%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:37:27 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 90 ( 27 ~; 24 |; 31 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_distribution,conjecture,
! [X1] :
( ( ! [X2] : product(inverse(X2),X2,X1)
& ! [X2] : product(X2,inverse(X2),X1)
& ! [X2] : product(X1,X2,X2)
& ! [X2] : product(X2,X1,X2)
& ! [X2,X3,X4,X5,X6,X7] :
( ( product(X2,X6,X7)
& product(X3,X4,X6)
& product(X2,X3,X5) )
=> product(X5,X4,X7) )
& ! [X2,X3,X4,X5,X6,X7] :
( ( product(X5,X4,X7)
& product(X3,X4,X6)
& product(X2,X3,X5) )
=> product(X2,X6,X7) )
& ! [X2,X3] :
? [X4] : product(X2,X3,X4) )
=> ! [X5,X6,X7,X2] :
( ( product(X6,X5,X2)
& product(inverse(X5),inverse(X6),X7) )
=> product(inverse(X7),inverse(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distribution) ).
fof(c_0_1,negated_conjecture,
~ ! [X1] :
( ( ! [X2] : product(inverse(X2),X2,X1)
& ! [X2] : product(X2,inverse(X2),X1)
& ! [X2] : product(X1,X2,X2)
& ! [X2] : product(X2,X1,X2)
& ! [X2,X3,X4,X5,X6,X7] :
( ( product(X2,X6,X7)
& product(X3,X4,X6)
& product(X2,X3,X5) )
=> product(X5,X4,X7) )
& ! [X2,X3,X4,X5,X6,X7] :
( ( product(X5,X4,X7)
& product(X3,X4,X6)
& product(X2,X3,X5) )
=> product(X2,X6,X7) )
& ! [X2,X3] :
? [X4] : product(X2,X3,X4) )
=> ! [X5,X6,X7,X2] :
( ( product(X6,X5,X2)
& product(inverse(X5),inverse(X6),X7) )
=> product(inverse(X7),inverse(X2),X1) ) ),
inference(assume_negation,[status(cth)],[prove_distribution]) ).
fof(c_0_2,negated_conjecture,
! [X9,X10,X12,X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24,X25,X26,X27] :
( ~ product(inverse(esk5_0),inverse(esk6_0),esk1_0)
& product(esk4_0,esk3_0,esk6_0)
& product(inverse(esk3_0),inverse(esk4_0),esk5_0)
& product(inverse(X27),X27,esk1_0)
& product(X26,inverse(X26),esk1_0)
& product(esk1_0,X25,X25)
& product(X24,esk1_0,X24)
& ( product(X21,X20,X23)
| ~ product(X18,X22,X23)
| ~ product(X19,X20,X22)
| ~ product(X18,X19,X21) )
& ( product(X12,X16,X17)
| ~ product(X15,X14,X17)
| ~ product(X13,X14,X16)
| ~ product(X12,X13,X15) )
& product(X9,X10,esk2_2(X9,X10)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
product(inverse(X1),X1,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( ~ product(X4,esk1_0,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_7,negated_conjecture,
product(X1,esk1_0,X1),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
product(esk1_0,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( ~ product(X3,X4,X2)
| ~ product(X1,X3,inverse(X4))
| product(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_10,negated_conjecture,
product(esk4_0,esk3_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_11,negated_conjecture,
( ~ product(X3,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,negated_conjecture,
product(inverse(esk3_0),inverse(esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,esk1_0)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
product(X1,inverse(X1),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( ~ product(X1,esk4_0,inverse(esk3_0))
| product(X1,esk6_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
product(esk5_0,esk4_0,inverse(esk3_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ product(X1,X4,X3)
| ~ product(X4,esk1_0,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_18,negated_conjecture,
( ~ product(X1,X2,esk1_0)
| product(X1,esk1_0,inverse(X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
product(esk5_0,esk6_0,esk1_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( ~ product(X1,esk1_0,X2)
| product(inverse(X1),X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_4]) ).
cnf(c_0_21,negated_conjecture,
product(esk5_0,esk1_0,inverse(esk6_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
~ product(inverse(esk5_0),inverse(esk6_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n005.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 20 19:53:34 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 0.16/0.47 % Version: 3.5.1
% 0.16/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.47 % Starting sh5l with 300s (1) cores
% 0.16/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1619652 completed with status 0
% 0.16/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.47 % No SInE strategy applied
% 0.16/0.47 % Search class: FHUNM-FFSF21-SFFFFFNN
% 0.16/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.16/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.16/0.47 % new_bool_1 with pid 1619663 completed with status 0
% 0.16/0.47 % Result found by new_bool_1
% 0.16/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.47 % No SInE strategy applied
% 0.16/0.47 % Search class: FHUNM-FFSF21-SFFFFFNN
% 0.16/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.16/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.16/0.47 % Preprocessing time : 0.001 s
% 0.16/0.47 % Presaturation interreduction done
% 0.16/0.47
% 0.16/0.47 % Proof found!
% 0.16/0.47 % SZS status Theorem
% 0.16/0.47 % SZS output start CNFRefutation
% See solution above
% 0.16/0.47 % Parsed axioms : 1
% 0.16/0.47 % Removed by relevancy pruning/SinE : 0
% 0.16/0.47 % Initial clauses : 10
% 0.16/0.47 % Removed in clause preprocessing : 0
% 0.16/0.47 % Initial clauses in saturation : 10
% 0.16/0.47 % Processed clauses : 167
% 0.16/0.47 % ...of these trivial : 15
% 0.16/0.47 % ...subsumed : 3
% 0.16/0.47 % ...remaining for further processing : 149
% 0.16/0.47 % Other redundant clauses eliminated : 0
% 0.16/0.47 % Clauses deleted for lack of memory : 0
% 0.16/0.47 % Backward-subsumed : 0
% 0.16/0.47 % Backward-rewritten : 1
% 0.16/0.47 % Generated clauses : 1525
% 0.16/0.47 % ...of the previous two non-redundant : 1240
% 0.16/0.47 % ...aggressively subsumed : 0
% 0.16/0.47 % Contextual simplify-reflections : 0
% 0.16/0.47 % Paramodulations : 1525
% 0.16/0.47 % Factorizations : 0
% 0.16/0.47 % NegExts : 0
% 0.16/0.47 % Equation resolutions : 0
% 0.16/0.47 % Disequality decompositions : 0
% 0.16/0.47 % Total rewrite steps : 290
% 0.16/0.47 % ...of those cached : 220
% 0.16/0.47 % Propositional unsat checks : 0
% 0.16/0.47 % Propositional check models : 0
% 0.16/0.47 % Propositional check unsatisfiable : 0
% 0.16/0.47 % Propositional clauses : 0
% 0.16/0.47 % Propositional clauses after purity: 0
% 0.16/0.47 % Propositional unsat core size : 0
% 0.16/0.47 % Propositional preprocessing time : 0.000
% 0.16/0.47 % Propositional encoding time : 0.000
% 0.16/0.47 % Propositional solver time : 0.000
% 0.16/0.47 % Success case prop preproc time : 0.000
% 0.16/0.47 % Success case prop encoding time : 0.000
% 0.16/0.47 % Success case prop solver time : 0.000
% 0.16/0.47 % Current number of processed clauses : 138
% 0.16/0.47 % Positive orientable unit clauses : 67
% 0.16/0.47 % Positive unorientable unit clauses: 0
% 0.16/0.47 % Negative unit clauses : 1
% 0.16/0.47 % Non-unit-clauses : 70
% 0.16/0.47 % Current number of unprocessed clauses: 1078
% 0.16/0.47 % ...number of literals in the above : 2059
% 0.16/0.47 % Current number of archived formulas : 0
% 0.16/0.47 % Current number of archived clauses : 11
% 0.16/0.47 % Clause-clause subsumption calls (NU) : 420
% 0.16/0.47 % Rec. Clause-clause subsumption calls : 402
% 0.16/0.47 % Non-unit clause-clause subsumptions : 3
% 0.16/0.47 % Unit Clause-clause subsumption calls : 5
% 0.16/0.47 % Rewrite failures with RHS unbound : 0
% 0.16/0.47 % BW rewrite match attempts : 62
% 0.16/0.47 % BW rewrite match successes : 1
% 0.16/0.47 % Condensation attempts : 0
% 0.16/0.47 % Condensation successes : 0
% 0.16/0.47 % Termbank termtop insertions : 18844
% 0.16/0.47 % Search garbage collected termcells : 355
% 0.16/0.47
% 0.16/0.47 % -------------------------------------------------
% 0.16/0.47 % User time : 0.024 s
% 0.16/0.47 % System time : 0.002 s
% 0.16/0.47 % Total time : 0.026 s
% 0.16/0.47 % Maximum resident set size: 3636 pages
% 0.16/0.47
% 0.16/0.47 % -------------------------------------------------
% 0.16/0.47 % User time : 0.101 s
% 0.16/0.47 % System time : 0.021 s
% 0.16/0.47 % Total time : 0.123 s
% 0.16/0.47 % Maximum resident set size: 4864 pages
% 0.16/0.47 % E exiting
%------------------------------------------------------------------------------