%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW191+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n027.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 18:18:50 EDT 2024

% Result   : Theorem 112.09s 112.47s
% Output   : Proof 112.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.23  % Problem    : SWW191+1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.24  % Command    : do_cvc5 %s %d
% 0.23/0.45  % Computer : n027.cluster.edu
% 0.23/0.45  % Model    : x86_64 x86_64
% 0.23/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.45  % Memory   : 8042.1875MB
% 0.23/0.45  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.23/0.45  % CPULimit   : 300
% 0.23/0.45  % WCLimit    : 300
% 0.23/0.45  % DateTime   : Sun May 26 04:35:24 EDT 2024
% 0.23/0.45  % CPUTime    : 
% 0.50/0.79  %----Proving TF0_NAR, FOF, or CNF
% 112.09/112.47  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 112.09/112.47  --- Run --no-e-matching --full-saturate-quant at 5...
% 112.09/112.47  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 112.09/112.47  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 112.09/112.47  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 112.09/112.47  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 112.09/112.47  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 112.09/112.47  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 112.09/112.47  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 112.09/112.47  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 112.09/112.47  --- Run --relevant-triggers --full-saturate-quant at 5...
% 112.09/112.47  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 112.09/112.47  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 112.09/112.47  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 112.09/112.47  --- Run --no-cbqi --full-saturate-quant at 10...
% 112.09/112.47  --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 112.09/112.47  % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.Lj9aQNll5p/cvc5---1.0.5_725.smt2
% 112.09/112.47  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.Lj9aQNll5p/cvc5---1.0.5_725.smt2
% 112.09/112.47  (assume a0 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))))
% 112.09/112.47  (assume a1 (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_z)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))))
% 112.09/112.47  (assume a2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_y____ tptp.v_L____))
% 112.09/112.47  (assume a3 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_Y____))
% 112.09/112.47  (assume a4 (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_x)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_x tptp.v_L____))))
% 112.09/112.47  (assume a5 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))))
% 112.09/112.47  (assume a6 (forall ((V_z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P V_z_2)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_y____ V_z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_y____ tptp.v_L____)))))
% 112.09/112.47  (assume a7 (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_w)))
% 112.09/112.47  (assume a8 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))))
% 112.09/112.47  (assume a9 (forall ((V_k $$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)))))
% 112.09/112.47  (assume a10 (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)))))
% 112.09/112.47  (assume a11 (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_z)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_y____ B_z)))))
% 112.09/112.47  (assume a12 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))))))
% 112.09/112.47  (assume a13 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 112.09/112.47  (assume a14 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_xa_2 V_ya_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2))))))
% 112.09/112.47  (assume a15 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 112.09/112.47  (assume a16 (tptp.hBOOL (tptp.hAPP tptp.v_P tptp.v_x____)))
% 112.09/112.47  (assume a17 (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.v_P B_x1))))
% 112.09/112.47  (assume a18 (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_x)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_x tptp.v_Y____))))
% 112.09/112.47  (assume a19 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P V_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x tptp.v_Y____))))
% 112.09/112.47  (assume a20 (exists ((B_z $$unsorted)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_x B_z)))))
% 112.09/112.47  (assume a21 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.v_x____ tptp.v_Y____))
% 112.09/112.47  (assume a22 (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)))))
% 112.09/112.47  (assume a23 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_xa_2 V_ya_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2))))))
% 112.09/112.47  (assume a24 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2) (= V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a25 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 112.09/112.47  (assume a26 (forall ((V_xa_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (= V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a27 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 112.09/112.47  (assume a28 (forall ((V_y $$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))))))
% 112.09/112.47  (assume a29 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 112.09/112.47  (assume a30 (forall ((V_y $$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))))))
% 112.09/112.47  (assume a31 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))))
% 112.09/112.47  (assume a32 (forall ((V_y $$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))))))
% 112.09/112.47  (assume a33 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (not (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 112.09/112.47  (assume a34 (forall ((V_a $$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))))))
% 112.09/112.47  (assume a35 (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))))))
% 112.09/112.47  (assume a36 (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))))))
% 112.09/112.47  (assume a37 (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))))))
% 112.09/112.47  (assume a38 (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))))))
% 112.09/112.47  (assume a39 (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))))))
% 112.09/112.47  (assume a40 (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))))))
% 112.09/112.47  (assume a41 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 112.09/112.47  (assume a42 (forall ((V_y $$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))))))
% 112.09/112.47  (assume a43 (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))))))
% 112.09/112.47  (assume a44 (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))))))
% 112.09/112.47  (assume a45 (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))))))
% 112.09/112.47  (assume a46 (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))))))
% 112.09/112.47  (assume a47 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 112.09/112.47  (assume a48 (forall ((V_b $$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))))))
% 112.09/112.47  (assume a49 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y))))))
% 112.09/112.47  (assume a50 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (= V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a51 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 112.09/112.47  (assume a52 (forall ((V_x $$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))))))
% 112.09/112.47  (assume a53 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 112.09/112.47  (assume a54 (forall ((V_b $$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))))))
% 112.09/112.47  (assume a55 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a56 (forall ((V_x $$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)))))
% 112.09/112.47  (assume a57 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 112.09/112.47  (assume a58 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (or (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (= V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a59 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2)))))))
% 112.09/112.47  (assume a60 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (not (= V_xa_2 V_ya_2)))))))
% 112.09/112.47  (assume a61 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 112.09/112.47  (assume a62 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2)))))
% 112.09/112.47  (assume a63 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2)))))
% 112.09/112.47  (assume a64 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (= V_xa_2 V_ya_2)))))
% 112.09/112.47  (assume a65 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (not (= V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a66 (forall ((V_y $$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)))))
% 112.09/112.47  (assume a67 (forall ((V_xa_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_g_2 V_xa_2))))))
% 112.09/112.47  (assume a68 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x))))))
% 112.09/112.47  (assume a69 (forall ((V_x $$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))))))
% 112.09/112.47  (assume a70 (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))))))
% 112.09/112.47  (assume a71 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= V_x V_y))))))
% 112.09/112.47  (assume a72 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))))
% 112.09/112.47  (assume a73 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))))
% 112.09/112.47  (assume a74 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))))
% 112.09/112.47  (assume a75 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))))
% 112.09/112.47  (assume a76 (forall ((V_xa_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a77 (forall ((V_xa_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_g_2 V_xa_2))))))
% 112.09/112.47  (assume a78 (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) tptp.v_L____))
% 112.09/112.47  (assume a79 (forall ((V_y $$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))))))
% 112.09/112.47  (assume a80 (not (=> (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.v_P B_x1))) (forall ((B_Y $$unsorted)) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_x)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_x B_Y))))))))
% 112.09/112.47  (assume a81 (forall ((T_a $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2)))))
% 112.09/112.47  (assume a82 (forall ((V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Odense__linorder T_a) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_x V_z))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z)))))
% 112.09/112.47  (assume a83 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Odense__linorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (forall ((B_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x B_w) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_w V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_w V_z)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z))))))
% 112.09/112.47  (assume a84 (forall ((V_f_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b V_c_2 (tptp.hAPP V_f_2 V_b_2)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_y B_x) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_f_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless T_b V_c_2 (tptp.hAPP V_f_2 V_a_2))))))))
% 112.09/112.47  (assume a85 (forall ((V_f_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_c_2 (tptp.hAPP V_f_2 V_b_2)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y B_x) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_f_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless T_b V_c_2 (tptp.hAPP V_f_2 V_a_2))))))))
% 112.09/112.47  (assume a86 (forall ((V_c_2 $$unsorted) (V_f_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_a) (tptp.class_Orderings_Oorder T_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_b_2) V_c_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_x B_y) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_a_2) V_c_2)))))))
% 112.09/112.47  (assume a87 (forall ((V_c_2 $$unsorted) (V_f_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_a) (tptp.class_Orderings_Oorder T_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_b_2) V_c_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a B_x B_y) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_a_2) V_c_2)))))))
% 112.09/112.47  (assume a88 (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_f_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_a) (tptp.class_Orderings_Oorder T_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.hAPP V_f_2 V_b_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b V_b_2 V_c_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b B_x B_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.hAPP V_f_2 V_c_2))))))))
% 112.09/112.47  (assume a89 (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_f_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_a) (tptp.class_Orderings_Oorder T_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.hAPP V_f_2 V_b_2)) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 V_c_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_b B_x B_y) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.hAPP V_f_2 V_c_2))))))))
% 112.09/112.47  (assume a90 (forall ((V_xa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b T_a)) V_xa_2) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 112.09/112.47  (assume a91 (forall ((V_g_2 $$unsorted) (V_f_2 $$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_f_2 V_g_2) (and (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (not (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_g_2 V_f_2)))))))
% 112.09/112.47  (assume a92 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 112.09/112.47  (assume a93 (not (forall ((B_L $$unsorted)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) B_L)))))
% 112.09/112.47  (assume a94 (exists ((B_x1 $$unsorted)) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) B_x1)))
% 112.09/112.47  (assume a95 (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_xa_2))))
% 112.09/112.47  (assume a96 (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P)) B_x1))))
% 112.09/112.47  (assume a97 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted)) (=> (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal V_R_2 V_S_2 V_xa_2) (=> (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal V_R_2 V_S_2 V_ya_2) (= V_xa_2 V_ya_2)))))
% 112.09/112.47  (assume a98 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a99 (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2)))
% 112.09/112.47  (assume a100 (exists ((B_x $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal B_x (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P))))
% 112.09/112.47  (assume a101 (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oord T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_f_2 V_b_2) V_a_2) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_c_2 V_b_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_b B_y B_x) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_f_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 V_c_2) V_a_2)))))))
% 112.09/112.47  (assume a102 (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 V_b_2) V_a_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b V_c_2 V_b_2) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_b B_y B_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_f_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP V_f_2 V_c_2) V_a_2)))))))
% 112.09/112.47  (assume a103 (forall ((V_c_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (=> (=> (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2))) (not (=> (not (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 V_B_2)))))))
% 112.09/112.47  (assume a104 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (= V_A_2 V_B_2)))))
% 112.09/112.47  (assume a105 (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_xa_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a106 (forall ((V_c_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))))
% 112.09/112.47  (assume a107 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (not (= V_A_2 V_B_2))))))
% 112.09/112.47  (assume a108 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (or (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= V_A_2 V_B_2)))))
% 112.09/112.47  (assume a109 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a110 (forall ((V_c_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))))
% 112.09/112.47  (assume a111 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a112 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a113 (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_xa_2 V_A_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)))))
% 112.09/112.47  (assume a114 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_xa_2 (tptp.c_fequal V_ya_2)) (= V_xa_2 V_ya_2))))
% 112.09/112.47  (assume a115 (forall ((V_xa_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (= (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_xa_2 V_B_2)))))
% 112.09/112.47  (assume a116 (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (=> (= V_xa_2 V_ya_2) (= (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_ya_2 V_A_2)))))
% 112.09/112.47  (assume a117 (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (= V_a_2 V_b_2) (=> (tptp.c_member T_a V_b_2 V_A_2) (tptp.c_member T_a V_a_2 V_A_2)))))
% 112.09/112.47  (assume a118 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (not (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)))))))
% 112.09/112.47  (assume a119 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a120 (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_xa_2 V_B_2)))))
% 112.09/112.47  (assume a121 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_xa_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_member T_a V_xa_2 V_B_2)))))
% 112.09/112.47  (assume a122 (forall ((V_xa_2 $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Pa_2 V_Q_2) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP V_Q_2 V_xa_2))))))
% 112.09/112.47  (assume a123 (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_xa_2 V_B_2)))))
% 112.09/112.47  (assume a124 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))))
% 112.09/112.47  (assume a125 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a126 (forall ((V_Q_2 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_xa_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Pa_2 V_Q_2) (tptp.hBOOL (tptp.hAPP V_Q_2 V_xa_2))))))
% 112.09/112.47  (assume a127 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (= (= V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)))))
% 112.09/112.47  (assume a128 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2)))
% 112.09/112.47  (assume a129 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a130 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (=> (tptp.c_member T_a V_ya_2 V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2))))))
% 112.09/112.47  (assume a131 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (=> (tptp.c_member T_a V_ya_2 V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2))))))
% 112.09/112.47  (assume a132 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2))))))
% 112.09/112.47  (assume a133 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (tptp.c_member T_a V_xa_2 V_R_2)))))
% 112.09/112.47  (assume a134 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_member T_a V_xa_2 V_R_2)))))
% 112.09/112.47  (assume a135 (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_xa_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a136 (forall ((V_S_2 $$unsorted)) (=> (exists ((B_X $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal B_X V_S_2)) (=> (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) V_S_2) B_x1))) (exists ((B_x1 $$unsorted)) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) V_S_2 B_x1))))))
% 112.09/112.47  (assume a137 (forall ((V_S_2 $$unsorted)) (=> (and (exists ((B_x $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal B_x V_S_2)) (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) V_S_2) B_x1)))) (exists ((B_x1 $$unsorted)) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) V_S_2 B_x1)))))
% 112.09/112.47  (assume a138 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a139 (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))))
% 112.09/112.47  (assume a140 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (=> (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))) (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2))))))
% 112.09/112.47  (assume a141 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OleastP T_a V_Pa_2 V_xa_2) (=> (tptp.c_member T_a V_ya_2 (tptp.c_Set_OCollect T_a V_Pa_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a142 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_OleastP T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)))))
% 112.09/112.47  (assume a143 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OleastP T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2) (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)))))
% 112.09/112.47  (assume a144 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_OleastP T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)))))
% 112.09/112.47  (assume a145 (forall ((V_R_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2) (=> (tptp.c_member T_a V_xa_2 V_R_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)))))))
% 112.09/112.47  (assume a146 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (and (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2) (tptp.c_member T_a V_xa_2 V_R_2))))))
% 112.09/112.47  (assume a147 (forall ((V_ya_2 $$unsorted) (V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (=> (tptp.c_member T_a V_ya_2 V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a148 (forall ((V_xa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OleastP T_a V_Pa_2 V_xa_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 V_xa_2))))))
% 112.09/112.47  (assume a149 (forall ((V_xa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_OleastP T_a V_Pa_2 V_xa_2) (and (tptp.hBOOL (tptp.hAPP V_Pa_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Set_OCollect T_a V_Pa_2)))))))
% 112.09/112.47  (assume a150 (forall ((V_xa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OleastP T_a V_Pa_2 V_xa_2) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Set_OCollect T_a V_Pa_2))))))
% 112.09/112.47  (assume a151 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))))
% 112.09/112.47  (assume a152 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_x V_xa_2)))))))
% 112.09/112.47  (assume a153 (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))
% 112.09/112.47  (assume a154 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2)))))
% 112.09/112.47  (assume a155 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) V_xa_2)) (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2)))))
% 112.09/112.47  (assume a156 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2) (=> (tptp.c_member T_a V_ya_2 V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2))))))
% 112.09/112.47  (assume a157 (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))))
% 112.09/112.47  (assume a158 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_Predicate_OPowp T_a V_A_2) (tptp.c_Predicate_OPowp T_a V_B_2)))))
% 112.09/112.47  (assume a159 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (tptp.c_member T_a B_x V_B_2))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a160 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_x V_xa_2))) (tptp.c_Lubs_Osetle T_a V_S_2 V_xa_2)))))
% 112.09/112.47  (assume a161 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))) (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2)))))
% 112.09/112.47  (assume a162 (forall ((T_a $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)) (tptp.hBOOL (tptp.hAPP V_Q_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_OCollect T_a V_Pa_2) (tptp.c_Set_OCollect T_a V_Q_2)))))
% 112.09/112.47  (assume a163 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (tptp.c_member T_a B_x V_A_2)) (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))))
% 112.09/112.47  (assume a164 (forall ((T_a $$unsorted)) (exists ((B_x $$unsorted)) (tptp.c_member T_a B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a165 (forall ((V_X_2 $$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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 B_m))))))))
% 112.09/112.47  (assume a166 (forall ((V_X_2 $$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 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m) (tptp.hAPP V_X_2 B_n))))))))
% 112.09/112.47  (assume a167 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_Set_OPow T_a V_A_2) (tptp.c_Set_OPow T_a V_B_2)))))
% 112.09/112.47  (assume a168 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)))))))
% 112.09/112.47  (assume a169 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Olinorder T_a)) (=> (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a170 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_c_2 V_d_2)) (and (or (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_d_2) (or (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_d_2)))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_d_2))))))
% 112.09/112.47  (assume a171 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Olinorder T_a)) (=> (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a172 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2) (and (tptp.c_member T_a V_xa_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a173 (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_A_2)) (=> (not (= V_a_2 V_b_2)) (tptp.c_member T_a V_a_2 V_A_2)))))
% 112.09/112.47  (assume a174 (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_a_2 V_B_2)) (= V_a_2 V_b_2)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))))
% 112.09/112.47  (assume a175 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_OPow T_a V_B_2)))))
% 112.09/112.47  (assume a176 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_OPow T_a V_A_2))))
% 112.09/112.47  (assume a177 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Olinorder T_a)) (=> (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2) (= (= (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)) (= V_xa_2 V_ya_2))))))
% 112.09/112.47  (assume a178 (forall ((V_xa_2 $$unsorted) (V_A_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert T_a V_ya_2 V_A_2) V_xa_2)) (or (= V_ya_2 V_xa_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))))))
% 112.09/112.47  (assume a179 (forall ((V_A_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Set_Oinsert T_a V_ya_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_ya_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2)))))
% 112.09/112.47  (assume a180 (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2))))
% 112.09/112.47  (assume a181 (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2))))
% 112.09/112.47  (assume a182 (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_A_2)) (or (= V_a_2 V_b_2) (tptp.c_member T_a V_a_2 V_A_2)))))
% 112.09/112.47  (assume a183 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (=> (not (tptp.c_member T_a V_xa_2 V_B_2)) (= (= (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (= V_A_2 V_B_2))))))
% 112.09/112.47  (assume a184 (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_B_2) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))))
% 112.09/112.47  (assume a185 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) V_A_2))))
% 112.09/112.47  (assume a186 (forall ((V_a_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 V_D_2)))))
% 112.09/112.47  (assume a187 (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))))
% 112.09/112.47  (assume a188 (forall ((V_a_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2))))
% 112.09/112.47  (assume a189 (forall ((T_a $$unsorted)) (= (tptp.c_Set_OPow T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a190 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_OPow T_a V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a191 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_OPow T_a V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a192 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_c_2 V_d_2)) (or (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_d_2)))))))
% 112.09/112.47  (assume a193 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a194 (forall ((V_k_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OatMost T_a V_less__eq_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_i_2) V_k_2)))))
% 112.09/112.47  (assume a195 (forall ((V_k_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OatLeast T_a V_less__eq_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_k_2) V_i_2)))))
% 112.09/112.47  (assume a196 (forall ((V_k_2 $$unsorted) (V_less_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OlessThan T_a V_less_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_i_2) V_k_2)))))
% 112.09/112.47  (assume a197 (forall ((V_k_2 $$unsorted) (V_less_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OgreaterThan T_a V_less_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_k_2) V_i_2)))))
% 112.09/112.47  (assume a198 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OatLeastAtMost T_a V_less__eq_2 V_l_2 V_u_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_l_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_i_2) V_u_2))))))
% 112.09/112.47  (assume a199 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (V_less_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OgreaterThanLessThan T_a V_less_2 V_l_2 V_u_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_l_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_i_2) V_u_2))))))
% 112.09/112.47  (assume a200 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (V_less_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OatLeastLessThan T_a V_less__eq_2 V_less_2 V_l_2 V_u_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_l_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_i_2) V_u_2))))))
% 112.09/112.47  (assume a201 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (V_less_2 $$unsorted) (V_less__eq_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord_OgreaterThanAtMost T_a V_less__eq_2 V_less_2 V_l_2 V_u_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less_2 V_l_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq_2 V_i_2) V_u_2))))))
% 112.09/112.47  (assume a202 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Omonoseq T_a V_X_2) (or (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)))) (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)))))))))
% 112.09/112.47  (assume a203 (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))))))
% 112.09/112.47  (assume a204 (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)))))
% 112.09/112.47  (assume a205 (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))))
% 112.09/112.47  (assume a206 (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))))
% 112.09/112.47  (assume a207 (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)))))
% 112.09/112.47  (assume a208 (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))))
% 112.09/112.47  (assume a209 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 112.09/112.47  (assume a210 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))))
% 112.09/112.47  (assume a211 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))))
% 112.09/112.47  (assume a212 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 112.09/112.47  (assume a213 (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)))))
% 112.09/112.47  (assume a214 (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)))))
% 112.09/112.47  (assume a215 (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_n_2) V_m_2))) (=> (=> (= V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_n_2) V_m_2))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_n_2) V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_n_2) V_m_2)))))))
% 112.09/112.47  (assume a216 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_SEQ_Oincseq T_a V_X_2) (tptp.c_SEQ_Omonoseq T_a V_X_2)))))
% 112.09/112.47  (assume a217 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_SEQ_Odecseq T_a V_X_2) (tptp.c_SEQ_Omonoseq T_a V_X_2)))))
% 112.09/112.47  (assume a218 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))))
% 112.09/112.47  (assume a219 (forall ((V_k $$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)))))
% 112.09/112.47  (assume a220 (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))))
% 112.09/112.47  (assume a221 (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))))
% 112.09/112.47  (assume a222 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)))
% 112.09/112.47  (assume a223 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 B_m)))) (tptp.c_SEQ_Omonoseq T_a V_X_2)))))
% 112.09/112.47  (assume a224 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m) (tptp.hAPP V_X_2 B_n)))) (tptp.c_SEQ_Omonoseq T_a V_X_2)))))
% 112.09/112.47  (assume a225 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_m_2) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_n_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_m_2 V_n_2)))))
% 112.09/112.47  (assume a226 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2)))))
% 112.09/112.47  (assume a227 (forall ((V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Orderings_Oorder T_b) (tptp.class_Orderings_Oorder T_a)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless T_a B_x B_y) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y)))) (tptp.c_Orderings_Oorder__class_Ostrict__mono T_a T_b V_f_2)))))
% 112.09/112.47  (assume a228 (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_k_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_k_2 V_i_2)))))
% 112.09/112.47  (assume a229 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2)))))
% 112.09/112.47  (assume a230 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OlessThan T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_ya_2)) (= V_xa_2 V_ya_2)))))
% 112.09/112.47  (assume a231 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_ya_2)) (= V_xa_2 V_ya_2)))))
% 112.09/112.47  (assume a232 (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord__class_OlessThan T_a V_k_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_i_2 V_k_2)))))
% 112.09/112.47  (assume a233 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OatMost T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2)))))
% 112.09/112.47  (assume a234 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_xa_2)))))
% 112.09/112.47  (assume a235 (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord__class_OatMost T_a V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_i_2 V_k_2)))))
% 112.09/112.47  (assume a236 (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_member T_a V_i_2 (tptp.c_SetInterval_Oord__class_OatLeast T_a V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_k_2 V_i_2)))))
% 112.09/112.47  (assume a237 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_RComplete_Onatceiling V_y)))))
% 112.09/112.47  (assume a238 (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_i) (tptp.hAPP V_f_2 B_j)))) (=> (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.hAPP V_f_2 V_i_2) (tptp.hAPP V_f_2 V_j_2))))))
% 112.09/112.47  (assume a239 (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_xa_2 V_A_2) (not (forall ((B_B $$unsorted)) (=> (= V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 B_B)) (tptp.c_member T_a V_xa_2 B_B)))))))
% 112.09/112.47  (assume a240 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatLeast T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_ya_2)) (= V_xa_2 V_ya_2)))))
% 112.09/112.47  (assume a241 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatMost T_a V_xa_2) (tptp.c_SetInterval_Oord__class_OatMost T_a V_ya_2)) (= V_xa_2 V_ya_2)))))
% 112.09/112.47  (assume a242 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_l_2))))))
% 112.09/112.47  (assume a243 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_l_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatMost T_a V_u_2))))))
% 112.09/112.47  (assume a244 (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))))
% 112.09/112.47  (assume a245 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x))))
% 112.09/112.47  (assume a246 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (exists ((B_B $$unsorted)) (and (= V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 B_B)) (not (tptp.c_member T_a V_a_2 B_B)))))))
% 112.09/112.47  (assume a247 (forall ((V_n_2 $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.c_SEQ_Osubseq V_f_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 (tptp.hAPP V_f_2 V_n_2)))))
% 112.09/112.47  (assume a248 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) (tptp.c_RComplete_Onatfloor V_y)))))
% 112.09/112.47  (assume a249 (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2))))))
% 112.09/112.47  (assume a250 (forall ((T_a $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (V_B_2 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)))))
% 112.09/112.47  (assume a251 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a252 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (=> (not (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 V_B_2)))))
% 112.09/112.47  (assume a253 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 112.09/112.47  (assume a254 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)))
% 112.09/112.47  (assume a255 (= (tptp.c_SetInterval_Oord__class_OatLeast tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))))
% 112.09/112.47  (assume a256 (forall ((V_n_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat V_n_2))))
% 112.09/112.47  (assume a257 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x))))
% 112.09/112.47  (assume a258 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 112.09/112.47  (assume a259 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)))
% 112.09/112.47  (assume a260 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))))
% 112.09/112.47  (assume a261 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a262 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a263 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 112.09/112.47  (assume a264 (forall ((V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (or (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x))))))))
% 112.09/112.47  (assume a265 (forall ((V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (and (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x))))))))
% 112.09/112.47  (assume a266 (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)))))
% 112.09/112.47  (assume a267 (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)))))
% 112.09/112.47  (assume a268 (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))))
% 112.09/112.47  (assume a269 (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)))))
% 112.09/112.47  (assume a270 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a271 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a272 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (or (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))))
% 112.09/112.47  (assume a273 (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a274 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 112.09/112.47  (assume a275 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a276 (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a277 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a278 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a279 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2))))
% 112.09/112.47  (assume a280 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2))))
% 112.09/112.47  (assume a281 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2))))
% 112.09/112.47  (assume a282 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2)))))
% 112.09/112.47  (assume a283 (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_D_2))))))
% 112.09/112.47  (assume a284 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_Set_OPow T_a V_A_2) (tptp.c_Set_OPow T_a V_B_2)) (tptp.c_Set_OPow T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a285 (forall ((V_n $$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))))
% 112.09/112.47  (assume a286 (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))))))
% 112.09/112.47  (assume a287 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 112.09/112.47  (assume a288 (forall ((V_n_2 $$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))))
% 112.09/112.47  (assume a289 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 112.09/112.47  (assume a290 (forall ((V_n_2 $$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)))))
% 112.09/112.47  (assume a291 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)))
% 112.09/112.47  (assume a292 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 112.09/112.47  (assume a293 (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))))
% 112.09/112.47  (assume a294 (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))))
% 112.09/112.47  (assume a295 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)))))
% 112.09/112.47  (assume a296 (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_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_f_2 B_m) (tptp.hAPP V_f_2 B_n)))))))
% 112.09/112.47  (assume a297 (forall ((V_xa_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_b T_a) V_f_2 V_g_2) V_xa_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_g_2 V_xa_2))))))
% 112.09/112.47  (assume a298 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 112.09/112.47  (assume a299 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Orderings_Otop__class_Otop T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 112.09/112.47  (assume a300 (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted)) (= (forall ((B_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m V_n_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_m)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member tptp.tc_Nat_Onat B_x (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))))
% 112.09/112.47  (assume a301 (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted)) (= (exists ((B_m $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m V_n_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_m)))) (exists ((B_x $$unsorted)) (and (tptp.c_member tptp.tc_Nat_Onat B_x (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))))
% 112.09/112.47  (assume a302 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))))
% 112.09/112.47  (assume a303 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))))
% 112.09/112.47  (assume a304 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_a) V_a))))
% 112.09/112.47  (assume a305 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_x) V_x))))
% 112.09/112.47  (assume a306 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_a)))))
% 112.09/112.47  (assume a307 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x)))))
% 112.09/112.47  (assume a308 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x)))))
% 112.09/112.47  (assume a309 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b)))))
% 112.09/112.47  (assume a310 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 112.09/112.47  (assume a311 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 112.09/112.47  (assume a312 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_c))))))
% 112.09/112.47  (assume a313 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))))
% 112.09/112.47  (assume a314 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))))
% 112.09/112.47  (assume a315 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_c) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_c))))))
% 112.09/112.47  (assume a316 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))))
% 112.09/112.47  (assume a317 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))))
% 112.09/112.47  (assume a318 (forall ((V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x))))))))
% 112.09/112.47  (assume a319 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_c V_d)))))))
% 112.09/112.47  (assume a320 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup 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_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x))))))
% 112.09/112.47  (assume a321 (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x))))))
% 112.09/112.47  (assume a322 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_x)))))
% 112.09/112.47  (assume a323 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_y)))))
% 112.09/112.47  (assume a324 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))))
% 112.09/112.47  (assume a325 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup 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_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))))
% 112.09/112.47  (assume a326 (forall ((V_z_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_xa_2 V_ya_2) V_z_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_z_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ya_2 V_z_2))))))
% 112.09/112.47  (assume a327 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_xa_2 V_ya_2) V_ya_2)))))
% 112.09/112.47  (assume a328 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 112.09/112.47  (assume a329 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 112.09/112.47  (assume a330 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 112.09/112.47  (assume a331 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 112.09/112.47  (assume a332 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_l_2))))))
% 112.09/112.47  (assume a333 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_l_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_u_2))))))
% 112.09/112.47  (assume a334 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_n)))))
% 112.09/112.47  (assume a335 (forall ((V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_l_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_l_2)) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_l_2)))))
% 112.09/112.47  (assume a336 (forall ((V_a_2 $$unsorted) (V_xa_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_xa_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_xa_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2))))))
% 112.09/112.47  (assume a337 (forall ((V_a_2 $$unsorted) (V_xa_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_xa_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_a_2 (tptp.c_RComplete_Onatfloor V_xa_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2) V_xa_2)))))
% 112.09/112.47  (assume a338 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_member T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a339 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2)))
% 112.09/112.47  (assume a340 (forall ((V_n $$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))))
% 112.09/112.47  (assume a341 (forall ((V_k_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_k_2) (= (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_k_2 V_l_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a342 (forall ((T_a $$unsorted)) (= (tptp.c_Set_OPow T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Set_Oinsert (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a343 (forall ((V_xa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b T_a)) V_xa_2) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 112.09/112.47  (assume a344 (forall ((V_a_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_member T_a V_a_2 V_A_2)))))
% 112.09/112.47  (assume a345 (forall ((V_c_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_member T_a V_c_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a346 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (tptp.c_member T_a B_x V_A_2)) (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a347 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (not (tptp.c_member T_a B_x V_A_2))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a348 (= (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))))
% 112.09/112.47  (assume a349 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2)))))
% 112.09/112.47  (assume a350 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a351 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Set_Oinsert T_a V_c_2 (tptp.c_Set_Oinsert T_a V_d_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (or (and (= V_a_2 V_c_2) (= V_b_2 V_d_2)) (and (= V_a_2 V_d_2) (= V_b_2 V_c_2))))))
% 112.09/112.47  (assume a352 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_a_2 V_b_2))))
% 112.09/112.47  (assume a353 (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Set_OCollect T_a V_Pa_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))))
% 112.09/112.47  (assume a354 (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect T_a V_Pa_2)) (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))))
% 112.09/112.47  (assume a355 (forall ((T_a $$unsorted)) (not (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a356 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a357 (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) V_B_2)))
% 112.09/112.47  (assume a358 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_A_2)))
% 112.09/112.47  (assume a359 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (and (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_B_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a360 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_OPow T_a V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a361 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a362 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x))))
% 112.09/112.47  (assume a363 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x) V_x))))
% 112.09/112.47  (assume a364 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))))
% 112.09/112.47  (assume a365 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Obot__class_Obot T_a)) (and (= V_xa_2 (tptp.c_Orderings_Obot__class_Obot T_a)) (= V_ya_2 (tptp.c_Orderings_Obot__class_Obot T_a)))))))
% 112.09/112.47  (assume a366 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))))
% 112.09/112.47  (assume a367 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))))
% 112.09/112.47  (assume a368 (forall ((V_xa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (or (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))))
% 112.09/112.47  (assume a369 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2)) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2))))))
% 112.09/112.47  (assume a370 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2))))))
% 112.09/112.47  (assume a371 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a372 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_A_2))))
% 112.09/112.47  (assume a373 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a_2 V_b_2) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))))
% 112.09/112.47  (assume a374 (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_b_2) (tptp.c_Set_Oinsert T_a V_c_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (and (= V_a_2 V_b_2) (= V_b_2 V_c_2))))))
% 112.09/112.47  (assume a375 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_a_2 V_a_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a376 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 112.09/112.47  (assume a377 (forall ((V_n_2 $$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)))))
% 112.09/112.47  (assume a378 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 112.09/112.47  (assume a379 (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Set_OPow T_a V_B_2))))
% 112.09/112.47  (assume a380 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 112.09/112.47  (assume a381 (= (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a382 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 112.09/112.47  (assume a383 (forall ((V_n_2 $$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)))))
% 112.09/112.47  (assume a384 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 112.09/112.47  (assume a385 (forall ((V_x $$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)))))
% 112.09/112.47  (assume a386 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) V_x))))
% 112.09/112.47  (assume a387 (forall ((V_n_2 $$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))))
% 112.09/112.47  (assume a388 (forall ((V_u_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_u_2) (tptp.c_Set_Oinsert T_a V_u_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_SetInterval_Oord__class_OatMost T_a V_u_2)))))
% 112.09/112.47  (assume a389 (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Othe__elem T_a (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_xa_2)))
% 112.09/112.47  (assume a390 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)))))))
% 112.09/112.47  (assume a391 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2) (tptp.c_Set_Oinsert T_a V_u_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2))))))
% 112.09/112.47  (assume a392 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_l_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2))))))
% 112.09/112.47  (assume a393 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)))))))
% 112.09/112.47  (assume a394 (forall ((V_n_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat V_n_2))))
% 112.09/112.47  (assume a395 (forall ((V_m_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a396 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_c_2 V_d_2)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2) (= V_b_2 V_d_2)))))))
% 112.09/112.47  (assume a397 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_c_2 V_d_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_d_2) (= V_a_2 V_c_2)))))))
% 112.09/112.47  (assume a398 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2) (= (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_c_2 V_d_2)) (and (= V_a_2 V_c_2) (= V_b_2 V_d_2))))))))
% 112.09/112.47  (assume a399 (= (tptp.c_Orderings_Obot__class_Obot tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 112.09/112.47  (assume a400 (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted)) (= (forall ((B_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m V_n_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_m)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member tptp.tc_Nat_Onat B_x (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))))
% 112.09/112.47  (assume a401 (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted)) (= (exists ((B_m $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m V_n_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_m)))) (exists ((B_x $$unsorted)) (and (tptp.c_member tptp.tc_Nat_Onat B_x (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))))))
% 112.09/112.47  (assume a402 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a403 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2))))))
% 112.09/112.47  (assume a404 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2))))))
% 112.09/112.47  (assume a405 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_a_2 V_b_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_c_2 V_d_2)) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_d_2)))))))
% 112.09/112.47  (assume a406 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)))))))
% 112.09/112.47  (assume a407 (forall ((V_k_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_k_2) (= (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_k_2 V_l_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a408 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_k_2 V_l_2)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_k_2 V_l_2))))))
% 112.09/112.47  (assume a409 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_k_2 V_l_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_Orderings_Oord__class_Oless T_a V_k_2 V_l_2))))))
% 112.09/112.47  (assume a410 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)))))))
% 112.09/112.47  (assume a411 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)))))))
% 112.09/112.47  (assume a412 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_l_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_u_2))))))
% 112.09/112.47  (assume a413 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_l_2))))))
% 112.09/112.47  (assume a414 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)))))))
% 112.09/112.47  (assume a415 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_l_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatMost T_a V_u_2))))))
% 112.09/112.47  (assume a416 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_l_2))))))
% 112.09/112.47  (assume a417 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)))))))
% 112.09/112.47  (assume a418 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_m_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_m_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)))))))
% 112.09/112.47  (assume a419 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2) (tptp.c_Set_Oinsert T_a V_u_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2))))))
% 112.09/112.47  (assume a420 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_l_2 V_u_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_l_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2))))))
% 112.09/112.47  (assume a421 (forall ((V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (and (=> (tptp.c_member T_a V_xa_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (=> (not (tptp.c_member T_a V_xa_2 V_B_2)) (and (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_B_2)) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))))
% 112.09/112.47  (assume a422 (forall ((V_n_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_n_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_n_2)) (tptp.c_Set_Oinsert T_a V_n_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a423 (forall ((V_n_2 $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Nat_Osemiring__1__class_ONats tptp.tc_RealDef_Oreal))))
% 112.09/112.47  (assume a424 (forall ((T_a $$unsorted)) (=> (tptp.class_GCD_Ogcd T_a) (= (tptp.c_GCD_Ogcd__class_OGcd T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 112.09/112.47  (assume a425 (forall ((V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_B_2) (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2))))))
% 112.09/112.47  (assume a426 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2))))))
% 112.09/112.47  (assume a427 (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (not (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)) (not (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2))))))))
% 112.09/112.47  (assume a428 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2)))))))
% 112.09/112.47  (assume a429 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 112.09/112.47  (assume a430 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2))))))
% 112.09/112.47  (assume a431 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 112.09/112.47  (assume a432 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a433 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2))))
% 112.09/112.47  (assume a434 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Orderings_Obot__class_Obot T_a)) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 112.09/112.47  (assume a435 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 112.09/112.47  (assume a436 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z) V_x) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_z V_x))))))
% 112.09/112.47  (assume a437 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_z V_x))))))
% 112.09/112.47  (assume a438 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))))
% 112.09/112.47  (assume a439 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))))
% 112.09/112.47  (assume a440 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) V_x))))
% 112.09/112.47  (assume a441 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)) V_x))))
% 112.09/112.47  (assume a442 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Orderings_Otop__class_Otop T_a) V_x) V_x))))
% 112.09/112.47  (assume a443 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))))
% 112.09/112.47  (assume a444 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Otop__class_Otop T_a)) (and (= V_xa_2 (tptp.c_Orderings_Otop__class_Otop T_a)) (= V_ya_2 (tptp.c_Orderings_Otop__class_Otop T_a)))))))
% 112.09/112.47  (assume a445 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (and (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))))
% 112.09/112.47  (assume a446 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2))))
% 112.09/112.47  (assume a447 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_B_2))))
% 112.09/112.47  (assume a448 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (and (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2))))))
% 112.09/112.47  (assume a449 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2))))
% 112.09/112.47  (assume a450 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (tptp.c_member T_a V_c_2 V_B_2)))))
% 112.09/112.47  (assume a451 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_B_2) (not (= B_x B_xa)))))))))
% 112.09/112.47  (assume a452 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a453 (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a454 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a455 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_A_2)))
% 112.09/112.47  (assume a456 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a457 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a458 (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) V_B_2)))
% 112.09/112.47  (assume a459 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_A_2)))
% 112.09/112.47  (assume a460 (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_D_2))))))
% 112.09/112.47  (assume a461 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 112.09/112.47  (assume a462 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2))))
% 112.09/112.47  (assume a463 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2))))
% 112.09/112.47  (assume a464 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2)))
% 112.09/112.47  (assume a465 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2)))
% 112.09/112.47  (assume a466 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)) V_A_2)))))
% 112.09/112.47  (assume a467 (forall ((V_B_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_D_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_D_2))))))
% 112.09/112.47  (assume a468 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2)))
% 112.09/112.47  (assume a469 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)))))
% 112.09/112.47  (assume a470 (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)))))
% 112.09/112.47  (assume a471 (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)))))
% 112.09/112.47  (assume a472 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a473 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a474 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 112.09/112.47  (assume a475 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))))
% 112.09/112.47  (assume a476 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a477 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a478 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a479 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) V_A_2)))
% 112.09/112.47  (assume a480 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_a) V_a))))
% 112.09/112.47  (assume a481 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_x) V_x))))
% 112.09/112.47  (assume a482 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_a)))))
% 112.09/112.47  (assume a483 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))))
% 112.09/112.47  (assume a484 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))))
% 112.09/112.47  (assume a485 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)))))
% 112.09/112.47  (assume a486 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)))))
% 112.09/112.47  (assume a487 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)))))
% 112.09/112.47  (assume a488 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))))
% 112.09/112.47  (assume a489 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))))
% 112.09/112.47  (assume a490 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))))
% 112.09/112.47  (assume a491 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_c) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))))
% 112.09/112.47  (assume a492 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))))
% 112.09/112.47  (assume a493 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))))
% 112.09/112.47  (assume a494 (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a) V_A_2 V_B_2) V_xa_2) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP V_A_2 V_xa_2) (tptp.hAPP V_B_2 V_xa_2))))))
% 112.09/112.47  (assume a495 (forall ((V_xa_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b T_a) V_f_2 V_g_2) V_xa_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_g_2 V_xa_2))))))
% 112.09/112.47  (assume a496 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OPow T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_Set_OPow T_a V_A_2) (tptp.c_Set_OPow T_a V_B_2)))))
% 112.09/112.47  (assume a497 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)))
% 112.09/112.47  (assume a498 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))))
% 112.09/112.47  (assume a499 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a500 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 112.09/112.47  (assume a501 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_B_2)))))
% 112.09/112.47  (assume a502 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 112.09/112.47  (assume a503 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 112.09/112.47  (assume a504 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 112.09/112.47  (assume a505 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 112.09/112.47  (assume a506 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) V_B_2))))
% 112.09/112.47  (assume a507 (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)))))
% 112.09/112.47  (assume a508 (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2)))))
% 112.09/112.47  (assume a509 (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))))
% 112.09/112.47  (assume a510 (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))))
% 112.09/112.47  (assume a511 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b))))))))
% 112.09/112.47  (assume a512 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_c V_d)))))))
% 112.09/112.47  (assume a513 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)))))))
% 112.09/112.47  (assume a514 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)))))))
% 112.09/112.47  (assume a515 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y)))))
% 112.09/112.47  (assume a516 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x)))))
% 112.09/112.47  (assume a517 (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))))
% 112.09/112.47  (assume a518 (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))))
% 112.09/112.47  (assume a519 (forall ((V_z_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_ya_2 V_z_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_z_2))))))
% 112.09/112.47  (assume a520 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_xa_2 V_ya_2) V_xa_2)))))
% 112.09/112.47  (assume a521 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))))
% 112.09/112.47  (assume a522 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))))
% 112.09/112.47  (assume a523 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x))))
% 112.09/112.47  (assume a524 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x))))
% 112.09/112.47  (assume a525 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))))
% 112.09/112.47  (assume a526 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))))
% 112.09/112.47  (assume a527 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_C_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2))))))
% 112.09/112.47  (assume a528 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 112.09/112.47  (assume a529 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_a_2 V_C_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 112.09/112.47  (assume a530 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_a_2 V_A_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a531 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (and (=> (tptp.c_member T_a V_a_2 V_C_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))) (=> (not (tptp.c_member T_a V_a_2 V_C_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2))))))
% 112.09/112.47  (assume a532 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (and (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (=> (not (tptp.c_member T_a V_a_2 V_A_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 112.09/112.47  (assume a533 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_xa_2 V_B_2) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 112.09/112.47  (assume a534 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (and (=> (tptp.c_member T_a V_xa_2 V_B_2) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (=> (not (tptp.c_member T_a V_xa_2 V_B_2)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2) (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))))
% 112.09/112.47  (assume a535 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2))))
% 112.09/112.47  (assume a536 (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_B_2))))
% 112.09/112.47  (assume a537 (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a538 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 112.09/112.47  (assume a539 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_i_2 V_n_2) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_i_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_i_2 V_n_2)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_n_2 V_m_2))))))
% 112.09/112.47  (assume a540 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2))))
% 112.09/112.47  (assume a541 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a542 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)) V_B_2))))
% 112.09/112.47  (assume a543 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 112.09/112.47  (assume a544 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a545 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) V_A_2))))
% 112.09/112.47  (assume a546 (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_A_2))))
% 112.09/112.47  (assume a547 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a548 (forall ((V_k_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_k_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_k_2)) (tptp.c_Set_Oinsert T_a V_k_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a549 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_l_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a550 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OlessThan T_a V_l_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a551 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a552 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a553 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a554 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a555 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a556 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a557 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_l_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a558 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatMost T_a V_l_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a559 (forall ((V_u_2 $$unsorted) (V_m_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_m_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_m_2 V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a560 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OatLeast T_a V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a561 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost T_a V_l_2 V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThan T_a V_u_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a562 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (tptp.c_member T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_ONats T_a)))))
% 112.09/112.47  (assume a563 (forall ((V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (and (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_B_2)) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 112.09/112.47  (assume a564 (forall ((V_b_2 $$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))))))
% 112.09/112.47  (assume a565 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 112.09/112.47  (assume a566 (forall ((V_d_2 $$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_d_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_d_2))))))
% 112.09/112.47  (assume a567 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_d_2))))))
% 112.09/112.47  (assume a568 (forall ((V_b_2 $$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)))))
% 112.09/112.47  (assume a569 (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)))))
% 112.09/112.47  (assume a570 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 112.09/112.47  (assume a571 (forall ((V_m $$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)))
% 112.09/112.47  (assume a572 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 112.09/112.47  (assume a573 (forall ((V_n $$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))))
% 112.09/112.47  (assume a574 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m))))))
% 112.09/112.47  (assume a575 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m)))
% 112.09/112.47  (assume a576 (forall ((V_l $$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)))))
% 112.09/112.47  (assume a577 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_l)))))
% 112.09/112.47  (assume a578 (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_i)) V_i))))
% 112.09/112.47  (assume a579 (forall ((V_n_2 $$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))))))
% 112.09/112.47  (assume a580 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_m) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))))
% 112.09/112.47  (assume a581 (forall ((V_n_2 $$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))))))
% 112.09/112.47  (assume a582 (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))))))
% 112.09/112.47  (assume a583 (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)))))
% 112.09/112.47  (assume a584 (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)))))
% 112.09/112.47  (assume a585 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_xa_2 V_ya_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 112.09/112.47  (assume a586 (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)))))
% 112.09/112.47  (assume a587 (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))))
% 112.09/112.47  (assume a588 (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)))))
% 112.09/112.47  (assume a589 (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))))
% 112.09/112.47  (assume a590 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_c V_a) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a V_c) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_b V_c))))))
% 112.09/112.47  (assume a591 (forall ((V_n_2 $$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))))))
% 112.09/112.47  (assume a592 (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) V_xa_2) (= V_xa_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 112.09/112.47  (assume a593 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (= V_a_2 V_b_2) (= V_c_2 V_d_2))))))
% 112.09/112.47  (assume a594 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 112.09/112.47  (assume a595 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 112.09/112.47  (assume a596 (forall ((V_b_2 $$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))))))
% 112.09/112.47  (assume a597 (forall ((V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)) (tptp.hBOOL (tptp.hAPP V_Q_2 B_x))))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_OCollect T_a V_Pa_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Set_OCollect T_a V_Q_2)))))))
% 112.09/112.47  (assume a598 (forall ((V_ya_2 $$unsorted) (V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_xa_2 V_A_2) (=> (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_ya_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 V_A_2 (tptp.hAPP (tptp.hAPP V_f_2 V_xa_2) V_ya_2))))))
% 112.09/112.47  (assume a599 (forall ((V_p_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_p_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_p_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 112.09/112.47  (assume a600 (forall ((V_k $$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))))
% 112.09/112.47  (assume a601 (forall ((V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_z_2)))
% 112.09/112.47  (assume a602 (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a1_2 V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_a2_2)))
% 112.09/112.47  (assume a603 (forall ((V_a5_2 $$unsorted) (V_a1_2 $$unsorted) (V_a2_2 $$unsorted) (V_a4_2 $$unsorted) (V_a3_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 V_a2_2 (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2)) (or (and (= V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2) V_a4_2)) (exists ((B_x $$unsorted) (B_y $$unsorted)) (and (= (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2) (tptp.hAPP (tptp.hAPP V_a3_2 B_x) B_y)) (tptp.c_member T_a B_x V_a2_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_a2_2 (tptp.c_Set_Oinsert T_a B_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) B_y)))))))
% 112.09/112.47  (assume a604 (forall ((V_x $$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)))))
% 112.09/112.47  (assume a605 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat V_n_2 (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 V_n_2)))) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a606 (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)))))
% 112.09/112.47  (assume a607 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_n))))
% 112.09/112.47  (assume a608 (forall ((V_n $$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))))
% 112.09/112.47  (assume a609 (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))))
% 112.09/112.47  (assume a610 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_k))))
% 112.09/112.47  (assume a611 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 112.09/112.47  (assume a612 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 112.09/112.47  (assume a613 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))))
% 112.09/112.47  (assume a614 (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_nat_H)))))
% 112.09/112.47  (assume a615 (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 112.09/112.47  (assume a616 (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 112.09/112.47  (assume a617 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))))
% 112.09/112.47  (assume a618 (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 112.09/112.47  (assume a619 (forall ((T_a $$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))))))
% 112.09/112.47  (assume a620 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 112.09/112.47  (assume a621 (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeast tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_SetInterval_Oord__class_OgreaterThan tptp.tc_Nat_Onat V_k_2))))
% 112.09/112.47  (assume a622 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_l_2) V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan tptp.tc_Nat_Onat V_l_2 V_u_2))))
% 112.09/112.47  (assume a623 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Nat_OSuc V_x) (tptp.c_Nat_OSuc V_y)) (= V_x V_y))))
% 112.09/112.47  (assume a624 (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))))
% 112.09/112.47  (assume a625 (forall ((V_n $$unsorted)) (not (= (tptp.c_Nat_OSuc V_n) V_n))))
% 112.09/112.47  (assume a626 (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Nat_OSuc V_n)))))
% 112.09/112.47  (assume a627 (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))))
% 112.09/112.47  (assume a628 (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))))))
% 112.09/112.47  (assume a629 (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)))))
% 112.09/112.47  (assume a630 (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))))
% 112.09/112.47  (assume a631 (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))))))
% 112.09/112.47  (assume a632 (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))))
% 112.09/112.47  (assume a633 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) V_n))))
% 112.09/112.47  (assume a634 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 112.09/112.47  (assume a635 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 112.09/112.47  (assume a636 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= V_m V_n)))))
% 112.09/112.47  (assume a637 (forall ((V_k $$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)))))
% 112.09/112.47  (assume a638 (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)))))
% 112.09/112.47  (assume a639 (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)))))
% 112.09/112.47  (assume a640 (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)))))
% 112.09/112.47  (assume a641 (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)))))
% 112.09/112.47  (assume a642 (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))))
% 112.09/112.47  (assume a643 (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)))))
% 112.09/112.47  (assume a644 (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)))))
% 112.09/112.47  (assume a645 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_l_2) V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost tptp.tc_Nat_Onat V_l_2 V_u_2))))
% 112.09/112.47  (assume a646 (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oone T_a) (= (= (tptp.c_Groups_Oone__class_Oone T_a) V_xa_2) (= V_xa_2 (tptp.c_Groups_Oone__class_Oone T_a))))))
% 112.09/112.47  (assume a647 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 112.09/112.47  (assume a648 (forall ((T_a $$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))))))
% 112.09/112.47  (assume a649 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 112.09/112.47  (assume a650 (forall ((T_a $$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))))))
% 112.09/112.47  (assume a651 (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 $$unsorted)) (and (= V_m_2 (tptp.c_Nat_OSuc B_j)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_n_2)))))))
% 112.09/112.47  (assume a652 (forall ((V_n_2 $$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)))))
% 112.09/112.47  (assume a653 (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))))))
% 112.09/112.47  (assume a654 (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))))
% 112.09/112.47  (assume a655 (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))))
% 112.09/112.47  (assume a656 (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))))
% 112.09/112.47  (assume a657 (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)))))
% 112.09/112.47  (assume a658 (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))))
% 112.09/112.47  (assume a659 (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)))))
% 112.09/112.47  (assume a660 (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))))
% 112.09/112.47  (assume a661 (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))))
% 112.09/112.47  (assume a662 (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))))))
% 112.09/112.47  (assume a663 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Omonoseq T_a V_X_2) (or (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n) (tptp.hAPP V_X_2 (tptp.c_Nat_OSuc B_n)))) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 (tptp.c_Nat_OSuc B_n)) (tptp.hAPP V_X_2 B_n))))))))
% 112.09/112.47  (assume a664 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_l_2 (tptp.c_Nat_OSuc V_u_2)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_l_2 V_u_2))))
% 112.09/112.47  (assume a665 (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OgreaterThan tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OgreaterThan tptp.tc_Nat_Onat V_k_2) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a666 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (tptp.c_member T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Nat_Osemiring__1__class_ONats T_a)))))
% 112.09/112.47  (assume a667 (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat V_k_2 (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat V_k_2)))))
% 112.09/112.47  (assume a668 (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2) (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat V_k_2)))))
% 112.09/112.47  (assume a669 (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_n) (tptp.hAPP V_f_2 (tptp.c_Nat_OSuc B_n)))))))
% 112.09/112.47  (assume a670 (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat V_k_2))))
% 112.09/112.47  (assume a671 (forall ((V_n $$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))))
% 112.09/112.47  (assume a672 (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))))
% 112.09/112.47  (assume a673 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)))))
% 112.09/112.47  (assume a674 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_m_2 V_n_2))))))
% 112.09/112.47  (assume a675 (forall ((V_m_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_m_2)) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat V_m_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))))))
% 112.09/112.47  (assume a676 (forall ((V_k_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeast tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeast tptp.tc_Nat_Onat V_k_2) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat V_k_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))))))
% 112.09/112.47  (assume a677 (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 (tptp.c_Nat_OSuc V_j_2)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_i_2 (tptp.c_Nat_OSuc V_j_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_i_2 V_j_2) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_j_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))))))))
% 112.09/112.47  (assume a678 (forall ((V_x $$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)))))))
% 112.09/112.47  (assume a679 (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))))
% 112.09/112.47  (assume a680 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 112.09/112.47  (assume a681 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))
% 112.09/112.47  (assume a682 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 112.09/112.47  (assume a683 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 112.09/112.47  (assume a684 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 112.09/112.47  (assume a685 (forall ((V_n $$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)))))))
% 112.09/112.47  (assume a686 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n))))
% 112.09/112.47  (assume a687 (forall ((V_xa_2 $$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_xa_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_xa_2))))
% 112.09/112.47  (assume a688 (forall ((V_xa_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_xa_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_xa_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 112.09/112.47  (assume a689 (forall ((T_a $$unsorted)) (=> (tptp.class_GCD_Ogcd T_a) (= (tptp.c_GCD_Ogcd__class_OLcm T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 112.09/112.47  (assume a690 (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)))))))
% 112.09/112.47  (assume a691 (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))))))))
% 112.09/112.47  (assume a692 (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_i_2 V_j_2) (tptp.c_Set_Oinsert tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))))))))
% 112.09/112.47  (assume a693 (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)))))
% 112.09/112.48  (assume a694 (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)))))
% 112.09/112.48  (assume a695 (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))))))
% 112.09/112.48  (assume a696 (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))))))))
% 112.09/112.48  (assume a697 (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))))))))
% 112.09/112.48  (assume a698 (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)))))
% 112.09/112.48  (assume a699 (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 $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k)))))))
% 112.09/112.48  (assume a700 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_i)))))
% 112.09/112.48  (assume a701 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_m)))))
% 112.09/112.48  (assume a702 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 112.09/112.48  (assume a703 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 112.09/112.48  (assume a704 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 112.09/112.48  (assume a705 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 112.09/112.48  (assume a706 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 112.09/112.48  (assume a707 (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2)) (= V_b_2 V_c_2)))))
% 112.09/112.48  (assume a708 (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2)) (= V_b_2 V_c_2)))))
% 112.09/112.48  (assume a709 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 112.09/112.48  (assume a710 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 112.09/112.48  (assume a711 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))))
% 112.09/112.48  (assume a712 (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))))
% 112.09/112.48  (assume a713 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))))
% 112.09/112.48  (assume a714 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 112.09/112.48  (assume a715 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 112.09/112.48  (assume a716 (forall ((V_d $$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)))))))
% 112.09/112.48  (assume a717 (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)))))
% 112.09/112.48  (assume a718 (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)))))
% 112.09/112.48  (assume a719 (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)))))
% 112.09/112.48  (assume a720 (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)))))
% 112.09/112.48  (assume a721 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 112.09/112.48  (assume a722 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 112.09/112.48  (assume a723 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 112.09/112.48  (assume a724 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))))
% 112.09/112.48  (assume a725 (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))))
% 112.09/112.48  (assume a726 (forall ((V_z $$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)))))
% 112.09/112.48  (assume a727 (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))))
% 112.09/112.48  (assume a728 (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))))
% 112.09/112.48  (assume a729 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 112.09/112.48  (assume a730 (forall ((V_m $$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)))))
% 112.09/112.48  (assume a731 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))))
% 112.09/112.48  (assume a732 (forall ((V_z $$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)))))
% 112.09/112.48  (assume a733 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 112.09/112.48  (assume a734 (forall ((V_k $$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)))))
% 112.09/112.48  (assume a735 (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))))))
% 112.09/112.48  (assume a736 (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)))))
% 112.09/112.48  (assume a737 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_k))))
% 112.09/112.48  (assume a738 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))))
% 112.09/112.48  (assume a739 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 112.09/112.48  (assume a740 (forall ((V_n_2 $$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))))))
% 112.09/112.48  (assume a741 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 112.09/112.48  (assume a742 (forall ((V_m $$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)))))
% 112.09/112.48  (assume a743 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))))
% 112.09/112.48  (assume a744 (forall ((V_z $$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)))))
% 112.09/112.48  (assume a745 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 112.09/112.48  (assume a746 (forall ((V_k $$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)))))
% 112.09/112.48  (assume a747 (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))))))
% 112.09/112.48  (assume a748 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n))))
% 112.09/112.48  (assume a749 (forall ((V_n $$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))))
% 112.09/112.48  (assume a750 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n)))))))
% 112.09/112.48  (assume a751 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 112.09/112.48  (assume a752 (forall ((V_z $$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)))))
% 112.09/112.48  (assume a753 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)))))
% 112.09/112.48  (assume a754 (forall ((V_n_2 $$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))))
% 112.09/112.48  (assume a755 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))
% 112.09/112.48  (assume a756 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 112.09/112.48  (assume a757 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 112.09/112.48  (assume a758 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 112.09/112.48  (assume a759 (forall ((V_m $$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)))
% 112.09/112.48  (assume a760 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) V_n)))
% 112.09/112.48  (assume a761 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 112.09/112.48  (assume a762 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 112.09/112.48  (assume a763 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 112.09/112.48  (assume a764 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 112.09/112.48  (assume a765 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 112.09/112.48  (assume a766 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a)))))
% 112.09/112.48  (assume a767 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a)))))
% 112.09/112.48  (assume a768 (forall ((V_d $$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)))))))
% 112.09/112.48  (assume a769 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 112.09/112.48  (assume a770 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))))
% 112.09/112.48  (assume a771 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 112.09/112.48  (assume a772 (forall ((V_b $$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)))))))
% 112.09/112.48  (assume a773 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 112.09/112.48  (assume a774 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 112.09/112.48  (assume a775 (forall ((V_b $$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)))))))
% 112.09/112.48  (assume a776 (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)))))))
% 112.09/112.48  (assume a777 (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)))))))
% 112.09/112.48  (assume a778 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_xa_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_ya_2) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_xa_2 V_ya_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_xa_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ya_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 112.09/112.48  (assume a779 (forall ((V_b $$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)))))))
% 112.09/112.48  (assume a780 (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))))))
% 112.09/112.48  (assume a781 (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)))))
% 112.09/112.48  (assume a782 (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)))
% 112.09/112.48  (assume a783 (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)))
% 112.09/112.48  (assume a784 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 112.09/112.48  (assume a785 (forall ((V_n $$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))))
% 112.09/112.48  (assume a786 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 112.09/112.48  (assume a787 (forall ((V_b $$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))))
% 112.09/112.48  (assume a788 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))))
% 112.09/112.48  (assume a789 (forall ((V_d $$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))))))
% 112.09/112.48  (assume a790 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2))))
% 112.09/112.48  (assume a791 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 112.09/112.48  (assume a792 (forall ((V_n $$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)))))
% 112.09/112.48  (assume a793 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n))))
% 112.09/112.48  (assume a794 (forall ((V_i $$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)))))
% 112.09/112.48  (assume a795 (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted) (V_j_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2) V_i_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2)))))
% 112.09/112.48  (assume a796 (forall ((V_m $$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)))))
% 112.09/112.48  (assume a797 (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))))
% 112.09/112.48  (assume a798 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k)))))
% 112.09/112.48  (assume a799 (forall ((V_i_2 $$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)))))
% 112.09/112.48  (assume a800 (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))))
% 112.09/112.48  (assume a801 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2) V_k_2) (= V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_i_2))))))
% 112.09/112.48  (assume a802 (forall ((V_i $$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))))))
% 112.09/112.48  (assume a803 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k)))))
% 112.09/112.48  (assume a804 (forall ((V_i $$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)))))
% 112.09/112.48  (assume a805 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Nat_Osemiring__1__class_ONats T_a)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Nat_Osemiring__1__class_ONats T_a)) (tptp.c_member T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Nat_Osemiring__1__class_ONats T_a)))))))
% 112.09/112.48  (assume a806 (forall ((V_x $$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))))))
% 112.09/112.48  (assume a807 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 112.09/112.48  (assume a808 (forall ((V_b $$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)))))))
% 112.09/112.48  (assume a809 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 112.09/112.48  (assume a810 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 112.09/112.48  (assume a811 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 112.09/112.48  (assume a812 (forall ((V_b $$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)))))))
% 112.09/112.48  (assume a813 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 112.09/112.48  (assume a814 (forall ((T_a $$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))))))
% 112.09/112.48  (assume a815 (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)))))))
% 112.09/112.48  (assume a816 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_Pa_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_d $$unsorted)) (=> (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_d))))))))
% 112.09/112.48  (assume a817 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_Pa_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (not (or (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (exists ((B_d $$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_Pa_2 B_d))))))))))
% 112.09/112.48  (assume a818 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_j) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m))))))
% 112.09/112.48  (assume a819 (forall ((V_m $$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))))))
% 112.09/112.48  (assume a820 (forall ((V_n $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 112.09/112.48  (assume a821 (forall ((V_k_2 $$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_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_i_2 V_j_2) (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j_2 V_k_2)))))))
% 112.09/112.48  (assume a822 (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)))))
% 112.09/112.48  (assume a823 (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)))))))
% 112.09/112.48  (assume a824 (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))))))
% 112.09/112.48  (assume a825 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 112.09/112.48  (assume a826 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 112.09/112.48  (assume a827 (forall ((V_l_2 $$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))))))
% 112.09/112.48  (assume a828 (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))))))
% 112.09/112.48  (assume a829 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone 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)))))))
% 112.09/112.48  (assume a830 (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))))
% 112.09/112.48  (assume a831 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (tptp.c_member T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Oring__1__class_OInts T_a)))))
% 112.09/112.48  (assume a832 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (tptp.c_member T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Int_Oring__1__class_OInts T_a)))))))
% 112.09/112.48  (assume a833 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (tptp.c_member T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Int_Oring__1__class_OInts T_a)))))))
% 112.09/112.48  (assume a834 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (tptp.c_member T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Oring__1__class_OInts T_a)))))
% 112.09/112.48  (assume a835 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))))
% 112.09/112.48  (assume a836 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))))
% 112.09/112.48  (assume a837 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 112.09/112.48  (assume a838 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))))
% 112.09/112.48  (assume a839 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))))
% 112.09/112.48  (assume a840 (forall ((V_c $$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)))))
% 112.09/112.48  (assume a841 (forall ((V_n_2 $$unsorted)) (tptp.c_member tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Int_Oring__1__class_OInts tptp.tc_RealDef_Oreal))))
% 112.09/112.48  (assume a842 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Oring__char__0 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 112.09/112.48  (assume a843 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Oring__char__0 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 112.09/112.48  (assume a844 (forall ((V_a_2 $$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))))))
% 112.09/112.48  (assume a845 (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))))
% 112.09/112.48  (assume a846 (forall ((V_n_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.hBOOL (tptp.hAPP V_Pa_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_Pa_2 B_i))))) (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_k (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 112.09/112.48  (assume a847 (forall ((V_v $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 112.09/112.48  (assume a848 (forall ((V_w_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (tptp.c_member T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2) (tptp.c_Int_Oring__1__class_OInts T_a)))))
% 112.09/112.48  (assume a849 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_xa_2 V_ya_2)))))
% 112.09/112.48  (assume a850 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_xa_2 V_ya_2)))))
% 112.09/112.48  (assume a851 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_xa_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_ya_2)) (= V_xa_2 V_ya_2)))))
% 112.09/112.48  (assume a852 (forall ((V_xa_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2) V_xa_2) (= V_xa_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))))))
% 112.09/112.48  (assume a853 (forall ((V_w_2 $$unsorted) (V_v_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber T_a) (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2)) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v_2)))))))
% 112.09/112.48  (assume a854 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))))
% 112.09/112.48  (assume a855 (forall ((V_c $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_c)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_c)))))
% 112.09/112.48  (assume a856 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))))
% 112.09/112.48  (assume a857 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w))))))
% 112.09/112.48  (assume a858 (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_z)))))
% 112.09/112.48  (assume a859 (forall ((V_M_2 $$unsorted)) (=> (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_M_2) (= (tptp.c_GCD_Ogcd__class_OGcd tptp.tc_Nat_Onat V_M_2) (tptp.c_GCD_Ogcd__class_OGcd tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) V_M_2 (tptp.c_Set_Oinsert tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))))))))
% 112.09/112.48  (assume a860 (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.c_Groups_Otimes__class_Otimes T_a V_u V_x) (tptp.c_Groups_Otimes__class_Otimes T_a V_v V_y)) V_a)))))))))
% 112.09/112.48  (assume a861 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Nat_Onat V_l_2 V_u_2))))
% 112.09/112.48  (assume a862 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Nat_Onat V_l_2 V_u_2))))
% 112.09/112.48  (assume a863 (forall ((V_k_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OlessThan tptp.tc_Nat_Onat V_k_2))))
% 112.09/112.48  (assume a864 (forall ((V_k_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OatMost tptp.tc_Nat_Onat V_k_2))))
% 112.09/112.48  (assume a865 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost tptp.tc_Nat_Onat V_l_2 V_u_2))))
% 112.09/112.48  (assume a866 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan tptp.tc_Nat_Onat V_l_2 V_u_2))))
% 112.09/112.48  (assume a867 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Int_Oring__1__class_OInts T_a)) (tptp.c_member T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_b_2) (tptp.c_Int_Oring__1__class_OInts T_a)))))))
% 112.09/112.48  (assume a868 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n))))
% 112.09/112.48  (assume a869 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n))))
% 112.09/112.48  (assume a870 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))))
% 112.09/112.48  (assume a871 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))))
% 112.09/112.48  (assume a872 (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w)) V_z)))))
% 112.09/112.48  (assume a873 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w))))))
% 112.09/112.48  (assume a874 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))))
% 112.09/112.48  (assume a875 (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Oring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Groups_Ominus__class_Ominus T_b V_a V_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.c_Groups_Otimes__class_Otimes T_b V_a (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.c_Groups_Otimes__class_Otimes T_b V_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)))))))
% 112.09/112.48  (assume a876 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Oring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v) (tptp.c_Groups_Ominus__class_Ominus T_b V_b V_c)) (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v) V_b) (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v) V_c))))))
% 112.09/112.48  (assume a877 (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)))))
% 112.09/112.48  (assume a878 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v) (tptp.c_Groups_Oplus__class_Oplus T_b V_b V_c)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v) V_b) (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v) V_c))))))
% 112.09/112.48  (assume a879 (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Groups_Oplus__class_Oplus T_b V_a V_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.c_Groups_Otimes__class_Otimes T_b V_a (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.c_Groups_Otimes__class_Otimes T_b V_b (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)))))))
% 112.09/112.48  (assume a880 (forall ((V_z $$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)))))
% 112.09/112.48  (assume a881 (forall ((V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z)))))
% 112.09/112.48  (assume a882 (forall ((V_z_2 $$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_z_2) V_z_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 112.09/112.48  (assume a883 (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Int_Oint V_i_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun tptp.tc_Int_Oint tptp.tc_HOL_Obool) (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Int_Oint V_i_2 V_j_2) (tptp.c_Set_Oinsert tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Int_Oint tptp.tc_HOL_Obool))))))))
% 112.09/112.48  (assume a884 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_l_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan tptp.tc_Int_Oint V_l_2 V_u_2))))
% 112.09/112.48  (assume a885 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.tc_Int_Oint V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_u_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Int_Oint V_l_2 V_u_2))))
% 112.09/112.48  (assume a886 (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))))
% 112.09/112.48  (assume a887 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2))))
% 112.09/112.48  (assume a888 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2 V_z_2))))
% 112.09/112.48  (assume a889 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2) (= V_w_2 V_z_2)))))
% 112.09/112.48  (assume a890 (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_l_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_u_2) (tptp.c_SetInterval_Oord__class_OgreaterThanAtMost tptp.tc_Int_Oint V_l_2 V_u_2))))
% 112.09/112.48  (assume a891 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (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.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)))))
% 112.09/112.48  (assume a892 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (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.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)))))
% 112.09/112.48  (assume a893 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j V_k)))))
% 112.09/112.48  (assume a894 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (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.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_n)))))
% 112.09/112.48  (assume a895 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n V_k)))))
% 112.09/112.48  (assume a896 (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_H V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_H V_z_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))))
% 112.09/112.48  (assume a897 (forall ((V_k $$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)))))
% 112.09/112.48  (assume a898 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z1 V_z2) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z2 V_w)))))
% 112.09/112.48  (assume a899 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (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.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2 V_w)))))
% 112.09/112.48  (assume a900 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z2 V_z3)))))
% 112.09/112.48  (assume a901 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (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.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z1) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z2)))))
% 112.09/112.48  (assume a902 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))))
% 112.09/112.48  (assume a903 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))
% 112.09/112.48  (assume a904 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c))))))
% 112.09/112.48  (assume a905 (forall ((V_c $$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.c_Groups_Otimes__class_Otimes T_a V_a V_e) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_e) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_e) V_c)))))
% 112.09/112.48  (assume a906 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)))
% 112.09/112.48  (assume a907 (forall ((V_z $$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)))
% 112.09/112.48  (assume a908 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a) V_b))))))
% 112.09/112.48  (assume a909 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_d_2)) (= V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_a_2) V_e_2) V_d_2))))))
% 112.09/112.48  (assume a910 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_d_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) V_e_2) V_c_2) V_d_2)))))
% 112.09/112.48  (assume a911 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_xa_2 V_xa_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_ya_2 V_ya_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_xa_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ya_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 112.09/112.48  (assume a912 (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)))))
% 112.09/112.48  (assume a913 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z1) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z2)))))
% 112.09/112.48  (assume a914 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (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.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2 V_w)))))
% 112.09/112.48  (assume a915 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k V_j))))))
% 112.09/112.48  (assume a916 (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_w)))
% 112.09/112.48  (assume a917 (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))))
% 112.09/112.48  (assume a918 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_k)))))
% 112.09/112.48  (assume a919 (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z) (= V_z V_w)))))
% 112.09/112.48  (assume a920 (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z_2 V_w_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_2 V_w_2) (not (= V_z_2 V_w_2))))))
% 112.09/112.48  (assume a921 (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))))
% 112.09/112.48  (assume a922 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))
% 112.09/112.48  (assume a923 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m_2) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_m_2 V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 112.09/112.48  (assume a924 (forall ((V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z_2))))
% 112.09/112.48  (assume a925 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2))))
% 112.09/112.48  (assume a926 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_xa_2 V_xa_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_ya_2 V_ya_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (and (= V_xa_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_ya_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 112.09/112.48  (assume a927 (forall ((V_M_2 $$unsorted)) (=> (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_M_2) (=> (not (= V_M_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)))) (= (= (tptp.c_GCD_Ogcd__class_OLcm tptp.tc_Nat_Onat V_M_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_member tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_M_2))))))
% 112.09/112.48  (assume a928 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (=> (tptp.c_member T_a V_a_2 (tptp.c_Nat_Osemiring__1__class_ONats T_a)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Nat_Osemiring__1__class_ONats T_a)) (tptp.c_member T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_b_2) (tptp.c_Nat_Osemiring__1__class_ONats T_a)))))))
% 112.09/112.48  (assume a929 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_z) V_z)))
% 112.09/112.48  (assume a930 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 112.09/112.48  (assume a931 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))
% 112.09/112.48  (assume a932 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (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))))))
% 112.09/112.48  (assume a933 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n) V_n)))
% 112.09/112.48  (assume a934 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 112.09/112.48  (assume a935 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 112.09/112.48  (assume a936 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) V_a))))
% 112.09/112.48  (assume a937 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) V_a))))
% 112.09/112.48  (assume a938 (forall ((V_n $$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.c_Groups_Otimes__class_Otimes T_a V_m V_n)))))))
% 112.09/112.48  (assume a939 (forall ((V_M_2 $$unsorted)) (=> (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_M_2) (=> (tptp.c_member tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_M_2) (= (tptp.c_GCD_Ogcd__class_OLcm tptp.tc_Nat_Onat V_M_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 112.09/112.48  (assume a940 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 112.09/112.48  (assume a941 (forall ((V_k $$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.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_j))))))
% 112.09/112.48  (assume a942 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_k))))))
% 112.09/112.48  (assume a943 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_k_2) (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)))))
% 112.09/112.48  (assume a944 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 112.09/112.48  (assume a945 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)))))
% 112.09/112.48  (assume a946 (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_xa_2 V_z_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_ya_2 V_z_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_xa_2 V_ya_2)))))
% 112.09/112.48  (assume a947 (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.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x V_y))))))
% 112.09/112.48  (assume a948 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z V_y))))))
% 112.09/112.48  (assume a949 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2) V_m_2) (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))))
% 112.09/112.48  (assume a950 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2) V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 112.09/112.48  (assume a951 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_k_2) V_m_2) (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))))
% 112.09/112.48  (assume a952 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c))))))
% 112.09/112.48  (assume a953 (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_m))))
% 112.09/112.48  (assume a954 (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_m)))))
% 112.09/112.48  (assume a955 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_k)))))
% 112.09/112.48  (assume a956 (forall ((V_k $$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_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_j)))))
% 112.09/112.48  (assume a957 (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_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_l))))))
% 112.09/112.48  (assume a958 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_a) V_a))))
% 112.09/112.48  (assume a959 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_x) V_x))))
% 112.09/112.48  (assume a960 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Oab__semigroup__idem__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)))))
% 112.09/112.48  (assume a961 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 112.09/112.48  (assume a962 (forall ((V_N_2 $$unsorted)) (= (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_N_2) (exists ((B_m $$unsorted)) (forall ((B_x $$unsorted)) (=> (tptp.c_member tptp.tc_Nat_Onat B_x V_N_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_x B_m)))))))
% 112.09/112.48  (assume a963 (forall ((V_N_2 $$unsorted)) (= (tptp.c_Finite__Set_Ofinite tptp.tc_Nat_Onat V_N_2) (exists ((B_m $$unsorted)) (forall ((B_x $$unsorted)) (=> (tptp.c_member tptp.tc_Nat_Onat B_x V_N_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_x B_m)))))))
% 112.09/112.48  (assume a964 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (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)))))))
% 112.09/112.48  (assume a965 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 112.09/112.48  (assume a966 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (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)))))))
% 112.09/112.48  (assume a967 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (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)))))
% 112.09/112.48  (assume a968 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (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)))))
% 112.09/112.48  (assume a969 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n_2 V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 112.09/112.48  (assume a970 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_m_2) (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))))))
% 112.09/112.48  (assume a971 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (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))))))
% 112.09/112.48  (assume a972 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 112.09/112.48  (assume a973 (forall ((V_n $$unsorted)) (= (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))))
% 112.09/112.48  (assume a974 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_a_2 V_c_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_b_2 V_c_2)) (= V_a_2 V_b_2)))))
% 112.09/112.48  (assume a975 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c_2 V_b_2)) (= V_a_2 V_b_2)))))
% 112.09/112.48  (assume a976 (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.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.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_a V_b)))))))
% 112.09/112.48  (assume a977 (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.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))))
% 112.09/112.48  (assume a978 (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.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)))))))
% 112.09/112.48  (assume a979 (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.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))))
% 112.09/112.48  (assume a980 (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.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))))
% 112.09/112.48  (assume a981 (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.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)))))))
% 112.09/112.48  (assume a982 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)))))))
% 112.09/112.48  (assume a983 (forall ((V_b $$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.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 112.09/112.48  (assume a984 (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.c_Groups_Otimes__class_Otimes T_a V_c_2 V_a_2) (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))))))
% 112.09/112.48  (assume a985 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 112.09/112.48  (assume a986 (forall ((V_b $$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.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))))))
% 112.09/112.48  (assume a987 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 112.09/112.48  (assume a988 (forall ((V_b $$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.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 112.09/112.48  (assume a989 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)))))))
% 112.09/112.48  (assume a990 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oidom (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a991 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a992 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a993 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a994 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a995 (tptp.class_Rings_Oidom tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a996 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a997 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a998 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a999 (tptp.class_Rings_Ocomm__ring tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1000 (tptp.class_Lattices_Obounded__lattice tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1001 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1002 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1003 (tptp.class_Rings_Oidom tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1004 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1005 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1006 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1007 (tptp.class_Rings_Ocomm__ring tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1008 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1009 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__top (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1010 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__bot (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1011 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__sup (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1012 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__inf (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1013 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_1) (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1014 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1015 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1016 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1017 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Otop T_1) (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1018 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1019 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Obot T_1) (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1020 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ominus T_1) (tptp.class_Groups_Ominus (tptp.tc_fun T_2 T_1)))))
% 112.09/112.48  (assume a1021 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1022 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1023 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1024 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1025 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1026 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1027 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1028 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1029 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1030 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1031 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1032 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1033 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1034 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1035 (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1036 (tptp.class_Lattices_Osemilattice__sup tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1037 (tptp.class_Lattices_Osemilattice__inf tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1038 (tptp.class_Lattices_Odistrib__lattice tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1039 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1040 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1041 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1042 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1043 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1044 (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1045 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1046 (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1047 (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1048 (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1049 (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1050 (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1051 (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1052 (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1053 (tptp.class_Rings_Osemiring__1 tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1054 (tptp.class_Lattices_Olattice tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1055 (tptp.class_Groups_Ogroup__add tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1056 (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1057 (tptp.class_Orderings_Oorder tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1058 (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1059 (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1060 (tptp.class_Rings_Osemiring tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1061 (tptp.class_Orderings_Oord tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1062 (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1063 (tptp.class_Groups_Ominus tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1064 (tptp.class_Groups_Ozero tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1065 (tptp.class_Rings_Oring tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1066 (tptp.class_Int_Onumber tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1067 (tptp.class_Groups_Oone tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1068 (tptp.class_GCD_Ogcd tptp.tc_Int_Oint))
% 112.09/112.48  (assume a1069 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1070 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1071 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1072 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1073 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1074 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1075 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1076 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1077 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1078 (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1079 (tptp.class_Lattices_Osemilattice__sup tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1080 (tptp.class_Lattices_Osemilattice__inf tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1081 (tptp.class_Lattices_Odistrib__lattice tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1082 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1083 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1084 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1085 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1086 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1087 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1088 (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1089 (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1090 (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1091 (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1092 (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1093 (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1094 (tptp.class_Rings_Osemiring__1 tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1095 (tptp.class_Lattices_Olattice tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1096 (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1097 (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1098 (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1099 (tptp.class_Orderings_Oord tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1100 (tptp.class_Orderings_Obot tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1101 (tptp.class_Groups_Ominus tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1102 (tptp.class_Groups_Ozero tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1103 (tptp.class_Int_Onumber tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1104 (tptp.class_Groups_Oone tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1105 (tptp.class_GCD_Ogcd tptp.tc_Nat_Onat))
% 112.09/112.48  (assume a1106 (tptp.class_Lattices_Obounded__lattice__top tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1107 (tptp.class_Lattices_Obounded__lattice__bot tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1108 (tptp.class_Lattices_Osemilattice__sup tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1109 (tptp.class_Lattices_Osemilattice__inf tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1110 (tptp.class_Lattices_Odistrib__lattice tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1111 (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1112 (tptp.class_Lattices_Olattice tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1113 (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1114 (tptp.class_Orderings_Otop tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1115 (tptp.class_Orderings_Oord tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1116 (tptp.class_Orderings_Obot tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1117 (tptp.class_Groups_Ominus tptp.tc_HOL_Obool))
% 112.09/112.48  (assume a1118 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1119 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1120 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1121 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1122 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1123 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1124 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1125 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1126 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1127 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1128 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1129 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1130 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1131 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1132 (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1133 (tptp.class_Orderings_Odense__linorder tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1134 (tptp.class_Lattices_Osemilattice__sup tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1135 (tptp.class_Lattices_Osemilattice__inf tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1136 (tptp.class_Lattices_Odistrib__lattice tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1137 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1138 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1139 (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1140 (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1141 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1142 (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1143 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1144 (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1145 (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1146 (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1147 (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1148 (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1149 (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1150 (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1151 (tptp.class_Rings_Osemiring__1 tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1152 (tptp.class_Lattices_Olattice tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1153 (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1154 (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1155 (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1156 (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1157 (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1158 (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1159 (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1160 (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1161 (tptp.class_Groups_Ominus tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1162 (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1163 (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1164 (tptp.class_Int_Onumber tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1165 (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal))
% 112.09/112.48  (assume a1166 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1167 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1168 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1169 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1170 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1171 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1172 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1173 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1174 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Olinordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1175 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1176 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1177 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1178 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1179 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1180 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semidom (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1181 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Groups_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1182 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1183 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1184 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1185 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1186 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__idom (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1187 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1188 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1189 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1190 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1191 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1192 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1193 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1194 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1195 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Osemiring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1196 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1197 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Omult__zero (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1198 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1199 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Int_Oring__char__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1200 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Int_Onumber__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1201 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1202 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oord (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1203 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Oring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1204 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Ominus (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1205 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ozero T_1) (tptp.class_Groups_Ozero (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1206 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Oring (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1207 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Int_Onumber (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1208 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Oone (tptp.tc_Polynomial_Opoly T_1)))))
% 112.09/112.48  (assume a1209 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x_2) V_y_2))) (= V_x_2 V_y_2))))
% 112.09/112.48  (assume a1210 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x_2) V_y_2)))))
% 112.09/112.48  (assume a1211 (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____)))
% 112.09/112.48  (assume a1212 true)
% 112.09/112.48  (step t1 (cl (not (= (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) (not (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule equiv_pos2)
% 112.09/112.48  (step t2 (cl (= (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule refl)
% 112.09/112.48  (step t3 (cl (= (= (= (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) true) (= (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule equiv_simplify)
% 112.09/112.48  (step t4 (cl (not (= (= (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) true)) (= (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule equiv1 :premises (t3))
% 112.09/112.48  (step t5 (cl (= (= (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))))) :rule all_simplify)
% 112.09/112.48  (step t6 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule refl)
% 112.09/112.48  (step t7 (cl (= (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule all_simplify)
% 112.09/112.48  (step t8 (cl (= (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule cong :premises (t6 t7))
% 112.09/112.48  (step t9 (cl (= (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) true)) :rule all_simplify)
% 112.09/112.48  (step t10 (cl (= (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) true)) :rule trans :premises (t8 t9))
% 112.09/112.48  (step t11 (cl (= (= (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) true)) :rule trans :premises (t5 t10))
% 112.09/112.48  (step t12 (cl (= (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule resolution :premises (t4 t11))
% 112.09/112.48  (step t13 (cl (= (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule refl)
% 112.09/112.48  (step t14 (cl (= (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule cong :premises (t2 t12 t13))
% 112.09/112.48  (step t15 (cl (not (= (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) (not (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule equiv_pos2)
% 112.09/112.48  (step t16 (cl (= (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule refl)
% 112.09/112.48  (step t17 (cl (= (= (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))))) :rule equiv_simplify)
% 112.09/112.48  (step t18 (cl (= (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) (not (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))))) :rule equiv2 :premises (t17))
% 112.09/112.48  (step t19 (cl (not (not (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule not_not)
% 112.09/112.48  (step t20 (cl (= (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule resolution :premises (t18 t19))
% 112.09/112.48  (step t21 (cl (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule implies_neg1)
% 112.09/112.48  (anchor :step t22)
% 112.09/112.48  (assume t22.a0 (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))
% 112.09/112.48  (assume t22.a1 (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))
% 112.09/112.48  (assume t22.a2 (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))
% 112.09/112.48  (step t22.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 112.09/112.48  (step t22.t2 (cl (= (= false true) false)) :rule all_simplify)
% 112.09/112.48  (step t22.t3 (cl (= (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) false) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule equiv_simplify)
% 112.09/112.48  (step t22.t4 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) false) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule equiv2 :premises (t22.t3))
% 112.09/112.48  (step t22.t5 (cl (not (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) :rule not_not)
% 112.09/112.48  (step t22.t6 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) false) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) :rule resolution :premises (t22.t4 t22.t5))
% 112.09/112.48  (step t22.t7 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) false)) :rule resolution :premises (t22.t6 t22.a2))
% 112.09/112.48  (step t22.t8 (cl (= false (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule symm :premises (t22.t7))
% 112.09/112.48  (step t22.t9 (cl (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) :rule symm :premises (t22.a1))
% 112.09/112.48  (step t22.t10 (cl (= tptp.v_y____ tptp.v_y____)) :rule refl)
% 112.09/112.48  (step t22.t11 (cl (= (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____) (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) :rule cong :premises (t22.t9 t22.t10))
% 112.09/112.48  (step t22.t12 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule cong :premises (t22.t11))
% 112.09/112.48  (step t22.t13 (cl (= (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) true) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule equiv_simplify)
% 112.09/112.48  (step t22.t14 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) true) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule equiv2 :premises (t22.t13))
% 112.09/112.48  (step t22.t15 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) true)) :rule resolution :premises (t22.t14 t22.a0))
% 112.09/112.48  (step t22.t16 (cl (= false true)) :rule trans :premises (t22.t8 t22.t12 t22.t15))
% 112.09/112.48  (step t22.t17 (cl false) :rule resolution :premises (t22.t1 t22.t2 t22.t16))
% 112.09/112.48  (step t22 (cl (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2))
% 112.09/112.48  (step t23 (cl (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) :rule and_pos)
% 112.09/112.48  (step t24 (cl (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) :rule and_pos)
% 112.09/112.48  (step t25 (cl (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule and_pos)
% 112.09/112.48  (step t26 (cl false (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule resolution :premises (t22 t23 t24 t25))
% 112.09/112.48  (step t27 (cl (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) false) :rule reordering :premises (t26))
% 112.09/112.48  (step t28 (cl (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) false) :rule contraction :premises (t27))
% 112.09/112.48  (step t29 (cl (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) false) :rule resolution :premises (t21 t28))
% 112.09/112.48  (step t30 (cl (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) (not false)) :rule implies_neg2)
% 112.09/112.48  (step t31 (cl (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false)) :rule resolution :premises (t29 t30))
% 112.09/112.48  (step t32 (cl (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false)) :rule contraction :premises (t31))
% 112.09/112.48  (step t33 (cl (= (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false) (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))))) :rule implies_simplify)
% 112.09/112.48  (step t34 (cl (not (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false)) (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule equiv1 :premises (t33))
% 112.09/112.48  (step t35 (cl (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule resolution :premises (t32 t34))
% 112.09/112.48  (step t36 (cl (= (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) false)) :rule resolution :premises (t20 t35))
% 112.09/112.48  (step t37 (cl (= (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) false))) :rule cong :premises (t16 t36))
% 112.09/112.48  (step t38 (cl (= (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) false) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule all_simplify)
% 112.09/112.48  (step t39 (cl (= (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule trans :premises (t37 t38))
% 112.09/112.48  (step t40 (cl (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule implies_neg1)
% 112.09/112.48  (anchor :step t41)
% 112.09/112.48  (assume t41.a0 (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))
% 112.09/112.48  (assume t41.a1 (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))
% 112.09/112.48  (assume t41.a2 (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))
% 112.09/112.48  (step t41.t1 (cl (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule and_neg)
% 112.09/112.48  (step t41.t2 (cl (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule resolution :premises (t41.t1 t41.a2 t41.a0 t41.a1))
% 112.09/112.48  (step t41 (cl (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule subproof :discharge (t41.a0 t41.a1 t41.a2))
% 112.09/112.48  (step t42 (cl (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) :rule and_pos)
% 112.09/112.48  (step t43 (cl (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule and_pos)
% 112.09/112.48  (step t44 (cl (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) :rule and_pos)
% 112.09/112.48  (step t45 (cl (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule resolution :premises (t41 t42 t43 t44))
% 112.09/112.48  (step t46 (cl (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule reordering :premises (t45))
% 112.09/112.48  (step t47 (cl (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule contraction :premises (t46))
% 112.09/112.48  (step t48 (cl (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule resolution :premises (t40 t47))
% 112.09/112.48  (step t49 (cl (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (not (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule implies_neg2)
% 112.09/112.48  (step t50 (cl (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule resolution :premises (t48 t49))
% 112.09/112.48  (step t51 (cl (=> (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule contraction :premises (t50))
% 112.09/112.48  (step t52 (cl (not (and (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule resolution :premises (t15 t39 t51))
% 112.09/112.48  (step t53 (cl (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule not_and :premises (t52))
% 112.09/112.48  (step t54 (cl (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule or_neg)
% 112.09/112.48  (step t55 (cl (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))))) :rule or_neg)
% 112.09/112.48  (step t56 (cl (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule or_neg)
% 112.09/112.48  (step t57 (cl (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule resolution :premises (t53 t54 t55 t56))
% 112.09/112.48  (step t58 (cl (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (not (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule contraction :premises (t57))
% 112.09/112.48  (step t59 (cl (or (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule resolution :premises (t1 t14 t58))
% 112.09/112.48  (step t60 (cl (not (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule or :premises (t59))
% 112.09/112.48  (step t61 (cl (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) :rule or_pos)
% 112.09/112.48  (step t62 (cl (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule reordering :premises (t61))
% 112.09/112.48  (step t63 (cl (= (forall ((B_z $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_z))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))) (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____))))) :rule hole :args ((forall ((B_z $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_z))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))) (= B_z B_y)))
% 112.09/112.48  (step t64 (cl (not (forall ((B_z $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_z))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____)))) (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) :rule equiv1 :premises (t63))
% 112.09/112.48  (step t65 (cl (not (= (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_z)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))) (forall ((B_z $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_z))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))))) (not (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_z)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____)))) (forall ((B_z $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_z))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____)))) :rule equiv_pos2)
% 112.09/112.48  (step t66 (cl (= (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.v_P B_z)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))) (forall ((B_z $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_z))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____))))) :rule all_simplify)
% 112.09/112.48  (step t67 (cl (forall ((B_z $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_z))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_z tptp.v_y____)))) :rule resolution :premises (t65 t66 a1))
% 112.09/112.48  (step t68 (cl (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) :rule resolution :premises (t64 t67))
% 112.09/112.48  (step t69 (cl (=> (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) :rule implies_neg1)
% 112.09/112.48  (anchor :step t70)
% 112.09/112.48  (assume t70.a0 (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))
% 112.09/112.48  (step t70.t1 (cl (or (not (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule forall_inst :args ((:= V_u_2 tptp.v_y____) (:= V_S_2 tptp.v_P) (:= T_a tptp.tc_RealDef_Oreal)))
% 112.09/112.48  (step t70.t2 (cl (not (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule or :premises (t70.t1))
% 112.09/112.48  (step t70.t3 (cl (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule resolution :premises (t70.t2 t70.a0))
% 112.09/112.48  (step t70 (cl (not (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule subproof :discharge (t70.a0))
% 112.09/112.48  (step t71 (cl (=> (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule resolution :premises (t69 t70))
% 112.09/112.48  (step t72 (cl (=> (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule implies_neg2)
% 112.09/112.48  (step t73 (cl (=> (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) (=> (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule resolution :premises (t71 t72))
% 112.09/112.48  (step t74 (cl (=> (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))))) :rule contraction :premises (t73))
% 112.09/112.48  (step t75 (cl (not (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule implies :premises (t74))
% 112.09/112.48  (step t76 (cl (not (= (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) (not (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) :rule equiv_pos2)
% 112.09/112.48  (anchor :step t77 :args ((V_u_2 $$unsorted) (:= V_u_2 V_u_2) (V_S_2 $$unsorted) (:= V_S_2 V_S_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t77.t1 (cl (= V_u_2 V_u_2)) :rule refl)
% 112.09/112.48  (step t77.t2 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t77.t3 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t77.t4 (cl (= (tptp.class_Orderings_Oord T_a) (tptp.class_Orderings_Oord T_a))) :rule refl)
% 112.09/112.48  (step t77.t5 (cl (= (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))))) :rule all_simplify)
% 112.09/112.48  (step t77.t6 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) :rule refl)
% 112.09/112.48  (step t77.t7 (cl (= (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))) (=> (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) :rule cong :premises (t77.t5 t77.t6))
% 112.09/112.48  (step t77.t8 (cl (= (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) :rule cong :premises (t77.t4 t77.t7))
% 112.09/112.48  (step t77 (cl (= (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))))) :rule bind)
% 112.09/112.48  (step t78 (cl (= (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) :rule all_simplify)
% 112.09/112.48  (step t79 (cl (= (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) :rule trans :premises (t77 t78))
% 112.09/112.48  (anchor :step t80 :args ((V_u_2 $$unsorted) (:= V_u_2 V_u_2) (V_S_2 $$unsorted) (:= V_S_2 V_S_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t80.t1 (cl (= V_u_2 V_u_2)) :rule refl)
% 112.09/112.48  (step t80.t2 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t80.t3 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t80.t4 (cl (= (not (tptp.class_Orderings_Oord T_a)) (not (tptp.class_Orderings_Oord T_a)))) :rule refl)
% 112.09/112.48  (anchor :step t80.t5 :args ((B_y $$unsorted) (:= B_y B_y)))
% 112.09/112.48  (step t80.t5.t1 (cl (= B_y B_y)) :rule refl)
% 112.09/112.48  (step t80.t5.t2 (cl (and (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))) (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))) (not (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))) (not (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))) :rule and_neg)
% 112.09/112.48  (step t80.t5.t3 (cl (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))) :rule hole :premises (a113) :args ((= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))))
% 112.09/112.48  (step t80.t5.t4 (cl (not (= (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2)) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2))))) (not (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2))) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2)))) :rule equiv_pos2)
% 112.09/112.48  (anchor :step t80.t5.t5 :args ((V_Pa_2 $$unsorted) (:= V_Pa_2 V_Pa_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t80.t5.t5.t1 (cl (= V_Pa_2 V_Pa_2)) :rule refl)
% 112.09/112.48  (step t80.t5.t5.t2 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t80.t5.t5.t3 (cl (= (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2)))) :rule all_simplify)
% 112.09/112.48  (step t80.t5.t5 (cl (= (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2)) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2))))) :rule bind)
% 112.09/112.48  (step t80.t5.t6 (cl (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2)))) :rule resolution :premises (t80.t5.t4 t80.t5.t5 a99))
% 112.09/112.48  (step t80.t5.t7 (cl (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))) :rule hole :premises (t80.t5.t6) :args ((= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))))
% 112.09/112.48  (step t80.t5.t8 (cl (and (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))) (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))) :rule resolution :premises (t80.t5.t2 t80.t5.t3 t80.t5.t7))
% 112.09/112.48  (step t80.t5.t9 (cl (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))) :rule and :premises (t80.t5.t8))
% 112.09/112.48  (step t80.t5.t10 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t80.t5.t11 (cl (= B_y B_y)) :rule refl)
% 112.09/112.48  (step t80.t5.t12 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t80.t5.t13 (cl (= (tptp.c_member T_a B_y V_S_2) (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2))) :rule hole :premises (t80.t5.t9 t80.t5.t10 t80.t5.t11 t80.t5.t12) :args (24))
% 112.09/112.48  (step t80.t5.t14 (cl (= (not (tptp.c_member T_a B_y V_S_2)) (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)))) :rule cong :premises (t80.t5.t13))
% 112.09/112.48  (step t80.t5.t15 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) :rule refl)
% 112.09/112.48  (step t80.t5.t16 (cl (= (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) :rule cong :premises (t80.t5.t14 t80.t5.t15))
% 112.09/112.48  (step t80.t5 (cl (= (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (forall ((B_y $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))))) :rule bind)
% 112.09/112.48  (step t80.t6 (cl (= (not (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (not (forall ((B_y $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))))) :rule cong :premises (t80.t5))
% 112.09/112.48  (step t80.t7 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) :rule refl)
% 112.09/112.48  (step t80.t8 (cl (= (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) :rule cong :premises (t80.t4 t80.t6 t80.t7))
% 112.09/112.48  (step t80 (cl (= (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) :rule bind)
% 112.09/112.48  (anchor :step t81 :args ((V_u_2 $$unsorted) (:= V_u_2 V_u_2) (V_S_2 $$unsorted) (:= V_S_2 V_S_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t81.t1 (cl (= V_u_2 V_u_2)) :rule refl)
% 112.09/112.48  (step t81.t2 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t81.t3 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t81.t4 (cl (= (not (tptp.class_Orderings_Oord T_a)) (not (tptp.class_Orderings_Oord T_a)))) :rule refl)
% 112.09/112.48  (anchor :step t81.t5 :args ((B_y $$unsorted) (:= B_y B_y)))
% 112.09/112.48  (step t81.t5.t1 (cl (= B_y B_y)) :rule refl)
% 112.09/112.48  (step t81.t5.t2 (cl (= (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2) (tptp.hBOOL (tptp.hAPP V_S_2 B_y)))) :rule all_simplify)
% 112.09/112.48  (step t81.t5.t3 (cl (= (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))))) :rule cong :premises (t81.t5.t2))
% 112.09/112.48  (step t81.t5.t4 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) :rule refl)
% 112.09/112.48  (step t81.t5.t5 (cl (= (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) :rule cong :premises (t81.t5.t3 t81.t5.t4))
% 112.09/112.48  (step t81.t5 (cl (= (forall ((B_y $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))))) :rule bind)
% 112.09/112.48  (step t81.t6 (cl (= (not (forall ((B_y $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))))) :rule cong :premises (t81.t5))
% 112.09/112.48  (step t81.t7 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) :rule refl)
% 112.09/112.48  (step t81.t8 (cl (= (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) :rule cong :premises (t81.t4 t81.t6 t81.t7))
% 112.09/112.48  (step t81 (cl (= (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_y) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) :rule bind)
% 112.09/112.48  (step t82 (cl (= (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.c_member T_a B_y V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) :rule trans :premises (t80 t81))
% 112.09/112.48  (step t83 (cl (= (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member T_a B_y V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2)))))) :rule trans :premises (t79 t82))
% 112.09/112.48  (step t84 (cl (forall ((V_u_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_y))) (tptp.c_Orderings_Oord__class_Oless__eq T_a B_y V_u_2)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_S_2) V_u_2))))) :rule resolution :premises (t76 t83 a157))
% 112.09/112.48  (step t85 (cl (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (forall ((B_y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.v_P B_y))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y tptp.v_y____)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule resolution :premises (t75 t84))
% 112.09/112.48  (step t86 (cl (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) :rule resolution :premises (t62 a1159 t68 t85))
% 112.09/112.48  (step t87 (cl (not (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____)) :rule or_pos)
% 112.09/112.48  (step t88 (cl (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (not (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____)))) :rule reordering :premises (t87))
% 112.09/112.48  (step t89 (cl (=> (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))) :rule implies_neg1)
% 112.09/112.48  (anchor :step t90)
% 112.09/112.48  (assume t90.a0 (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))
% 112.09/112.48  (step t90.t1 (cl (or (not (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____)))) :rule forall_inst :args ((:= B_x tptp.v_y____)))
% 112.09/112.48  (step t90.t2 (cl (not (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) :rule or :premises (t90.t1))
% 112.09/112.48  (step t90.t3 (cl (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) :rule resolution :premises (t90.t2 t90.a0))
% 112.09/112.48  (step t90 (cl (not (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) :rule subproof :discharge (t90.a0))
% 112.09/112.48  (step t91 (cl (=> (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) :rule resolution :premises (t89 t90))
% 112.09/112.48  (step t92 (cl (=> (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) (not (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____)))) :rule implies_neg2)
% 112.09/112.48  (step t93 (cl (=> (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) (=> (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____)))) :rule resolution :premises (t91 t92))
% 112.09/112.48  (step t94 (cl (=> (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____)))) :rule contraction :premises (t93))
% 112.09/112.48  (step t95 (cl (not (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) :rule implies :premises (t94))
% 112.09/112.48  (step t96 (cl (not (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))) (not (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))) :rule equiv_pos2)
% 112.09/112.48  (step t97 (cl (not (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))) (not (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) :rule reordering :premises (t96))
% 112.09/112.48  (step t98 (cl (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) :rule or_pos)
% 112.09/112.48  (step t99 (cl (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule reordering :premises (t98))
% 112.09/112.48  (step t100 (cl (not (= (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) tptp.v_L____) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____))) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) tptp.v_L____)) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) :rule equiv_pos2)
% 112.09/112.48  (step t101 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 112.09/112.48  (step t102 (cl (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)))) :rule refl)
% 112.09/112.48  (step t103 (cl (and (= tptp.c_Nat_OSuc (lambda ((BOUND_VARIABLE_19872 $$unsorted)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat BOUND_VARIABLE_19872 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (= tptp.c_SEQ_Osubseq (lambda ((BOUND_VARIABLE_19269 $$unsorted)) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP BOUND_VARIABLE_19269 B_m) (tptp.hAPP BOUND_VARIABLE_19269 B_n)))))) (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))) (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))) (not (= tptp.c_Nat_OSuc (lambda ((BOUND_VARIABLE_19872 $$unsorted)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat BOUND_VARIABLE_19872 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))) (not (= tptp.c_SEQ_Osubseq (lambda ((BOUND_VARIABLE_19269 $$unsorted)) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (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 BOUND_VARIABLE_19269 B_m) (tptp.hAPP BOUND_VARIABLE_19269 B_n))))))) (not (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))) (not (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))) :rule and_neg)
% 112.09/112.48  (step t104 (cl (= tptp.c_Nat_OSuc (lambda ((BOUND_VARIABLE_19872 $$unsorted)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat BOUND_VARIABLE_19872 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))) :rule hole :premises (a792) :args ((= tptp.c_Nat_OSuc (lambda ((BOUND_VARIABLE_19872 $$unsorted)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat BOUND_VARIABLE_19872 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 112.09/112.48  (step t105 (cl (not (= (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_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_f_2 B_m) (tptp.hAPP V_f_2 B_n)))))) (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_m) (tptp.hAPP V_f_2 B_n)))))))) (not (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_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_f_2 B_m) (tptp.hAPP V_f_2 B_n))))))) (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_m) (tptp.hAPP V_f_2 B_n))))))) :rule equiv_pos2)
% 112.09/112.48  (anchor :step t106 :args ((V_f_2 $$unsorted) (:= V_f_2 V_f_2)))
% 112.09/112.48  (step t106.t1 (cl (= V_f_2 V_f_2)) :rule refl)
% 112.09/112.48  (step t106.t2 (cl (= (tptp.c_SEQ_Osubseq V_f_2) (tptp.c_SEQ_Osubseq V_f_2))) :rule refl)
% 112.09/112.48  (step t106.t3 (cl (= (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_f_2 B_m) (tptp.hAPP V_f_2 B_n)))) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (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_f_2 B_m) (tptp.hAPP V_f_2 B_n)))))) :rule all_simplify)
% 112.09/112.48  (step t106.t4 (cl (= (= (tptp.c_SEQ_Osubseq V_f_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_f_2 B_m) (tptp.hAPP V_f_2 B_n))))) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (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_f_2 B_m) (tptp.hAPP V_f_2 B_n))))))) :rule cong :premises (t106.t2 t106.t3))
% 112.09/112.48  (step t106 (cl (= (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_m) (tptp.hAPP V_f_2 B_n)))))) (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (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_f_2 B_m) (tptp.hAPP V_f_2 B_n)))))))) :rule bind)
% 112.09/112.48  (step t107 (cl (forall ((V_f_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_f_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 B_m) (tptp.hAPP V_f_2 B_n))))))) :rule resolution :premises (t105 t106 a296))
% 112.09/112.48  (step t108 (cl (= tptp.c_SEQ_Osubseq (lambda ((BOUND_VARIABLE_19269 $$unsorted)) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (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 BOUND_VARIABLE_19269 B_m) (tptp.hAPP BOUND_VARIABLE_19269 B_n))))))) :rule hole :premises (t107) :args ((= tptp.c_SEQ_Osubseq (lambda ((BOUND_VARIABLE_19269 $$unsorted)) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP BOUND_VARIABLE_19269 B_m) (tptp.hAPP BOUND_VARIABLE_19269 B_n))))))))
% 112.09/112.48  (step t109 (cl (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))) :rule hole :premises (a113) :args ((= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))))
% 112.09/112.48  (step t110 (cl (not (= (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2)) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2))))) (not (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2))) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2)))) :rule equiv_pos2)
% 112.09/112.48  (anchor :step t111 :args ((V_Pa_2 $$unsorted) (:= V_Pa_2 V_Pa_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t111.t1 (cl (= V_Pa_2 V_Pa_2)) :rule refl)
% 112.09/112.48  (step t111.t2 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t111.t3 (cl (= (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2)))) :rule all_simplify)
% 112.09/112.48  (step t111 (cl (= (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_OCollect T_a V_Pa_2) V_Pa_2)) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2))))) :rule bind)
% 112.09/112.48  (step t112 (cl (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (= V_Pa_2 (tptp.c_Set_OCollect T_a V_Pa_2)))) :rule resolution :premises (t110 t111 a99))
% 112.09/112.48  (step t113 (cl (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))) :rule hole :premises (t112) :args ((= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))))
% 112.09/112.48  (step t114 (cl (and (= tptp.c_Nat_OSuc (lambda ((BOUND_VARIABLE_19872 $$unsorted)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat BOUND_VARIABLE_19872 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (= tptp.c_SEQ_Osubseq (lambda ((BOUND_VARIABLE_19269 $$unsorted)) (forall ((B_m $$unsorted) (B_n $$unsorted)) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP BOUND_VARIABLE_19269 B_m) (tptp.hAPP BOUND_VARIABLE_19269 B_n)))))) (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))) (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))) :rule resolution :premises (t103 t104 t108 t109 t113))
% 112.09/112.48  (step t115 (cl (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))) :rule and :premises (t114))
% 112.09/112.48  (step t116 (cl (= tptp.v_P tptp.v_P)) :rule refl)
% 112.09/112.48  (step t117 (cl (= (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) tptp.tc_RealDef_Oreal) tptp.v_P))) :rule hole :premises (t115 t101 t116) :args (24))
% 112.09/112.48  (step t118 (cl (= tptp.v_L____ tptp.v_L____)) :rule refl)
% 112.09/112.48  (step t119 (cl (= (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) tptp.v_L____) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) tptp.tc_RealDef_Oreal) tptp.v_P) tptp.v_L____))) :rule cong :premises (t101 t102 t117 t118))
% 112.09/112.48  (step t120 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 112.09/112.48  (step t121 (cl (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)))) :rule refl)
% 112.09/112.48  (step t122 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) tptp.tc_RealDef_Oreal) tptp.v_P) tptp.v_P)) :rule all_simplify)
% 112.09/112.48  (step t123 (cl (= tptp.v_L____ tptp.v_L____)) :rule refl)
% 112.09/112.48  (step t124 (cl (= (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) tptp.tc_RealDef_Oreal) tptp.v_P) tptp.v_L____) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____))) :rule cong :premises (t120 t121 t122 t123))
% 112.09/112.48  (step t125 (cl (= (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) (tptp.c_Set_OCollect tptp.tc_RealDef_Oreal tptp.v_P) tptp.v_L____) (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____))) :rule trans :premises (t119 t124))
% 112.09/112.48  (step t126 (cl (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) :rule resolution :premises (t100 t125 a78))
% 112.09/112.48  (step t127 (cl (=> (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) :rule implies_neg1)
% 112.09/112.48  (anchor :step t128)
% 112.09/112.48  (assume t128.a0 (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))))
% 112.09/112.48  (step t128.t1 (cl (or (not (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule forall_inst :args ((:= V_xa_2 tptp.v_L____) (:= V_S_2 tptp.v_P) (:= V_R_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool))) (:= T_a tptp.tc_RealDef_Oreal)))
% 112.09/112.48  (step t128.t2 (cl (not (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule or :premises (t128.t1))
% 112.09/112.48  (step t128.t3 (cl (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule resolution :premises (t128.t2 t128.a0))
% 112.09/112.48  (step t128 (cl (not (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule subproof :discharge (t128.a0))
% 112.09/112.48  (step t129 (cl (=> (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule resolution :premises (t127 t128))
% 112.09/112.48  (step t130 (cl (=> (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule implies_neg2)
% 112.09/112.48  (step t131 (cl (=> (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (=> (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule resolution :premises (t129 t130))
% 112.09/112.48  (step t132 (cl (=> (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule contraction :premises (t131))
% 112.09/112.48  (step t133 (cl (not (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule implies :premises (t132))
% 112.09/112.48  (step t134 (cl (not (= (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))))) (not (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) :rule equiv_pos2)
% 112.09/112.48  (step t135 (cl (= (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2)))))) :rule all_simplify)
% 112.09/112.48  (step t136 (cl (forall ((V_xa_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_Lubs_OisLub T_a V_R_2 V_S_2 V_xa_2)) (tptp.c_Lubs_Osetge T_a V_xa_2 (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))))) :rule resolution :premises (t134 t135 a151))
% 112.09/112.48  (step t137 (cl (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.c_Lubs_OisLub tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P tptp.v_L____)) (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule resolution :premises (t133 t136))
% 112.09/112.48  (step t138 (cl (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) :rule resolution :premises (t99 t126 a1159 t137))
% 112.09/112.48  (step t139 (cl (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))) :rule or_pos)
% 112.09/112.48  (step t140 (cl (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))) (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))))) :rule reordering :premises (t139))
% 112.09/112.48  (step t141 (cl (=> (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) :rule implies_neg1)
% 112.09/112.48  (anchor :step t142)
% 112.09/112.48  (assume t142.a0 (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))
% 112.09/112.48  (step t142.t1 (cl (or (not (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))))) :rule forall_inst :args ((:= V_S_2 (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (:= V_xa_2 tptp.v_L____) (:= T_a tptp.tc_RealDef_Oreal)))
% 112.09/112.48  (step t142.t2 (cl (not (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) :rule or :premises (t142.t1))
% 112.09/112.48  (step t142.t3 (cl (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) :rule resolution :premises (t142.t2 t142.a0))
% 112.09/112.48  (step t142 (cl (not (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) :rule subproof :discharge (t142.a0))
% 112.09/112.48  (step t143 (cl (=> (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) :rule resolution :premises (t141 t142))
% 112.09/112.48  (step t144 (cl (=> (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))))) :rule implies_neg2)
% 112.09/112.48  (step t145 (cl (=> (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) (=> (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))))) :rule resolution :premises (t143 t144))
% 112.09/112.48  (step t146 (cl (=> (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))))) :rule contraction :premises (t145))
% 112.09/112.48  (step t147 (cl (not (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) :rule implies :premises (t146))
% 112.09/112.48  (step t148 (cl (not (= (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) (not (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) :rule equiv_pos2)
% 112.09/112.48  (anchor :step t149 :args ((V_S_2 $$unsorted) (:= V_S_2 V_S_2) (V_xa_2 $$unsorted) (:= V_xa_2 V_xa_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t149.t1 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t149.t2 (cl (= V_xa_2 V_xa_2)) :rule refl)
% 112.09/112.48  (step t149.t3 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t149.t4 (cl (= (tptp.class_Orderings_Oord T_a) (tptp.class_Orderings_Oord T_a))) :rule refl)
% 112.09/112.48  (step t149.t5 (cl (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2))) :rule refl)
% 112.09/112.48  (step t149.t6 (cl (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))) :rule all_simplify)
% 112.09/112.48  (step t149.t7 (cl (= (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) :rule cong :premises (t149.t5 t149.t6))
% 112.09/112.48  (step t149.t8 (cl (= (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) :rule cong :premises (t149.t4 t149.t7))
% 112.09/112.48  (step t149 (cl (= (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) :rule bind)
% 112.09/112.48  (step t150 (cl (= (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) :rule all_simplify)
% 112.09/112.48  (step t151 (cl (= (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) :rule trans :premises (t149 t150))
% 112.09/112.48  (anchor :step t152 :args ((V_S_2 $$unsorted) (:= V_S_2 V_S_2) (V_xa_2 $$unsorted) (:= V_xa_2 V_xa_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t152.t1 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t152.t2 (cl (= V_xa_2 V_xa_2)) :rule refl)
% 112.09/112.48  (step t152.t3 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t152.t4 (cl (= (not (tptp.class_Orderings_Oord T_a)) (not (tptp.class_Orderings_Oord T_a)))) :rule refl)
% 112.09/112.48  (step t152.t5 (cl (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2))) :rule refl)
% 112.09/112.48  (anchor :step t152.t6 :args ((B_x $$unsorted) (:= B_x B_x)))
% 112.09/112.48  (step t152.t6.t1 (cl (= B_x B_x)) :rule refl)
% 112.09/112.48  (step t152.t6.t2 (cl (and (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))) (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))) (not (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))) (not (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))) :rule and_neg)
% 112.09/112.48  (step t152.t6.t3 (cl (and (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))) (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))) :rule resolution :premises (t152.t6.t2 t109 t113))
% 112.09/112.48  (step t152.t6.t4 (cl (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))) :rule and :premises (t152.t6.t3))
% 112.09/112.48  (step t152.t6.t5 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t152.t6.t6 (cl (= B_x B_x)) :rule refl)
% 112.09/112.48  (step t152.t6.t7 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t152.t6.t8 (cl (= (tptp.c_member T_a B_x V_S_2) (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2))) :rule hole :premises (t152.t6.t4 t152.t6.t5 t152.t6.t6 t152.t6.t7) :args (24))
% 112.09/112.48  (step t152.t6.t9 (cl (= (not (tptp.c_member T_a B_x V_S_2)) (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)))) :rule cong :premises (t152.t6.t8))
% 112.09/112.48  (step t152.t6.t10 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))) :rule refl)
% 112.09/112.48  (step t152.t6.t11 (cl (= (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))) :rule cong :premises (t152.t6.t9 t152.t6.t10))
% 112.09/112.48  (step t152.t6 (cl (= (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))) (forall ((B_x $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))) :rule bind)
% 112.09/112.48  (step t152.t7 (cl (= (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) :rule cong :premises (t152.t5 t152.t6))
% 112.09/112.48  (step t152.t8 (cl (= (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) :rule cong :premises (t152.t4 t152.t7))
% 112.09/112.48  (step t152 (cl (= (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) :rule bind)
% 112.09/112.48  (anchor :step t153 :args ((V_S_2 $$unsorted) (:= V_S_2 V_S_2) (V_xa_2 $$unsorted) (:= V_xa_2 V_xa_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t153.t1 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t153.t2 (cl (= V_xa_2 V_xa_2)) :rule refl)
% 112.09/112.48  (step t153.t3 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t153.t4 (cl (= (not (tptp.class_Orderings_Oord T_a)) (not (tptp.class_Orderings_Oord T_a)))) :rule refl)
% 112.09/112.48  (step t153.t5 (cl (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2))) :rule refl)
% 112.09/112.48  (anchor :step t153.t6 :args ((B_x $$unsorted) (:= B_x B_x)))
% 112.09/112.48  (step t153.t6.t1 (cl (= B_x B_x)) :rule refl)
% 112.09/112.48  (step t153.t6.t2 (cl (= (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2) (tptp.hBOOL (tptp.hAPP V_S_2 B_x)))) :rule all_simplify)
% 112.09/112.48  (step t153.t6.t3 (cl (= (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))))) :rule cong :premises (t153.t6.t2))
% 112.09/112.48  (step t153.t6.t4 (cl (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))) :rule refl)
% 112.09/112.48  (step t153.t6.t5 (cl (= (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))) :rule cong :premises (t153.t6.t3 t153.t6.t4))
% 112.09/112.48  (step t153.t6 (cl (= (forall ((B_x $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))) :rule bind)
% 112.09/112.48  (step t153.t7 (cl (= (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) :rule cong :premises (t153.t5 t153.t6))
% 112.09/112.48  (step t153.t8 (cl (= (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) :rule cong :premises (t153.t4 t153.t7))
% 112.09/112.48  (step t153 (cl (= (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (@ (@ (@ (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))) T_a) B_x) V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) :rule bind)
% 112.09/112.48  (step t154 (cl (= (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) :rule trans :premises (t152 t153))
% 112.09/112.48  (step t155 (cl (= (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_S_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))) (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x)))))))) :rule trans :premises (t151 t154))
% 112.09/112.48  (step t156 (cl (forall ((V_S_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Osetge T_a V_xa_2 V_S_2) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_S_2 B_x))) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 B_x))))))) :rule resolution :premises (t148 t155 a153))
% 112.09/112.48  (step t157 (cl (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))))) :rule resolution :premises (t147 t156))
% 112.09/112.48  (step t158 (cl (= (tptp.c_Lubs_Osetge tptp.tc_RealDef_Oreal tptp.v_L____ (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x))))) :rule resolution :premises (t140 a1159 t157))
% 112.09/112.48  (step t159 (cl (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) B_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ B_x)))) :rule resolution :premises (t97 t138 t158))
% 112.09/112.48  (step t160 (cl (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal tptp.v_L____ tptp.v_y____))) :rule resolution :premises (t95 t159))
% 112.09/112.48  (step t161 (cl (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) tptp.v_y____)))) :rule resolution :premises (t88 a1211 t160))
% 112.09/112.48  (step t162 (cl (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) :rule or_pos)
% 112.09/112.48  (step t163 (cl (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule reordering :premises (t162))
% 112.09/112.48  (step t164 (cl (not (= (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))))) (not (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule equiv_pos2)
% 112.09/112.48  (step t165 (cl (= (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))) :rule refl)
% 112.09/112.48  (step t166 (cl (= (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)))) :rule refl)
% 112.09/112.48  (step t167 (cl (= (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule all_simplify)
% 112.09/112.48  (step t168 (cl (= (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule cong :premises (t166 t167))
% 112.09/112.48  (step t169 (cl (= (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))))) :rule cong :premises (t165 t168))
% 112.09/112.48  (step t170 (cl (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) :rule implies_neg1)
% 112.09/112.48  (anchor :step t171)
% 112.09/112.48  (assume t171.a0 (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))
% 112.09/112.48  (step t171.t1 (cl (or (not (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule forall_inst :args ((:= V_S_2 tptp.v_P) (:= V_R_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool))) (:= T_a tptp.tc_RealDef_Oreal)))
% 112.09/112.48  (step t171.t2 (cl (not (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule or :premises (t171.t1))
% 112.09/112.48  (step t171.t3 (cl (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule resolution :premises (t171.t2 t171.a0))
% 112.09/112.48  (step t171 (cl (not (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule subproof :discharge (t171.a0))
% 112.09/112.48  (step t172 (cl (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule resolution :premises (t170 t171))
% 112.09/112.48  (step t173 (cl (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (not (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule implies_neg2)
% 112.09/112.48  (step t174 (cl (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule resolution :premises (t172 t173))
% 112.09/112.48  (step t175 (cl (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule contraction :premises (t174))
% 112.09/112.48  (step t176 (cl (=> (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))))) :rule resolution :premises (t164 t169 t175))
% 112.09/112.48  (step t177 (cl (not (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule implies :premises (t176))
% 112.09/112.48  (step t178 (cl (not (= (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))) (not (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) :rule equiv_pos2)
% 112.09/112.48  (step t179 (cl (= (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))))) :rule all_simplify)
% 112.09/112.48  (anchor :step t180 :args ((V_S_2 $$unsorted) (:= V_S_2 V_S_2) (V_R_2 $$unsorted) (:= V_R_2 V_R_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t180.t1 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t180.t2 (cl (= V_R_2 V_R_2)) :rule refl)
% 112.09/112.48  (step t180.t3 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t180.t4 (cl (= (not (tptp.class_Orderings_Oord T_a)) (not (tptp.class_Orderings_Oord T_a)))) :rule refl)
% 112.09/112.48  (step t180.t5 (cl (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))) :rule refl)
% 112.09/112.48  (step t180.t6 (cl (and (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))) (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))) (not (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475))))) (not (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))) :rule and_neg)
% 112.09/112.48  (step t180.t7 (cl (and (= tptp.c_member (lambda ((BOUND_VARIABLE_18474 $$unsorted) (BOUND_VARIABLE_18475 $$unsorted) (BOUND_VARIABLE_18476 $$unsorted)) (tptp.hBOOL (tptp.hAPP BOUND_VARIABLE_18476 BOUND_VARIABLE_18475)))) (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468)))) :rule resolution :premises (t180.t6 t109 t113))
% 112.09/112.48  (step t180.t8 (cl (= tptp.c_Set_OCollect (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468))) :rule and :premises (t180.t7))
% 112.09/112.48  (step t180.t9 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t180.t10 (cl (= (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))) :rule refl)
% 112.09/112.48  (step t180.t11 (cl (= (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) T_a) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) :rule hole :premises (t180.t8 t180.t9 t180.t10) :args (24))
% 112.09/112.48  (step t180.t12 (cl (= (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) T_a) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) :rule cong :premises (t180.t5 t180.t11))
% 112.09/112.48  (step t180.t13 (cl (= (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) T_a) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))) :rule cong :premises (t180.t4 t180.t12))
% 112.09/112.48  (step t180 (cl (= (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) T_a) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))))) :rule bind)
% 112.09/112.48  (anchor :step t181 :args ((V_S_2 $$unsorted) (:= V_S_2 V_S_2) (V_R_2 $$unsorted) (:= V_R_2 V_R_2) (T_a $$unsorted) (:= T_a T_a)))
% 112.09/112.48  (step t181.t1 (cl (= V_S_2 V_S_2)) :rule refl)
% 112.09/112.48  (step t181.t2 (cl (= V_R_2 V_R_2)) :rule refl)
% 112.09/112.48  (step t181.t3 (cl (= T_a T_a)) :rule refl)
% 112.09/112.48  (step t181.t4 (cl (= (not (tptp.class_Orderings_Oord T_a)) (not (tptp.class_Orderings_Oord T_a)))) :rule refl)
% 112.09/112.48  (step t181.t5 (cl (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2))) :rule refl)
% 112.09/112.48  (step t181.t6 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) T_a) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))) :rule all_simplify)
% 112.09/112.48  (step t181.t7 (cl (= (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) T_a) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) :rule cong :premises (t181.t5 t181.t6))
% 112.09/112.48  (step t181.t8 (cl (= (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) T_a) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) :rule cong :premises (t181.t4 t181.t7))
% 112.16/112.51  (step t181 (cl (= (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (@ (@ (lambda ((BOUND_VARIABLE_18467 $$unsorted) (BOUND_VARIABLE_18468 $$unsorted)) BOUND_VARIABLE_18468) T_a) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))) :rule bind)
% 112.16/112.51  (step t182 (cl (= (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))) :rule trans :premises (t180 t181))
% 112.16/112.51  (step t183 (cl (= (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Set_OCollect T_a (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2)))))) :rule trans :premises (t179 t182))
% 112.16/112.51  (step t184 (cl (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (= (tptp.c_Lubs_Oubs T_a V_R_2 V_S_2) (tptp.c_Lubs_OisUb T_a V_R_2 V_S_2))))) :rule resolution :premises (t178 t183 a139))
% 112.16/112.51  (step t185 (cl (or (not (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal)) (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P)))) :rule resolution :premises (t177 t184))
% 112.16/112.51  (step t186 (cl (= (tptp.c_Lubs_OisUb tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P) (tptp.c_Lubs_Oubs tptp.tc_RealDef_Oreal (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_RealDef_Oreal tptp.tc_HOL_Obool)) tptp.v_P))) :rule resolution :premises (t163 a1159 t185))
% 112.16/112.51  (step t187 (cl) :rule resolution :premises (t60 t86 t161 t186))
% 112.16/112.51  
% 112.16/112.51  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.Lj9aQNll5p/cvc5---1.0.5_725.smt2
% 112.16/112.51  % cvc5---1.0.5 exiting
% 112.16/112.52  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------