cl (= V_b_2 V_b_2)) :rule refl)
% 29.97/30.20  (step t383.t2 (cl (= V_a_2 V_a_2)) :rule refl)
% 29.97/30.20  (step t383.t3 (cl (= T_a T_a)) :rule refl)
% 29.97/30.20  (step t383.t4 (cl (= (tptp.class_Groups_Oab__group__add T_a) (tptp.class_Groups_Oab__group__add T_a))) :rule refl)
% 29.97/30.20  (step t383.t5 (cl (= (= V_a_2 V_b_2) (= V_b_2 V_a_2))) :rule all_simplify)
% 29.97/30.20  (step t383.t6 (cl (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))) :rule refl)
% 29.97/30.20  (step t383.t7 (cl (= (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= V_b_2 V_a_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) :rule cong :premises (t383.t5 t383.t6))
% 29.97/30.20  (step t383.t8 (cl (= (= (= V_b_2 V_a_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) :rule all_simplify)
% 29.97/30.20  (step t383.t9 (cl (= (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) :rule trans :premises (t383.t7 t383.t8))
% 29.97/30.20  (step t383.t10 (cl (= (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2))))) :rule cong :premises (t383.t4 t383.t9))
% 29.97/30.20  (step t383 (cl (= (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))))) :rule bind)
% 29.97/30.20  (step t384 (cl (= (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))))) :rule all_simplify)
% 29.97/30.20  (step t385 (cl (= (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))))) :rule trans :premises (t383 t384))
% 29.97/30.20  (step t386 (cl (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2))))) :rule resolution :premises (t382 t385 a143))
% 29.97/30.20  (step t387 (cl (or (not (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal)) (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t381 t386))
% 29.97/30.20  (step t388 (cl (= (= tptp.v_m tptp.v_x) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t363 a1133 t387))
% 29.97/30.20  (step t389 (cl (not (= tptp.v_m tptp.v_x)) (not (= tptp.v_m tptp.v_x))) :rule resolution :premises (t359 t361 t388))
% 29.97/30.20  (step t390 (cl (not (= tptp.v_m tptp.v_x))) :rule contraction :premises (t389))
% 29.97/30.20  (step t391 (cl (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) :rule or_pos)
% 29.97/30.20  (step t392 (cl (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))))) :rule reordering :premises (t391))
% 29.97/30.20  (step t393 (cl (not (= (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))))) (not (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m))))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))))) :rule equiv_pos2)
% 29.97/30.20  (step t394 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))))) :rule refl)
% 29.97/30.20  (step t395 (cl (= (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) :rule refl)
% 29.97/30.20  (step t396 (cl (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) :rule refl)
% 29.97/30.20  (step t397 (cl (= (= tptp.v_x tptp.v_m) (= tptp.v_m tptp.v_x))) :rule all_simplify)
% 29.97/30.20  (step t398 (cl (= (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_m tptp.v_x)))) :rule cong :premises (t396 t397))
% 29.97/30.20  (step t399 (cl (= (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) :rule all_simplify)
% 29.97/30.20  (step t400 (cl (= (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) :rule trans :premises (t398 t399))
% 29.97/30.20  (step t401 (cl (= (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))))) :rule cong :premises (t335 t395 t400))
% 29.97/30.20  (step t402 (cl (= (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))))) :rule cong :premises (t394 t401))
% 29.97/30.20  (step t403 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t404)
% 29.97/30.20  (assume t404.a0 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))))
% 29.97/30.20  (step t404.t1 (cl (or (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m))))) :rule forall_inst :args ((:= V_y_2 tptp.v_x) (:= V_x_2 tptp.v_m) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t404.t2 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) :rule or :premises (t404.t1))
% 29.97/30.20  (step t404.t3 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) :rule resolution :premises (t404.t2 t404.a0))
% 29.97/30.20  (step t404 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) :rule subproof :discharge (t404.a0))
% 29.97/30.20  (step t405 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) :rule resolution :premises (t403 t404))
% 29.97/30.20  (step t406 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m))))) :rule implies_neg2)
% 29.97/30.20  (step t407 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m)))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m))))) :rule resolution :premises (t405 t406))
% 29.97/30.20  (step t408 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= tptp.v_x tptp.v_m))))) :rule contraction :premises (t407))
% 29.97/30.20  (step t409 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))))) :rule resolution :premises (t393 t402 t408))
% 29.97/30.20  (step t410 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) :rule implies :premises (t409))
% 29.97/30.20  (step t411 (cl (not (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))))) (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) :rule equiv_pos2)
% 29.97/30.20  (anchor :step t412 :args ((V_y_2 $$unsorted) (:= V_y_2 V_y_2) (V_x_2 $$unsorted) (:= V_x_2 V_x_2) (T_a $$unsorted) (:= T_a T_a)))
% 29.97/30.20  (step t412.t1 (cl (= V_y_2 V_y_2)) :rule refl)
% 29.97/30.20  (step t412.t2 (cl (= V_x_2 V_x_2)) :rule refl)
% 29.97/30.20  (step t412.t3 (cl (= T_a T_a)) :rule refl)
% 29.97/30.20  (step t412.t4 (cl (= (tptp.class_Orderings_Olinorder T_a) (tptp.class_Orderings_Olinorder T_a))) :rule refl)
% 29.97/30.20  (step t412.t5 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2))) :rule refl)
% 29.97/30.20  (step t412.t6 (cl (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)))) :rule refl)
% 29.97/30.20  (step t412.t7 (cl (= (= V_x_2 V_y_2) (= V_y_2 V_x_2))) :rule all_simplify)
% 29.97/30.20  (step t412.t8 (cl (= (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))) :rule cong :premises (t412.t6 t412.t7))
% 29.97/30.20  (step t412.t9 (cl (= (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) :rule cong :premises (t412.t5 t412.t8))
% 29.97/30.20  (step t412.t10 (cl (= (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2)))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))))) :rule cong :premises (t412.t4 t412.t9))
% 29.97/30.20  (step t412 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))))) :rule bind)
% 29.97/30.20  (step t413 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))))) :rule all_simplify)
% 29.97/30.20  (step t414 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2)))))) :rule trans :premises (t412 t413))
% 29.97/30.20  (step t415 (cl (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_y_2 V_x_2))))) :rule resolution :premises (t411 t414 a69))
% 29.97/30.20  (step t416 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x))))) :rule resolution :premises (t410 t415))
% 29.97/30.20  (step t417 (cl (= (= tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)))) :rule resolution :premises (t392 a1137 a1185 t416))
% 29.97/30.20  (step t418 (cl (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x)) :rule resolution :premises (t63 t390 t417))
% 29.97/30.20  (step t419 (cl (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule or_pos)
% 29.97/30.20  (step t420 (cl (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) :rule reordering :premises (t419))
% 29.97/30.20  (step t421 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t422)
% 29.97/30.20  (assume t422.a0 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))))
% 29.97/30.20  (step t422.t1 (cl (or (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) :rule forall_inst :args ((:= V_y_2 tptp.v_x) (:= V_x_2 tptp.v_m) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t422.t2 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule or :premises (t422.t1))
% 29.97/30.20  (step t422.t3 (cl (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t422.t2 t422.a0))
% 29.97/30.20  (step t422 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule subproof :discharge (t422.a0))
% 29.97/30.20  (step t423 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t421 t422))
% 29.97/30.20  (step t424 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) (not (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) :rule implies_neg2)
% 29.97/30.20  (step t425 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) :rule resolution :premises (t423 t424))
% 29.97/30.20  (step t426 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))))) :rule contraction :premises (t425))
% 29.97/30.20  (step t427 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))) (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule implies :premises (t426))
% 29.97/30.20  (step t428 (cl (not (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))))) (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))) :rule equiv_pos2)
% 29.97/30.20  (step t429 (cl (= (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))))) :rule all_simplify)
% 29.97/30.20  (step t430 (cl (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))) :rule resolution :premises (t428 t429 a78))
% 29.97/30.20  (step t431 (cl (or (not (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t427 t430))
% 29.97/30.20  (step t432 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t420 a1136 t431))
% 29.97/30.20  (step t433 (cl (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_m tptp.v_x) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t40 t418 t432))
% 29.97/30.20  (step t434 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule resolution :premises (t38 t433))
% 29.97/30.20  (step t435 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t436)
% 29.97/30.20  (assume t436.a0 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 29.97/30.20  (step t436.t1 (cl (or (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule forall_inst :args ((:= V_y_2 tptp.v_m) (:= V_x_2 tptp.v_x)))
% 29.97/30.20  (step t436.t2 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule or :premises (t436.t1))
% 29.97/30.20  (step t436.t3 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule resolution :premises (t436.t2 t436.a0))
% 29.97/30.20  (step t436 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule subproof :discharge (t436.a0))
% 29.97/30.20  (step t437 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule resolution :premises (t435 t436))
% 29.97/30.20  (step t438 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule implies_neg2)
% 29.97/30.20  (step t439 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t437 t438))
% 29.97/30.20  (step t440 (cl (=> (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) :rule contraction :premises (t439))
% 29.97/30.20  (step t441 (cl (not (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule implies :premises (t440))
% 29.97/30.20  (step t442 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule resolution :premises (t441 a170))
% 29.97/30.20  (step t443 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) :rule resolution :premises (t36 t434 t442))
% 29.97/30.20  (step t444 (cl (=> (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z)))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t445)
% 29.97/30.20  (assume t445.a0 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))))
% 29.97/30.20  (step t445.t1 (cl (or (not (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z)))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule forall_inst :args ((:= V_w (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (:= V_z (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))
% 29.97/30.20  (step t445.t2 (cl (not (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z)))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule or :premises (t445.t1))
% 29.97/30.20  (step t445.t3 (cl (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t445.t2 t445.a0))
% 29.97/30.20  (step t445 (cl (not (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z)))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule subproof :discharge (t445.a0))
% 29.97/30.20  (step t446 (cl (=> (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t444 t445))
% 29.97/30.20  (step t447 (cl (=> (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (not (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies_neg2)
% 29.97/30.20  (step t448 (cl (=> (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) (=> (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t446 t447))
% 29.97/30.20  (step t449 (cl (=> (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule contraction :premises (t448))
% 29.97/30.20  (step t450 (cl (not (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z)))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule implies :premises (t449))
% 29.97/30.20  (step t451 (cl (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t450 a59))
% 29.97/30.20  (step t452 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule resolution :premises (t34 t443 t451))
% 29.97/30.20  (step t453 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t454)
% 29.97/30.20  (assume t454.a0 (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 29.97/30.20  (step t454.t1 (cl (or (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule forall_inst :args ((:= V_a (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t454.t2 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule or :premises (t454.t1))
% 29.97/30.20  (step t454.t3 (cl (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t454.t2 t454.a0))
% 29.97/30.20  (step t454 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule subproof :discharge (t454.a0))
% 29.97/30.20  (step t455 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t453 t454))
% 29.97/30.20  (step t456 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (not (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule implies_neg2)
% 29.97/30.20  (step t457 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule resolution :premises (t455 t456))
% 29.97/30.20  (step t458 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))))) :rule contraction :premises (t457))
% 29.97/30.20  (step t459 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule implies :premises (t458))
% 29.97/30.20  (step t460 (cl (not (= (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))) (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) :rule equiv_pos2)
% 29.97/30.20  (anchor :step t461 :args ((V_a $$unsorted) (:= V_a V_a) (T_a $$unsorted) (:= T_a T_a)))
% 29.97/30.20  (step t461.t1 (cl (= V_a V_a)) :rule refl)
% 29.97/30.20  (step t461.t2 (cl (= T_a T_a)) :rule refl)
% 29.97/30.20  (step t461.t3 (cl (= (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.class_Groups_Oordered__ab__group__add__abs T_a))) :rule refl)
% 29.97/30.20  (step t461.t4 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a))) :rule refl)
% 29.97/30.20  (step t461.t5 (cl (= (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) :rule all_simplify)
% 29.97/30.20  (step t461.t6 (cl (= (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) :rule cong :premises (t461.t4 t461.t5))
% 29.97/30.20  (step t461.t7 (cl (= (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a))) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))) :rule cong :premises (t461.t3 t461.t6))
% 29.97/30.20  (step t461 (cl (= (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))))) :rule bind)
% 29.97/30.20  (step t462 (cl (= (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))) :rule all_simplify)
% 29.97/30.20  (step t463 (cl (= (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))) :rule trans :premises (t461 t462))
% 29.97/30.20  (step t464 (cl (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__group__add__abs T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a)) (= V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))) :rule resolution :premises (t460 t463 a166))
% 29.97/30.20  (step t465 (cl (or (not (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))))) :rule resolution :premises (t459 t464))
% 29.97/30.20  (step t466 (cl (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)))) :rule resolution :premises (t32 a1106 t452 t465))
% 29.97/30.20  (step t467 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) :rule resolution :premises (t16 t30 t466))
% 29.97/30.20  (step t468 (cl (not (= (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))))) (not (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule equiv_pos2)
% 29.97/30.20  (step t469 (cl (= (= (= (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) true) (= (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule equiv_simplify)
% 29.97/30.20  (step t470 (cl (not (= (= (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) true)) (= (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule equiv1 :premises (t469))
% 29.97/30.20  (step t471 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))))) :rule all_simplify)
% 29.97/30.20  (step t472 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule refl)
% 29.97/30.20  (step t473 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule all_simplify)
% 29.97/30.20  (step t474 (cl (= (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule cong :premises (t472 t473))
% 29.97/30.20  (step t475 (cl (= (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) true)) :rule all_simplify)
% 29.97/30.20  (step t476 (cl (= (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) true)) :rule trans :premises (t474 t475))
% 29.97/30.20  (step t477 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) true)) :rule trans :premises (t471 t476))
% 29.97/30.20  (step t478 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule resolution :premises (t470 t477))
% 29.97/30.20  (step t479 (cl (= (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule refl)
% 29.97/30.20  (step t480 (cl (= (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))))) :rule cong :premises (t478 t217 t218 t479))
% 29.97/30.20  (step t481 (cl (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule and_neg)
% 29.97/30.20  (step t482 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t483)
% 29.97/30.20  (assume t483.a0 (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))
% 29.97/30.20  (assume t483.a1 (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))
% 29.97/30.20  (assume t483.a2 (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))
% 29.97/30.20  (step t483.t1 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t483.t2)
% 29.97/30.20  (assume t483.t2.a0 (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))
% 29.97/30.20  (assume t483.t2.a1 (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))
% 29.97/30.20  (assume t483.t2.a2 (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))
% 29.97/30.20  (step t483.t2.t1 (cl (= (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) false) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule equiv_simplify)
% 29.97/30.20  (step t483.t2.t2 (cl (not (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) false)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule equiv1 :premises (t483.t2.t1))
% 29.97/30.20  (step t483.t2.t3 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 29.97/30.20  (step t483.t2.t4 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) :rule symm :premises (t483.t2.a1))
% 29.97/30.20  (step t483.t2.t5 (cl (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m) tptp.v_x)) :rule symm :premises (t483.t2.a2))
% 29.97/30.20  (step t483.t2.t6 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule cong :premises (t483.t2.t3 t483.t2.t4 t483.t2.t5))
% 29.97/30.20  (step t483.t2.t7 (cl (= (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) false) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule equiv_simplify)
% 29.97/30.20  (step t483.t2.t8 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) false) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) :rule equiv2 :premises (t483.t2.t7))
% 29.97/30.20  (step t483.t2.t9 (cl (not (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) :rule not_not)
% 29.97/30.20  (step t483.t2.t10 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) false) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) :rule resolution :premises (t483.t2.t8 t483.t2.t9))
% 29.97/30.20  (step t483.t2.t11 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) false)) :rule resolution :premises (t483.t2.t10 t483.t2.a0))
% 29.97/30.20  (step t483.t2.t12 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) false)) :rule trans :premises (t483.t2.t6 t483.t2.t11))
% 29.97/30.20  (step t483.t2.t13 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t483.t2.t2 t483.t2.t12))
% 29.97/30.20  (step t483.t2 (cl (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule subproof :discharge (t483.t2.a0 t483.t2.a1 t483.t2.a2))
% 29.97/30.20  (step t483.t3 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule and_pos)
% 29.97/30.20  (step t483.t4 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t483.t5 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t483.t6 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule resolution :premises (t483.t2 t483.t3 t483.t4 t483.t5))
% 29.97/30.20  (step t483.t7 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule reordering :premises (t483.t6))
% 29.97/30.20  (step t483.t8 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule contraction :premises (t483.t7))
% 29.97/30.20  (step t483.t9 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t483.t1 t483.t8))
% 29.97/30.20  (step t483.t10 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule implies_neg2)
% 29.97/30.20  (step t483.t11 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule resolution :premises (t483.t9 t483.t10))
% 29.97/30.20  (step t483.t12 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule contraction :premises (t483.t11))
% 29.97/30.20  (step t483.t13 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule implies :premises (t483.t12))
% 29.97/30.20  (step t483.t14 (cl (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule and_neg)
% 29.97/30.20  (step t483.t15 (cl (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t483.t14 t483.a0 t483.a2 t483.a1))
% 29.97/30.20  (step t483.t16 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t483.t13 t483.t15))
% 29.97/30.20  (step t483 (cl (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule subproof :discharge (t483.a0 t483.a1 t483.a2))
% 29.97/30.20  (step t484 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule and_pos)
% 29.97/30.20  (step t485 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t486 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) :rule and_pos)
% 29.97/30.20  (step t487 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule resolution :premises (t483 t484 t485 t486))
% 29.97/30.20  (step t488 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule reordering :premises (t487))
% 29.97/30.20  (step t489 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule contraction :premises (t488))
% 29.97/30.20  (step t490 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t482 t489))
% 29.97/30.20  (step t491 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule implies_neg2)
% 29.97/30.20  (step t492 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule resolution :premises (t490 t491))
% 29.97/30.20  (step t493 (cl (=> (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule contraction :premises (t492))
% 29.97/30.20  (step t494 (cl (not (and (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m)))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule implies :premises (t493))
% 29.97/30.20  (step t495 (cl (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t481 t494))
% 29.97/30.20  (step t496 (cl (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))))) :rule or_neg)
% 29.97/30.20  (step t497 (cl (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule or_neg)
% 29.97/30.20  (step t498 (cl (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))))) :rule or_neg)
% 29.97/30.20  (step t499 (cl (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule or_neg)
% 29.97/30.20  (step t500 (cl (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule resolution :premises (t495 t496 t497 t498 t499))
% 29.97/30.20  (step t501 (cl (or (not (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule contraction :premises (t500))
% 29.97/30.20  (step t502 (cl (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule resolution :premises (t468 t480 t501))
% 29.97/30.20  (step t503 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x) (not (= tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule or :premises (t502))
% 29.97/30.20  (step t504 (cl (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))) :rule or_pos)
% 29.97/30.20  (step t505 (cl (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule reordering :premises (t504))
% 29.97/30.20  (step t506 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t507)
% 29.97/30.20  (assume t507.a0 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))))
% 29.97/30.20  (step t507.t1 (cl (or (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule forall_inst :args ((:= V_x tptp.v_x) (:= V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t507.t2 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule or :premises (t507.t1))
% 29.97/30.20  (step t507.t3 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule resolution :premises (t507.t2 t507.a0))
% 29.97/30.20  (step t507 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule subproof :discharge (t507.a0))
% 29.97/30.20  (step t508 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule resolution :premises (t506 t507))
% 29.97/30.20  (step t509 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (not (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule implies_neg2)
% 29.97/30.20  (step t510 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule resolution :premises (t508 t509))
% 29.97/30.20  (step t511 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e)))))) :rule contraction :premises (t510))
% 29.97/30.20  (step t512 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule implies :premises (t511))
% 29.97/30.20  (step t513 (cl (not (= (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))))) (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) :rule equiv_pos2)
% 29.97/30.20  (step t514 (cl (= (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))))) :rule all_simplify)
% 29.97/30.20  (step t515 (cl (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) :rule resolution :premises (t513 t514 a71))
% 29.97/30.20  (step t516 (cl (or (not (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e))))) :rule resolution :premises (t512 t515))
% 29.97/30.20  (step t517 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_m tptp.v_e) tptp.v_x))) :rule resolution :premises (t505 a1137 a1186 t516))
% 29.97/30.20  (step t518 (cl (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t503 t517 t277 t261))
% 29.97/30.20  (step t519 (cl (=> (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) :rule implies_neg1)
% 29.97/30.20  (anchor :step t520)
% 29.97/30.20  (assume t520.a0 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))))
% 29.97/30.20  (step t520.t1 (cl (or (not (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule forall_inst :args ((:= V_c tptp.v_m) (:= V_b (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m)) (:= V_a tptp.v_e) (:= T_a tptp.tc_RealDef_Oreal)))
% 29.97/30.20  (step t520.t2 (cl (not (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule or :premises (t520.t1))
% 29.97/30.20  (step t520.t3 (cl (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t520.t2 t520.a0))
% 29.97/30.20  (step t520 (cl (not (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule subproof :discharge (t520.a0))
% 29.97/30.20  (step t521 (cl (=> (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t519 t520))
% 29.97/30.20  (step t522 (cl (=> (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (not (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule implies_neg2)
% 29.97/30.20  (step t523 (cl (=> (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) (=> (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule resolution :premises (t521 t522))
% 29.97/30.20  (step t524 (cl (=> (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m))))) :rule contraction :premises (t523))
% 29.97/30.20  (step t525 (cl (not (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule implies :premises (t524))
% 29.97/30.20  (step t526 (cl (not (= (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))))) (not (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) :rule equiv_pos2)
% 29.97/30.20  (step t527 (cl (= (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))))) :rule all_simplify)
% 29.97/30.20  (step t528 (cl (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oordered__ab__semigroup__add T_a)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) :rule resolution :premises (t526 t527 a87))
% 29.97/30.20  (step t529 (cl (or (not (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_e (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal tptp.v_e tptp.v_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal tptp.v_x tptp.v_m) tptp.v_m)))) :rule resolution :premises (t525 t528))
% 29.97/30.22  (step t530 (cl) :rule resolution :premises (t2 t467 t518 t529 a1105))
% 29.97/30.22  
% 29.97/30.22  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.8f6EC8uEMZ/cvc5---1.0.5_7543.smt2
% 29.97/30.22  % cvc5---1.0.5 exiting
% 29.97/30.22  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------