%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP401-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:43:33 PM UTC 2026
% Result : Unsatisfiable 56.45s 8.71s
% Output : CNFRefutation 56.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 6
% Syntax : Number of clauses : 123 ( 102 unt; 0 nHn; 22 RR)
% Number of literals : 144 ( 143 equ; 24 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 316 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_cancellation,axiom,
( multiply(X1,X2) != multiply(X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-1.ax',left_cancellation) ).
cnf(commutator,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
cnf(commutator_distributes_over_product,axiom,
commutator(multiply(X1,X2),X3) = multiply(commutator(X1,X3),commutator(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator_distributes_over_product) ).
cnf(right_cancellation,axiom,
( multiply(X1,X2) != multiply(X3,X2)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-1.ax',right_cancellation) ).
cnf(prove_nilpotency,negated_conjecture,
multiply(commutator(a,b),c) != multiply(c,commutator(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_nilpotency) ).
cnf(c_0_6,plain,
( multiply(X1,X2) != multiply(X1,X3)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[left_cancellation]) ).
cnf(c_0_7,plain,
( multiply(X1,X2) != multiply(X1,X3)
| X2 = X3 ),
c_0_6 ).
cnf(c_0_8,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
commutator ).
cnf(c_0_9,plain,
( multiply(X3,X1) != multiply(X2,X3)
| X1 = multiply(X2,commutator(X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_11,plain,
multiply(X1,commutator(X1,X1)) = X1,
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
multiply(X1,multiply(commutator(X1,X1),X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
commutator(multiply(X1,X2),X3) = multiply(commutator(X1,X3),commutator(X2,X3)),
commutator_distributes_over_product ).
cnf(c_0_14,plain,
( multiply(X1,X2) != multiply(X3,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[right_cancellation]) ).
cnf(c_0_15,plain,
multiply(X1,commutator(multiply(X1,X2),X1)) = multiply(X1,commutator(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
multiply(X1,commutator(commutator(X1,X1),X1)) = multiply(commutator(X1,X1),X1),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_17,plain,
( multiply(X1,X2) != multiply(X3,X2)
| X1 = X3 ),
c_0_14 ).
cnf(c_0_18,plain,
multiply(commutator(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_11]),c_0_11]),c_0_16]) ).
cnf(c_0_19,plain,
( multiply(X2,X1) != X1
| commutator(X1,X1) = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
multiply(commutator(X1,X1),multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_21,plain,
( multiply(X2,X1) != X2
| X1 = commutator(X2,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_22,plain,
multiply(X1,commutator(commutator(X1,X1),commutator(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_11]),c_0_11]) ).
cnf(c_0_23,plain,
commutator(multiply(X1,X2),multiply(X1,X2)) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
multiply(commutator(X1,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_8]) ).
cnf(c_0_25,plain,
commutator(commutator(X1,X1),commutator(X1,X1)) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
commutator(X1,X1) = commutator(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_23]),c_0_25]) ).
cnf(c_0_27,plain,
multiply(commutator(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_28,plain,
multiply(X1,commutator(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
cnf(c_0_29,plain,
( multiply(X3,multiply(X4,X1)) != multiply(X3,multiply(X4,X2))
| X1 = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_10]) ).
cnf(c_0_30,plain,
commutator(multiply(X1,X2),X1) = commutator(X2,X1),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_31,plain,
commutator(multiply(X1,X2),X2) = commutator(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_32,plain,
multiply(X1,commutator(multiply(X2,commutator(X2,X1)),X1)) = multiply(commutator(X2,X1),X1),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_33,plain,
( multiply(X3,multiply(X2,X1)) != multiply(X2,X3)
| X1 = commutator(X2,X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_8]) ).
cnf(c_0_34,plain,
commutator(multiply(X1,commutator(X1,X2)),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_8]),c_0_31]) ).
cnf(c_0_35,plain,
commutator(multiply(X1,multiply(X2,X3)),X2) = commutator(multiply(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_31]),c_0_13]),c_0_10]) ).
cnf(c_0_36,plain,
multiply(X1,multiply(X2,multiply(commutator(X2,X1),X3))) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_8]),c_0_10]),c_0_10]) ).
cnf(c_0_37,plain,
multiply(commutator(X1,X2),X2) = multiply(X2,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_10]),c_0_8]),c_0_31]) ).
cnf(c_0_38,plain,
( multiply(X3,X2) != multiply(X2,X3)
| commutator(X1,X1) = commutator(X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_39,plain,
commutator(multiply(X1,multiply(X2,commutator(X2,X3))),X3) = commutator(multiply(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_34]),c_0_13]) ).
cnf(c_0_40,plain,
commutator(multiply(X1,multiply(commutator(X2,X1),X3)),X2) = commutator(multiply(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_30]) ).
cnf(c_0_41,plain,
commutator(multiply(X1,commutator(X2,X1)),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_8]),c_0_30]) ).
cnf(c_0_42,plain,
multiply(commutator(X1,X2),multiply(X2,X3)) = multiply(X2,multiply(commutator(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_37]),c_0_10]) ).
cnf(c_0_43,plain,
commutator(X1,X1) = commutator(commutator(X2,X3),X3),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_44,plain,
commutator(multiply(X1,commutator(commutator(X2,X1),X2)),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_45,plain,
multiply(X1,commutator(X1,commutator(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_20]),c_0_11]) ).
cnf(c_0_46,plain,
( multiply(X2,multiply(commutator(X3,X2),X1)) != multiply(X2,commutator(X3,X2))
| X1 = commutator(X2,commutator(X3,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_47,plain,
commutator(multiply(commutator(X1,X2),X3),X2) = commutator(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_43]),c_0_27]) ).
cnf(c_0_48,plain,
( multiply(X3,multiply(X4,X1)) != multiply(X3,X4)
| X1 = commutator(X2,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_49,plain,
multiply(X1,multiply(X2,commutator(commutator(X2,X1),X2))) = multiply(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_44]),c_0_10]),c_0_13]),c_0_37]),c_0_41]),c_0_8]),c_0_10]),c_0_37]) ).
cnf(c_0_50,plain,
commutator(X1,commutator(X1,X1)) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_51,plain,
commutator(commutator(X1,X2),X2) = commutator(X2,commutator(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_8]),c_0_37])]) ).
cnf(c_0_52,plain,
commutator(commutator(multiply(X1,X2),X3),X3) = commutator(commutator(X2,X3),X3),
inference(spm,[status(thm)],[c_0_47,c_0_13]) ).
cnf(c_0_53,plain,
commutator(commutator(X1,X2),X1) = commutator(X3,X3),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
commutator(X1,commutator(X2,X2)) = commutator(X2,X2),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_55,plain,
commutator(X1,commutator(multiply(X2,X3),X1)) = commutator(X1,commutator(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_35]),c_0_52]),c_0_51]) ).
cnf(c_0_56,plain,
multiply(commutator(X1,X2),X1) = multiply(X1,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_53]),c_0_28]) ).
cnf(c_0_57,plain,
multiply(X1,multiply(X2,multiply(X1,commutator(X2,X1)))) = multiply(X2,multiply(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_31]),c_0_10]),c_0_10]) ).
cnf(c_0_58,plain,
multiply(X1,commutator(commutator(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_53]) ).
cnf(c_0_59,plain,
multiply(commutator(X1,X2),multiply(X1,X3)) = multiply(X1,multiply(commutator(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_53]),c_0_27]) ).
cnf(c_0_60,plain,
commutator(X1,commutator(commutator(X2,X3),X2)) = commutator(commutator(X2,X3),X2),
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_61,plain,
commutator(X1,commutator(commutator(X2,X3),X1)) = commutator(X1,commutator(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_55]) ).
cnf(c_0_62,plain,
commutator(multiply(X1,multiply(X2,X3)),multiply(X1,X2)) = commutator(X3,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_10]) ).
cnf(c_0_63,plain,
commutator(X1,X1) = commutator(X2,commutator(X2,X3)),
inference(spm,[status(thm)],[c_0_38,c_0_56]) ).
cnf(c_0_64,plain,
( multiply(X3,multiply(X4,multiply(X2,X1))) != multiply(X2,multiply(X3,X4))
| X1 = commutator(X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_33,c_0_10]) ).
cnf(c_0_65,plain,
multiply(X1,multiply(X2,multiply(X2,commutator(X2,X1)))) = multiply(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_57]),c_0_58]),c_0_59]),c_0_56]) ).
cnf(c_0_66,plain,
commutator(commutator(X1,X2),X1) = commutator(X1,commutator(X2,X1)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
commutator(commutator(X1,X2),multiply(X2,X1)) = commutator(multiply(X1,X2),multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_62,c_0_8]) ).
cnf(c_0_68,plain,
commutator(multiply(X1,X2),commutator(X1,X3)) = commutator(X2,commutator(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_63]),c_0_27]) ).
cnf(c_0_69,plain,
commutator(X1,multiply(X2,X1)) = commutator(X1,X2),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,plain,
commutator(multiply(X1,X2),commutator(X2,X3)) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_63]),c_0_28]) ).
cnf(c_0_71,plain,
( multiply(X1,X4) != multiply(X2,multiply(X3,X4))
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_72,plain,
( multiply(X1,multiply(X2,X3)) != multiply(X2,X1)
| multiply(commutator(X1,X2),X3) = commutator(X4,X4) ),
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
cnf(c_0_73,plain,
commutator(X1,commutator(X2,multiply(X2,X1))) = commutator(multiply(X1,X2),multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_30]),c_0_67]),c_0_68]) ).
cnf(c_0_74,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = commutator(X2,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_69]),c_0_67]),c_0_70]) ).
cnf(c_0_75,plain,
commutator(X1,X1) = commutator(X2,commutator(X3,X2)),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_76,plain,
( multiply(X1,commutator(X3,X2)) != multiply(X3,X2)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_71,c_0_8]) ).
cnf(c_0_77,plain,
multiply(commutator(X1,X2),commutator(X2,X1)) = commutator(X3,X3),
inference(spm,[status(thm)],[c_0_72,c_0_8]) ).
cnf(c_0_78,plain,
commutator(X1,commutator(X2,multiply(X2,X1))) = commutator(X2,commutator(X1,X2)),
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,plain,
commutator(multiply(X1,X2),commutator(X3,X1)) = commutator(X2,commutator(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_75]),c_0_27]) ).
cnf(c_0_80,plain,
commutator(multiply(X1,commutator(X2,X3)),X3) = commutator(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_43]),c_0_28]) ).
cnf(c_0_81,plain,
( multiply(X1,commutator(X4,X3)) != commutator(multiply(X2,X4),X3)
| X1 = commutator(X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_82,plain,
( commutator(X3,X3) != multiply(X2,X1)
| commutator(X1,X2) = multiply(X1,X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,plain,
commutator(commutator(X1,X2),commutator(X2,X1)) = commutator(X2,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_8]),c_0_69]),c_0_79]),c_0_80]) ).
cnf(c_0_84,plain,
( multiply(X1,commutator(X3,X2)) != commutator(X4,X4)
| X1 = commutator(X2,multiply(X2,X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_26]),c_0_69]) ).
cnf(c_0_85,plain,
commutator(multiply(X1,commutator(X2,X3)),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_53]),c_0_28]) ).
cnf(c_0_86,plain,
multiply(commutator(X1,X2),commutator(X2,X1)) = commutator(X2,commutator(X1,X2)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_77]),c_0_83]),c_0_26]) ).
cnf(c_0_87,plain,
multiply(X1,commutator(X2,commutator(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_75]) ).
cnf(c_0_88,plain,
commutator(X1,multiply(X1,X2)) = commutator(X1,X2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_77]),c_0_26]) ).
cnf(c_0_89,plain,
multiply(X1,commutator(commutator(X1,X1),X1)) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_90,plain,
commutator(commutator(multiply(X1,X2),X3),X2) = commutator(commutator(X1,X3),X2),
inference(spm,[status(thm)],[c_0_85,c_0_13]) ).
cnf(c_0_91,plain,
commutator(X1,multiply(X2,multiply(X3,X1))) = commutator(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_69,c_0_10]) ).
cnf(c_0_92,plain,
commutator(commutator(X1,X2),multiply(X3,commutator(X2,X1))) = commutator(X3,commutator(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_86]),c_0_87]),c_0_88]) ).
cnf(c_0_93,plain,
commutator(commutator(X1,X1),X1) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_89]) ).
cnf(c_0_94,plain,
commutator(commutator(X1,multiply(X2,multiply(X1,X3))),X3) = commutator(commutator(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_69]),c_0_90]) ).
cnf(c_0_95,plain,
commutator(X1,commutator(X2,X3)) = commutator(commutator(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_86]),c_0_87]),c_0_92]) ).
cnf(c_0_96,plain,
multiply(commutator(X1,commutator(X2,X1)),X3) = X3,
inference(spm,[status(thm)],[c_0_27,c_0_75]) ).
cnf(c_0_97,plain,
commutator(multiply(X1,X2),commutator(X3,X2)) = commutator(X1,commutator(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_75]),c_0_28]) ).
cnf(c_0_98,plain,
commutator(commutator(X1,X1),X2) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_93,c_0_26]) ).
cnf(c_0_99,plain,
commutator(X1,commutator(multiply(X2,X1),X3)) = commutator(commutator(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_35]) ).
cnf(c_0_100,plain,
commutator(commutator(X1,X2),multiply(X1,X3)) = commutator(X3,commutator(X2,X1)),
inference(spm,[status(thm)],[c_0_79,c_0_95]) ).
cnf(c_0_101,plain,
commutator(X1,commutator(X2,multiply(X3,X1))) = commutator(commutator(X3,X2),X1),
inference(rw,[status(thm)],[c_0_90,c_0_95]) ).
cnf(c_0_102,plain,
multiply(commutator(X1,multiply(X2,X3)),commutator(X3,X2)) = commutator(multiply(X1,X3),multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_13,c_0_69]) ).
cnf(c_0_103,plain,
multiply(commutator(X1,X2),multiply(commutator(X2,X1),X3)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_86]),c_0_96]) ).
cnf(c_0_104,plain,
commutator(multiply(commutator(X1,X2),X3),commutator(X4,X1)) = commutator(X3,commutator(X4,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_85]),c_0_10]),c_0_68]) ).
cnf(c_0_105,plain,
commutator(multiply(X1,multiply(X2,X3)),X3) = commutator(multiply(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_31]),c_0_13]) ).
cnf(c_0_106,plain,
multiply(commutator(X1,X2),multiply(commutator(X3,X2),X4)) = multiply(commutator(multiply(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_107,plain,
commutator(multiply(X1,commutator(X1,X2)),commutator(X3,X2)) = commutator(X1,commutator(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_8]),c_0_97]) ).
cnf(c_0_108,plain,
commutator(multiply(commutator(X1,X2),X3),commutator(X4,X2)) = commutator(X3,commutator(X4,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_80]),c_0_10]),c_0_68]) ).
cnf(c_0_109,plain,
commutator(commutator(commutator(X1,X2),X2),X3) = commutator(commutator(X1,X2),X2),
inference(spm,[status(thm)],[c_0_98,c_0_43]) ).
cnf(c_0_110,plain,
multiply(X1,multiply(X2,multiply(commutator(X1,X3),commutator(X2,X1)))) = multiply(X2,multiply(X1,commutator(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_85]),c_0_10]),c_0_10]),c_0_56]) ).
cnf(c_0_111,plain,
commutator(commutator(X1,X2),X3) = commutator(X2,commutator(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_62]),c_0_70]),c_0_30]),c_0_100]),c_0_101]) ).
cnf(c_0_112,plain,
multiply(commutator(X1,X2),commutator(X2,commutator(X3,X4))) = commutator(multiply(X1,commutator(X4,X3)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_105]) ).
cnf(c_0_113,plain,
multiply(commutator(X1,X2),multiply(X3,commutator(X3,X2))) = multiply(commutator(multiply(X1,X3),X2),X3),
inference(spm,[status(thm)],[c_0_106,c_0_56]) ).
cnf(c_0_114,plain,
commutator(commutator(X1,X2),commutator(X3,X2)) = commutator(X2,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_51]) ).
cnf(c_0_115,plain,
multiply(commutator(multiply(X1,X2),X3),X2) = multiply(X2,commutator(multiply(X2,X1),X3)),
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_110,c_0_106]),c_0_111]),c_0_112]),c_0_10]),c_0_8]),c_0_113]) ).
cnf(c_0_116,plain,
commutator(X1,commutator(multiply(X2,X1),X3)) = commutator(X2,commutator(X3,X1)),
inference(rw,[status(thm)],[c_0_99,c_0_111]) ).
cnf(c_0_117,plain,
commutator(multiply(X1,X2),X3) = commutator(multiply(X2,X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_106]),c_0_13]),c_0_114]),c_0_87]) ).
cnf(c_0_118,negated_conjecture,
multiply(commutator(a,b),c) != multiply(c,commutator(a,b)),
inference(fof_simplification,[status(thm)],[prove_nilpotency]) ).
cnf(c_0_119,plain,
commutator(X1,X1) = commutator(X2,commutator(X3,X4)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_115]),c_0_116]),c_0_117]) ).
cnf(c_0_120,negated_conjecture,
multiply(commutator(a,b),c) != multiply(c,commutator(a,b)),
c_0_118 ).
cnf(c_0_121,plain,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_119]),c_0_28]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP401-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:11:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 56.45/8.71 % Version: 3.5.1
% 56.45/8.71 % Preprocessing class: FSSSSMSSSSSNFFN.
% 56.45/8.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 56.45/8.71 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 56.45/8.71 % Starting new_bool_3 with 300s (1) cores
% 56.45/8.71 % Starting new_bool_1 with 300s (1) cores
% 56.45/8.71 % Starting sh5l with 300s (1) cores
% 56.45/8.71 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1663337 completed with status 0
% 56.45/8.71 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 56.45/8.71 % Preprocessing class: FSSSSMSSSSSNFFN.
% 56.45/8.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 56.45/8.71 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 56.45/8.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 56.45/8.71 % No SInE strategy applied
% 56.45/8.71 % Search class: FHUPS-FFSF22-MFFFFFNN
% 56.45/8.71 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 56.45/8.71 % Starting SubtermCWHack with 136s (1) cores
% 56.45/8.71 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 56.45/8.71 % Starting G----_0008_C18_F1_SE_CS_SP_S0Y with 248s (1) cores
% 56.45/8.71 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 136s (1) cores
% 56.45/8.71 % Starting new_bool_3 with 136s (1) cores
% 56.45/8.71 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 1663346 completed with status 0
% 56.45/8.71 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 56.45/8.71 % Preprocessing class: FSSSSMSSSSSNFFN.
% 56.45/8.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 56.45/8.71 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 56.45/8.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 56.45/8.71 % No SInE strategy applied
% 56.45/8.71 % Search class: FHUPS-FFSF22-MFFFFFNN
% 56.45/8.71 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 56.45/8.71 % Starting SubtermCWHack with 136s (1) cores
% 56.45/8.71 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 56.45/8.71 % Starting G----_0008_C18_F1_SE_CS_SP_S0Y with 248s (1) cores
% 56.45/8.71 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 136s (1) cores
% 56.45/8.71 % Preprocessing time : 0.001 s
% 56.45/8.71 % Presaturation interreduction done
% 56.45/8.71
% 56.45/8.71 % Proof found!
% 56.45/8.71 % SZS status Unsatisfiable
% 56.45/8.71 % SZS output start CNFRefutation
% See solution above
% 56.45/8.72 % Parsed axioms : 6
% 56.45/8.72 % Removed by relevancy pruning/SinE : 0
% 56.45/8.72 % Initial clauses : 6
% 56.45/8.72 % Removed in clause preprocessing : 0
% 56.45/8.72 % Initial clauses in saturation : 6
% 56.45/8.72 % Processed clauses : 14557
% 56.45/8.72 % ...of these trivial : 803
% 56.45/8.72 % ...subsumed : 12712
% 56.45/8.72 % ...remaining for further processing : 1042
% 56.45/8.72 % Other redundant clauses eliminated : 128
% 56.45/8.72 % Clauses deleted for lack of memory : 0
% 56.45/8.72 % Backward-subsumed : 57
% 56.45/8.72 % Backward-rewritten : 403
% 56.45/8.72 % Generated clauses : 384553
% 56.45/8.72 % ...of the previous two non-redundant : 320918
% 56.45/8.72 % ...aggressively subsumed : 0
% 56.45/8.72 % Contextual simplify-reflections : 0
% 56.45/8.72 % Paramodulations : 384325
% 56.45/8.72 % Factorizations : 0
% 56.45/8.72 % NegExts : 0
% 56.45/8.72 % Equation resolutions : 228
% 56.45/8.72 % Disequality decompositions : 0
% 56.45/8.72 % Total rewrite steps : 816386
% 56.45/8.72 % ...of those cached : 653100
% 56.45/8.72 % Propositional unsat checks : 0
% 56.45/8.72 % Propositional check models : 0
% 56.45/8.72 % Propositional check unsatisfiable : 0
% 56.45/8.72 % Propositional clauses : 0
% 56.45/8.72 % Propositional clauses after purity: 0
% 56.45/8.72 % Propositional unsat core size : 0
% 56.45/8.72 % Propositional preprocessing time : 0.000
% 56.45/8.72 % Propositional encoding time : 0.000
% 56.45/8.72 % Propositional solver time : 0.000
% 56.45/8.72 % Success case prop preproc time : 0.000
% 56.45/8.72 % Success case prop encoding time : 0.000
% 56.45/8.72 % Success case prop solver time : 0.000
% 56.45/8.72 % Current number of processed clauses : 576
% 56.45/8.72 % Positive orientable unit clauses : 131
% 56.45/8.72 % Positive unorientable unit clauses: 22
% 56.45/8.72 % Negative unit clauses : 0
% 56.45/8.72 % Non-unit-clauses : 423
% 56.45/8.72 % Current number of unprocessed clauses: 299782
% 56.45/8.72 % ...number of literals in the above : 496387
% 56.45/8.72 % Current number of archived formulas : 0
% 56.45/8.72 % Current number of archived clauses : 466
% 56.45/8.72 % Clause-clause subsumption calls (NU) : 70197
% 56.45/8.72 % Rec. Clause-clause subsumption calls : 70197
% 56.45/8.72 % Non-unit clause-clause subsumptions : 6736
% 56.45/8.72 % Unit Clause-clause subsumption calls : 2751
% 56.45/8.72 % Rewrite failures with RHS unbound : 5822
% 56.45/8.72 % BW rewrite match attempts : 10628
% 56.45/8.72 % BW rewrite match successes : 1798
% 56.45/8.72 % Condensation attempts : 0
% 56.45/8.72 % Condensation successes : 0
% 56.45/8.72 % Termbank termtop insertions : 6100455
% 56.45/8.72 % Search garbage collected termcells : 8
% 56.45/8.72
% 56.45/8.72 % -------------------------------------------------
% 56.45/8.72 % User time : 7.642 s
% 56.45/8.72 % System time : 0.303 s
% 56.45/8.72 % Total time : 7.945 s
% 56.45/8.72 % Maximum resident set size: 3636 pages
% 56.45/8.72
% 56.45/8.72 % -------------------------------------------------
% 56.45/8.72 % User time : 38.821 s
% 56.45/8.72 % System time : 1.424 s
% 56.45/8.72 % Total time : 40.245 s
% 56.45/8.72 % Maximum resident set size: 4608 pages
% 56.45/8.72 % E exiting
%------------------------------------------------------------------------------