%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:41:19 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 7 RR)
% Number of literals : 42 ( 41 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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 : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_cubed_is_identity,hypothesis,
multiply(X1,multiply(X1,X1)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
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(prove_commutator,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator) ).
cnf(commutator,axiom,
commutator(X1,X2) = multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
cnf(c_0_6,hypothesis,
multiply(X1,multiply(X1,X1)) = identity,
x_cubed_is_identity ).
cnf(c_0_7,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_8,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_9,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_10,hypothesis,
multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2))))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_11,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_12,hypothesis,
multiply(X1,inverse(X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_13,hypothesis,
multiply(inverse(X1),identity) = inverse(X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_13]) ).
cnf(c_0_15,negated_conjecture,
commutator(commutator(a,b),b) != identity,
inference(fof_simplification,[status(thm)],[prove_commutator]) ).
cnf(c_0_16,hypothesis,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_17,hypothesis,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
commutator(commutator(a,b),b) != identity,
c_0_15 ).
cnf(c_0_19,axiom,
commutator(X1,X2) = multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))),
commutator ).
cnf(c_0_20,hypothesis,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_16]),c_0_17]) ).
cnf(c_0_21,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X2))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_9]),c_0_7]) ).
cnf(c_0_22,hypothesis,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_12]),c_0_9]) ).
cnf(c_0_23,hypothesis,
inverse(X1) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_6]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
multiply(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b)))) != identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_25,hypothesis,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_26,hypothesis,
multiply(X1,multiply(X1,inverse(X2))) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_27,hypothesis,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_28,hypothesis,
inverse(multiply(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))))) != identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_7]),c_0_7]),c_0_7]) ).
cnf(c_0_30,hypothesis,
multiply(inverse(X1),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_7,c_0_25]) ).
cnf(c_0_31,hypothesis,
multiply(X1,multiply(X1,multiply(X2,X2))) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_32,hypothesis,
inverse(multiply(X1,multiply(X2,inverse(X3)))) = multiply(X3,inverse(multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_27,c_0_7]) ).
cnf(c_0_33,hypothesis,
multiply(inverse(X1),multiply(X2,X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_34,hypothesis,
inverse(multiply(X1,multiply(X1,X2))) = multiply(inverse(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_7]) ).
cnf(c_0_35,hypothesis,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_20]),c_0_14]) ).
cnf(c_0_36,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_37,negated_conjecture,
multiply(a,multiply(b,multiply(inverse(multiply(b,a)),multiply(b,multiply(b,multiply(a,inverse(multiply(b,multiply(a,b))))))))) != 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_23]),c_0_23]),c_0_7]),c_0_31]),c_0_32]),c_0_7]),c_0_23]),c_0_7]),c_0_7]),c_0_33]) ).
cnf(c_0_38,hypothesis,
multiply(X1,multiply(X2,X1)) = inverse(multiply(X2,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_34,c_0_35]),c_0_25]),c_0_14]),c_0_25]),c_0_7]) ).
cnf(c_0_39,hypothesis,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_36,c_0_22]) ).
cnf(c_0_40,hypothesis,
multiply(X1,multiply(X2,multiply(X3,multiply(X1,multiply(X2,multiply(X3,multiply(X1,multiply(X2,X3)))))))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_7]),c_0_7]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_23]),c_0_7]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:53:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.44 % Version: 3.5.1
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.44 % Starting sh5l with 300s (1) cores
% 0.13/0.44 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3372900 completed with status 0
% 0.13/0.44 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.44 % No SInE strategy applied
% 0.13/0.44 % Search class: FUUPM-FFSF21-DFFFFFNN
% 0.13/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.44 % Starting G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with 136s (1) cores
% 0.13/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.44 % G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with pid 3372908 completed with status 0
% 0.13/0.44 % Result found by G-E--_201_C45_F1_AE_CS_SP_PI_S0Y
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.44 % No SInE strategy applied
% 0.13/0.44 % Search class: FUUPM-FFSF21-DFFFFFNN
% 0.13/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.44 % Starting G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with 136s (1) cores
% 0.13/0.44 % Preprocessing time : 0.001 s
% 0.13/0.44
% 0.13/0.44 % Proof found!
% 0.13/0.44 % SZS status Unsatisfiable
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.13/0.44 % Parsed axioms : 6
% 0.13/0.44 % Removed by relevancy pruning/SinE : 0
% 0.13/0.44 % Initial clauses : 6
% 0.13/0.44 % Removed in clause preprocessing : 1
% 0.13/0.44 % Initial clauses in saturation : 5
% 0.13/0.44 % Processed clauses : 271
% 0.13/0.44 % ...of these trivial : 82
% 0.13/0.44 % ...subsumed : 135
% 0.13/0.44 % ...remaining for further processing : 54
% 0.13/0.44 % Other redundant clauses eliminated : 0
% 0.13/0.44 % Clauses deleted for lack of memory : 0
% 0.13/0.44 % Backward-subsumed : 0
% 0.13/0.44 % Backward-rewritten : 8
% 0.13/0.44 % Generated clauses : 1733
% 0.13/0.44 % ...of the previous two non-redundant : 657
% 0.13/0.44 % ...aggressively subsumed : 0
% 0.13/0.44 % Contextual simplify-reflections : 0
% 0.13/0.44 % Paramodulations : 1733
% 0.13/0.44 % Factorizations : 0
% 0.13/0.44 % NegExts : 0
% 0.13/0.44 % Equation resolutions : 0
% 0.13/0.44 % Disequality decompositions : 0
% 0.13/0.44 % Total rewrite steps : 5093
% 0.13/0.44 % ...of those cached : 4001
% 0.13/0.44 % Propositional unsat checks : 0
% 0.13/0.44 % Propositional check models : 0
% 0.13/0.44 % Propositional check unsatisfiable : 0
% 0.13/0.44 % Propositional clauses : 0
% 0.13/0.44 % Propositional clauses after purity: 0
% 0.13/0.44 % Propositional unsat core size : 0
% 0.13/0.44 % Propositional preprocessing time : 0.000
% 0.13/0.44 % Propositional encoding time : 0.000
% 0.13/0.44 % Propositional solver time : 0.000
% 0.13/0.44 % Success case prop preproc time : 0.000
% 0.13/0.44 % Success case prop encoding time : 0.000
% 0.13/0.44 % Success case prop solver time : 0.000
% 0.13/0.44 % Current number of processed clauses : 46
% 0.13/0.44 % Positive orientable unit clauses : 32
% 0.13/0.44 % Positive unorientable unit clauses: 3
% 0.13/0.44 % Negative unit clauses : 11
% 0.13/0.44 % Non-unit-clauses : 0
% 0.13/0.44 % Current number of unprocessed clauses: 354
% 0.13/0.44 % ...number of literals in the above : 354
% 0.13/0.44 % Current number of archived formulas : 0
% 0.13/0.44 % Current number of archived clauses : 9
% 0.13/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.13/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.13/0.44 % Non-unit clause-clause subsumptions : 0
% 0.13/0.44 % Unit Clause-clause subsumption calls : 38
% 0.13/0.44 % Rewrite failures with RHS unbound : 0
% 0.13/0.44 % BW rewrite match attempts : 256
% 0.13/0.44 % BW rewrite match successes : 26
% 0.13/0.44 % Condensation attempts : 0
% 0.13/0.44 % Condensation successes : 0
% 0.13/0.44 % Termbank termtop insertions : 19958
% 0.13/0.44 % Search garbage collected termcells : 2
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.023 s
% 0.13/0.44 % System time : 0.003 s
% 0.13/0.44 % Total time : 0.025 s
% 0.13/0.44 % Maximum resident set size: 3636 pages
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.102 s
% 0.13/0.44 % System time : 0.023 s
% 0.13/0.44 % Total time : 0.125 s
% 0.13/0.44 % Maximum resident set size: 4608 pages
% 0.13/0.44 % E exiting
%------------------------------------------------------------------------------