%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET985+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 02:15:54 PM UTC 2026
% Result : Theorem 0.24s 5.60s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 62 ( 24 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 55 ( 17 ~; 24 |; 6 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 3 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t139_zfmisc_1,conjecture,
! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3))
| subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) )
=> subset(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
fof(t138_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( ( subset(X2,X4)
& subset(X1,X3) )
| cartesian_product2(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(t113_zfmisc_1,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X2 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3))
| subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) )
=> subset(X2,X4) ) ),
inference(assume_negation,[status(cth)],[t139_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3))
| subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) )
=> subset(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X10,X11,X12,X13] :
( ( ~ subset(cartesian_product2(X10,X11),cartesian_product2(X12,X13))
| cartesian_product2(X10,X11) = empty_set
| subset(X11,X13) )
& ( ~ subset(cartesian_product2(X10,X11),cartesian_product2(X12,X13))
| cartesian_product2(X10,X11) = empty_set
| subset(X10,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t138_zfmisc_1])])])]) ).
fof(c_0_8,negated_conjecture,
( ~ subset(esk2_0,esk4_0)
& ( subset(cartesian_product2(esk2_0,esk1_0),cartesian_product2(esk4_0,esk3_0))
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) )
& ~ empty(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_9,plain,
( ~ subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| cartesian_product2(X1,X3) = empty_set
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( subset(cartesian_product2(esk2_0,esk1_0),cartesian_product2(esk4_0,esk3_0))
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ subset(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X15,X16] :
( ( cartesian_product2(X15,X16) = empty_set
| X16 != empty_set )
& ( cartesian_product2(X15,X16) = empty_set
| X15 != empty_set )
& ( X16 = empty_set
| X15 = empty_set
| cartesian_product2(X15,X16) != empty_set ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])])]) ).
cnf(c_0_13,plain,
( ~ subset(cartesian_product2(X3,X1),cartesian_product2(X4,X2))
| cartesian_product2(X3,X1) = empty_set
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| cartesian_product2(esk2_0,esk1_0) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_15,plain,
( cartesian_product2(X1,X2) != empty_set
| X2 = empty_set
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) = empty_set
| cartesian_product2(esk2_0,esk1_0) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
fof(c_0_17,plain,
! [X14] : subset(empty_set,X14),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_18,negated_conjecture,
( esk2_0 = empty_set
| esk1_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_15]) ).
cnf(c_0_19,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
esk1_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_19])]) ).
cnf(c_0_22,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/5.47 % Computer : n002.cluster.edu
% 0.20/5.47 % Model : x86_64 x86_64
% 0.20/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.47 % Memory : 8046.5625MB
% 0.20/5.47 % OS : Linux 6.8.0-71-generic
% 0.20/5.47 % CPULimit : 300
% 0.20/5.47 % WCLimit : 300
% 0.20/5.47 % DateTime : Mon Sep 21 05:48:52 UTC 2026
% 0.20/5.47 % CPUTime :
% 0.20/5.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/5.54 Running first-order theorem proving
% 0.24/5.54 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
% 0.24/5.60 % Version: 3.5.1
% 0.24/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.60 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.60 % Starting sh5l with 300s (1) cores
% 0.24/5.60 % new_bool_3 with pid 2559516 completed with status 0
% 0.24/5.60 % Result found by new_bool_3
% 0.24/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/5.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/5.60 % Search class: FGUSS-FFSS22-SFFFFFNN
% 0.24/5.60 % partial match(1): FGUSS-FFSF22-SFFFFFNN
% 0.24/5.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/5.60 % Starting SubtermCWHack with 31s (1) cores
% 0.24/5.60 % SubtermCWHack with pid 2559524 completed with status 0
% 0.24/5.60 % Result found by SubtermCWHack
% 0.24/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/5.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/5.60 % Search class: FGUSS-FFSS22-SFFFFFNN
% 0.24/5.60 % partial match(1): FGUSS-FFSF22-SFFFFFNN
% 0.24/5.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/5.60 % Starting SubtermCWHack with 31s (1) cores
% 0.24/5.60 % Preprocessing time : 0.002 s
% 0.24/5.60
% 0.24/5.60 % Proof found!
% 0.24/5.60 % SZS status Theorem
% 0.24/5.60 % SZS output start CNFRefutation
% See solution above
% 0.24/5.60 % Parsed axioms : 8
% 0.24/5.60 % Removed by relevancy pruning/SinE : 0
% 0.24/5.60 % Initial clauses : 13
% 0.24/5.60 % Removed in clause preprocessing : 0
% 0.24/5.60 % Initial clauses in saturation : 13
% 0.24/5.60 % Processed clauses : 21
% 0.24/5.60 % ...of these trivial : 0
% 0.24/5.60 % ...subsumed : 1
% 0.24/5.60 % ...remaining for further processing : 20
% 0.24/5.60 % Other redundant clauses eliminated : 2
% 0.24/5.60 % Clauses deleted for lack of memory : 0
% 0.24/5.60 % Backward-subsumed : 0
% 0.24/5.60 % Backward-rewritten : 4
% 0.24/5.60 % Generated clauses : 21
% 0.24/5.60 % ...of the previous two non-redundant : 14
% 0.24/5.60 % ...aggressively subsumed : 0
% 0.24/5.60 % Contextual simplify-reflections : 1
% 0.24/5.60 % Paramodulations : 19
% 0.24/5.60 % Factorizations : 0
% 0.24/5.60 % NegExts : 0
% 0.24/5.60 % Equation resolutions : 2
% 0.24/5.60 % Disequality decompositions : 0
% 0.24/5.60 % Total rewrite steps : 25
% 0.24/5.60 % ...of those cached : 14
% 0.24/5.60 % Propositional unsat checks : 0
% 0.24/5.60 % Propositional check models : 0
% 0.24/5.60 % Propositional check unsatisfiable : 0
% 0.24/5.60 % Propositional clauses : 0
% 0.24/5.60 % Propositional clauses after purity: 0
% 0.24/5.60 % Propositional unsat core size : 0
% 0.24/5.60 % Propositional preprocessing time : 0.000
% 0.24/5.60 % Propositional encoding time : 0.000
% 0.24/5.60 % Propositional solver time : 0.000
% 0.24/5.60 % Success case prop preproc time : 0.000
% 0.24/5.60 % Success case prop encoding time : 0.000
% 0.24/5.60 % Success case prop solver time : 0.000
% 0.24/5.60 % Current number of processed clauses : 14
% 0.24/5.60 % Positive orientable unit clauses : 7
% 0.24/5.60 % Positive unorientable unit clauses: 0
% 0.24/5.60 % Negative unit clauses : 2
% 0.24/5.60 % Non-unit-clauses : 5
% 0.24/5.60 % Current number of unprocessed clauses: 6
% 0.24/5.60 % ...number of literals in the above : 20
% 0.24/5.60 % Current number of archived formulas : 0
% 0.24/5.60 % Current number of archived clauses : 4
% 0.24/5.60 % Clause-clause subsumption calls (NU) : 6
% 0.24/5.60 % Rec. Clause-clause subsumption calls : 6
% 0.24/5.60 % Non-unit clause-clause subsumptions : 2
% 0.24/5.60 % Unit Clause-clause subsumption calls : 1
% 0.24/5.60 % Rewrite failures with RHS unbound : 0
% 0.24/5.60 % BW rewrite match attempts : 2
% 0.24/5.60 % BW rewrite match successes : 1
% 0.24/5.60 % Condensation attempts : 0
% 0.24/5.60 % Condensation successes : 0
% 0.24/5.60 % Termbank termtop insertions : 928
% 0.24/5.60 % Search garbage collected termcells : 130
% 0.24/5.60
% 0.24/5.60 % -------------------------------------------------
% 0.24/5.60 % User time : 0.009 s
% 0.24/5.60 % System time : 0.002 s
% 0.24/5.60 % Total time : 0.011 s
% 0.24/5.60 % Maximum resident set size: 3632 pages
% 0.24/5.60
% 0.24/5.60 % -------------------------------------------------
% 0.24/5.60 % User time : 0.013 s
% 0.24/5.60 % System time : 0.007 s
% 0.24/5.60 % Total time : 0.020 s
% 0.24/5.60 % Maximum resident set size: 4864 pages
% 0.24/5.60 % E exiting
%------------------------------------------------------------------------------