%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET950+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 : n011.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 0.16s 15.79s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% Number of atoms : 90 ( 23 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 114 ( 46 ~; 43 |; 21 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 70 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t103_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
~ ( ! [X5,X6] :
~ ( X4 = ordered_pair(X5,X6)
& in(X6,X3)
& in(X5,X2) )
& in(X4,X1)
& subset(X1,cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_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/sandbox2/benchmark/theBenchmark.p',d2_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,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( ! [X5,X6] :
~ ( X4 = ordered_pair(X5,X6)
& in(X6,X3)
& in(X5,X2) )
& in(X4,X1)
& subset(X1,cartesian_product2(X2,X3)) ),
inference(assume_negation,[status(cth)],[t103_zfmisc_1]) ).
fof(c_0_4,plain,
! [X24,X25,X26,X27,X30,X31,X32,X33,X34,X35,X37,X38] :
( ( X35 = cartesian_product2(X33,X34)
| in(esk8_3(X33,X34,X35),X35)
| esk8_3(X33,X34,X35) = ordered_pair(esk9_3(X33,X34,X35),esk10_3(X33,X34,X35)) )
& ( X35 = cartesian_product2(X33,X34)
| in(esk8_3(X33,X34,X35),X35)
| in(esk10_3(X33,X34,X35),X34) )
& ( X35 = cartesian_product2(X33,X34)
| in(esk8_3(X33,X34,X35),X35)
| in(esk9_3(X33,X34,X35),X33) )
& ( X35 = cartesian_product2(X33,X34)
| esk8_3(X33,X34,X35) != ordered_pair(X37,X38)
| ~ in(X38,X34)
| ~ in(X37,X33)
| ~ in(esk8_3(X33,X34,X35),X35) )
& ( X26 != cartesian_product2(X24,X25)
| in(X30,X26)
| X30 != ordered_pair(X31,X32)
| ~ in(X32,X25)
| ~ in(X31,X24) )
& ( X26 != cartesian_product2(X24,X25)
| ~ in(X27,X26)
| X27 = ordered_pair(esk6_4(X24,X25,X26,X27),esk7_4(X24,X25,X26,X27)) )
& ( X26 != cartesian_product2(X24,X25)
| ~ in(X27,X26)
| in(esk7_4(X24,X25,X26,X27),X25) )
& ( X26 != cartesian_product2(X24,X25)
| ~ in(X27,X26)
| in(esk6_4(X24,X25,X26,X27),X24) ) ),
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] :
( ( esk4_0 != ordered_pair(X11,X12)
| ~ in(X12,esk3_0)
| ~ in(X11,esk2_0) )
& in(esk4_0,esk1_0)
& subset(esk1_0,cartesian_product2(esk2_0,esk3_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,
( X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4)
| X1 = ordered_pair(esk6_4(X2,X3,X4,X1),esk7_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( esk4_0 != ordered_pair(X1,X2)
| ~ in(X2,esk3_0)
| ~ in(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| ordered_pair(esk6_4(X1,X2,cartesian_product2(X1,X2),X3),esk7_4(X1,X2,cartesian_product2(X1,X2),X3)) = X3 ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( X3 != cartesian_product2(X1,X2)
| ~ in(X4,X3)
| in(esk7_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( ~ in(esk4_0,cartesian_product2(X1,X2))
| ~ in(esk6_4(X1,X2,cartesian_product2(X1,X2),esk4_0),esk2_0)
| ~ in(esk7_4(X1,X2,cartesian_product2(X1,X2),esk4_0),esk3_0) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8])]) ).
cnf(c_0_11,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| in(esk7_4(X1,X2,cartesian_product2(X1,X2),X3),X2) ),
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),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_13,plain,
! [X17,X18,X19,X20,X21] :
( ( subset(X20,X21)
| ~ in(esk5_2(X20,X21),X21) )
& ( subset(X20,X21)
| in(esk5_2(X20,X21),X20) )
& ( in(X19,X18)
| ~ in(X19,X17)
| ~ subset(X17,X18) ) ),
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])])])])])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ in(esk4_0,cartesian_product2(X1,esk3_0))
| ~ in(esk6_4(X1,esk3_0,cartesian_product2(X1,esk3_0),esk4_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| in(esk6_4(X1,X2,cartesian_product2(X1,X2),X3),X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
subset(esk1_0,cartesian_product2(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
~ in(esk4_0,cartesian_product2(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(X1,esk1_0)
| in(X1,cartesian_product2(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
in(esk4_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET950+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.16/15.72 % CPULimit : 300
% 0.16/15.72 % WCLimit : 300
% 0.16/15.72 % DateTime : Mon Sep 21 05:45:06 UTC 2026
% 0.16/15.72 % CPUTime :
% 0.16/15.72 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/15.76 Running first-order theorem proving
% 0.16/15.76 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
% 0.16/15.79 % Version: 3.5.1
% 0.16/15.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/15.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/15.79 % Starting new_bool_3 with 300s (1) cores
% 0.16/15.79 % Starting new_bool_1 with 300s (1) cores
% 0.16/15.79 % Starting sh5l with 300s (1) cores
% 0.16/15.79 % new_bool_3 with pid 3264330 completed with status 0
% 0.16/15.79 % Result found by new_bool_3
% 0.16/15.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/15.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/15.79 % Starting new_bool_3 with 300s (1) cores
% 0.16/15.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/15.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/15.79 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.16/15.79 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/15.79 % Starting SubtermCWHack with 31s (1) cores
% 0.16/15.79 % SubtermCWHack with pid 3264338 completed with status 0
% 0.16/15.79 % Result found by SubtermCWHack
% 0.16/15.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/15.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/15.79 % Starting new_bool_3 with 300s (1) cores
% 0.16/15.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/15.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/15.79 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.16/15.79 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/15.79 % Starting SubtermCWHack with 31s (1) cores
% 0.16/15.79 % Preprocessing time : 0.001 s
% 0.16/15.79
% 0.16/15.79 % Proof found!
% 0.16/15.79 % SZS status Theorem
% 0.16/15.79 % SZS output start CNFRefutation
% See solution above
% 0.16/15.79 % Parsed axioms : 10
% 0.16/15.79 % Removed by relevancy pruning/SinE : 2
% 0.16/15.79 % Initial clauses : 19
% 0.16/15.79 % Removed in clause preprocessing : 0
% 0.16/15.79 % Initial clauses in saturation : 19
% 0.16/15.79 % Processed clauses : 51
% 0.16/15.79 % ...of these trivial : 0
% 0.16/15.79 % ...subsumed : 1
% 0.16/15.79 % ...remaining for further processing : 50
% 0.16/15.79 % Other redundant clauses eliminated : 6
% 0.16/15.79 % Clauses deleted for lack of memory : 0
% 0.16/15.79 % Backward-subsumed : 0
% 0.16/15.79 % Backward-rewritten : 0
% 0.16/15.79 % Generated clauses : 45
% 0.16/15.79 % ...of the previous two non-redundant : 40
% 0.16/15.79 % ...aggressively subsumed : 0
% 0.16/15.79 % Contextual simplify-reflections : 0
% 0.16/15.79 % Paramodulations : 40
% 0.16/15.79 % Factorizations : 0
% 0.16/15.79 % NegExts : 0
% 0.16/15.79 % Equation resolutions : 6
% 0.16/15.79 % Disequality decompositions : 0
% 0.16/15.79 % Total rewrite steps : 3
% 0.16/15.79 % ...of those cached : 0
% 0.16/15.79 % Propositional unsat checks : 0
% 0.16/15.79 % Propositional check models : 0
% 0.16/15.79 % Propositional check unsatisfiable : 0
% 0.16/15.79 % Propositional clauses : 0
% 0.16/15.79 % Propositional clauses after purity: 0
% 0.16/15.79 % Propositional unsat core size : 0
% 0.16/15.79 % Propositional preprocessing time : 0.000
% 0.16/15.79 % Propositional encoding time : 0.000
% 0.16/15.79 % Propositional solver time : 0.000
% 0.16/15.79 % Success case prop preproc time : 0.000
% 0.16/15.79 % Success case prop encoding time : 0.000
% 0.16/15.79 % Success case prop solver time : 0.000
% 0.16/15.79 % Current number of processed clauses : 46
% 0.16/15.79 % Positive orientable unit clauses : 4
% 0.16/15.79 % Positive unorientable unit clauses: 0
% 0.16/15.79 % Negative unit clauses : 6
% 0.16/15.79 % Non-unit-clauses : 36
% 0.16/15.79 % Current number of unprocessed clauses: 8
% 0.16/15.79 % ...number of literals in the above : 38
% 0.16/15.79 % Current number of archived formulas : 0
% 0.16/15.79 % Current number of archived clauses : 0
% 0.16/15.79 % Clause-clause subsumption calls (NU) : 185
% 0.16/15.79 % Rec. Clause-clause subsumption calls : 139
% 0.16/15.79 % Non-unit clause-clause subsumptions : 0
% 0.16/15.79 % Unit Clause-clause subsumption calls : 24
% 0.16/15.79 % Rewrite failures with RHS unbound : 0
% 0.16/15.79 % BW rewrite match attempts : 0
% 0.16/15.79 % BW rewrite match successes : 0
% 0.16/15.79 % Condensation attempts : 0
% 0.16/15.79 % Condensation successes : 0
% 0.16/15.79 % Termbank termtop insertions : 2100
% 0.16/15.79 % Search garbage collected termcells : 406
% 0.16/15.79
% 0.16/15.79 % -------------------------------------------------
% 0.16/15.79 % User time : 0.009 s
% 0.16/15.79 % System time : 0.002 s
% 0.16/15.79 % Total time : 0.011 s
% 0.16/15.79 % Maximum resident set size: 3896 pages
% 0.16/15.79
% 0.16/15.79 % -------------------------------------------------
% 0.16/15.79 % User time : 0.012 s
% 0.16/15.79 % System time : 0.006 s
% 0.16/15.79 % Total time : 0.017 s
% 0.16/15.79 % Maximum resident set size: 4864 pages
% 0.16/15.79 % E exiting
%------------------------------------------------------------------------------