%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP024-5 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:23:35 PM UTC 2026
% Result : Unsatisfiable 30.01s 18.12s
% Output : CNFRefutation 30.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of clauses : 129 ( 129 unt; 0 nHn; 4 RR)
% Number of literals : 129 ( 128 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 311 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(name,axiom,
commutator(X1,X2) = multiply(inverse(X1),multiply(inverse(X2),multiply(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',name) ).
cnf(associativity_of_commutator,hypothesis,
commutator(commutator(X1,X2),X3) = commutator(X1,commutator(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_commutator) ).
cnf(prove_center,negated_conjecture,
multiply(a,commutator(b,c)) != multiply(commutator(b,c),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_center) ).
cnf(c_0_6,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_7,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_8,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_9,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_10,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_11,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_12,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
cnf(c_0_14,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_15,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_14]) ).
cnf(c_0_16,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_15]),c_0_12]) ).
cnf(c_0_17,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_18,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_19,axiom,
commutator(X1,X2) = multiply(inverse(X1),multiply(inverse(X2),multiply(X1,X2))),
name ).
cnf(c_0_20,plain,
multiply(inverse(X1),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_6,c_0_17]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_16]),c_0_13]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_23,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(X1,X2)),multiply(X2,X1)) = commutator(X2,X1),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_7,c_0_23]) ).
cnf(c_0_27,plain,
commutator(X1,multiply(inverse(X1),X2)) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_6]),c_0_25]),c_0_6]),c_0_24]) ).
cnf(c_0_28,hypothesis,
commutator(commutator(X1,X2),X3) = commutator(X1,commutator(X2,X3)),
associativity_of_commutator ).
cnf(c_0_29,plain,
commutator(X1,X1) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_13]),c_0_7]),c_0_13]) ).
cnf(c_0_30,plain,
commutator(identity,X1) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_8]),c_0_26]),c_0_7]),c_0_8]) ).
cnf(c_0_31,plain,
inverse(commutator(X1,X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_24]) ).
cnf(c_0_32,plain,
commutator(X1,multiply(X1,X2)) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_13]) ).
cnf(c_0_33,hypothesis,
commutator(X1,commutator(X1,X2)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_34,plain,
commutator(multiply(X1,X2),X1) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_31]) ).
cnf(c_0_35,hypothesis,
commutator(X1,commutator(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_26]),c_0_28]) ).
cnf(c_0_36,plain,
multiply(X1,multiply(X2,commutator(X2,X1))) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_24]),c_0_13]),c_0_6]) ).
cnf(c_0_37,hypothesis,
commutator(multiply(X1,X2),commutator(X2,X1)) = identity,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,hypothesis,
commutator(multiply(X1,X2),commutator(X1,X2)) = identity,
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_39,plain,
commutator(inverse(multiply(X1,X2)),X2) = commutator(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_40,hypothesis,
multiply(commutator(X1,X2),multiply(X2,X1)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_6]),c_0_12]),c_0_6]),c_0_36]) ).
cnf(c_0_41,hypothesis,
commutator(X1,commutator(X2,multiply(X1,X2))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_26]),c_0_28]) ).
cnf(c_0_42,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_43,hypothesis,
commutator(inverse(multiply(X1,X2)),multiply(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31]),c_0_28]),c_0_41]) ).
cnf(c_0_44,hypothesis,
multiply(commutator(X1,X2),X2) = multiply(X2,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_35]),c_0_12]) ).
cnf(c_0_45,plain,
multiply(inverse(multiply(commutator(X1,X2),X3)),X4) = multiply(inverse(X3),multiply(commutator(X2,X1),X4)),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_46,hypothesis,
multiply(commutator(X1,X2),X1) = multiply(X1,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_12]) ).
cnf(c_0_47,plain,
multiply(inverse(multiply(X1,commutator(X2,X3))),X4) = multiply(commutator(X3,X2),multiply(inverse(X1),X4)),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_48,plain,
inverse(multiply(X1,multiply(X2,inverse(X3)))) = multiply(X3,inverse(multiply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_42]),c_0_6]),c_0_17]) ).
cnf(c_0_49,hypothesis,
commutator(multiply(inverse(multiply(X1,X2)),X2),X1) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_22]),c_0_6]),c_0_25]) ).
cnf(c_0_50,plain,
multiply(X1,multiply(inverse(multiply(X2,X1)),X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_6,c_0_16]) ).
cnf(c_0_51,hypothesis,
multiply(X1,multiply(X2,inverse(multiply(X2,X1)))) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_43]),c_0_12]),c_0_6]),c_0_24]) ).
cnf(c_0_52,plain,
commutator(X1,inverse(multiply(X2,X1))) = commutator(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_53,plain,
multiply(commutator(X1,X2),inverse(X3)) = inverse(multiply(X3,commutator(X2,X1))),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_54,hypothesis,
multiply(X1,inverse(multiply(X1,commutator(X2,X1)))) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_44]),c_0_31]) ).
cnf(c_0_55,plain,
commutator(multiply(X1,commutator(X1,X2)),X2) = commutator(multiply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_56,plain,
commutator(multiply(inverse(X1),X2),X1) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_6]),c_0_20]),c_0_24]) ).
cnf(c_0_57,hypothesis,
multiply(commutator(X1,X2),multiply(inverse(X2),X3)) = multiply(inverse(X2),multiply(commutator(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_58,plain,
multiply(commutator(X1,X2),multiply(commutator(X2,X1),X3)) = X3,
inference(spm,[status(thm)],[c_0_9,c_0_31]) ).
cnf(c_0_59,plain,
multiply(inverse(X1),multiply(X2,multiply(X3,inverse(X4)))) = inverse(multiply(X4,multiply(inverse(multiply(X2,X3)),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_48]),c_0_6]) ).
cnf(c_0_60,hypothesis,
multiply(X1,multiply(inverse(multiply(X1,X2)),X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_49]),c_0_6]),c_0_12]),c_0_6]),c_0_24]) ).
cnf(c_0_61,hypothesis,
commutator(X1,inverse(X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_25]),c_0_20]),c_0_24]) ).
cnf(c_0_62,hypothesis,
commutator(multiply(X1,X2),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_36]),c_0_16]),c_0_6]),c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_63,plain,
commutator(inverse(X1),multiply(X2,X1)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_21]),c_0_32]) ).
cnf(c_0_64,hypothesis,
commutator(X1,multiply(commutator(X2,X1),X3)) = commutator(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_57]),c_0_6]),c_0_45]),c_0_25]),c_0_58]),c_0_6]),c_0_59]),c_0_60]),c_0_31]),c_0_61]) ).
cnf(c_0_65,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,X1)))) = inverse(multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_6]) ).
cnf(c_0_66,hypothesis,
commutator(multiply(X1,multiply(X2,X3)),X3) = commutator(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_62,c_0_6]) ).
cnf(c_0_67,plain,
commutator(multiply(X1,X2),inverse(X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_63]),c_0_31]) ).
cnf(c_0_68,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_24]),c_0_28]),c_0_32]),c_0_35]) ).
cnf(c_0_69,hypothesis,
commutator(multiply(X1,multiply(X2,commutator(X3,X4))),X4) = commutator(multiply(X1,X2),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_61]),c_0_61]) ).
cnf(c_0_70,plain,
multiply(inverse(X1),multiply(X2,X1)) = multiply(X2,commutator(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_36]) ).
cnf(c_0_71,hypothesis,
commutator(multiply(X1,multiply(X2,multiply(X3,X4))),X4) = commutator(multiply(X1,multiply(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_66,c_0_6]) ).
cnf(c_0_72,plain,
commutator(X1,multiply(X2,X1)) = commutator(X1,X2),
inference(rw,[status(thm)],[c_0_67,c_0_61]) ).
cnf(c_0_73,hypothesis,
commutator(multiply(X1,X2),commutator(multiply(X2,X1),X3)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_68]),c_0_30]) ).
cnf(c_0_74,hypothesis,
commutator(multiply(X1,multiply(inverse(X2),X3)),X2) = commutator(multiply(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_75,plain,
multiply(commutator(X1,X2),commutator(X2,X1)) = identity,
inference(spm,[status(thm)],[c_0_7,c_0_31]) ).
cnf(c_0_76,hypothesis,
commutator(X1,commutator(X2,X3)) = commutator(X2,commutator(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_31]),c_0_28]) ).
cnf(c_0_77,plain,
multiply(X1,multiply(X2,multiply(X2,commutator(X2,X1)))) = multiply(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_72]),c_0_6]) ).
cnf(c_0_78,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_6,c_0_21]) ).
cnf(c_0_79,plain,
multiply(inverse(multiply(X1,X2)),multiply(X2,multiply(X1,X3))) = multiply(commutator(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_24]),c_0_6]) ).
cnf(c_0_80,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X3,multiply(X1,X2))) = commutator(X3,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_6]) ).
cnf(c_0_81,hypothesis,
multiply(commutator(multiply(X1,X2),X3),multiply(X2,X1)) = multiply(X2,multiply(X1,commutator(multiply(X1,X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_73]),c_0_6]),c_0_12]),c_0_6]) ).
cnf(c_0_82,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X2,multiply(X3,X1))) = commutator(multiply(X2,X3),X1),
inference(spm,[status(thm)],[c_0_24,c_0_6]) ).
cnf(c_0_83,hypothesis,
commutator(X1,multiply(X2,multiply(X1,X3))) = commutator(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_74]),c_0_61]),c_0_13]) ).
cnf(c_0_84,plain,
multiply(inverse(X1),multiply(X2,inverse(X3))) = inverse(multiply(X3,multiply(inverse(X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_42]),c_0_6]) ).
cnf(c_0_85,hypothesis,
multiply(commutator(X1,commutator(X2,X3)),commutator(X1,commutator(X2,X3))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_28]) ).
cnf(c_0_86,plain,
multiply(commutator(X1,X2),commutator(X1,X2)) = commutator(multiply(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_77]),c_0_6]),c_0_6]),c_0_44]),c_0_78]),c_0_79]),c_0_69]) ).
cnf(c_0_87,hypothesis,
commutator(multiply(X1,multiply(X2,X3)),X2) = commutator(multiply(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_22]),c_0_13]) ).
cnf(c_0_88,hypothesis,
commutator(multiply(X1,commutator(multiply(X1,X2),X3)),X2) = commutator(X1,multiply(commutator(multiply(X1,X2),X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_89,hypothesis,
commutator(X1,multiply(commutator(multiply(X1,X2),X3),X2)) = commutator(X1,multiply(X2,commutator(multiply(X1,X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_46]),c_0_6]),c_0_32]) ).
cnf(c_0_90,hypothesis,
commutator(X1,multiply(X2,multiply(X3,multiply(X1,X4)))) = commutator(X1,multiply(X2,multiply(X3,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_6]),c_0_6]) ).
cnf(c_0_91,plain,
multiply(inverse(X1),multiply(X2,multiply(X3,multiply(X1,inverse(multiply(X2,X3)))))) = commutator(multiply(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_65]),c_0_25]),c_0_6]),c_0_6]),c_0_6]),c_0_61]),c_0_66]) ).
cnf(c_0_92,hypothesis,
commutator(X1,multiply(X2,inverse(multiply(X1,X3)))) = commutator(X1,multiply(X2,inverse(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_17]),c_0_61]),c_0_61]) ).
cnf(c_0_93,plain,
multiply(inverse(multiply(X1,X2)),multiply(X3,commutator(X1,X3))) = inverse(multiply(X1,multiply(inverse(X3),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_36]),c_0_61]),c_0_84]) ).
cnf(c_0_94,hypothesis,
commutator(X1,commutator(multiply(X1,X2),X3)) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_28]) ).
cnf(c_0_95,plain,
multiply(X1,multiply(X2,multiply(X2,X1))) = multiply(X2,multiply(X1,multiply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_68]),c_0_6]),c_0_12]),c_0_6]),c_0_6]) ).
cnf(c_0_96,hypothesis,
commutator(multiply(X1,X1),commutator(X2,X3)) = identity,
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_97,hypothesis,
commutator(multiply(commutator(multiply(X1,X2),X3),X1),X2) = commutator(X1,multiply(X2,commutator(multiply(X1,X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_81]),c_0_34]),c_0_88]),c_0_89]) ).
cnf(c_0_98,hypothesis,
commutator(X1,multiply(X2,commutator(multiply(X1,X3),X4))) = commutator(X1,multiply(X2,commutator(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_59]),c_0_6]),c_0_60]),c_0_92]),c_0_31]) ).
cnf(c_0_99,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1)))) = multiply(inverse(X3),multiply(X2,commutator(multiply(X3,X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_61]) ).
cnf(c_0_100,plain,
multiply(inverse(X1),commutator(X2,X3)) = inverse(multiply(commutator(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_17,c_0_31]) ).
cnf(c_0_101,hypothesis,
commutator(multiply(X1,commutator(X2,X3)),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_64]),c_0_61]),c_0_34]),c_0_53]),c_0_61]) ).
cnf(c_0_102,hypothesis,
commutator(multiply(X1,X2),multiply(X3,commutator(X1,X3))) = multiply(commutator(X2,X3),commutator(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_93]),c_0_13]),c_0_6]),c_0_6]),c_0_78]),c_0_20]),c_0_79]),c_0_61]) ).
cnf(c_0_103,hypothesis,
commutator(inverse(X1),X2) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_16]),c_0_13]),c_0_24]),c_0_39]) ).
cnf(c_0_104,plain,
commutator(X1,multiply(X2,multiply(X3,X1))) = commutator(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_72,c_0_6]) ).
cnf(c_0_105,hypothesis,
multiply(commutator(multiply(X1,X2),X3),multiply(X1,commutator(X1,commutator(X2,X3)))) = multiply(X1,commutator(multiply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_36,c_0_94]) ).
cnf(c_0_106,plain,
commutator(X1,multiply(X2,X2)) = commutator(multiply(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_95]),c_0_6]),c_0_6]),c_0_78]),c_0_80]),c_0_66]) ).
cnf(c_0_107,hypothesis,
commutator(X1,commutator(X2,multiply(X3,X3))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_96]),c_0_26]),c_0_28]) ).
cnf(c_0_108,hypothesis,
commutator(multiply(commutator(multiply(X1,X2),X3),X1),X2) = commutator(X1,multiply(X2,commutator(X2,X3))),
inference(rw,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_109,hypothesis,
multiply(commutator(X1,X2),multiply(X2,X3)) = multiply(X2,multiply(commutator(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_44]),c_0_6]) ).
cnf(c_0_110,plain,
multiply(X1,multiply(commutator(multiply(X2,X3),X1),X2)) = multiply(X2,multiply(X1,commutator(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_99]),c_0_16]),c_0_13]),c_0_61]),c_0_100]),c_0_44]),c_0_17]),c_0_6]),c_0_13]) ).
cnf(c_0_111,hypothesis,
commutator(multiply(X1,multiply(X2,commutator(X3,X4))),X3) = commutator(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_101,c_0_6]) ).
cnf(c_0_112,hypothesis,
multiply(commutator(X1,multiply(X2,X3)),commutator(X3,X1)) = commutator(multiply(X1,commutator(X3,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_16]),c_0_103]),c_0_103]) ).
cnf(c_0_113,plain,
multiply(X1,multiply(X2,multiply(inverse(multiply(X1,multiply(X2,X3))),X3))) = commutator(X3,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_65]),c_0_13]),c_0_6]),c_0_103]),c_0_104]) ).
cnf(c_0_114,hypothesis,
multiply(commutator(multiply(X1,multiply(X2,X2)),X3),X1) = multiply(X1,commutator(multiply(X1,multiply(X2,X2)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_12]) ).
cnf(c_0_115,plain,
multiply(X1,multiply(inverse(multiply(X2,multiply(X3,X1))),X4)) = multiply(inverse(multiply(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_50,c_0_6]) ).
cnf(c_0_116,hypothesis,
multiply(commutator(multiply(X1,X2),X3),commutator(X3,X1)) = commutator(X2,multiply(X3,commutator(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_9]),c_0_103]),c_0_103]) ).
cnf(c_0_117,hypothesis,
commutator(multiply(X1,X2),multiply(X3,commutator(X3,X1))) = commutator(multiply(X2,X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_6]),c_0_34]),c_0_110]),c_0_111]) ).
cnf(c_0_118,plain,
commutator(multiply(X1,commutator(X1,X2)),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[c_0_55,c_0_62]) ).
cnf(c_0_119,hypothesis,
multiply(commutator(multiply(X1,X2),X3),commutator(X3,X2)) = commutator(X1,multiply(X3,commutator(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_61]),c_0_103]),c_0_100]),c_0_44]),c_0_103]) ).
cnf(c_0_120,hypothesis,
commutator(X1,multiply(X2,commutator(multiply(X3,X3),X4))) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115]),c_0_60]),c_0_98]) ).
cnf(c_0_121,plain,
commutator(X1,multiply(X2,commutator(X2,X1))) = commutator(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_36]) ).
cnf(c_0_122,hypothesis,
commutator(X1,multiply(X2,commutator(X3,X2))) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_119]),c_0_118]),c_0_6]),c_0_86]),c_0_120]) ).
cnf(c_0_123,plain,
commutator(X1,multiply(X2,commutator(X2,X1))) = commutator(X1,X2),
inference(rw,[status(thm)],[c_0_121,c_0_72]) ).
cnf(c_0_124,hypothesis,
multiply(commutator(X1,X2),multiply(X3,commutator(X2,commutator(X3,X1)))) = multiply(X3,commutator(X1,X2)),
inference(spm,[status(thm)],[c_0_36,c_0_76]) ).
cnf(c_0_125,hypothesis,
commutator(X1,commutator(X2,X3)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_122]),c_0_116]),c_0_28]),c_0_123]) ).
cnf(c_0_126,negated_conjecture,
multiply(a,commutator(b,c)) != multiply(commutator(b,c),a),
prove_center ).
cnf(c_0_127,hypothesis,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125]),c_0_12]) ).
cnf(c_0_128,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP024-5 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.30 % Computer : n003.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Mon May 4 18:17:11 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 % start to proof: theBenchmark
% 30.01/18.12 % Version : CSE_E---1.7
% 30.01/18.12 % Problem : theBenchmark.p
% 30.01/18.12 % SZS status Unsatisfiable for theBenchmark.p
% 30.01/18.12 % SZS output start CNFRefutation
% See solution above
% 30.19/18.24 % Total time : 13.397s
%------------------------------------------------------------------------------