%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP004-2 : 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 : n003.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 12:37:25 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 9 unt; 0 nHn; 22 RR)
% Number of literals : 60 ( 0 equ; 36 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity2) ).
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity1) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(prove_right_inverse,negated_conjecture,
~ product(a,inverse(a),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_inverse) ).
cnf(c_0_5,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity2]) ).
cnf(c_0_6,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity1]) ).
cnf(c_0_7,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_5 ).
cnf(c_0_8,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_9,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_6 ).
cnf(c_0_10,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_11,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ~ product(inverse(inverse(X1)),identity,X2)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_14,plain,
( ~ product(X1,X3,X2)
| product(inverse(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_15,plain,
( ~ product(inverse(X1),X2,identity)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( ~ product(X1,identity,X2)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_17,plain,
( ~ product(X4,X1,inverse(X2))
| ~ product(inverse(X4),identity,X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_18,plain,
( ~ product(identity,X2,X1)
| product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_19,plain,
( ~ product(X1,X2,identity)
| product(identity,inverse(X1),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,plain,
( ~ product(identity,X1,inverse(X2))
| product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_8]) ).
cnf(c_0_21,plain,
( ~ product(X2,X1,identity)
| product(identity,X1,inverse(X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
~ product(a,inverse(a),identity),
inference(fof_simplification,[status(thm)],[prove_right_inverse]) ).
cnf(c_0_23,plain,
( ~ product(X2,X1,identity)
| product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
~ product(a,inverse(a),identity),
c_0_22 ).
cnf(c_0_25,plain,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_23,c_0_8]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 19:54:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % new_bool_3 with pid 2435512 completed with status 0
% 0.14/0.44 % Result found by new_bool_3
% 0.14/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FHUNS-FFSF11-SFFFFFNN
% 0.14/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 2435519 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FHUNS-FFSF11-SFFFFFNN
% 0.14/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 8
% 0.14/0.44 % Removed by relevancy pruning/SinE : 3
% 0.14/0.44 % Initial clauses : 5
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 5
% 0.14/0.44 % Processed clauses : 74
% 0.14/0.44 % ...of these trivial : 1
% 0.14/0.44 % ...subsumed : 27
% 0.14/0.44 % ...remaining for further processing : 46
% 0.14/0.44 % Other redundant clauses eliminated : 0
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 1
% 0.14/0.44 % Backward-rewritten : 2
% 0.14/0.44 % Generated clauses : 242
% 0.14/0.44 % ...of the previous two non-redundant : 169
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 242
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 0
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 72
% 0.14/0.44 % ...of those cached : 58
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 43
% 0.14/0.44 % Positive orientable unit clauses : 10
% 0.14/0.44 % Positive unorientable unit clauses: 0
% 0.14/0.44 % Negative unit clauses : 0
% 0.14/0.44 % Non-unit-clauses : 33
% 0.14/0.44 % Current number of unprocessed clauses: 100
% 0.14/0.44 % ...number of literals in the above : 300
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 3
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 294
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 289
% 0.14/0.44 % Non-unit clause-clause subsumptions : 28
% 0.14/0.44 % Unit Clause-clause subsumption calls : 6
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 31
% 0.14/0.44 % BW rewrite match successes : 2
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 2837
% 0.14/0.44 % Search garbage collected termcells : 31
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.005 s
% 0.14/0.44 % System time : 0.001 s
% 0.14/0.44 % Total time : 0.006 s
% 0.14/0.44 % Maximum resident set size: 3640 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.007 s
% 0.14/0.44 % System time : 0.004 s
% 0.14/0.44 % Total time : 0.012 s
% 0.14/0.44 % Maximum resident set size: 4608 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------