%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:37:24 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 8 RR)
% Number of literals : 39 ( 38 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 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 : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_commutator,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator) ).
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(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(commutator,axiom,
commutator(X1,X2) = multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_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(c_0_8,negated_conjecture,
commutator(commutator(a,b),b) != identity,
inference(fof_simplification,[status(thm)],[prove_commutator]) ).
cnf(c_0_9,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_10,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_11,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_12,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse ).
cnf(c_0_13,negated_conjecture,
commutator(commutator(a,b),b) != identity,
c_0_8 ).
cnf(c_0_14,axiom,
commutator(X1,X2) = multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))),
commutator ).
cnf(c_0_15,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_17,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_18,hypothesis,
multiply(X1,multiply(X1,X1)) = identity,
x_cubed_is_identity ).
cnf(c_0_19,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_13,c_0_14]),c_0_14]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_11]) ).
cnf(c_0_22,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_17]) ).
cnf(c_0_23,hypothesis,
inverse(X1) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_18]),c_0_17]) ).
cnf(c_0_24,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_19,c_0_9]),c_0_9]),c_0_9]) ).
cnf(c_0_25,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_26,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_27,hypothesis,
inverse(multiply(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(inverse(multiply(a,multiply(b,inverse(multiply(b,a))))),multiply(b,b))))))))) != identity,
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_25]),c_0_23]),c_0_23]),c_0_23]),c_0_9]),c_0_9]) ).
cnf(c_0_29,plain,
inverse(multiply(X1,multiply(X2,inverse(X3)))) = multiply(X3,inverse(multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_9]) ).
cnf(c_0_30,hypothesis,
multiply(inverse(X1),multiply(X2,X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_31,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X2))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_18]),c_0_11]),c_0_9]) ).
cnf(c_0_32,hypothesis,
inverse(multiply(X1,multiply(X1,X2))) = multiply(inverse(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_9]) ).
cnf(c_0_33,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_20]),c_0_22]) ).
cnf(c_0_34,hypothesis,
multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2))))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_9]),c_0_9]) ).
cnf(c_0_35,negated_conjecture,
multiply(a,multiply(b,multiply(a,multiply(a,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(spm,[status(thm)],[c_0_28,c_0_29]),c_0_9]),c_0_9]),c_0_9]),c_0_30]),c_0_31]) ).
cnf(c_0_36,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_32,c_0_33]),c_0_25]),c_0_22]),c_0_25]),c_0_9]) ).
cnf(c_0_37,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_9,c_0_34]),c_0_9]),c_0_9]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n001.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 20 19:58:42 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 0.19/0.49 % Version: 3.5.1
% 0.19/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.49 % Starting sh5l with 300s (1) cores
% 0.19/0.49 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1259743 completed with status 0
% 0.19/0.49 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.19/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.49 % No SInE strategy applied
% 0.19/0.49 % Search class: FUUPM-FFSF21-DFFFFFNN
% 0.19/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.19/0.49 % Starting G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with 136s (1) cores
% 0.19/0.49 % Starting new_bool_3 with 136s (1) cores
% 0.19/0.49 % Starting new_bool_1 with 136s (1) cores
% 0.19/0.49 % G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with pid 1259750 completed with status 0
% 0.19/0.49 % Result found by G-E--_201_C45_F1_AE_CS_SP_PI_S0Y
% 0.19/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.49 % No SInE strategy applied
% 0.19/0.49 % Search class: FUUPM-FFSF21-DFFFFFNN
% 0.19/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.19/0.49 % Starting G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with 136s (1) cores
% 0.19/0.49 % Preprocessing time : 0.001 s
% 0.19/0.49
% 0.19/0.49 % Proof found!
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49 % SZS output start CNFRefutation
% See solution above
% 0.19/0.49 % Parsed axioms : 8
% 0.19/0.49 % Removed by relevancy pruning/SinE : 0
% 0.19/0.49 % Initial clauses : 8
% 0.19/0.49 % Removed in clause preprocessing : 1
% 0.19/0.49 % Initial clauses in saturation : 7
% 0.19/0.49 % Processed clauses : 271
% 0.19/0.49 % ...of these trivial : 68
% 0.19/0.49 % ...subsumed : 147
% 0.19/0.49 % ...remaining for further processing : 56
% 0.19/0.49 % Other redundant clauses eliminated : 0
% 0.19/0.49 % Clauses deleted for lack of memory : 0
% 0.19/0.49 % Backward-subsumed : 0
% 0.19/0.49 % Backward-rewritten : 7
% 0.19/0.49 % Generated clauses : 1857
% 0.19/0.49 % ...of the previous two non-redundant : 675
% 0.19/0.49 % ...aggressively subsumed : 0
% 0.19/0.49 % Contextual simplify-reflections : 0
% 0.19/0.49 % Paramodulations : 1857
% 0.19/0.49 % Factorizations : 0
% 0.19/0.49 % NegExts : 0
% 0.19/0.49 % Equation resolutions : 0
% 0.19/0.49 % Disequality decompositions : 0
% 0.19/0.49 % Total rewrite steps : 5625
% 0.19/0.49 % ...of those cached : 4463
% 0.19/0.49 % Propositional unsat checks : 0
% 0.19/0.49 % Propositional check models : 0
% 0.19/0.49 % Propositional check unsatisfiable : 0
% 0.19/0.49 % Propositional clauses : 0
% 0.19/0.49 % Propositional clauses after purity: 0
% 0.19/0.49 % Propositional unsat core size : 0
% 0.19/0.49 % Propositional preprocessing time : 0.000
% 0.19/0.49 % Propositional encoding time : 0.000
% 0.19/0.49 % Propositional solver time : 0.000
% 0.19/0.49 % Success case prop preproc time : 0.000
% 0.19/0.49 % Success case prop encoding time : 0.000
% 0.19/0.49 % Success case prop solver time : 0.000
% 0.19/0.49 % Current number of processed clauses : 49
% 0.19/0.49 % Positive orientable unit clauses : 33
% 0.19/0.49 % Positive unorientable unit clauses: 3
% 0.19/0.49 % Negative unit clauses : 13
% 0.19/0.49 % Non-unit-clauses : 0
% 0.19/0.49 % Current number of unprocessed clauses: 377
% 0.19/0.49 % ...number of literals in the above : 377
% 0.19/0.49 % Current number of archived formulas : 0
% 0.19/0.49 % Current number of archived clauses : 8
% 0.19/0.49 % Clause-clause subsumption calls (NU) : 0
% 0.19/0.49 % Rec. Clause-clause subsumption calls : 0
% 0.19/0.49 % Non-unit clause-clause subsumptions : 0
% 0.19/0.49 % Unit Clause-clause subsumption calls : 47
% 0.19/0.49 % Rewrite failures with RHS unbound : 0
% 0.19/0.49 % BW rewrite match attempts : 339
% 0.19/0.49 % BW rewrite match successes : 24
% 0.19/0.49 % Condensation attempts : 0
% 0.19/0.49 % Condensation successes : 0
% 0.19/0.49 % Termbank termtop insertions : 21532
% 0.19/0.49 % Search garbage collected termcells : 2
% 0.19/0.49
% 0.19/0.49 % -------------------------------------------------
% 0.19/0.49 % User time : 0.023 s
% 0.19/0.49 % System time : 0.004 s
% 0.19/0.49 % Total time : 0.026 s
% 0.19/0.49 % Maximum resident set size: 3636 pages
% 0.19/0.49
% 0.19/0.49 % -------------------------------------------------
% 0.19/0.49 % User time : 0.087 s
% 0.19/0.49 % System time : 0.019 s
% 0.19/0.49 % Total time : 0.105 s
% 0.19/0.49 % Maximum resident set size: 4608 pages
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------