%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 02:23:47 PM UTC 2026
% Result : Theorem 0.27s 0.54s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 33 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 10 ~; 6 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t20_finset_1,conjecture,
! [X1,X2,X3] :
( ( finite(X3)
& finite(X2)
& finite(X1) )
=> finite(cartesian_product3(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finset_1) ).
fof(fc14_finset_1,axiom,
! [X1,X2] :
( ( finite(X2)
& finite(X1) )
=> finite(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(d3_zfmisc_1,axiom,
! [X1,X2,X3] : cartesian_product3(X1,X2,X3) = cartesian_product2(cartesian_product2(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( finite(X3)
& finite(X2)
& finite(X1) )
=> finite(cartesian_product3(X1,X2,X3)) ),
inference(assume_negation,[status(cth)],[t20_finset_1]) ).
fof(c_0_4,plain,
! [X35,X36] :
( finite(cartesian_product2(X35,X36))
| ~ finite(X36)
| ~ finite(X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc14_finset_1])])]) ).
fof(c_0_5,plain,
! [X13,X14,X15] : cartesian_product3(X13,X14,X15) = cartesian_product2(cartesian_product2(X13,X14),X15),
inference(variable_rename,[status(thm)],[d3_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
( ~ finite(cartesian_product3(esk1_0,esk2_0,esk3_0))
& finite(esk3_0)
& finite(esk2_0)
& finite(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_7,plain,
( ~ finite(X2)
| ~ finite(X1)
| finite(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
cartesian_product3(X1,X2,X3) = cartesian_product2(cartesian_product2(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
~ finite(cartesian_product3(esk1_0,esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ finite(X3)
| ~ finite(cartesian_product2(X1,X2))
| finite(cartesian_product3(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
finite(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
~ finite(cartesian_product2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
cnf(c_0_13,negated_conjecture,
finite(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
finite(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_7]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.43 % Computer : n002.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 21 05:52:48 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.50 Running first-order theorem proving
% 0.27/0.51 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
% 0.27/0.54 % Version: 3.5.1
% 0.27/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.54 % Starting sh5l with 300s (1) cores
% 0.27/0.54 % new_bool_3 with pid 2565588 completed with status 0
% 0.27/0.54 % Result found by new_bool_3
% 0.27/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.54 % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.27/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.54 % SubtermCWHack with pid 2565591 completed with status 0
% 0.27/0.54 % Result found by SubtermCWHack
% 0.27/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.54 % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.27/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.54 % Preprocessing time : 0.001 s
% 0.27/0.54
% 0.27/0.54 % Proof found!
% 0.27/0.54 % SZS status Theorem
% 0.27/0.54 % SZS output start CNFRefutation
% See solution above
% 0.27/0.54 % Parsed axioms : 60
% 0.27/0.54 % Removed by relevancy pruning/SinE : 31
% 0.27/0.54 % Initial clauses : 52
% 0.27/0.54 % Removed in clause preprocessing : 0
% 0.27/0.54 % Initial clauses in saturation : 52
% 0.27/0.54 % Processed clauses : 87
% 0.27/0.54 % ...of these trivial : 0
% 0.27/0.54 % ...subsumed : 7
% 0.27/0.54 % ...remaining for further processing : 80
% 0.27/0.54 % Other redundant clauses eliminated : 0
% 0.27/0.54 % Clauses deleted for lack of memory : 0
% 0.27/0.54 % Backward-subsumed : 0
% 0.27/0.54 % Backward-rewritten : 6
% 0.27/0.54 % Generated clauses : 58
% 0.27/0.54 % ...of the previous two non-redundant : 52
% 0.27/0.54 % ...aggressively subsumed : 0
% 0.27/0.54 % Contextual simplify-reflections : 0
% 0.27/0.54 % Paramodulations : 58
% 0.27/0.54 % Factorizations : 0
% 0.27/0.54 % NegExts : 0
% 0.27/0.54 % Equation resolutions : 0
% 0.27/0.54 % Disequality decompositions : 0
% 0.27/0.54 % Total rewrite steps : 20
% 0.27/0.54 % ...of those cached : 6
% 0.27/0.54 % Propositional unsat checks : 0
% 0.27/0.54 % Propositional check models : 0
% 0.27/0.54 % Propositional check unsatisfiable : 0
% 0.27/0.54 % Propositional clauses : 0
% 0.27/0.54 % Propositional clauses after purity: 0
% 0.27/0.54 % Propositional unsat core size : 0
% 0.27/0.54 % Propositional preprocessing time : 0.000
% 0.27/0.54 % Propositional encoding time : 0.000
% 0.27/0.54 % Propositional solver time : 0.000
% 0.27/0.54 % Success case prop preproc time : 0.000
% 0.27/0.54 % Success case prop encoding time : 0.000
% 0.27/0.54 % Success case prop solver time : 0.000
% 0.27/0.54 % Current number of processed clauses : 74
% 0.27/0.54 % Positive orientable unit clauses : 25
% 0.27/0.54 % Positive unorientable unit clauses: 0
% 0.27/0.54 % Negative unit clauses : 8
% 0.27/0.54 % Non-unit-clauses : 41
% 0.27/0.54 % Current number of unprocessed clauses: 8
% 0.27/0.54 % ...number of literals in the above : 20
% 0.27/0.54 % Current number of archived formulas : 0
% 0.27/0.54 % Current number of archived clauses : 6
% 0.27/0.54 % Clause-clause subsumption calls (NU) : 100
% 0.27/0.54 % Rec. Clause-clause subsumption calls : 93
% 0.27/0.54 % Non-unit clause-clause subsumptions : 4
% 0.27/0.54 % Unit Clause-clause subsumption calls : 18
% 0.27/0.54 % Rewrite failures with RHS unbound : 0
% 0.27/0.54 % BW rewrite match attempts : 5
% 0.27/0.54 % BW rewrite match successes : 4
% 0.27/0.54 % Condensation attempts : 0
% 0.27/0.54 % Condensation successes : 0
% 0.27/0.54 % Termbank termtop insertions : 3389
% 0.27/0.54 % Search garbage collected termcells : 566
% 0.27/0.54
% 0.27/0.54 % -------------------------------------------------
% 0.27/0.54 % User time : 0.010 s
% 0.27/0.54 % System time : 0.003 s
% 0.27/0.54 % Total time : 0.013 s
% 0.27/0.54 % Maximum resident set size: 3684 pages
% 0.27/0.54
% 0.27/0.54 % -------------------------------------------------
% 0.27/0.54 % User time : 0.013 s
% 0.27/0.54 % System time : 0.010 s
% 0.27/0.54 % Total time : 0.022 s
% 0.27/0.54 % Maximum resident set size: 4608 pages
% 0.27/0.54 % E exiting
%------------------------------------------------------------------------------