%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU090+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:23:47 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 49 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 45 ( 16 ~; 12 |; 13 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 39 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t21_finset_1,conjecture,
! [X1,X2,X3,X4] :
( ( finite(X4)
& finite(X3)
& finite(X2)
& finite(X1) )
=> finite(cartesian_product4(X1,X2,X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finset_1) ).
fof(fc14_finset_1,axiom,
! [X1,X2] :
( ( finite(X2)
& finite(X1) )
=> finite(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(d4_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product4(X1,X2,X3,X4) = cartesian_product2(cartesian_product3(X1,X2,X3),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_zfmisc_1) ).
fof(fc15_finset_1,axiom,
! [X1,X2,X3] :
( ( finite(X3)
& finite(X2)
& finite(X1) )
=> finite(cartesian_product3(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_finset_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( finite(X4)
& finite(X3)
& finite(X2)
& finite(X1) )
=> finite(cartesian_product4(X1,X2,X3,X4)) ),
inference(assume_negation,[status(cth)],[t21_finset_1]) ).
fof(c_0_5,plain,
! [X39,X40] :
( finite(cartesian_product2(X39,X40))
| ~ finite(X40)
| ~ finite(X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc14_finset_1])])]) ).
fof(c_0_6,plain,
! [X15,X16,X17,X18] : cartesian_product4(X15,X16,X17,X18) = cartesian_product2(cartesian_product3(X15,X16,X17),X18),
inference(variable_rename,[status(thm)],[d4_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( ~ finite(cartesian_product4(esk1_0,esk2_0,esk3_0,esk4_0))
& finite(esk4_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_4])])])]) ).
cnf(c_0_8,plain,
( ~ finite(X2)
| ~ finite(X1)
| finite(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
cartesian_product4(X1,X2,X3,X4) = cartesian_product2(cartesian_product3(X1,X2,X3),X4),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ finite(cartesian_product4(esk1_0,esk2_0,esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ finite(X4)
| ~ finite(cartesian_product3(X1,X2,X3))
| finite(cartesian_product4(X1,X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
finite(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X45,X46,X47] :
( finite(cartesian_product3(X45,X46,X47))
| ~ finite(X47)
| ~ finite(X46)
| ~ finite(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc15_finset_1])])]) ).
cnf(c_0_14,negated_conjecture,
~ finite(cartesian_product3(esk1_0,esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_15,plain,
( ~ finite(X3)
| ~ finite(X2)
| ~ finite(X1)
| finite(cartesian_product3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
finite(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
finite(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
finite(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU090+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:50:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.46 % Version: 3.5.1
% 0.14/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % Starting sh5l with 300s (1) cores
% 0.14/0.46 % new_bool_3 with pid 2689478 completed with status 0
% 0.14/0.46 % Result found by new_bool_3
% 0.14/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.14/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.46 % SubtermCWHack with pid 2689481 completed with status 0
% 0.14/0.46 % Result found by SubtermCWHack
% 0.14/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.14/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.46 % Preprocessing time : 0.003 s
% 0.14/0.46
% 0.14/0.46 % Proof found!
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.46 % Parsed axioms : 63
% 0.14/0.46 % Removed by relevancy pruning/SinE : 31
% 0.14/0.46 % Initial clauses : 56
% 0.14/0.46 % Removed in clause preprocessing : 0
% 0.14/0.46 % Initial clauses in saturation : 56
% 0.14/0.46 % Processed clauses : 92
% 0.14/0.46 % ...of these trivial : 0
% 0.14/0.46 % ...subsumed : 10
% 0.14/0.46 % ...remaining for further processing : 82
% 0.14/0.46 % Other redundant clauses eliminated : 0
% 0.14/0.46 % Clauses deleted for lack of memory : 0
% 0.14/0.46 % Backward-subsumed : 0
% 0.14/0.46 % Backward-rewritten : 6
% 0.14/0.46 % Generated clauses : 58
% 0.14/0.46 % ...of the previous two non-redundant : 52
% 0.14/0.46 % ...aggressively subsumed : 0
% 0.14/0.46 % Contextual simplify-reflections : 0
% 0.14/0.46 % Paramodulations : 58
% 0.14/0.46 % Factorizations : 0
% 0.14/0.46 % NegExts : 0
% 0.14/0.46 % Equation resolutions : 0
% 0.14/0.46 % Disequality decompositions : 0
% 0.14/0.46 % Total rewrite steps : 21
% 0.14/0.46 % ...of those cached : 6
% 0.14/0.46 % Propositional unsat checks : 0
% 0.14/0.46 % Propositional check models : 0
% 0.14/0.46 % Propositional check unsatisfiable : 0
% 0.14/0.46 % Propositional clauses : 0
% 0.14/0.46 % Propositional clauses after purity: 0
% 0.14/0.46 % Propositional unsat core size : 0
% 0.14/0.46 % Propositional preprocessing time : 0.000
% 0.14/0.46 % Propositional encoding time : 0.000
% 0.14/0.46 % Propositional solver time : 0.000
% 0.14/0.46 % Success case prop preproc time : 0.000
% 0.14/0.46 % Success case prop encoding time : 0.000
% 0.14/0.46 % Success case prop solver time : 0.000
% 0.14/0.46 % Current number of processed clauses : 76
% 0.14/0.46 % Positive orientable unit clauses : 26
% 0.14/0.46 % Positive unorientable unit clauses: 0
% 0.14/0.46 % Negative unit clauses : 8
% 0.14/0.46 % Non-unit-clauses : 42
% 0.14/0.46 % Current number of unprocessed clauses: 6
% 0.14/0.46 % ...number of literals in the above : 16
% 0.14/0.46 % Current number of archived formulas : 0
% 0.14/0.46 % Current number of archived clauses : 6
% 0.14/0.46 % Clause-clause subsumption calls (NU) : 98
% 0.14/0.46 % Rec. Clause-clause subsumption calls : 89
% 0.14/0.46 % Non-unit clause-clause subsumptions : 7
% 0.14/0.46 % Unit Clause-clause subsumption calls : 38
% 0.14/0.46 % Rewrite failures with RHS unbound : 0
% 0.14/0.46 % BW rewrite match attempts : 5
% 0.14/0.46 % BW rewrite match successes : 4
% 0.14/0.46 % Condensation attempts : 0
% 0.14/0.46 % Condensation successes : 0
% 0.14/0.46 % Termbank termtop insertions : 3872
% 0.14/0.46 % Search garbage collected termcells : 637
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.015 s
% 0.14/0.46 % System time : 0.003 s
% 0.14/0.46 % Total time : 0.018 s
% 0.14/0.46 % Maximum resident set size: 3688 pages
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.017 s
% 0.14/0.46 % System time : 0.007 s
% 0.14/0.46 % Total time : 0.024 s
% 0.14/0.46 % Maximum resident set size: 4608 pages
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------