%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP002-3 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 04:23:31 PM UTC 2026
% Result : Unsatisfiable 1.61s 1.84s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of clauses : 68 ( 68 unt; 0 nHn; 4 RR)
% Number of literals : 68 ( 67 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 124 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(x_cubed_is_identity,hypothesis,
multiply(X1,multiply(X1,X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity) ).
cnf(commutator,axiom,
commutator(X1,X2) = multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
cnf(prove_commutator,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator) ).
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(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_18,hypothesis,
multiply(X1,multiply(X1,X1)) = identity,
x_cubed_is_identity ).
cnf(c_0_19,axiom,
commutator(X1,X2) = multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))),
commutator ).
cnf(c_0_20,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_21,hypothesis,
multiply(inverse(X1),inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(X2,inverse(multiply(X2,X1)))) = commutator(X1,X2),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
commutator(X1,multiply(X2,inverse(X1))) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_6]),c_0_19]) ).
cnf(c_0_24,hypothesis,
multiply(X1,X1) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_13]) ).
cnf(c_0_25,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_26,plain,
commutator(multiply(X1,X2),inverse(X1)) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_9]),c_0_20]),c_0_6]),c_0_22]) ).
cnf(c_0_27,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_28,plain,
commutator(inverse(X1),multiply(X2,X1)) = commutator(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_29,hypothesis,
multiply(X1,multiply(X1,X2)) = multiply(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_6,c_0_24]) ).
cnf(c_0_30,hypothesis,
multiply(X1,multiply(X2,multiply(X1,X2))) = inverse(multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_24]) ).
cnf(c_0_31,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_25,c_0_25]),c_0_6]),c_0_20]) ).
cnf(c_0_32,plain,
commutator(inverse(multiply(X1,X2)),X1) = commutator(inverse(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_13]),c_0_28]) ).
cnf(c_0_33,hypothesis,
multiply(inverse(X1),multiply(X2,multiply(X1,X2))) = multiply(X1,inverse(multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
inverse(commutator(X1,X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_22]),c_0_6]),c_0_22]) ).
cnf(c_0_35,plain,
commutator(multiply(X1,X2),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_16]),c_0_13]),c_0_13]) ).
cnf(c_0_36,hypothesis,
commutator(multiply(X1,multiply(X2,X1)),inverse(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_25]),c_0_6]),c_0_9]),c_0_6]),c_0_6]),c_0_29]),c_0_20]),c_0_22]) ).
cnf(c_0_37,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_6,c_0_27]) ).
cnf(c_0_38,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_39,plain,
inverse(multiply(commutator(X1,X2),X3)) = multiply(inverse(X3),commutator(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_40,plain,
commutator(X1,inverse(multiply(X1,X2))) = commutator(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_41,plain,
commutator(multiply(X1,multiply(X2,X3)),X3) = commutator(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_35,c_0_6]) ).
cnf(c_0_42,plain,
commutator(inverse(multiply(X1,X2)),X2) = commutator(inverse(X2),inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_13]) ).
cnf(c_0_43,plain,
commutator(inverse(multiply(X1,X2)),inverse(X1)) = commutator(inverse(X2),inverse(X1)),
inference(spm,[status(thm)],[c_0_32,c_0_9]) ).
cnf(c_0_44,hypothesis,
commutator(inverse(X1),X2) = commutator(X1,inverse(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_36,c_0_37]),c_0_20]),c_0_6]),c_0_24]),c_0_25]),c_0_35]),c_0_32]) ).
cnf(c_0_45,plain,
multiply(inverse(multiply(X1,X2)),commutator(X1,X2)) = inverse(multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_20]),c_0_39]) ).
cnf(c_0_46,plain,
commutator(X1,multiply(X2,X1)) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_16]),c_0_13]),c_0_13]) ).
cnf(c_0_47,hypothesis,
commutator(multiply(X1,multiply(X2,X1)),X2) = commutator(inverse(X2),inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_24]),c_0_42]),c_0_6]) ).
cnf(c_0_48,plain,
commutator(multiply(X1,X2),X1) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_13]),c_0_44]),c_0_13]) ).
cnf(c_0_49,plain,
multiply(commutator(X1,X2),multiply(X2,X1)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_45]),c_0_13]),c_0_13]) ).
cnf(c_0_50,plain,
commutator(multiply(X1,X2),commutator(X2,X1)) = commutator(commutator(X1,X2),multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_45]),c_0_13]),c_0_34]),c_0_13]) ).
cnf(c_0_51,plain,
commutator(X1,multiply(X2,multiply(X3,X1))) = commutator(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_46,c_0_6]) ).
cnf(c_0_52,plain,
commutator(inverse(X1),multiply(X1,X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_9]),c_0_13]) ).
cnf(c_0_53,plain,
multiply(X1,multiply(inverse(multiply(X1,X2)),X2)) = commutator(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_13]),c_0_40]) ).
cnf(c_0_54,plain,
commutator(X1,inverse(X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_44]),c_0_44]),c_0_26]) ).
cnf(c_0_55,hypothesis,
commutator(multiply(X1,multiply(X2,X1)),X2) = commutator(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_44]),c_0_13]) ).
cnf(c_0_56,plain,
commutator(multiply(X1,X2),commutator(X1,X2)) = commutator(commutator(X2,X1),multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_57,plain,
commutator(multiply(X1,inverse(X2)),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_52]) ).
cnf(c_0_58,plain,
multiply(X1,multiply(inverse(multiply(X1,X2)),X2)) = commutator(X2,X1),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,hypothesis,
multiply(X1,multiply(X2,commutator(X2,X1))) = multiply(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(spm,[status(thm)],[c_0_45,c_0_55]),c_0_6]),c_0_6]),c_0_30]),c_0_13]),c_0_6]),c_0_30]),c_0_13]) ).
cnf(c_0_60,plain,
commutator(inverse(X1),inverse(multiply(X1,X2))) = commutator(inverse(X1),inverse(X2)),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_61,negated_conjecture,
commutator(commutator(a,b),b) != identity,
prove_commutator ).
cnf(c_0_62,plain,
commutator(commutator(X1,X2),X2) = commutator(X2,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(spm,[status(thm)],[c_0_56,c_0_57]),c_0_6]),c_0_7]),c_0_12]),c_0_23]),c_0_6]),c_0_7]),c_0_12]) ).
cnf(c_0_63,plain,
commutator(commutator(X1,X2),multiply(X2,X1)) = 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_58,c_0_45]),c_0_13]),c_0_6]),c_0_59]),c_0_7]),c_0_54]),c_0_56]) ).
cnf(c_0_64,plain,
commutator(X1,multiply(X1,X2)) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_44]),c_0_13]),c_0_44]),c_0_13]) ).
cnf(c_0_65,negated_conjecture,
commutator(b,commutator(b,a)) != identity,
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,plain,
commutator(X1,commutator(X1,X2)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_9]),c_0_54]),c_0_64]),c_0_62]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP002-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:14:42 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.61/1.84 % Version : CSE_E---1.7
% 1.61/1.84 % Problem : theBenchmark.p
% 1.61/1.84 % SZS status Unsatisfiable for theBenchmark.p
% 1.61/1.84 % SZS output start CNFRefutation
% See solution above
% 1.61/1.84 % Total time : 1.371s
%------------------------------------------------------------------------------