%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP031-2 : 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 : n007.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 12:37:30 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.58s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 9 unt; 0 nHn; 15 RR)
% Number of literals : 46 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 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 : 61 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
cnf(right_inverse,hypothesis,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(right_identity,hypothesis,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(prove_a_has_a_left_inverse,negated_conjecture,
~ product(X1,a,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_has_a_left_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,hypothesis,
product(X1,inverse(X1),identity),
right_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,hypothesis,
( ~ product(X4,X2,X1)
| ~ product(X4,identity,X3)
| product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,hypothesis,
product(X1,identity,X1),
right_identity ).
cnf(c_0_12,hypothesis,
( ~ product(X1,X3,X4)
| ~ product(X3,inverse(X4),X2)
| product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_13,hypothesis,
( ~ product(X3,X2,X1)
| product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,hypothesis,
( ~ product(X2,X4,X3)
| ~ product(X1,X3,X4)
| product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
~ product(X1,a,identity),
inference(fof_simplification,[status(thm)],[prove_a_has_a_left_inverse]) ).
cnf(c_0_16,hypothesis,
( ~ product(X2,X1,identity)
| product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
~ product(X1,a,identity),
c_0_15 ).
cnf(c_0_18,hypothesis,
product(inverse(X1),X1,identity),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_17,c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.47 % Computer : n007.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 20 19:52:35 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.55 Running first-order theorem proving
% 0.25/0.55 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
% 0.25/0.58 % Version: 3.5.1
% 0.25/0.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.58 % Starting sh5l with 300s (1) cores
% 0.25/0.58 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3437536 completed with status 0
% 0.25/0.58 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.25/0.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.58 % No SInE strategy applied
% 0.25/0.58 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.25/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.58 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 0.25/0.58 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.58 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.58 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3437542 completed with status 0
% 0.25/0.58 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.25/0.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.58 % No SInE strategy applied
% 0.25/0.58 % Search class: FHUNS-FFSF21-SFFFFFNN
% 0.25/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.58 % Preprocessing time : 0.002 s
% 0.25/0.58
% 0.25/0.58 % Proof found!
% 0.25/0.58 % SZS status Unsatisfiable
% 0.25/0.58 % SZS output start CNFRefutation
% See solution above
% 0.25/0.58 % Parsed axioms : 7
% 0.25/0.58 % Removed by relevancy pruning/SinE : 0
% 0.25/0.58 % Initial clauses : 7
% 0.25/0.58 % Removed in clause preprocessing : 0
% 0.25/0.58 % Initial clauses in saturation : 7
% 0.25/0.58 % Processed clauses : 38
% 0.25/0.58 % ...of these trivial : 0
% 0.25/0.58 % ...subsumed : 1
% 0.25/0.58 % ...remaining for further processing : 37
% 0.25/0.58 % Other redundant clauses eliminated : 0
% 0.25/0.58 % Clauses deleted for lack of memory : 0
% 0.25/0.58 % Backward-subsumed : 0
% 0.25/0.58 % Backward-rewritten : 1
% 0.25/0.58 % Generated clauses : 140
% 0.25/0.58 % ...of the previous two non-redundant : 106
% 0.25/0.58 % ...aggressively subsumed : 0
% 0.25/0.58 % Contextual simplify-reflections : 0
% 0.25/0.58 % Paramodulations : 140
% 0.25/0.58 % Factorizations : 0
% 0.25/0.58 % NegExts : 0
% 0.25/0.58 % Equation resolutions : 0
% 0.25/0.58 % Disequality decompositions : 0
% 0.25/0.58 % Total rewrite steps : 18
% 0.25/0.58 % ...of those cached : 7
% 0.25/0.58 % Propositional unsat checks : 0
% 0.25/0.58 % Propositional check models : 0
% 0.25/0.58 % Propositional check unsatisfiable : 0
% 0.25/0.58 % Propositional clauses : 0
% 0.25/0.58 % Propositional clauses after purity: 0
% 0.25/0.58 % Propositional unsat core size : 0
% 0.25/0.58 % Propositional preprocessing time : 0.000
% 0.25/0.58 % Propositional encoding time : 0.000
% 0.25/0.58 % Propositional solver time : 0.000
% 0.25/0.58 % Success case prop preproc time : 0.000
% 0.25/0.58 % Success case prop encoding time : 0.000
% 0.25/0.58 % Success case prop solver time : 0.000
% 0.25/0.58 % Current number of processed clauses : 36
% 0.25/0.58 % Positive orientable unit clauses : 11
% 0.25/0.58 % Positive unorientable unit clauses: 0
% 0.25/0.58 % Negative unit clauses : 1
% 0.25/0.58 % Non-unit-clauses : 24
% 0.25/0.58 % Current number of unprocessed clauses: 75
% 0.25/0.58 % ...number of literals in the above : 179
% 0.25/0.58 % Current number of archived formulas : 0
% 0.25/0.58 % Current number of archived clauses : 1
% 0.25/0.58 % Clause-clause subsumption calls (NU) : 38
% 0.25/0.58 % Rec. Clause-clause subsumption calls : 27
% 0.25/0.58 % Non-unit clause-clause subsumptions : 1
% 0.25/0.58 % Unit Clause-clause subsumption calls : 1
% 0.25/0.58 % Rewrite failures with RHS unbound : 0
% 0.25/0.58 % BW rewrite match attempts : 9
% 0.25/0.58 % BW rewrite match successes : 1
% 0.25/0.58 % Condensation attempts : 0
% 0.25/0.58 % Condensation successes : 0
% 0.25/0.58 % Termbank termtop insertions : 1674
% 0.25/0.58 % Search garbage collected termcells : 18
% 0.25/0.58
% 0.25/0.58 % -------------------------------------------------
% 0.25/0.58 % User time : 0.010 s
% 0.25/0.58 % System time : 0.003 s
% 0.25/0.58 % Total time : 0.013 s
% 0.25/0.58 % Maximum resident set size: 3632 pages
% 0.25/0.58
% 0.25/0.58 % -------------------------------------------------
% 0.25/0.58 % User time : 0.039 s
% 0.25/0.58 % System time : 0.016 s
% 0.25/0.58 % Total time : 0.055 s
% 0.25/0.58 % Maximum resident set size: 4608 pages
% 0.25/0.58 % E exiting
%------------------------------------------------------------------------------