%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP039-5 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n002.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 16:50:33 EDT 2024

% Result   : Unsatisfiable 11.97s 12.20s
% Output   : Proof 11.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : GRP039-5 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun May 26 19:09:54 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.21/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.67/10.89  --- Run --no-e-matching --full-saturate-quant at 5...
% 11.97/12.20  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.OPES6AXeOq/cvc5---1.0.5_24349.smt2
% 11.97/12.20  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.OPES6AXeOq/cvc5---1.0.5_24349.smt2
% 11.97/12.23  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 11.97/12.23  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 11.97/12.23  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 11.97/12.23  (assume a3 (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))))
% 11.97/12.23  (assume a4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) Z)) (tptp.subgroup_member Z))))
% 11.97/12.23  (assume a5 (forall ((X $$unsorted)) (= (tptp.multiply X tptp.identity) X)))
% 11.97/12.23  (assume a6 (forall ((X $$unsorted)) (= (tptp.multiply X (tptp.inverse X)) tptp.identity)))
% 11.97/12.23  (assume a7 (tptp.subgroup_member tptp.identity))
% 11.97/12.23  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y)))))
% 11.97/12.23  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= (tptp.multiply X (tptp.element_in_O2 X Y)) Y))))
% 11.97/12.23  (assume a10 (tptp.subgroup_member tptp.b))
% 11.97/12.23  (assume a11 (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) tptp.c))
% 11.97/12.23  (assume a12 (= (tptp.multiply tptp.a tptp.c) tptp.d))
% 11.97/12.23  (assume a13 (not (tptp.subgroup_member tptp.d)))
% 11.97/12.23  (step t1 (cl (not (= (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (or (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))))) (not (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) (or (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule equiv_pos2)
% 11.97/12.23  (step t2 (cl (= (= (= (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) true) (= (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule equiv_simplify)
% 11.97/12.23  (step t3 (cl (not (= (= (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) true)) (= (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule equiv1 :premises (t2))
% 11.97/12.23  (step t4 (cl (= (= (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule all_simplify)
% 11.97/12.23  (step t5 (cl (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule refl)
% 11.97/12.23  (step t6 (cl (= (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule all_simplify)
% 11.97/12.23  (step t7 (cl (= (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule cong :premises (t5 t6))
% 11.97/12.23  (step t8 (cl (= (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) true)) :rule all_simplify)
% 11.97/12.23  (step t9 (cl (= (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) true)) :rule trans :premises (t7 t8))
% 11.97/12.23  (step t10 (cl (= (= (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) true)) :rule trans :premises (t4 t9))
% 11.97/12.23  (step t11 (cl (= (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t3 t10))
% 11.97/12.23  (step t12 (cl (= (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule refl)
% 11.97/12.23  (step t13 (cl (= (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule refl)
% 11.97/12.23  (step t14 (cl (= (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule refl)
% 11.97/12.23  (step t15 (cl (= (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule refl)
% 11.97/12.23  (step t16 (cl (= (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule refl)
% 11.97/12.23  (step t17 (cl (= (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (or (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))))) :rule cong :premises (t11 t12 t13 t14 t15 t16))
% 11.97/12.23  (step t18 (cl (not (= (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))))) (not (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule equiv_pos2)
% 11.97/12.23  (step t19 (cl (= (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule refl)
% 11.97/12.23  (step t20 (cl (= (= (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule equiv_simplify)
% 11.97/12.23  (step t21 (cl (= (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) (not (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule equiv2 :premises (t20))
% 11.97/12.23  (step t22 (cl (not (not (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule not_not)
% 11.97/12.23  (step t23 (cl (= (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t21 t22))
% 11.97/12.23  (step t24 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t25)
% 11.97/12.23  (assume t25.a0 (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))
% 11.97/12.23  (assume t25.a1 (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))
% 11.97/12.23  (assume t25.a2 (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))
% 11.97/12.23  (assume t25.a3 (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))))
% 11.97/12.23  (assume t25.a4 (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))
% 11.97/12.23  (assume t25.a5 (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))
% 11.97/12.23  (step t25.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 11.97/12.23  (step t25.t2 (cl (= (= true false) false)) :rule all_simplify)
% 11.97/12.23  (step t25.t3 (cl (= (= (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) true) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule equiv_simplify)
% 11.97/12.23  (step t25.t4 (cl (= (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) true) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule equiv2 :premises (t25.t3))
% 11.97/12.23  (step t25.t5 (cl (= (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) true)) :rule resolution :premises (t25.t4 t25.a5))
% 11.97/12.23  (step t25.t6 (cl (= true (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule symm :premises (t25.t5))
% 11.97/12.23  (step t25.t7 (cl (= (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule symm :premises (t25.a4))
% 11.97/12.23  (step t25.t8 (cl (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule symm :premises (t25.t7))
% 11.97/12.23  (step t25.t9 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t25.a3))
% 11.97/12.23  (step t25.t10 (cl (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule symm :premises (t25.t9))
% 11.97/12.23  (step t25.t11 (cl (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule refl)
% 11.97/12.23  (step t25.t12 (cl (= (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule cong :premises (t25.t10 t25.t11))
% 11.97/12.23  (step t25.t13 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule symm :premises (t25.a2))
% 11.97/12.23  (step t25.t14 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule symm :premises (t25.t13))
% 11.97/12.23  (step t25.t15 (cl (= tptp.a tptp.a)) :rule refl)
% 11.97/12.23  (step t25.t16 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) :rule symm :premises (t25.a1))
% 11.97/12.23  (step t25.t17 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule cong :premises (t25.t15 t25.t16))
% 11.97/12.23  (step t25.t18 (cl (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule trans :premises (t25.t8 t25.t12 t25.t14 t25.t17))
% 11.97/12.23  (step t25.t19 (cl (= (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule cong :premises (t25.t18))
% 11.97/12.23  (step t25.t20 (cl (= (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) false) (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule equiv_simplify)
% 11.97/12.23  (step t25.t21 (cl (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) false) (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule equiv2 :premises (t25.t20))
% 11.97/12.23  (step t25.t22 (cl (not (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule not_not)
% 11.97/12.23  (step t25.t23 (cl (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) false) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t25.t21 t25.t22))
% 11.97/12.23  (step t25.t24 (cl (= (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) false)) :rule resolution :premises (t25.t23 t25.a0))
% 11.97/12.23  (step t25.t25 (cl (= true false)) :rule trans :premises (t25.t6 t25.t19 t25.t24))
% 11.97/12.23  (step t25.t26 (cl false) :rule resolution :premises (t25.t1 t25.t2 t25.t25))
% 11.97/12.23  (step t25 (cl (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) :rule subproof :discharge (t25.a0 t25.a1 t25.a2 t25.a3 t25.a4 t25.a5))
% 11.97/12.23  (step t26 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule and_pos)
% 11.97/12.23  (step t27 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule and_pos)
% 11.97/12.23  (step t28 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule and_pos)
% 11.97/12.23  (step t29 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t30 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule and_pos)
% 11.97/12.23  (step t31 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule and_pos)
% 11.97/12.23  (step t32 (cl false (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t25 t26 t27 t28 t29 t30 t31))
% 11.97/12.23  (step t33 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) false) :rule reordering :premises (t32))
% 11.97/12.23  (step t34 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) false) :rule contraction :premises (t33))
% 11.97/12.23  (step t35 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) false) :rule resolution :premises (t24 t34))
% 11.97/12.23  (step t36 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) (not false)) :rule implies_neg2)
% 11.97/12.23  (step t37 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false)) :rule resolution :premises (t35 t36))
% 11.97/12.23  (step t38 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false)) :rule contraction :premises (t37))
% 11.97/12.23  (step t39 (cl (= (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule implies_simplify)
% 11.97/12.23  (step t40 (cl (not (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false)) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule equiv1 :premises (t39))
% 11.97/12.23  (step t41 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t38 t40))
% 11.97/12.23  (step t42 (cl (= (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) false)) :rule resolution :premises (t23 t41))
% 11.97/12.23  (step t43 (cl (= (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) false))) :rule cong :premises (t19 t42))
% 11.97/12.23  (step t44 (cl (= (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) false) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))))) :rule all_simplify)
% 11.97/12.23  (step t45 (cl (= (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))))) :rule trans :premises (t43 t44))
% 11.97/12.23  (step t46 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t47)
% 11.97/12.23  (assume t47.a0 (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))
% 11.97/12.23  (assume t47.a1 (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))))
% 11.97/12.23  (assume t47.a2 (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))
% 11.97/12.23  (assume t47.a3 (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))
% 11.97/12.23  (assume t47.a4 (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))
% 11.97/12.23  (assume t47.a5 (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))
% 11.97/12.23  (step t47.t1 (cl (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule and_neg)
% 11.97/12.23  (step t47.t2 (cl (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t47.t1 t47.a0 t47.a3 t47.a5 t47.a1 t47.a4 t47.a2))
% 11.97/12.23  (step t47 (cl (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule subproof :discharge (t47.a0 t47.a1 t47.a2 t47.a3 t47.a4 t47.a5))
% 11.97/12.23  (step t48 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule and_pos)
% 11.97/12.23  (step t49 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t50 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule and_pos)
% 11.97/12.23  (step t51 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule and_pos)
% 11.97/12.23  (step t52 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule and_pos)
% 11.97/12.23  (step t53 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule and_pos)
% 11.97/12.23  (step t54 (cl (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule resolution :premises (t47 t48 t49 t50 t51 t52 t53))
% 11.97/12.23  (step t55 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule reordering :premises (t54))
% 11.97/12.23  (step t56 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule contraction :premises (t55))
% 11.97/12.23  (step t57 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t46 t56))
% 11.97/12.23  (step t58 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 11.97/12.23  (step t59 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t57 t58))
% 11.97/12.23  (step t60 (cl (=> (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule contraction :premises (t59))
% 11.97/12.23  (step t61 (cl (not (and (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule resolution :premises (t18 t45 t60))
% 11.97/12.23  (step t62 (cl (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule not_and :premises (t61))
% 11.97/12.23  (step t63 (cl (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule or_neg)
% 11.97/12.23  (step t64 (cl (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule or_neg)
% 11.97/12.23  (step t65 (cl (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule or_neg)
% 11.97/12.23  (step t66 (cl (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule or_neg)
% 11.97/12.23  (step t67 (cl (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule or_neg)
% 11.97/12.23  (step t68 (cl (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule or_neg)
% 11.97/12.23  (step t69 (cl (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule resolution :premises (t62 t63 t64 t65 t66 t67 t68))
% 11.97/12.23  (step t70 (cl (or (not (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule contraction :premises (t69))
% 11.97/12.23  (step t71 (cl (or (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))))) :rule resolution :premises (t1 t17 t70))
% 11.97/12.23  (step t72 (cl (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule or :premises (t71))
% 11.97/12.23  (step t73 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t74)
% 11.97/12.23  (assume t74.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 11.97/12.23  (step t74.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.inverse tptp.a)) (:= Z (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))
% 11.97/12.23  (step t74.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule or :premises (t74.t1))
% 11.97/12.23  (step t74.t3 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t74.t2 t74.a0))
% 11.97/12.23  (step t74 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule subproof :discharge (t74.a0))
% 11.97/12.23  (step t75 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t73 t74))
% 11.97/12.23  (step t76 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule implies_neg2)
% 11.97/12.23  (step t77 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule resolution :premises (t75 t76))
% 11.97/12.23  (step t78 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule contraction :premises (t77))
% 11.97/12.23  (step t79 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies :premises (t78))
% 11.97/12.23  (step t80 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t79 a2))
% 11.97/12.23  (step t81 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t82)
% 11.97/12.23  (assume t82.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 11.97/12.23  (step t82.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule forall_inst :args ((:= X (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))
% 11.97/12.23  (step t82.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule or :premises (t82.t1))
% 11.97/12.23  (step t82.t3 (cl (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t82.t2 t82.a0))
% 11.97/12.23  (step t82 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule subproof :discharge (t82.a0))
% 11.97/12.23  (step t83 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t81 t82))
% 11.97/12.23  (step t84 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 11.97/12.23  (step t85 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t83 t84))
% 11.97/12.23  (step t86 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule contraction :premises (t85))
% 11.97/12.23  (step t87 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies :premises (t86))
% 11.97/12.23  (step t88 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) (not (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule equiv_pos2)
% 11.97/12.23  (anchor :step t89 :args ((X $$unsorted) (:= X X)))
% 11.97/12.23  (step t89.t1 (cl (= X X)) :rule refl)
% 11.97/12.23  (step t89.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 11.97/12.23  (step t89 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 11.97/12.23  (step t90 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t88 t89 a0))
% 11.97/12.23  (step t91 (cl (= (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t87 t90))
% 11.97/12.23  (step t92 (cl (not (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule or_pos)
% 11.97/12.23  (step t93 (cl (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule reordering :premises (t92))
% 11.97/12.23  (step t94 (cl (not (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))) :rule or_pos)
% 11.97/12.23  (step t95 (cl (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))) (not (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule reordering :premises (t94))
% 11.97/12.23  (step t96 (cl (not (= (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (tptp.subgroup_member tptp.a) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))))) (not (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) (or (tptp.subgroup_member tptp.a) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule equiv_pos2)
% 11.97/12.23  (step t97 (cl (= (= (= (not (not (tptp.subgroup_member tptp.a))) (tptp.subgroup_member tptp.a)) true) (= (not (not (tptp.subgroup_member tptp.a))) (tptp.subgroup_member tptp.a)))) :rule equiv_simplify)
% 11.97/12.23  (step t98 (cl (not (= (= (not (not (tptp.subgroup_member tptp.a))) (tptp.subgroup_member tptp.a)) true)) (= (not (not (tptp.subgroup_member tptp.a))) (tptp.subgroup_member tptp.a))) :rule equiv1 :premises (t97))
% 11.97/12.23  (step t99 (cl (= (= (not (not (tptp.subgroup_member tptp.a))) (tptp.subgroup_member tptp.a)) (= (tptp.subgroup_member tptp.a) (not (not (tptp.subgroup_member tptp.a)))))) :rule all_simplify)
% 11.97/12.23  (step t100 (cl (= (tptp.subgroup_member tptp.a) (tptp.subgroup_member tptp.a))) :rule refl)
% 11.97/12.23  (step t101 (cl (= (not (not (tptp.subgroup_member tptp.a))) (tptp.subgroup_member tptp.a))) :rule all_simplify)
% 11.97/12.23  (step t102 (cl (= (= (tptp.subgroup_member tptp.a) (not (not (tptp.subgroup_member tptp.a)))) (= (tptp.subgroup_member tptp.a) (tptp.subgroup_member tptp.a)))) :rule cong :premises (t100 t101))
% 11.97/12.23  (step t103 (cl (= (= (tptp.subgroup_member tptp.a) (tptp.subgroup_member tptp.a)) true)) :rule all_simplify)
% 11.97/12.23  (step t104 (cl (= (= (tptp.subgroup_member tptp.a) (not (not (tptp.subgroup_member tptp.a)))) true)) :rule trans :premises (t102 t103))
% 11.97/12.23  (step t105 (cl (= (= (not (not (tptp.subgroup_member tptp.a))) (tptp.subgroup_member tptp.a)) true)) :rule trans :premises (t99 t104))
% 11.97/12.23  (step t106 (cl (= (not (not (tptp.subgroup_member tptp.a))) (tptp.subgroup_member tptp.a))) :rule resolution :premises (t98 t105))
% 11.97/12.23  (step t107 (cl (= (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule refl)
% 11.97/12.23  (step t108 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule refl)
% 11.97/12.23  (step t109 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule refl)
% 11.97/12.23  (step t110 (cl (= (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))))) :rule refl)
% 11.97/12.23  (step t111 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 11.97/12.23  (step t112 (cl (= (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule refl)
% 11.97/12.23  (step t113 (cl (= (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (tptp.subgroup_member tptp.a) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))))) :rule cong :premises (t106 t107 t108 t109 t110 t111 t112))
% 11.97/12.23  (step t114 (cl (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_neg)
% 11.97/12.23  (step t115 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t116)
% 11.97/12.23  (assume t116.a0 (not (tptp.subgroup_member tptp.a)))
% 11.97/12.23  (assume t116.a1 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 11.97/12.23  (assume t116.a2 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 11.97/12.23  (assume t116.a3 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 11.97/12.23  (assume t116.a4 (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))
% 11.97/12.23  (assume t116.a5 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 11.97/12.23  (step t116.t1 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t116.t2)
% 11.97/12.23  (assume t116.t2.a0 (not (tptp.subgroup_member tptp.a)))
% 11.97/12.23  (assume t116.t2.a1 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 11.97/12.23  (assume t116.t2.a2 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 11.97/12.23  (assume t116.t2.a3 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 11.97/12.23  (assume t116.t2.a4 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 11.97/12.23  (assume t116.t2.a5 (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))
% 11.97/12.23  (step t116.t2.t1 (cl (= (= (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))) false) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule equiv_simplify)
% 11.97/12.23  (step t116.t2.t2 (cl (not (= (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))) false)) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule equiv1 :premises (t116.t2.t1))
% 11.97/12.23  (step t116.t2.t3 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse (tptp.inverse tptp.a)))) :rule symm :premises (t116.t2.a5))
% 11.97/12.23  (step t116.t2.t4 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule symm :premises (t116.t2.t3))
% 11.97/12.23  (step t116.t2.t5 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a)))) :rule refl)
% 11.97/12.23  (step t116.t2.t6 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)) :rule symm :premises (t116.t2.a4))
% 11.97/12.23  (step t116.t2.t7 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule symm :premises (t116.t2.t6))
% 11.97/12.23  (step t116.t2.t8 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t116.t2.t5 t116.t2.t7))
% 11.97/12.23  (step t116.t2.t9 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t116.t2.a3))
% 11.97/12.23  (step t116.t2.t10 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t116.t2.a2))
% 11.97/12.23  (step t116.t2.t11 (cl (= tptp.a tptp.a)) :rule refl)
% 11.97/12.23  (step t116.t2.t12 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity tptp.a))) :rule cong :premises (t116.t2.t10 t116.t2.t11))
% 11.97/12.23  (step t116.t2.t13 (cl (= (tptp.multiply tptp.identity tptp.a) tptp.a)) :rule symm :premises (t116.t2.a1))
% 11.97/12.23  (step t116.t2.t14 (cl (= (tptp.inverse (tptp.inverse tptp.a)) tptp.a)) :rule trans :premises (t116.t2.t4 t116.t2.t8 t116.t2.t9 t116.t2.t12 t116.t2.t13))
% 11.97/12.23  (step t116.t2.t15 (cl (= (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))) (tptp.subgroup_member tptp.a))) :rule cong :premises (t116.t2.t14))
% 11.97/12.23  (step t116.t2.t16 (cl (= (= (tptp.subgroup_member tptp.a) false) (not (tptp.subgroup_member tptp.a)))) :rule equiv_simplify)
% 11.97/12.23  (step t116.t2.t17 (cl (= (tptp.subgroup_member tptp.a) false) (not (not (tptp.subgroup_member tptp.a)))) :rule equiv2 :premises (t116.t2.t16))
% 11.97/12.23  (step t116.t2.t18 (cl (not (not (not (tptp.subgroup_member tptp.a)))) (tptp.subgroup_member tptp.a)) :rule not_not)
% 11.97/12.23  (step t116.t2.t19 (cl (= (tptp.subgroup_member tptp.a) false) (tptp.subgroup_member tptp.a)) :rule resolution :premises (t116.t2.t17 t116.t2.t18))
% 11.97/12.23  (step t116.t2.t20 (cl (= (tptp.subgroup_member tptp.a) false)) :rule resolution :premises (t116.t2.t19 t116.t2.a0))
% 11.97/12.23  (step t116.t2.t21 (cl (= (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))) false)) :rule trans :premises (t116.t2.t15 t116.t2.t20))
% 11.97/12.23  (step t116.t2.t22 (cl (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t116.t2.t2 t116.t2.t21))
% 11.97/12.23  (step t116.t2 (cl (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t116.t2.a0 t116.t2.a1 t116.t2.a2 t116.t2.a3 t116.t2.a4 t116.t2.a5))
% 11.97/12.23  (step t116.t3 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (tptp.subgroup_member tptp.a))) :rule and_pos)
% 11.97/12.23  (step t116.t4 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 11.97/12.23  (step t116.t5 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t116.t6 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t116.t7 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 11.97/12.23  (step t116.t8 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule and_pos)
% 11.97/12.23  (step t116.t9 (cl (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))))) :rule resolution :premises (t116.t2 t116.t3 t116.t4 t116.t5 t116.t6 t116.t7 t116.t8))
% 11.97/12.23  (step t116.t10 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule reordering :premises (t116.t9))
% 11.97/12.23  (step t116.t11 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule contraction :premises (t116.t10))
% 11.97/12.23  (step t116.t12 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t116.t1 t116.t11))
% 11.97/12.23  (step t116.t13 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 11.97/12.23  (step t116.t14 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t116.t12 t116.t13))
% 11.97/12.23  (step t116.t15 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t116.t14))
% 11.97/12.23  (step t116.t16 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t116.t15))
% 11.97/12.23  (step t116.t17 (cl (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) :rule and_neg)
% 11.97/12.23  (step t116.t18 (cl (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) :rule resolution :premises (t116.t17 t116.a0 t116.a1 t116.a3 t116.a5 t116.a2 t116.a4))
% 11.97/12.23  (step t116.t19 (cl (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t116.t16 t116.t18))
% 11.97/12.23  (step t116 (cl (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t116.a0 t116.a1 t116.a2 t116.a3 t116.a4 t116.a5))
% 11.97/12.23  (step t117 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (tptp.subgroup_member tptp.a))) :rule and_pos)
% 11.97/12.23  (step t118 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 11.97/12.23  (step t119 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 11.97/12.23  (step t120 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t121 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule and_pos)
% 11.97/12.23  (step t122 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t123 (cl (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t116 t117 t118 t119 t120 t121 t122))
% 11.97/12.23  (step t124 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule reordering :premises (t123))
% 11.97/12.23  (step t125 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule contraction :premises (t124))
% 11.97/12.23  (step t126 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t115 t125))
% 11.97/12.23  (step t127 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 11.97/12.23  (step t128 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t126 t127))
% 11.97/12.23  (step t129 (cl (=> (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t128))
% 11.97/12.23  (step t130 (cl (not (and (not (tptp.subgroup_member tptp.a)) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t129))
% 11.97/12.23  (step t131 (cl (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t114 t130))
% 11.97/12.23  (step t132 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (not (tptp.subgroup_member tptp.a))))) :rule or_neg)
% 11.97/12.23  (step t133 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (= tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule or_neg)
% 11.97/12.23  (step t134 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or_neg)
% 11.97/12.23  (step t135 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule or_neg)
% 11.97/12.23  (step t136 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))))) :rule or_neg)
% 11.97/12.23  (step t137 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 11.97/12.23  (step t138 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule or_neg)
% 11.97/12.23  (step t139 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t131 t132 t133 t134 t135 t136 t137 t138))
% 11.97/12.23  (step t140 (cl (or (not (not (tptp.subgroup_member tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t139))
% 11.97/12.23  (step t141 (cl (or (tptp.subgroup_member tptp.a) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t96 t113 t140))
% 11.97/12.23  (step t142 (cl (tptp.subgroup_member tptp.a) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule or :premises (t141))
% 11.97/12.23  (step t143 (cl (tptp.subgroup_member tptp.a) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule reordering :premises (t142))
% 11.97/12.23  (step t144 (cl (not (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) :rule or_pos)
% 11.97/12.23  (step t145 (cl (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (not (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule reordering :premises (t144))
% 11.97/12.23  (step t146 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t147)
% 11.97/12.23  (assume t147.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))))
% 11.97/12.23  (step t147.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X tptp.b) (:= Y (tptp.inverse tptp.a))))
% 11.97/12.23  (step t147.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule or :premises (t147.t1))
% 11.97/12.23  (step t147.t3 (cl (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t147.t2 t147.a0))
% 11.97/12.23  (step t147 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule subproof :discharge (t147.a0))
% 11.97/12.23  (step t148 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t146 t147))
% 11.97/12.23  (step t149 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 11.97/12.23  (step t150 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t148 t149))
% 11.97/12.23  (step t151 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule contraction :premises (t150))
% 11.97/12.23  (step t152 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule implies :premises (t151))
% 11.97/12.23  (step t153 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) Z)) (tptp.subgroup_member Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))))) (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) Z)) (tptp.subgroup_member Z)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) :rule equiv_pos2)
% 11.97/12.23  (anchor :step t154 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (Z $$unsorted) (:= Z Z)))
% 11.97/12.23  (step t154.t1 (cl (= X X)) :rule refl)
% 11.97/12.23  (step t154.t2 (cl (= Y Y)) :rule refl)
% 11.97/12.23  (step t154.t3 (cl (= Z Z)) :rule refl)
% 11.97/12.23  (step t154.t4 (cl (= (not (tptp.subgroup_member X)) (not (tptp.subgroup_member X)))) :rule refl)
% 11.97/12.23  (step t154.t5 (cl (= (not (tptp.subgroup_member Y)) (not (tptp.subgroup_member Y)))) :rule refl)
% 11.97/12.23  (step t154.t6 (cl (= (= (tptp.multiply X Y) Z) (= Z (tptp.multiply X Y)))) :rule all_simplify)
% 11.97/12.23  (step t154.t7 (cl (= (not (= (tptp.multiply X Y) Z)) (not (= Z (tptp.multiply X Y))))) :rule cong :premises (t154.t6))
% 11.97/12.23  (step t154.t8 (cl (= (tptp.subgroup_member Z) (tptp.subgroup_member Z))) :rule refl)
% 11.97/12.23  (step t154.t9 (cl (= (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) Z)) (tptp.subgroup_member Z)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= Z (tptp.multiply X Y))) (tptp.subgroup_member Z)))) :rule cong :premises (t154.t4 t154.t5 t154.t7 t154.t8))
% 11.97/12.23  (step t154 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) Z)) (tptp.subgroup_member Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= Z (tptp.multiply X Y))) (tptp.subgroup_member Z))))) :rule bind)
% 11.97/12.23  (step t155 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= Z (tptp.multiply X Y))) (tptp.subgroup_member Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) (tptp.multiply X Y))) (tptp.subgroup_member (tptp.multiply X Y)))))) :rule all_simplify)
% 11.97/12.23  (anchor :step t156 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 11.97/12.23  (step t156.t1 (cl (= X X)) :rule refl)
% 11.97/12.23  (step t156.t2 (cl (= Y Y)) :rule refl)
% 11.97/12.23  (step t156.t3 (cl (= (not (tptp.subgroup_member X)) (not (tptp.subgroup_member X)))) :rule refl)
% 11.97/12.23  (step t156.t4 (cl (= (not (tptp.subgroup_member Y)) (not (tptp.subgroup_member Y)))) :rule refl)
% 11.97/12.23  (step t156.t5 (cl (= (= (tptp.multiply X Y) (tptp.multiply X Y)) true)) :rule all_simplify)
% 11.97/12.23  (step t156.t6 (cl (= (not (= (tptp.multiply X Y) (tptp.multiply X Y))) (not true))) :rule cong :premises (t156.t5))
% 11.97/12.23  (step t156.t7 (cl (= (not true) false)) :rule all_simplify)
% 11.97/12.23  (step t156.t8 (cl (= (not (= (tptp.multiply X Y) (tptp.multiply X Y))) false)) :rule trans :premises (t156.t6 t156.t7))
% 11.97/12.23  (step t156.t9 (cl (= (tptp.subgroup_member (tptp.multiply X Y)) (tptp.subgroup_member (tptp.multiply X Y)))) :rule refl)
% 11.97/12.23  (step t156.t10 (cl (= (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) (tptp.multiply X Y))) (tptp.subgroup_member (tptp.multiply X Y))) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) false (tptp.subgroup_member (tptp.multiply X Y))))) :rule cong :premises (t156.t3 t156.t4 t156.t8 t156.t9))
% 11.97/12.23  (step t156.t11 (cl (= (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) false (tptp.subgroup_member (tptp.multiply X Y))) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) :rule all_simplify)
% 11.97/12.23  (step t156.t12 (cl (= (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) (tptp.multiply X Y))) (tptp.subgroup_member (tptp.multiply X Y))) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) :rule trans :premises (t156.t10 t156.t11))
% 11.97/12.23  (step t156 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) (tptp.multiply X Y))) (tptp.subgroup_member (tptp.multiply X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))))) :rule bind)
% 11.97/12.23  (step t157 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= Z (tptp.multiply X Y))) (tptp.subgroup_member Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))))) :rule trans :premises (t155 t156))
% 11.97/12.23  (step t158 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (not (= (tptp.multiply X Y) Z)) (tptp.subgroup_member Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))))) :rule trans :premises (t154 t157))
% 11.97/12.23  (step t159 (cl (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) :rule resolution :premises (t153 t158 a4))
% 11.97/12.23  (step t160 (cl (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t152 t159))
% 11.97/12.23  (step t161 (cl (not (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))) :rule or_pos)
% 11.97/12.23  (step t162 (cl (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)) (not (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule reordering :premises (t161))
% 11.97/12.23  (step t163 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t164)
% 11.97/12.23  (assume t164.a0 (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))))
% 11.97/12.23  (step t164.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 11.97/12.23  (step t164.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule or :premises (t164.t1))
% 11.97/12.23  (step t164.t3 (cl (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t164.t2 t164.a0))
% 11.97/12.23  (step t164 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule subproof :discharge (t164.a0))
% 11.97/12.23  (step t165 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t163 t164))
% 11.97/12.23  (step t166 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule implies_neg2)
% 11.97/12.23  (step t167 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule resolution :premises (t165 t166))
% 11.97/12.23  (step t168 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule contraction :premises (t167))
% 11.97/12.23  (step t169 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule implies :premises (t168))
% 11.97/12.23  (step t170 (cl (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t169 a3))
% 11.97/12.23  (step t171 (cl (not (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule or_pos)
% 11.97/12.23  (step t172 (cl (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule reordering :premises (t171))
% 11.97/12.23  (step t173 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t174)
% 11.97/12.23  (assume t174.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))))
% 11.97/12.23  (step t174.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply tptp.b (tptp.inverse tptp.a)))))
% 11.97/12.23  (step t174.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule or :premises (t174.t1))
% 11.97/12.23  (step t174.t3 (cl (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t174.t2 t174.a0))
% 11.97/12.23  (step t174 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule subproof :discharge (t174.a0))
% 11.97/12.23  (step t175 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t173 t174))
% 11.97/12.23  (step t176 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 11.97/12.23  (step t177 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t175 t176))
% 11.97/12.23  (step t178 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule contraction :premises (t177))
% 11.97/12.23  (step t179 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies :premises (t178))
% 11.97/12.23  (step t180 (cl (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t179 t159))
% 11.97/12.23  (step t181 (cl (not (= (not (tptp.subgroup_member tptp.d)) (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (not (not (tptp.subgroup_member tptp.d))) (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule equiv_pos2)
% 11.97/12.23  (step t182 (cl (and (= tptp.d (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= tptp.c (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (= tptp.d (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= tptp.c (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule and_neg)
% 11.97/12.23  (step t183 (cl (not (= (= tptp.d (tptp.multiply tptp.a tptp.c)) (= tptp.d (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (= tptp.d (tptp.multiply tptp.a tptp.c))) (= tptp.d (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule equiv_pos2)
% 11.97/12.23  (step t184 (cl (= tptp.d tptp.d)) :rule refl)
% 11.97/12.23  (step t185 (cl (= tptp.a tptp.a)) :rule refl)
% 11.97/12.23  (step t186 (cl (= tptp.c (tptp.multiply tptp.b (tptp.inverse tptp.a)))) :rule symm :premises (a11))
% 11.97/12.23  (step t187 (cl (= (tptp.multiply tptp.a tptp.c) (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule cong :premises (t185 t186))
% 11.97/12.23  (step t188 (cl (= (= tptp.d (tptp.multiply tptp.a tptp.c)) (= tptp.d (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule cong :premises (t184 t187))
% 11.97/12.23  (step t189 (cl (= tptp.d (tptp.multiply tptp.a tptp.c))) :rule symm :premises (a12))
% 11.97/12.23  (step t190 (cl (= tptp.d (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t183 t188 t189))
% 11.97/12.23  (step t191 (cl (= tptp.c (tptp.multiply tptp.b (tptp.inverse tptp.a)))) :rule symm :premises (a11))
% 11.97/12.23  (step t192 (cl (and (= tptp.d (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= tptp.c (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t182 t190 t191))
% 11.97/12.23  (step t193 (cl (= tptp.d (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule and :premises (t192))
% 11.97/12.23  (step t194 (cl (= (tptp.subgroup_member tptp.d) (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule cong :premises (t193))
% 11.97/12.23  (step t195 (cl (= (not (tptp.subgroup_member tptp.d)) (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule cong :premises (t194))
% 11.97/12.23  (step t196 (cl (not (tptp.subgroup_member (tptp.multiply tptp.a (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t181 t195 a13))
% 11.97/12.23  (step t197 (cl (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.a))) :rule resolution :premises (t145 t160 a10 t162 t170 t172 t180 t196))
% 11.97/12.23  (step t198 (cl (not (tptp.subgroup_member tptp.a))) :rule contraction :premises (t197))
% 11.97/12.23  (step t199 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t200)
% 11.97/12.23  (assume t200.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 11.97/12.23  (step t200.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 11.97/12.23  (step t200.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule or :premises (t200.t1))
% 11.97/12.23  (step t200.t3 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t200.t2 t200.a0))
% 11.97/12.23  (step t200 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule subproof :discharge (t200.a0))
% 11.97/12.23  (step t201 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t199 t200))
% 11.97/12.23  (step t202 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule implies_neg2)
% 11.97/12.23  (step t203 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t201 t202))
% 11.97/12.23  (step t204 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule contraction :premises (t203))
% 11.97/12.23  (step t205 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule implies :premises (t204))
% 11.97/12.23  (step t206 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t205 t90))
% 11.97/12.23  (step t207 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t208)
% 11.97/12.23  (assume t208.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 11.97/12.23  (step t208.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 11.97/12.23  (step t208.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule or :premises (t208.t1))
% 11.97/12.23  (step t208.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t208.t2 t208.a0))
% 11.97/12.23  (step t208 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule subproof :discharge (t208.a0))
% 11.97/12.23  (step t209 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t207 t208))
% 11.97/12.23  (step t210 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies_neg2)
% 11.97/12.23  (step t211 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t209 t210))
% 11.97/12.23  (step t212 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule contraction :premises (t211))
% 11.97/12.23  (step t213 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule implies :premises (t212))
% 11.97/12.23  (step t214 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) (not (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule equiv_pos2)
% 11.97/12.23  (anchor :step t215 :args ((X $$unsorted) (:= X X)))
% 11.97/12.23  (step t215.t1 (cl (= X X)) :rule refl)
% 11.97/12.23  (step t215.t2 (cl (= (= (tptp.multiply (tptp.inverse X) X) tptp.identity) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule all_simplify)
% 11.97/12.23  (step t215 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) :rule bind)
% 11.97/12.23  (step t216 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule resolution :premises (t214 t215 a1))
% 11.97/12.23  (step t217 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t213 t216))
% 11.97/12.23  (step t218 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t219)
% 11.97/12.23  (assume t219.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 11.97/12.23  (step t219.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 11.97/12.23  (step t219.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule or :premises (t219.t1))
% 11.97/12.23  (step t219.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t219.t2 t219.a0))
% 11.97/12.23  (step t219 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule subproof :discharge (t219.a0))
% 11.97/12.23  (step t220 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t218 t219))
% 11.97/12.23  (step t221 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 11.97/12.23  (step t222 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t220 t221))
% 11.97/12.23  (step t223 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule contraction :premises (t222))
% 11.97/12.23  (step t224 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule implies :premises (t223))
% 11.97/12.23  (step t225 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t224 t216))
% 11.97/12.23  (step t226 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t227)
% 11.97/12.23  (assume t227.a0 (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))))
% 11.97/12.23  (step t227.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a)))))
% 11.97/12.23  (step t227.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule or :premises (t227.t1))
% 11.97/12.23  (step t227.t3 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t227.t2 t227.a0))
% 11.97/12.23  (step t227 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule subproof :discharge (t227.a0))
% 11.97/12.23  (step t228 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t226 t227))
% 11.97/12.23  (step t229 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) :rule implies_neg2)
% 11.97/12.23  (step t230 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) :rule resolution :premises (t228 t229))
% 11.97/12.23  (step t231 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity)))) :rule contraction :premises (t230))
% 11.97/12.23  (step t232 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule implies :premises (t231))
% 11.97/12.23  (step t233 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply X tptp.identity) X)) (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))))) (not (forall ((X $$unsorted)) (= (tptp.multiply X tptp.identity) X))) (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) :rule equiv_pos2)
% 11.97/12.23  (anchor :step t234 :args ((X $$unsorted) (:= X X)))
% 11.97/12.23  (step t234.t1 (cl (= X X)) :rule refl)
% 11.97/12.23  (step t234.t2 (cl (= (= (tptp.multiply X tptp.identity) X) (= X (tptp.multiply X tptp.identity)))) :rule all_simplify)
% 11.97/12.23  (step t234 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply X tptp.identity) X)) (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))))) :rule bind)
% 11.97/12.23  (step t235 (cl (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) :rule resolution :premises (t233 t234 a5))
% 11.97/12.23  (step t236 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t232 t235))
% 11.97/12.23  (step t237 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t238)
% 11.97/12.23  (assume t238.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 11.97/12.23  (step t238.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.inverse tptp.a)) (:= Z tptp.a)))
% 11.97/12.23  (step t238.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t238.t1))
% 11.97/12.23  (step t238.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t238.t2 t238.a0))
% 11.97/12.23  (step t238 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t238.a0))
% 11.97/12.23  (step t239 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t237 t238))
% 11.97/12.23  (step t240 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 11.97/12.23  (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t239 t240))
% 11.97/12.23  (step t242 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t241))
% 11.97/12.23  (step t243 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t242))
% 11.97/12.23  (step t244 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t243 a2))
% 11.97/12.23  (step t245 (cl (not (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t143 t198 t206 t217 t225 t236 t244))
% 11.97/12.23  (step t246 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t247)
% 11.97/12.23  (assume t247.a0 (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))))
% 11.97/12.23  (step t247.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 11.97/12.23  (step t247.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule or :premises (t247.t1))
% 11.97/12.23  (step t247.t3 (cl (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t247.t2 t247.a0))
% 11.97/12.23  (step t247 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t247.a0))
% 11.97/12.23  (step t248 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t246 t247))
% 11.97/12.23  (step t249 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (not (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 11.97/12.23  (step t250 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t248 t249))
% 11.97/12.23  (step t251 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t250))
% 11.97/12.23  (step t252 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t251))
% 11.97/12.23  (step t253 (cl (or (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t252 a3))
% 11.97/12.23  (step t254 (cl (not (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t95 t245 t253))
% 11.97/12.23  (step t255 (cl (not (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule or_pos)
% 11.97/12.23  (step t256 (cl (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule reordering :premises (t255))
% 11.97/12.23  (step t257 (cl (not (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b))) :rule or_pos)
% 11.97/12.23  (step t258 (cl (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)) (not (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b))))) :rule reordering :premises (t257))
% 11.97/12.23  (step t259 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t260)
% 11.97/12.23  (assume t260.a0 (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))))
% 11.97/12.23  (step t260.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b))))) :rule forall_inst :args ((:= X tptp.b)))
% 11.97/12.23  (step t260.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) :rule or :premises (t260.t1))
% 11.97/12.23  (step t260.t3 (cl (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) :rule resolution :premises (t260.t2 t260.a0))
% 11.97/12.23  (step t260 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) :rule subproof :discharge (t260.a0))
% 11.97/12.23  (step t261 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) :rule resolution :premises (t259 t260))
% 11.97/12.23  (step t262 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) (not (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b))))) :rule implies_neg2)
% 11.97/12.23  (step t263 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b))))) :rule resolution :premises (t261 t262))
% 11.97/12.23  (step t264 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b))))) :rule contraction :premises (t263))
% 11.97/12.23  (step t265 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) :rule implies :premises (t264))
% 11.97/12.23  (step t266 (cl (or (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member (tptp.inverse tptp.b)))) :rule resolution :premises (t265 a3))
% 11.97/12.23  (step t267 (cl (tptp.subgroup_member (tptp.inverse tptp.b))) :rule resolution :premises (t258 a10 t266))
% 11.97/12.23  (step t268 (cl (not (= (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (tptp.subgroup_member (tptp.inverse tptp.a)) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) (not (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (tptp.subgroup_member (tptp.inverse tptp.a)) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule equiv_pos2)
% 11.97/12.23  (step t269 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))))) :rule refl)
% 11.97/12.23  (step t270 (cl (= (= (= (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a))) true) (= (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule equiv_simplify)
% 11.97/12.23  (step t271 (cl (not (= (= (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a))) true)) (= (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule equiv1 :premises (t270))
% 11.97/12.23  (step t272 (cl (= (= (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.subgroup_member (tptp.inverse tptp.a)) (not (not (tptp.subgroup_member (tptp.inverse tptp.a))))))) :rule all_simplify)
% 11.97/12.23  (step t273 (cl (= (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule refl)
% 11.97/12.23  (step t274 (cl (= (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule all_simplify)
% 11.97/12.23  (step t275 (cl (= (= (tptp.subgroup_member (tptp.inverse tptp.a)) (not (not (tptp.subgroup_member (tptp.inverse tptp.a))))) (= (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule cong :premises (t273 t274))
% 11.97/12.23  (step t276 (cl (= (= (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))) true)) :rule all_simplify)
% 11.97/12.23  (step t277 (cl (= (= (tptp.subgroup_member (tptp.inverse tptp.a)) (not (not (tptp.subgroup_member (tptp.inverse tptp.a))))) true)) :rule trans :premises (t275 t276))
% 11.97/12.23  (step t278 (cl (= (= (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a))) true)) :rule trans :premises (t272 t277))
% 11.97/12.23  (step t279 (cl (= (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t271 t278))
% 11.97/12.23  (step t280 (cl (= (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule refl)
% 11.97/12.23  (step t281 (cl (= (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))))) :rule refl)
% 11.97/12.23  (step t282 (cl (= (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule refl)
% 11.97/12.23  (step t283 (cl (= (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (tptp.subgroup_member (tptp.inverse tptp.a)) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule cong :premises (t269 t279 t280 t281 t282))
% 11.97/12.23  (step t284 (cl (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule and_neg)
% 11.97/12.23  (step t285 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t286)
% 11.97/12.23  (assume t286.a0 (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))
% 11.97/12.23  (assume t286.a1 (not (tptp.subgroup_member (tptp.inverse tptp.a))))
% 11.97/12.23  (assume t286.a2 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 11.97/12.23  (assume t286.a3 (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))
% 11.97/12.23  (step t286.t1 (cl (=> (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t286.t2)
% 11.97/12.23  (assume t286.t2.a0 (not (tptp.subgroup_member (tptp.inverse tptp.a))))
% 11.97/12.23  (assume t286.t2.a1 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 11.97/12.23  (assume t286.t2.a2 (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))
% 11.97/12.23  (assume t286.t2.a3 (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))
% 11.97/12.23  (step t286.t2.t1 (cl (= (= (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) false) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule equiv_simplify)
% 11.97/12.23  (step t286.t2.t2 (cl (not (= (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) false)) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule equiv1 :premises (t286.t2.t1))
% 11.97/12.23  (step t286.t2.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule symm :premises (t286.t2.a3))
% 11.97/12.23  (step t286.t2.t4 (cl (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) :rule symm :premises (t286.t2.t3))
% 11.97/12.23  (step t286.t2.t5 (cl (= (tptp.multiply (tptp.inverse tptp.b) tptp.b) tptp.identity)) :rule symm :premises (t286.t2.a2))
% 11.97/12.23  (step t286.t2.t6 (cl (= (tptp.inverse tptp.a) (tptp.inverse tptp.a))) :rule refl)
% 11.97/12.23  (step t286.t2.t7 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule cong :premises (t286.t2.t5 t286.t2.t6))
% 11.97/12.23  (step t286.t2.t8 (cl (= (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) :rule symm :premises (t286.t2.a1))
% 11.97/12.23  (step t286.t2.t9 (cl (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.inverse tptp.a))) :rule trans :premises (t286.t2.t4 t286.t2.t7 t286.t2.t8))
% 11.97/12.23  (step t286.t2.t10 (cl (= (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule cong :premises (t286.t2.t9))
% 11.97/12.23  (step t286.t2.t11 (cl (= (= (tptp.subgroup_member (tptp.inverse tptp.a)) false) (not (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule equiv_simplify)
% 11.97/12.23  (step t286.t2.t12 (cl (= (tptp.subgroup_member (tptp.inverse tptp.a)) false) (not (not (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule equiv2 :premises (t286.t2.t11))
% 11.97/12.23  (step t286.t2.t13 (cl (not (not (not (tptp.subgroup_member (tptp.inverse tptp.a))))) (tptp.subgroup_member (tptp.inverse tptp.a))) :rule not_not)
% 11.97/12.23  (step t286.t2.t14 (cl (= (tptp.subgroup_member (tptp.inverse tptp.a)) false) (tptp.subgroup_member (tptp.inverse tptp.a))) :rule resolution :premises (t286.t2.t12 t286.t2.t13))
% 11.97/12.23  (step t286.t2.t15 (cl (= (tptp.subgroup_member (tptp.inverse tptp.a)) false)) :rule resolution :premises (t286.t2.t14 t286.t2.a0))
% 11.97/12.23  (step t286.t2.t16 (cl (= (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) false)) :rule trans :premises (t286.t2.t10 t286.t2.t15))
% 11.97/12.23  (step t286.t2.t17 (cl (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t286.t2.t2 t286.t2.t16))
% 11.97/12.23  (step t286.t2 (cl (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule subproof :discharge (t286.t2.a0 t286.t2.a1 t286.t2.a2 t286.t2.a3))
% 11.97/12.23  (step t286.t3 (cl (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t286.t4 (cl (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t286.t5 (cl (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule and_pos)
% 11.97/12.23  (step t286.t6 (cl (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t286.t7 (cl (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))))) :rule resolution :premises (t286.t2 t286.t3 t286.t4 t286.t5 t286.t6))
% 11.97/12.23  (step t286.t8 (cl (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule reordering :premises (t286.t7))
% 11.97/12.23  (step t286.t9 (cl (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule contraction :premises (t286.t8))
% 11.97/12.23  (step t286.t10 (cl (=> (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t286.t1 t286.t9))
% 11.97/12.23  (step t286.t11 (cl (=> (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 11.97/12.23  (step t286.t12 (cl (=> (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t286.t10 t286.t11))
% 11.97/12.23  (step t286.t13 (cl (=> (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule contraction :premises (t286.t12))
% 11.97/12.23  (step t286.t14 (cl (not (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies :premises (t286.t13))
% 11.97/12.23  (step t286.t15 (cl (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule and_neg)
% 11.97/12.23  (step t286.t16 (cl (and (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule resolution :premises (t286.t15 t286.a1 t286.a2 t286.a0 t286.a3))
% 11.97/12.23  (step t286.t17 (cl (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t286.t14 t286.t16))
% 11.97/12.23  (step t286 (cl (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule subproof :discharge (t286.a0 t286.a1 t286.a2 t286.a3))
% 11.97/12.23  (step t287 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule and_pos)
% 11.97/12.23  (step t288 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t289 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t290 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) :rule and_pos)
% 11.97/12.23  (step t291 (cl (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))))) :rule resolution :premises (t286 t287 t288 t289 t290))
% 11.97/12.23  (step t292 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule reordering :premises (t291))
% 11.97/12.23  (step t293 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule contraction :premises (t292))
% 11.97/12.23  (step t294 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t285 t293))
% 11.97/12.23  (step t295 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 11.97/12.23  (step t296 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t294 t295))
% 11.97/12.23  (step t297 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule contraction :premises (t296))
% 11.97/12.23  (step t298 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies :premises (t297))
% 11.97/12.23  (step t299 (cl (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t284 t298))
% 11.97/12.23  (step t300 (cl (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))))) :rule or_neg)
% 11.97/12.23  (step t301 (cl (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))))) :rule or_neg)
% 11.97/12.23  (step t302 (cl (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule or_neg)
% 11.97/12.23  (step t303 (cl (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))))) :rule or_neg)
% 11.97/12.23  (step t304 (cl (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule or_neg)
% 11.97/12.23  (step t305 (cl (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t299 t300 t301 t302 t303 t304))
% 11.97/12.23  (step t306 (cl (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (not (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule contraction :premises (t305))
% 11.97/12.23  (step t307 (cl (or (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (tptp.subgroup_member (tptp.inverse tptp.a)) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t268 t283 t306))
% 11.97/12.23  (step t308 (cl (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (tptp.subgroup_member (tptp.inverse tptp.a)) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule or :premises (t307))
% 11.97/12.23  (step t309 (cl (tptp.subgroup_member (tptp.inverse tptp.a)) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule reordering :premises (t308))
% 11.97/12.23  (step t310 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t311)
% 11.97/12.23  (assume t311.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 11.97/12.23  (step t311.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule forall_inst :args ((:= X tptp.b)))
% 11.97/12.23  (step t311.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule or :premises (t311.t1))
% 11.97/12.23  (step t311.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule resolution :premises (t311.t2 t311.a0))
% 11.97/12.23  (step t311 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule subproof :discharge (t311.a0))
% 11.97/12.23  (step t312 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule resolution :premises (t310 t311))
% 11.97/12.23  (step t313 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule implies_neg2)
% 11.97/12.23  (step t314 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule resolution :premises (t312 t313))
% 11.97/12.23  (step t315 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule contraction :premises (t314))
% 11.97/12.23  (step t316 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule implies :premises (t315))
% 11.97/12.23  (step t317 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule resolution :premises (t316 t216))
% 11.97/12.23  (step t318 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t319)
% 11.97/12.23  (assume t319.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 11.97/12.23  (step t319.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 11.97/12.23  (step t319.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule or :premises (t319.t1))
% 11.97/12.23  (step t319.t3 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t319.t2 t319.a0))
% 11.97/12.23  (step t319 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule subproof :discharge (t319.a0))
% 11.97/12.23  (step t320 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t318 t319))
% 11.97/12.23  (step t321 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule implies_neg2)
% 11.97/12.23  (step t322 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t320 t321))
% 11.97/12.23  (step t323 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule contraction :premises (t322))
% 11.97/12.23  (step t324 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule implies :premises (t323))
% 11.97/12.23  (step t325 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t324 t90))
% 11.97/12.23  (step t326 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule equiv_pos2)
% 11.97/12.23  (step t327 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))) :rule refl)
% 11.97/12.23  (step t328 (cl (= (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule all_simplify)
% 11.97/12.23  (step t329 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))))) :rule cong :premises (t327 t328))
% 11.97/12.23  (step t330 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t331)
% 11.97/12.23  (assume t331.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 11.97/12.23  (step t331.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.b)) (:= Y tptp.b) (:= Z (tptp.inverse tptp.a))))
% 11.97/12.23  (step t331.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule or :premises (t331.t1))
% 11.97/12.23  (step t331.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t331.t2 t331.a0))
% 11.97/12.23  (step t331 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule subproof :discharge (t331.a0))
% 11.97/12.23  (step t332 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t330 t331))
% 11.97/12.23  (step t333 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 11.97/12.23  (step t334 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t332 t333))
% 11.97/12.23  (step t335 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule contraction :premises (t334))
% 11.97/12.23  (step t336 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a))))) :rule resolution :premises (t326 t329 t335))
% 11.97/12.23  (step t337 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) :rule implies :premises (t336))
% 11.97/12.23  (step t338 (cl (= (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) tptp.b) (tptp.inverse tptp.a)))) :rule resolution :premises (t337 a2))
% 11.97/12.23  (step t339 (cl (not (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t309 t254 t317 t325 t338))
% 11.97/12.23  (step t340 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t341)
% 11.97/12.23  (assume t341.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))))
% 11.97/12.23  (step t341.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.b)) (:= Y (tptp.multiply tptp.b (tptp.inverse tptp.a)))))
% 11.97/12.23  (step t341.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule or :premises (t341.t1))
% 11.97/12.23  (step t341.t3 (cl (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t341.t2 t341.a0))
% 11.97/12.23  (step t341 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule subproof :discharge (t341.a0))
% 11.97/12.23  (step t342 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t340 t341))
% 11.97/12.23  (step t343 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 11.97/12.23  (step t344 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t342 t343))
% 11.97/12.23  (step t345 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule contraction :premises (t344))
% 11.97/12.23  (step t346 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subgroup_member X)) (not (tptp.subgroup_member Y)) (tptp.subgroup_member (tptp.multiply X Y))))) (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies :premises (t345))
% 11.97/12.23  (step t347 (cl (or (not (tptp.subgroup_member (tptp.inverse tptp.b))) (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.multiply (tptp.inverse tptp.b) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t346 t159))
% 11.97/12.23  (step t348 (cl (not (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t256 t267 t339 t347))
% 11.97/12.23  (step t349 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y)))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t350)
% 11.97/12.23  (assume t350.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))))
% 11.97/12.23  (step t350.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y)))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.multiply tptp.b (tptp.inverse tptp.a)))))
% 11.97/12.23  (step t350.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y)))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule or :premises (t350.t1))
% 11.97/12.23  (step t350.t3 (cl (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t350.t2 t350.a0))
% 11.97/12.23  (step t350 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y)))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule subproof :discharge (t350.a0))
% 11.97/12.23  (step t351 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t349 t350))
% 11.97/12.23  (step t352 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (not (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule implies_neg2)
% 11.97/12.23  (step t353 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule resolution :premises (t351 t352))
% 11.97/12.23  (step t354 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))))) :rule contraction :premises (t353))
% 11.97/12.23  (step t355 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y)))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies :premises (t354))
% 11.97/12.23  (step t356 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= (tptp.multiply X (tptp.element_in_O2 X Y)) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= (tptp.multiply X (tptp.element_in_O2 X Y)) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y)))))) :rule equiv_pos2)
% 11.97/12.23  (anchor :step t357 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 11.97/12.23  (step t357.t1 (cl (= X X)) :rule refl)
% 11.97/12.23  (step t357.t2 (cl (= Y Y)) :rule refl)
% 11.97/12.23  (step t357.t3 (cl (= (tptp.subgroup_member X) (tptp.subgroup_member X))) :rule refl)
% 11.97/12.23  (step t357.t4 (cl (= (tptp.subgroup_member Y) (tptp.subgroup_member Y))) :rule refl)
% 11.97/12.23  (step t357.t5 (cl (= (= (tptp.multiply X (tptp.element_in_O2 X Y)) Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))) :rule all_simplify)
% 11.97/12.23  (step t357.t6 (cl (= (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= (tptp.multiply X (tptp.element_in_O2 X Y)) Y)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y)))))) :rule cong :premises (t357.t3 t357.t4 t357.t5))
% 11.97/12.23  (step t357 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= (tptp.multiply X (tptp.element_in_O2 X Y)) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y))))))) :rule bind)
% 11.97/12.23  (step t358 (cl (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (= Y (tptp.multiply X (tptp.element_in_O2 X Y)))))) :rule resolution :premises (t356 t357 a9))
% 11.97/12.23  (step t359 (cl (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t355 t358))
% 11.97/12.23  (step t360 (cl (= (tptp.multiply tptp.b (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t93 t254 t348 t359))
% 11.97/12.23  (step t361 (cl (not (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule or_pos)
% 11.97/12.23  (step t362 (cl (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))) (not (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule reordering :premises (t361))
% 11.97/12.23  (step t363 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y)))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t364)
% 11.97/12.23  (assume t364.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y)))))
% 11.97/12.23  (step t364.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.multiply tptp.b (tptp.inverse tptp.a)))))
% 11.97/12.23  (step t364.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule or :premises (t364.t1))
% 11.97/12.23  (step t364.t3 (cl (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t364.t2 t364.a0))
% 11.97/12.23  (step t364 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule subproof :discharge (t364.a0))
% 11.97/12.23  (step t365 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y)))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t363 t364))
% 11.97/12.23  (step t366 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y)))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (not (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 11.97/12.23  (step t367 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y)))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y)))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule resolution :premises (t365 t366))
% 11.97/12.23  (step t368 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y)))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))))) :rule contraction :premises (t367))
% 11.97/12.23  (step t369 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subgroup_member X) (tptp.subgroup_member Y) (tptp.subgroup_member (tptp.element_in_O2 X Y))))) (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule implies :premises (t368))
% 11.97/12.23  (step t370 (cl (or (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member (tptp.multiply tptp.b (tptp.inverse tptp.a))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a)))))) :rule resolution :premises (t369 a8))
% 11.97/12.23  (step t371 (cl (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) (tptp.multiply tptp.b (tptp.inverse tptp.a))))) :rule resolution :premises (t362 t254 t348 t370))
% 11.97/12.23  (step t372 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X))))) :rule implies_neg1)
% 11.97/12.23  (anchor :step t373)
% 11.97/12.23  (assume t373.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))))
% 11.97/12.23  (step t373.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 11.97/12.23  (step t373.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule or :premises (t373.t1))
% 11.97/12.23  (step t373.t3 (cl (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule resolution :premises (t373.t2 t373.a0))
% 11.97/12.23  (step t373 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule subproof :discharge (t373.a0))
% 11.97/12.23  (step t374 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule resolution :premises (t372 t373))
% 11.97/12.23  (step t375 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule implies_neg2)
% 11.97/12.23  (step t376 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t374 t375))
% 11.97/12.23  (step t377 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule contraction :premises (t376))
% 11.97/12.23  (step t378 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X))))) (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule implies :premises (t377))
% 11.97/12.23  (step t379 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply X (tptp.inverse X)) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))))) (not (forall ((X $$unsorted)) (= (tptp.multiply X (tptp.inverse X)) tptp.identity))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X))))) :rule equiv_pos2)
% 11.97/12.23  (anchor :step t380 :args ((X $$unsorted) (:= X X)))
% 11.97/12.23  (step t380.t1 (cl (= X X)) :rule refl)
% 11.97/12.23  (step t380.t2 (cl (= (= (tptp.multiply X (tptp.inverse X)) tptp.identity) (= tptp.identity (tptp.multiply X (tptp.inverse X))))) :rule all_simplify)
% 11.97/12.23  (step t380 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply X (tptp.inverse X)) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X)))))) :rule bind)
% 11.97/12.23  (step t381 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply X (tptp.inverse X))))) :rule resolution :premises (t379 t380 a6))
% 11.97/12.23  (step t382 (cl (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule resolution :premises (t378 t381))
% 11.97/12.23  (step t383 (cl) :rule resolution :premises (t72 t80 t91 t360 t371 t382 t196))
% 11.97/12.23  
% 11.97/12.23  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.OPES6AXeOq/cvc5---1.0.5_24349.smt2
% 12.06/12.23  % cvc5---1.0.5 exiting
% 12.06/12.24  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------