TSTP Solution File: GRP024-5 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : GRP024-5 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.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 : Mon May 20 20:43:40 EDT 2024
% Result : Unsatisfiable 59.05s 7.97s
% Output : CNFRefutation 59.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 6
% Syntax : Number of clauses : 166 ( 166 unt; 0 nHn; 5 RR)
% Number of literals : 166 ( 165 equ; 3 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 : 408 ( 23 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(spm,[status(thm)],[c_0_36,c_0_37]),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,
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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,plain,
commutator(X1,inverse(multiply(X2,X1))) = commutator(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_54,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_55,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_56,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_57,plain,
commutator(inverse(X1),multiply(X2,X1)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_21]),c_0_32]) ).
cnf(c_0_58,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_46,c_0_47]),c_0_48]) ).
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_49]),c_0_6]) ).
cnf(c_0_60,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_61,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(spm,[status(thm)],[c_0_36,c_0_50]),c_0_12]),c_0_6]),c_0_24]) ).
cnf(c_0_62,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_51,c_0_52]),c_0_53]),c_0_25]),c_0_20]),c_0_24]) ).
cnf(c_0_63,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_52,c_0_36]),c_0_16]),c_0_6]),c_0_54]),c_0_55]),c_0_56]) ).
cnf(c_0_64,plain,
commutator(multiply(X1,X2),inverse(X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_57]),c_0_31]) ).
cnf(c_0_65,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(spm,[status(thm)],[c_0_24,c_0_58]),c_0_6]),c_0_59]),c_0_60]),c_0_20]),c_0_61]),c_0_31]),c_0_62]) ).
cnf(c_0_66,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_67,hypothesis,
commutator(multiply(X1,multiply(X2,X3)),X3) = commutator(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_63,c_0_6]) ).
cnf(c_0_68,plain,
commutator(X1,multiply(X2,X1)) = commutator(X1,X2),
inference(rw,[status(thm)],[c_0_64,c_0_62]) ).
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_65,c_0_66]),c_0_62]),c_0_62]) ).
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_67,c_0_6]) ).
cnf(c_0_72,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_73,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_45,c_0_24]),c_0_28]),c_0_32]),c_0_35]) ).
cnf(c_0_74,plain,
commutator(X1,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_26]),c_0_8]),c_0_7]) ).
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,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_68]),c_0_6]) ).
cnf(c_0_77,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_78,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_79,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_80,hypothesis,
commutator(multiply(X1,X2),commutator(X3,multiply(X2,X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_81,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_72]),c_0_28]) ).
cnf(c_0_82,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_76]),c_0_6]),c_0_6]),c_0_44]),c_0_60]),c_0_77]),c_0_69]) ).
cnf(c_0_83,hypothesis,
commutator(multiply(X1,X2),commutator(multiply(X2,X1),X3)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_73]),c_0_30]) ).
cnf(c_0_84,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_62,c_0_78]),c_0_62]),c_0_13]) ).
cnf(c_0_85,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_62]),c_0_79]) ).
cnf(c_0_86,hypothesis,
multiply(commutator(X1,multiply(X2,X3)),multiply(X3,X2)) = multiply(X3,multiply(X2,commutator(X1,multiply(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_80]),c_0_12]),c_0_6]) ).
cnf(c_0_87,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_52,c_0_16]),c_0_13]),c_0_24]),c_0_39]) ).
cnf(c_0_88,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_89,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_90,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(spm,[status(thm)],[c_0_36,c_0_73]),c_0_12]),c_0_6]),c_0_6]) ).
cnf(c_0_91,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_92,hypothesis,
commutator(multiply(X1,X1),commutator(X2,X3)) = identity,
inference(rw,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_93,plain,
commutator(inverse(X1),X1) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_19]),c_0_7]) ).
cnf(c_0_94,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_95,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(spm,[status(thm)],[c_0_36,c_0_83]),c_0_12]),c_0_6]) ).
cnf(c_0_96,plain,
commutator(multiply(inverse(multiply(X1,X2)),X3),X2) = commutator(multiply(inverse(X1),X3),X2),
inference(spm,[status(thm)],[c_0_45,c_0_20]) ).
cnf(c_0_97,hypothesis,
commutator(X1,multiply(commutator(X2,multiply(X1,X3)),X3)) = commutator(X1,multiply(X3,commutator(X2,multiply(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_44]),c_0_6]),c_0_32]) ).
cnf(c_0_98,plain,
commutator(X1,inverse(X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_14]) ).
cnf(c_0_99,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_61,c_0_85]),c_0_13]),c_0_6]),c_0_6]),c_0_60]),c_0_20]),c_0_77]),c_0_62]) ).
cnf(c_0_100,hypothesis,
multiply(commutator(X1,multiply(X2,X3)),commutator(X3,X2)) = multiply(commutator(X3,X2),commutator(X1,multiply(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_86]),c_0_24]),c_0_77]) ).
cnf(c_0_101,hypothesis,
multiply(X1,inverse(multiply(X2,commutator(X2,X1)))) = multiply(inverse(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_87]),c_0_88]),c_0_47]) ).
cnf(c_0_102,plain,
commutator(multiply(X1,X1),multiply(X1,X2)) = commutator(multiply(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_32]),c_0_82]) ).
cnf(c_0_103,plain,
commutator(X1,multiply(X2,multiply(X3,X1))) = commutator(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_68,c_0_6]) ).
cnf(c_0_104,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_89]) ).
cnf(c_0_105,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_90]),c_0_6]),c_0_6]),c_0_60]),c_0_91]),c_0_67]) ).
cnf(c_0_106,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_92]),c_0_26]),c_0_28]) ).
cnf(c_0_107,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_84,c_0_6]),c_0_6]) ).
cnf(c_0_108,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_66]),c_0_25]),c_0_6]),c_0_6]),c_0_6]),c_0_62]),c_0_67]) ).
cnf(c_0_109,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_67,c_0_17]),c_0_62]),c_0_62]) ).
cnf(c_0_110,hypothesis,
commutator(inverse(X1),commutator(X1,X2)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_93]),c_0_30]) ).
cnf(c_0_111,hypothesis,
commutator(multiply(X1,multiply(X2,X3)),X2) = commutator(multiply(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_22]),c_0_13]) ).
cnf(c_0_112,hypothesis,
commutator(multiply(X1,commutator(multiply(X2,X1),X3)),X2) = commutator(X1,multiply(commutator(multiply(X2,X1),X3),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_47]),c_0_6]),c_0_94]) ).
cnf(c_0_113,hypothesis,
commutator(X1,multiply(commutator(multiply(X2,X1),X3),X2)) = commutator(X1,multiply(X2,commutator(multiply(X2,X1),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_95]),c_0_32]) ).
cnf(c_0_114,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X2,X1)) = inverse(multiply(commutator(X1,X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_24]),c_0_6]),c_0_88]) ).
cnf(c_0_115,hypothesis,
commutator(X1,multiply(inverse(multiply(X1,X2)),X3)) = commutator(X1,multiply(inverse(X2),X3)),
inference(spm,[status(thm)],[c_0_84,c_0_60]) ).
cnf(c_0_116,hypothesis,
commutator(multiply(inverse(multiply(X1,X2)),X3),X1) = commutator(multiply(inverse(X2),X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_78]),c_0_96]),c_0_20]) ).
cnf(c_0_117,hypothesis,
commutator(multiply(X1,commutator(X2,multiply(X1,X3))),X3) = commutator(X1,multiply(X3,commutator(X2,multiply(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_86]),c_0_94]),c_0_97]) ).
cnf(c_0_118,hypothesis,
commutator(X1,commutator(inverse(X1),X2)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_98]),c_0_30]) ).
cnf(c_0_119,hypothesis,
multiply(commutator(X1,X2),commutator(X3,multiply(X2,X1))) = commutator(multiply(X1,X3),multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_68]),c_0_6]),c_0_36]),c_0_100]) ).
cnf(c_0_120,hypothesis,
commutator(multiply(X1,commutator(X1,X2)),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_63,c_0_101]),c_0_62]),c_0_62]),c_0_56]),c_0_63]) ).
cnf(c_0_121,plain,
commutator(multiply(inverse(X1),X2),multiply(X1,X1)) = commutator(X2,multiply(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_17]),c_0_87]),c_0_87]) ).
cnf(c_0_122,hypothesis,
multiply(X1,commutator(X2,X1)) = multiply(X2,multiply(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_52]),c_0_31]),c_0_44]),c_0_42]),c_0_6]) ).
cnf(c_0_123,plain,
commutator(multiply(X1,X2),multiply(X2,X2)) = commutator(X1,multiply(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_16]),c_0_62]),c_0_62]) ).
cnf(c_0_124,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_66]),c_0_13]),c_0_6]),c_0_87]),c_0_103]) ).
cnf(c_0_125,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_104,c_0_105]),c_0_106]),c_0_12]) ).
cnf(c_0_126,plain,
multiply(X1,multiply(inverse(multiply(X2,multiply(X3,X1))),X4)) = multiply(inverse(multiply(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_51,c_0_6]) ).
cnf(c_0_127,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_107,c_0_108]),c_0_59]),c_0_6]),c_0_61]),c_0_109]),c_0_31]) ).
cnf(c_0_128,hypothesis,
commutator(X1,commutator(X2,inverse(X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_110]),c_0_26]),c_0_28]) ).
cnf(c_0_129,hypothesis,
commutator(multiply(commutator(multiply(X1,X2),X3),X2),X1) = commutator(X2,multiply(X1,commutator(multiply(X1,X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_47]),c_0_6]),c_0_34]),c_0_112]),c_0_113]) ).
cnf(c_0_130,hypothesis,
commutator(multiply(commutator(multiply(X1,X2),X3),X4),X1) = commutator(multiply(commutator(X2,X3),X4),X1),
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_107,c_0_114]),c_0_62]),c_0_6]),c_0_115]),c_0_114]),c_0_62]) ).
cnf(c_0_131,hypothesis,
commutator(multiply(X1,multiply(X1,X2)),commutator(X3,X4)) = commutator(X2,commutator(X3,X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_92]),c_0_6]),c_0_12]),c_0_12]) ).
cnf(c_0_132,hypothesis,
commutator(multiply(X1,commutator(X2,X3)),multiply(X1,X2)) = commutator(X1,multiply(X2,commutator(X3,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_21]),c_0_62]),c_0_87]),c_0_21]),c_0_62]),c_0_88]),c_0_44]),c_0_87]) ).
cnf(c_0_133,hypothesis,
multiply(commutator(inverse(X1),X2),X1) = multiply(X1,commutator(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_118]),c_0_12]) ).
cnf(c_0_134,hypothesis,
commutator(multiply(X1,X2),multiply(X2,inverse(X1))) = commutator(multiply(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_62]),c_0_82]),c_0_36]) ).
cnf(c_0_135,hypothesis,
commutator(multiply(X1,commutator(X1,X2)),multiply(X2,X2)) = commutator(X1,multiply(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_87]),c_0_13]),c_0_123]) ).
cnf(c_0_136,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_124,c_0_125]),c_0_126]),c_0_61]),c_0_127]) ).
cnf(c_0_137,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_6,c_0_36]),c_0_6]),c_0_6]) ).
cnf(c_0_138,hypothesis,
commutator(multiply(X1,commutator(multiply(X1,X2),X3)),X2) = commutator(X1,multiply(X2,commutator(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_87]),c_0_127]) ).
cnf(c_0_139,hypothesis,
multiply(commutator(X1,inverse(X2)),X2) = multiply(X2,commutator(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_128]),c_0_12]) ).
cnf(c_0_140,hypothesis,
commutator(X1,multiply(X2,commutator(multiply(X2,X1),X3))) = commutator(multiply(X1,commutator(X1,X3)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130]),c_0_47]) ).
cnf(c_0_141,hypothesis,
commutator(multiply(inverse(X1),X2),commutator(X3,X4)) = commutator(multiply(X1,X2),commutator(X3,X4)),
inference(spm,[status(thm)],[c_0_131,c_0_9]) ).
cnf(c_0_142,hypothesis,
commutator(multiply(commutator(X1,X2),X3),multiply(X1,X3)) = commutator(X3,multiply(X1,commutator(X2,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_17]),c_0_88]),c_0_62]),c_0_62]),c_0_62]),c_0_88]),c_0_133]),c_0_87]),c_0_62]),c_0_62]) ).
cnf(c_0_143,hypothesis,
commutator(multiply(X1,X2),multiply(inverse(X1),X2)) = commutator(X1,multiply(X2,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_134,c_0_101]),c_0_17]),c_0_36]),c_0_62]),c_0_62]),c_0_135]) ).
cnf(c_0_144,hypothesis,
commutator(multiply(commutator(X1,multiply(X2,X2)),X3),X4) = commutator(X3,X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_136]),c_0_48]),c_0_78]),c_0_136]) ).
cnf(c_0_145,hypothesis,
commutator(multiply(inverse(X1),X2),multiply(X1,X2)) = commutator(multiply(X2,X2),X1),
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_134,c_0_17]),c_0_13]),c_0_87]),c_0_17]),c_0_62]),c_0_62]) ).
cnf(c_0_146,plain,
multiply(X1,multiply(X2,commutator(multiply(X2,X2),X1))) = multiply(X2,multiply(X1,commutator(X2,X1))),
inference(spm,[status(thm)],[c_0_137,c_0_82]) ).
cnf(c_0_147,hypothesis,
commutator(multiply(X1,commutator(X1,X2)),X3) = commutator(X1,multiply(X3,commutator(X3,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_17]),c_0_87]),c_0_88]),c_0_62]),c_0_62]),c_0_129]),c_0_88]),c_0_139]),c_0_62]),c_0_62]),c_0_62]),c_0_140]) ).
cnf(c_0_148,plain,
inverse(multiply(commutator(X1,X2),commutator(X3,X4))) = multiply(commutator(X4,X3),commutator(X2,X1)),
inference(spm,[status(thm)],[c_0_88,c_0_31]) ).
cnf(c_0_149,hypothesis,
commutator(multiply(X1,inverse(X2)),commutator(X3,X4)) = commutator(X3,commutator(X4,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_16]),c_0_87]),c_0_28]) ).
cnf(c_0_150,hypothesis,
commutator(X1,commutator(X2,multiply(inverse(X3),X4))) = commutator(X1,commutator(X2,multiply(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_141]),c_0_31]),c_0_28]),c_0_28]) ).
cnf(c_0_151,hypothesis,
commutator(X1,multiply(X2,multiply(X3,commutator(X2,X3)))) = commutator(X1,multiply(X3,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_142,c_0_143]),c_0_6]),c_0_144]),c_0_103]),c_0_145]),c_0_6]),c_0_146]) ).
cnf(c_0_152,hypothesis,
commutator(multiply(X1,commutator(X1,X2)),multiply(X2,X3)) = commutator(X1,multiply(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_34]),c_0_6]),c_0_36]) ).
cnf(c_0_153,hypothesis,
commutator(multiply(X1,commutator(X1,X2)),multiply(X3,X2)) = multiply(commutator(X1,X3),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_99,c_0_17]),c_0_87]),c_0_87]),c_0_87]),c_0_87]) ).
cnf(c_0_154,hypothesis,
commutator(multiply(X1,commutator(X2,X1)),multiply(X2,X3)) = multiply(commutator(X1,X2),commutator(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_99]),c_0_148]) ).
cnf(c_0_155,hypothesis,
commutator(X1,commutator(X2,multiply(X3,X4))) = commutator(multiply(X4,X3),commutator(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_13]),c_0_150]) ).
cnf(c_0_156,hypothesis,
multiply(commutator(X1,X2),commutator(X1,X3)) = commutator(X1,multiply(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_6]),c_0_47]),c_0_36]),c_0_153]) ).
cnf(c_0_157,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_99,c_0_9]),c_0_87]),c_0_87]) ).
cnf(c_0_158,hypothesis,
multiply(commutator(X1,X2),commutator(X2,multiply(X1,X3))) = commutator(multiply(X2,commutator(X2,X1)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_9]),c_0_87]),c_0_62]) ).
cnf(c_0_159,hypothesis,
commutator(multiply(X1,commutator(X1,X2)),commutator(X3,X4)) = commutator(X3,commutator(X4,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_70]),c_0_6]),c_0_14]),c_0_12]) ).
cnf(c_0_160,hypothesis,
commutator(X1,commutator(X2,commutator(X1,X3))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_35]),c_0_30]),c_0_28]) ).
cnf(c_0_161,negated_conjecture,
multiply(a,commutator(b,c)) != multiply(commutator(b,c),a),
inference(fof_simplification,[status(thm)],[prove_center]) ).
cnf(c_0_162,hypothesis,
commutator(X1,commutator(X2,X3)) = identity,
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_61,c_0_156]),c_0_31]),c_0_157]),c_0_158]),c_0_159]),c_0_28]),c_0_160]) ).
cnf(c_0_163,negated_conjecture,
multiply(a,commutator(b,c)) != multiply(commutator(b,c),a),
c_0_161 ).
cnf(c_0_164,hypothesis,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_162]),c_0_12]),c_0_162]),c_0_12]) ).
cnf(c_0_165,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP024-5 : TPTP v8.2.0. Released v2.2.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.38 % Computer : n019.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun May 19 05:15:08 EDT 2024
% 0.14/0.38 % CPUTime :
% 0.24/0.50 Running first-order theorem proving
% 0.24/0.50 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 59.05/7.97 # Version: 3.1.0
% 59.05/7.97 # Preprocessing class: FSSSSMSSSSSNFFN.
% 59.05/7.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.05/7.97 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 59.05/7.97 # Starting new_bool_3 with 300s (1) cores
% 59.05/7.97 # Starting new_bool_1 with 300s (1) cores
% 59.05/7.97 # Starting sh5l with 300s (1) cores
% 59.05/7.97 # sh5l with pid 32407 completed with status 0
% 59.05/7.97 # Result found by sh5l
% 59.05/7.97 # Preprocessing class: FSSSSMSSSSSNFFN.
% 59.05/7.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.05/7.97 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 59.05/7.97 # Starting new_bool_3 with 300s (1) cores
% 59.05/7.97 # Starting new_bool_1 with 300s (1) cores
% 59.05/7.97 # Starting sh5l with 300s (1) cores
% 59.05/7.97 # SinE strategy is gf500_gu_R04_F100_L20000
% 59.05/7.97 # Search class: FUUPM-FFSF21-MFFFFFNN
% 59.05/7.97 # Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 59.05/7.97 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 135s (1) cores
% 59.05/7.97 # H----_047_C09_12_F1_AE_ND_CS_SP_S2S with pid 32413 completed with status 0
% 59.05/7.97 # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S2S
% 59.05/7.97 # Preprocessing class: FSSSSMSSSSSNFFN.
% 59.05/7.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.05/7.97 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 59.05/7.97 # Starting new_bool_3 with 300s (1) cores
% 59.05/7.97 # Starting new_bool_1 with 300s (1) cores
% 59.05/7.97 # Starting sh5l with 300s (1) cores
% 59.05/7.97 # SinE strategy is gf500_gu_R04_F100_L20000
% 59.05/7.97 # Search class: FUUPM-FFSF21-MFFFFFNN
% 59.05/7.97 # Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 59.05/7.97 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 135s (1) cores
% 59.05/7.97 # Preprocessing time : 0.001 s
% 59.05/7.97 # Presaturation interreduction done
% 59.05/7.97
% 59.05/7.97 # Proof found!
% 59.05/7.97 # SZS status Unsatisfiable
% 59.05/7.97 # SZS output start CNFRefutation
% See solution above
% 59.05/7.97 # Parsed axioms : 6
% 59.05/7.97 # Removed by relevancy pruning/SinE : 0
% 59.05/7.97 # Initial clauses : 6
% 59.05/7.97 # Removed in clause preprocessing : 0
% 59.05/7.97 # Initial clauses in saturation : 6
% 59.05/7.97 # Processed clauses : 10469
% 59.05/7.97 # ...of these trivial : 3718
% 59.05/7.97 # ...subsumed : 5932
% 59.05/7.97 # ...remaining for further processing : 819
% 59.05/7.97 # Other redundant clauses eliminated : 0
% 59.05/7.97 # Clauses deleted for lack of memory : 0
% 59.05/7.97 # Backward-subsumed : 0
% 59.05/7.97 # Backward-rewritten : 577
% 59.05/7.97 # Generated clauses : 434760
% 59.05/7.97 # ...of the previous two non-redundant : 244479
% 59.05/7.97 # ...aggressively subsumed : 0
% 59.05/7.97 # Contextual simplify-reflections : 0
% 59.05/7.97 # Paramodulations : 434760
% 59.05/7.97 # Factorizations : 0
% 59.05/7.97 # NegExts : 0
% 59.05/7.97 # Equation resolutions : 0
% 59.05/7.97 # Disequality decompositions : 0
% 59.05/7.97 # Total rewrite steps : 1423624
% 59.05/7.97 # ...of those cached : 1124092
% 59.05/7.97 # Propositional unsat checks : 0
% 59.05/7.97 # Propositional check models : 0
% 59.05/7.97 # Propositional check unsatisfiable : 0
% 59.05/7.97 # Propositional clauses : 0
% 59.05/7.97 # Propositional clauses after purity: 0
% 59.05/7.97 # Propositional unsat core size : 0
% 59.05/7.97 # Propositional preprocessing time : 0.000
% 59.05/7.97 # Propositional encoding time : 0.000
% 59.05/7.97 # Propositional solver time : 0.000
% 59.05/7.97 # Success case prop preproc time : 0.000
% 59.05/7.97 # Success case prop encoding time : 0.000
% 59.05/7.97 # Success case prop solver time : 0.000
% 59.05/7.97 # Current number of processed clauses : 236
% 59.05/7.97 # Positive orientable unit clauses : 215
% 59.05/7.97 # Positive unorientable unit clauses: 21
% 59.05/7.97 # Negative unit clauses : 0
% 59.05/7.97 # Non-unit-clauses : 0
% 59.05/7.97 # Current number of unprocessed clauses: 231126
% 59.05/7.97 # ...number of literals in the above : 231126
% 59.05/7.97 # Current number of archived formulas : 0
% 59.05/7.97 # Current number of archived clauses : 583
% 59.05/7.97 # Clause-clause subsumption calls (NU) : 0
% 59.05/7.97 # Rec. Clause-clause subsumption calls : 0
% 59.05/7.97 # Non-unit clause-clause subsumptions : 0
% 59.05/7.97 # Unit Clause-clause subsumption calls : 2417
% 59.05/7.97 # Rewrite failures with RHS unbound : 0
% 59.05/7.97 # BW rewrite match attempts : 10052
% 59.05/7.97 # BW rewrite match successes : 2287
% 59.05/7.97 # Condensation attempts : 0
% 59.05/7.97 # Condensation successes : 0
% 59.05/7.97 # Termbank termtop insertions : 6619907
% 59.05/7.97 # Search garbage collected termcells : 2
% 59.05/7.97
% 59.05/7.97 # -------------------------------------------------
% 59.05/7.97 # User time : 7.036 s
% 59.05/7.97 # System time : 0.290 s
% 59.05/7.97 # Total time : 7.326 s
% 59.05/7.97 # Maximum resident set size: 1636 pages
% 59.05/7.97
% 59.05/7.97 # -------------------------------------------------
% 59.05/7.97 # User time : 7.037 s
% 59.05/7.97 # System time : 0.292 s
% 59.05/7.97 # Total time : 7.329 s
% 59.05/7.97 # Maximum resident set size: 1692 pages
% 59.05/7.97 % E---3.1 exiting
% 59.05/7.98 % E exiting
%------------------------------------------------------------------------------