%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP402-1 : 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 : 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 12:39:33 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 17 unt; 0 nHn; 15 RR)
% Number of literals : 37 ( 36 equ; 14 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 : 61 ( 1 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(nilpotency,axiom,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nilpotency) ).
cnf(prove_commutator_is_associative,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
cnf(c_0_5,plain,
( multiply(X1,X2) != multiply(X1,X3)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[left_cancellation]) ).
cnf(c_0_6,plain,
( multiply(X1,X2) != multiply(X1,X3)
| X2 = X3 ),
c_0_5 ).
cnf(c_0_7,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
commutator ).
cnf(c_0_8,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_9,plain,
( multiply(X3,X1) != multiply(X2,X3)
| X1 = multiply(X2,commutator(X2,X3)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
( multiply(X3,multiply(X4,X1)) != multiply(X3,multiply(X4,X2))
| X1 = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_8]),c_0_8]) ).
cnf(c_0_11,axiom,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
nilpotency ).
cnf(c_0_12,plain,
multiply(X1,commutator(X1,X1)) = X1,
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,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_8,c_0_7]),c_0_8]),c_0_8]) ).
cnf(c_0_14,plain,
( multiply(X3,multiply(commutator(X4,X5),X1)) != multiply(X3,multiply(X2,commutator(X4,X5)))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
multiply(X1,multiply(commutator(X1,X1),X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X2,commutator(commutator(X1,X2),X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_7]),c_0_11]),c_0_7]) ).
cnf(c_0_17,plain,
( multiply(X3,X1) != multiply(X3,multiply(X2,commutator(X3,X3)))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( multiply(X2,multiply(X3,X1)) != multiply(X2,X3)
| X1 = commutator(commutator(X2,X3),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_19,plain,
multiply(X1,commutator(X2,X2)) = X1,
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
commutator(X1,X1) = commutator(commutator(X2,X3),X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
inference(fof_simplification,[status(thm)],[prove_commutator_is_associative]) ).
cnf(c_0_22,plain,
( multiply(X2,multiply(X3,X1)) != multiply(X2,X3)
| X1 = commutator(a,a) ),
inference(rw,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
c_0_21 ).
cnf(c_0_24,plain,
( multiply(X1,X2) != multiply(X2,X1)
| commutator(X1,X2) = commutator(a,a) ),
inference(spm,[status(thm)],[c_0_22,c_0_7]) ).
cnf(c_0_25,negated_conjecture,
commutator(a,commutator(b,c)) != commutator(a,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_11]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 % Computer : n010.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 : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Sep 20 20:12:24 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.18/0.52 % Version: 3.5.1
% 0.18/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.52 % Starting sh5l with 300s (1) cores
% 0.18/0.52 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3415252 completed with status 0
% 0.18/0.52 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.18/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.52 % No SInE strategy applied
% 0.18/0.52 % Search class: FHUPS-FFSF22-MFFFFFNN
% 0.18/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.18/0.52 % Starting G----_0008_C18_F1_SE_CS_SP_S0Y with 248s (1) cores
% 0.18/0.52 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 136s (1) cores
% 0.18/0.52 % Starting new_bool_3 with 136s (1) cores
% 0.18/0.52 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3415257 completed with status 0
% 0.18/0.52 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.18/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.52 % No SInE strategy applied
% 0.18/0.52 % Search class: FHUPS-FFSF22-MFFFFFNN
% 0.18/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.18/0.52 % Preprocessing time : 0.001 s
% 0.18/0.52
% 0.18/0.52 % Proof found!
% 0.18/0.52 % SZS status Unsatisfiable
% 0.18/0.52 % SZS output start CNFRefutation
% See solution above
% 0.18/0.52 % Parsed axioms : 6
% 0.18/0.52 % Removed by relevancy pruning/SinE : 0
% 0.18/0.52 % Initial clauses : 6
% 0.18/0.52 % Removed in clause preprocessing : 0
% 0.18/0.52 % Initial clauses in saturation : 6
% 0.18/0.52 % Processed clauses : 292
% 0.18/0.52 % ...of these trivial : 26
% 0.18/0.52 % ...subsumed : 166
% 0.18/0.52 % ...remaining for further processing : 100
% 0.18/0.52 % Other redundant clauses eliminated : 14
% 0.18/0.52 % Clauses deleted for lack of memory : 0
% 0.18/0.52 % Backward-subsumed : 3
% 0.18/0.52 % Backward-rewritten : 24
% 0.18/0.52 % Generated clauses : 3796
% 0.18/0.52 % ...of the previous two non-redundant : 3512
% 0.18/0.52 % ...aggressively subsumed : 0
% 0.18/0.52 % Contextual simplify-reflections : 0
% 0.18/0.52 % Paramodulations : 3759
% 0.18/0.52 % Factorizations : 0
% 0.18/0.52 % NegExts : 0
% 0.18/0.52 % Equation resolutions : 37
% 0.18/0.52 % Disequality decompositions : 0
% 0.18/0.52 % Total rewrite steps : 8086
% 0.18/0.52 % ...of those cached : 7239
% 0.18/0.52 % Propositional unsat checks : 0
% 0.18/0.52 % Propositional check models : 0
% 0.18/0.52 % Propositional check unsatisfiable : 0
% 0.18/0.52 % Propositional clauses : 0
% 0.18/0.52 % Propositional clauses after purity: 0
% 0.18/0.52 % Propositional unsat core size : 0
% 0.18/0.52 % Propositional preprocessing time : 0.000
% 0.18/0.52 % Propositional encoding time : 0.000
% 0.18/0.52 % Propositional solver time : 0.000
% 0.18/0.52 % Success case prop preproc time : 0.000
% 0.18/0.52 % Success case prop encoding time : 0.000
% 0.18/0.52 % Success case prop solver time : 0.000
% 0.18/0.52 % Current number of processed clauses : 73
% 0.18/0.52 % Positive orientable unit clauses : 14
% 0.18/0.52 % Positive unorientable unit clauses: 5
% 0.18/0.52 % Negative unit clauses : 2
% 0.18/0.52 % Non-unit-clauses : 52
% 0.18/0.52 % Current number of unprocessed clauses: 3146
% 0.18/0.52 % ...number of literals in the above : 6983
% 0.18/0.52 % Current number of archived formulas : 0
% 0.18/0.52 % Current number of archived clauses : 27
% 0.18/0.52 % Clause-clause subsumption calls (NU) : 1013
% 0.18/0.52 % Rec. Clause-clause subsumption calls : 1013
% 0.18/0.52 % Non-unit clause-clause subsumptions : 131
% 0.18/0.52 % Unit Clause-clause subsumption calls : 28
% 0.18/0.52 % Rewrite failures with RHS unbound : 0
% 0.18/0.52 % BW rewrite match attempts : 233
% 0.18/0.52 % BW rewrite match successes : 42
% 0.18/0.52 % Condensation attempts : 0
% 0.18/0.52 % Condensation successes : 0
% 0.18/0.52 % Termbank termtop insertions : 56521
% 0.18/0.52 % Search garbage collected termcells : 8
% 0.18/0.52
% 0.18/0.52 % -------------------------------------------------
% 0.18/0.52 % User time : 0.070 s
% 0.18/0.52 % System time : 0.004 s
% 0.18/0.52 % Total time : 0.074 s
% 0.18/0.52 % Maximum resident set size: 3636 pages
% 0.18/0.52
% 0.18/0.52 % -------------------------------------------------
% 0.18/0.52 % User time : 0.345 s
% 0.18/0.52 % System time : 0.025 s
% 0.18/0.52 % Total time : 0.370 s
% 0.18/0.52 % Maximum resident set size: 4864 pages
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------