%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET955+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 02:15:50 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 108 ( 31 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 129 ( 50 ~; 59 |; 12 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 88 ( 2 sgn 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t108_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
<=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
=> cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(X6,X2)
& in(X5,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
<=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
=> cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
inference(assume_negation,[status(cth)],[t108_zfmisc_1]) ).
fof(c_0_4,plain,
! [X13,X14,X15,X16,X19,X20,X21,X22,X23,X24,X26,X27] :
( ( X24 = cartesian_product2(X22,X23)
| in(esk7_3(X22,X23,X24),X24)
| esk7_3(X22,X23,X24) = ordered_pair(esk8_3(X22,X23,X24),esk9_3(X22,X23,X24)) )
& ( X24 = cartesian_product2(X22,X23)
| in(esk7_3(X22,X23,X24),X24)
| in(esk9_3(X22,X23,X24),X23) )
& ( X24 = cartesian_product2(X22,X23)
| in(esk7_3(X22,X23,X24),X24)
| in(esk8_3(X22,X23,X24),X22) )
& ( X24 = cartesian_product2(X22,X23)
| esk7_3(X22,X23,X24) != ordered_pair(X26,X27)
| ~ in(X27,X23)
| ~ in(X26,X22)
| ~ in(esk7_3(X22,X23,X24),X24) )
& ( X15 != cartesian_product2(X13,X14)
| in(X19,X15)
| X19 != ordered_pair(X20,X21)
| ~ in(X21,X14)
| ~ in(X20,X13) )
& ( X15 != cartesian_product2(X13,X14)
| ~ in(X16,X15)
| X16 = ordered_pair(esk5_4(X13,X14,X15,X16),esk6_4(X13,X14,X15,X16)) )
& ( X15 != cartesian_product2(X13,X14)
| ~ in(X16,X15)
| in(esk6_4(X13,X14,X15,X16),X14) )
& ( X15 != cartesian_product2(X13,X14)
| ~ in(X16,X15)
| in(esk5_4(X13,X14,X15,X16),X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_zfmisc_1])])])])])])]) ).
fof(c_0_5,negated_conjecture,
! [X11,X12] :
( cartesian_product2(esk1_0,esk2_0) != cartesian_product2(esk3_0,esk4_0)
& ( in(ordered_pair(X11,X12),cartesian_product2(esk1_0,esk2_0))
| ~ in(ordered_pair(X11,X12),cartesian_product2(esk3_0,esk4_0)) )
& ( in(ordered_pair(X11,X12),cartesian_product2(esk3_0,esk4_0))
| ~ in(ordered_pair(X11,X12),cartesian_product2(esk1_0,esk2_0)) ) ),
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_3])])])])]) ).
cnf(c_0_6,plain,
( X6 != cartesian_product2(X2,X4)
| X5 != ordered_pair(X1,X3)
| ~ in(X3,X4)
| ~ in(X1,X2)
| in(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( ~ in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0))
| in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ in(X1,X3)
| ~ in(X2,X4)
| in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6])]) ).
cnf(c_0_9,plain,
( X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4)
| X1 = ordered_pair(esk5_4(X2,X3,X4,X1),esk6_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( ~ in(X1,esk3_0)
| ~ in(X2,esk4_0)
| in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| ordered_pair(esk5_4(X1,X2,cartesian_product2(X1,X2),X3),esk6_4(X1,X2,cartesian_product2(X1,X2),X3)) = X3 ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( X3 != cartesian_product2(X1,X2)
| ~ in(X4,X3)
| in(esk6_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( ~ in(X1,cartesian_product2(X2,X3))
| ~ in(esk5_4(X2,X3,cartesian_product2(X2,X3),X1),esk3_0)
| ~ in(esk6_4(X2,X3,cartesian_product2(X2,X3),X1),esk4_0)
| in(X1,cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| in(esk6_4(X1,X2,cartesian_product2(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( X3 != cartesian_product2(X1,X2)
| ~ in(X4,X3)
| in(esk5_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( ~ in(X1,cartesian_product2(X2,esk4_0))
| ~ in(esk5_4(X2,esk4_0,cartesian_product2(X2,esk4_0),X1),esk3_0)
| in(X1,cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| in(esk5_4(X1,X2,cartesian_product2(X1,X2),X3),X1) ),
inference(er,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X32,X33] :
( ( X32 = X33
| in(esk10_2(X32,X33),X33)
| in(esk10_2(X32,X33),X32) )
& ( X32 = X33
| ~ in(esk10_2(X32,X33),X33)
| ~ in(esk10_2(X32,X33),X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(X1,cartesian_product2(esk3_0,esk4_0))
| in(X1,cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( X1 = X2
| in(esk10_2(X1,X2),X2)
| in(esk10_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0))
| in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
( in(esk10_2(X1,cartesian_product2(esk3_0,esk4_0)),X1)
| in(esk10_2(X1,cartesian_product2(esk3_0,esk4_0)),cartesian_product2(esk1_0,esk2_0))
| X1 = cartesian_product2(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
cartesian_product2(esk1_0,esk2_0) != cartesian_product2(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(X1,cartesian_product2(X2,X3))
| ~ in(X1,cartesian_product2(esk1_0,esk2_0))
| in(X1,cartesian_product2(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_11]) ).
cnf(c_0_25,negated_conjecture,
in(esk10_2(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),cartesian_product2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
( ~ in(esk10_2(X1,X2),X2)
| ~ in(esk10_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
in(esk10_2(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),cartesian_product2(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET955+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n007.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 05:42:35 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42 % Version: 3.5.1
% 0.11/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.42 % Starting sh5l with 300s (1) cores
% 0.11/0.42 % new_bool_3 with pid 298085 completed with status 0
% 0.11/0.42 % Result found by new_bool_3
% 0.11/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.42 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.11/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.42 % SubtermCWHack with pid 298088 completed with status 0
% 0.11/0.42 % Result found by SubtermCWHack
% 0.11/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.42 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.11/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.42 % Preprocessing time : 0.001 s
% 0.11/0.42
% 0.11/0.42 % Proof found!
% 0.11/0.42 % SZS status Theorem
% 0.11/0.42 % SZS output start CNFRefutation
% See solution above
% 0.11/0.42 % Parsed axioms : 9
% 0.11/0.42 % Removed by relevancy pruning/SinE : 2
% 0.11/0.42 % Initial clauses : 17
% 0.11/0.42 % Removed in clause preprocessing : 0
% 0.11/0.42 % Initial clauses in saturation : 17
% 0.11/0.42 % Processed clauses : 75
% 0.11/0.42 % ...of these trivial : 1
% 0.11/0.42 % ...subsumed : 9
% 0.11/0.42 % ...remaining for further processing : 65
% 0.11/0.42 % Other redundant clauses eliminated : 5
% 0.11/0.42 % Clauses deleted for lack of memory : 0
% 0.11/0.42 % Backward-subsumed : 3
% 0.11/0.42 % Backward-rewritten : 0
% 0.11/0.42 % Generated clauses : 132
% 0.11/0.42 % ...of the previous two non-redundant : 121
% 0.11/0.42 % ...aggressively subsumed : 0
% 0.11/0.42 % Contextual simplify-reflections : 0
% 0.11/0.42 % Paramodulations : 124
% 0.11/0.42 % Factorizations : 4
% 0.11/0.42 % NegExts : 0
% 0.11/0.42 % Equation resolutions : 5
% 0.11/0.42 % Disequality decompositions : 0
% 0.11/0.42 % Total rewrite steps : 6
% 0.11/0.42 % ...of those cached : 4
% 0.11/0.42 % Propositional unsat checks : 0
% 0.11/0.42 % Propositional check models : 0
% 0.11/0.42 % Propositional check unsatisfiable : 0
% 0.11/0.42 % Propositional clauses : 0
% 0.11/0.42 % Propositional clauses after purity: 0
% 0.11/0.42 % Propositional unsat core size : 0
% 0.11/0.42 % Propositional preprocessing time : 0.000
% 0.11/0.42 % Propositional encoding time : 0.000
% 0.11/0.42 % Propositional solver time : 0.000
% 0.11/0.42 % Success case prop preproc time : 0.000
% 0.11/0.42 % Success case prop encoding time : 0.000
% 0.11/0.42 % Success case prop solver time : 0.000
% 0.11/0.42 % Current number of processed clauses : 58
% 0.11/0.42 % Positive orientable unit clauses : 3
% 0.11/0.42 % Positive unorientable unit clauses: 0
% 0.11/0.42 % Negative unit clauses : 5
% 0.11/0.42 % Non-unit-clauses : 50
% 0.11/0.42 % Current number of unprocessed clauses: 59
% 0.11/0.42 % ...number of literals in the above : 272
% 0.11/0.42 % Current number of archived formulas : 0
% 0.11/0.42 % Current number of archived clauses : 3
% 0.11/0.42 % Clause-clause subsumption calls (NU) : 476
% 0.11/0.42 % Rec. Clause-clause subsumption calls : 307
% 0.11/0.42 % Non-unit clause-clause subsumptions : 9
% 0.11/0.42 % Unit Clause-clause subsumption calls : 2
% 0.11/0.42 % Rewrite failures with RHS unbound : 0
% 0.11/0.42 % BW rewrite match attempts : 0
% 0.11/0.42 % BW rewrite match successes : 0
% 0.11/0.42 % Condensation attempts : 0
% 0.11/0.42 % Condensation successes : 0
% 0.11/0.42 % Termbank termtop insertions : 4010
% 0.11/0.42 % Search garbage collected termcells : 415
% 0.11/0.42
% 0.11/0.42 % -------------------------------------------------
% 0.11/0.42 % User time : 0.010 s
% 0.11/0.42 % System time : 0.001 s
% 0.11/0.42 % Total time : 0.011 s
% 0.11/0.42 % Maximum resident set size: 3636 pages
% 0.11/0.42
% 0.11/0.42 % -------------------------------------------------
% 0.11/0.42 % User time : 0.011 s
% 0.11/0.42 % System time : 0.006 s
% 0.11/0.42 % Total time : 0.016 s
% 0.11/0.42 % Maximum resident set size: 4864 pages
% 0.11/0.42 % E exiting
%------------------------------------------------------------------------------