%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU166+3 : 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 : n008.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 02:24:05 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 116 ( 21 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 140 ( 58 ~; 62 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 100 ( 0 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(t118_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
& subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_3,plain,
! [X17,X18,X19,X20,X23,X24,X25,X26,X27,X28,X30,X31] :
( ( X28 = cartesian_product2(X26,X27)
| in(esk7_3(X26,X27,X28),X28)
| esk7_3(X26,X27,X28) = ordered_pair(esk8_3(X26,X27,X28),esk9_3(X26,X27,X28)) )
& ( X28 = cartesian_product2(X26,X27)
| in(esk7_3(X26,X27,X28),X28)
| in(esk9_3(X26,X27,X28),X27) )
& ( X28 = cartesian_product2(X26,X27)
| in(esk7_3(X26,X27,X28),X28)
| in(esk8_3(X26,X27,X28),X26) )
& ( X28 = cartesian_product2(X26,X27)
| esk7_3(X26,X27,X28) != ordered_pair(X30,X31)
| ~ in(X31,X27)
| ~ in(X30,X26)
| ~ in(esk7_3(X26,X27,X28),X28) )
& ( X19 != cartesian_product2(X17,X18)
| in(X23,X19)
| X23 != ordered_pair(X24,X25)
| ~ in(X25,X18)
| ~ in(X24,X17) )
& ( X19 != cartesian_product2(X17,X18)
| ~ in(X20,X19)
| X20 = ordered_pair(esk5_4(X17,X18,X19,X20),esk6_4(X17,X18,X19,X20)) )
& ( X19 != cartesian_product2(X17,X18)
| ~ in(X20,X19)
| in(esk6_4(X17,X18,X19,X20),X18) )
& ( X19 != cartesian_product2(X17,X18)
| ~ in(X20,X19)
| in(esk5_4(X17,X18,X19,X20),X17) ) ),
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])])])])])])]) ).
cnf(c_0_4,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_3]) ).
cnf(c_0_5,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_3]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
& subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3)) ) ),
inference(assume_negation,[status(cth)],[t118_zfmisc_1]) ).
cnf(c_0_7,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_4])]) ).
cnf(c_0_8,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_5]) ).
cnf(c_0_9,plain,
( X3 != cartesian_product2(X1,X2)
| ~ in(X4,X3)
| in(esk6_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_10,plain,
! [X10,X11,X12,X13,X14] :
( ( subset(X13,X14)
| ~ in(esk4_2(X13,X14),X14) )
& ( subset(X13,X14)
| in(esk4_2(X13,X14),X13) )
& ( in(X12,X11)
| ~ in(X12,X10)
| ~ subset(X10,X11) ) ),
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)],[d3_tarski])])])])])])]) ).
fof(c_0_11,negated_conjecture,
( ( ~ subset(cartesian_product2(esk3_0,esk1_0),cartesian_product2(esk3_0,esk2_0))
| ~ subset(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk3_0)) )
& subset(esk1_0,esk2_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_12,plain,
( ~ in(X1,cartesian_product2(X4,X5))
| ~ in(esk5_4(X4,X5,cartesian_product2(X4,X5),X1),X2)
| ~ in(esk6_4(X4,X5,cartesian_product2(X4,X5),X1),X3)
| in(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| in(esk6_4(X1,X2,cartesian_product2(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ in(X1,cartesian_product2(X4,X3))
| ~ in(esk5_4(X4,X3,cartesian_product2(X4,X3),X1),X2)
| in(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(X1,esk1_0)
| in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( X3 != cartesian_product2(X1,X2)
| ~ in(X4,X3)
| in(esk5_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(X1,cartesian_product2(X3,X2))
| ~ in(esk5_4(X3,X2,cartesian_product2(X3,X2),X1),esk1_0)
| in(X1,cartesian_product2(esk2_0,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| in(esk5_4(X1,X2,cartesian_product2(X1,X2),X3),X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(X1,cartesian_product2(X3,X4))
| ~ in(esk5_4(X3,X4,cartesian_product2(X3,X4),X1),X2)
| ~ in(esk6_4(X3,X4,cartesian_product2(X3,X4),X1),esk1_0)
| in(X1,cartesian_product2(X2,esk2_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_22,plain,
( ~ in(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(X1,cartesian_product2(esk1_0,X2))
| in(X1,cartesian_product2(esk2_0,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(X1,cartesian_product2(X3,esk1_0))
| ~ in(esk5_4(X3,esk1_0,cartesian_product2(X3,esk1_0),X1),X2)
| in(X1,cartesian_product2(X2,esk2_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(esk4_2(X1,cartesian_product2(esk2_0,X2)),cartesian_product2(esk1_0,X2))
| subset(X1,cartesian_product2(esk2_0,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(X1,cartesian_product2(X2,esk1_0))
| in(X1,cartesian_product2(X2,esk2_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( ~ subset(cartesian_product2(esk3_0,esk1_0),cartesian_product2(esk3_0,esk2_0))
| ~ subset(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
subset(cartesian_product2(esk1_0,X1),cartesian_product2(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(esk4_2(X1,cartesian_product2(X2,esk2_0)),cartesian_product2(X2,esk1_0))
| subset(X1,cartesian_product2(X2,esk2_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
~ subset(cartesian_product2(esk3_0,esk1_0),cartesian_product2(esk3_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
subset(cartesian_product2(X1,esk1_0),cartesian_product2(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:55:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % new_bool_3 with pid 290236 completed with status 0
% 0.10/0.44 % Result found by new_bool_3
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 290243 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 10
% 0.10/0.44 % Removed by relevancy pruning/SinE : 2
% 0.10/0.44 % Initial clauses : 18
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 18
% 0.10/0.44 % Processed clauses : 118
% 0.10/0.44 % ...of these trivial : 0
% 0.10/0.44 % ...subsumed : 21
% 0.10/0.44 % ...remaining for further processing : 97
% 0.10/0.44 % Other redundant clauses eliminated : 7
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 2
% 0.10/0.44 % Backward-rewritten : 2
% 0.10/0.44 % Generated clauses : 205
% 0.10/0.44 % ...of the previous two non-redundant : 197
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 1
% 0.10/0.44 % Paramodulations : 195
% 0.10/0.44 % Factorizations : 4
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 7
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 4
% 0.10/0.44 % ...of those cached : 0
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 89
% 0.10/0.44 % Positive orientable unit clauses : 6
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 3
% 0.10/0.44 % Non-unit-clauses : 80
% 0.10/0.44 % Current number of unprocessed clauses: 97
% 0.10/0.44 % ...number of literals in the above : 405
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 4
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 1165
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 800
% 0.10/0.44 % Non-unit clause-clause subsumptions : 23
% 0.10/0.44 % Unit Clause-clause subsumption calls : 2
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 3
% 0.10/0.44 % BW rewrite match successes : 2
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 5379
% 0.10/0.44 % Search garbage collected termcells : 391
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.011 s
% 0.10/0.44 % System time : 0.006 s
% 0.10/0.44 % Total time : 0.016 s
% 0.10/0.44 % Maximum resident set size: 3640 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.012 s
% 0.10/0.44 % System time : 0.010 s
% 0.10/0.44 % Total time : 0.022 s
% 0.10/0.44 % Maximum resident set size: 4608 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------