%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET949+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 : n016.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 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 50 ( 22 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 66 ( 28 ~; 23 |; 13 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 46 ( 4 sgn 33 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t102_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( ! [X4,X5] : ordered_pair(X4,X5) != X1
& in(X1,cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_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(c_0_2,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ! [X4,X5] : ordered_pair(X4,X5) != X1
& in(X1,cartesian_product2(X2,X3)) ),
inference(assume_negation,[status(cth)],[t102_zfmisc_1]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ! [X4,X5] : ordered_pair(X4,X5) != X1
& in(X1,cartesian_product2(X2,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_4,plain,
! [X16,X17,X18,X19,X22,X23,X24,X25,X26,X27,X29,X30] :
( ( X27 = cartesian_product2(X25,X26)
| in(esk6_3(X25,X26,X27),X27)
| esk6_3(X25,X26,X27) = ordered_pair(esk7_3(X25,X26,X27),esk8_3(X25,X26,X27)) )
& ( X27 = cartesian_product2(X25,X26)
| in(esk6_3(X25,X26,X27),X27)
| in(esk8_3(X25,X26,X27),X26) )
& ( X27 = cartesian_product2(X25,X26)
| in(esk6_3(X25,X26,X27),X27)
| in(esk7_3(X25,X26,X27),X25) )
& ( X27 = cartesian_product2(X25,X26)
| esk6_3(X25,X26,X27) != ordered_pair(X29,X30)
| ~ in(X30,X26)
| ~ in(X29,X25)
| ~ in(esk6_3(X25,X26,X27),X27) )
& ( X18 != cartesian_product2(X16,X17)
| in(X22,X18)
| X22 != ordered_pair(X23,X24)
| ~ in(X24,X17)
| ~ in(X23,X16) )
& ( X18 != cartesian_product2(X16,X17)
| ~ in(X19,X18)
| X19 = ordered_pair(esk4_4(X16,X17,X18,X19),esk5_4(X16,X17,X18,X19)) )
& ( X18 != cartesian_product2(X16,X17)
| ~ in(X19,X18)
| in(esk5_4(X16,X17,X18,X19),X17) )
& ( X18 != cartesian_product2(X16,X17)
| ~ in(X19,X18)
| in(esk4_4(X16,X17,X18,X19),X16) ) ),
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,
! [X10,X11] :
( ordered_pair(X10,X11) != esk1_0
& in(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(esk4_4(X2,X3,X4,X1),esk5_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
ordered_pair(X1,X2) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ in(X3,cartesian_product2(X1,X2))
| ordered_pair(esk4_4(X1,X2,cartesian_product2(X1,X2),X3),esk5_4(X1,X2,cartesian_product2(X1,X2),X3)) = X3 ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
in(esk1_0,cartesian_product2(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
~ in(esk1_0,cartesian_product2(X1,X2)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8])]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_9,c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:49:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.43 % Version: 3.5.1
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.43 % Starting sh5l with 300s (1) cores
% 0.15/0.43 % new_bool_3 with pid 1689065 completed with status 0
% 0.15/0.43 % Result found by new_bool_3
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.43 % Search class: FGHSF-FFSF33-SFFFFFNN
% 0.15/0.43 % partial match(1): FGHSF-FFSF32-SFFFFFNN
% 0.15/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.43 % SubtermCWHack with pid 1689071 completed with status 0
% 0.15/0.43 % Result found by SubtermCWHack
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.43 % Search class: FGHSF-FFSF33-SFFFFFNN
% 0.15/0.43 % partial match(1): FGHSF-FFSF32-SFFFFFNN
% 0.15/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.43 % Preprocessing time : 0.001 s
% 0.15/0.43
% 0.15/0.43 % Proof found!
% 0.15/0.43 % SZS status Theorem
% 0.15/0.43 % SZS output start CNFRefutation
% See solution above
% 0.15/0.43 % Parsed axioms : 8
% 0.15/0.43 % Removed by relevancy pruning/SinE : 2
% 0.15/0.43 % Initial clauses : 14
% 0.15/0.43 % Removed in clause preprocessing : 0
% 0.15/0.43 % Initial clauses in saturation : 14
% 0.15/0.43 % Processed clauses : 26
% 0.15/0.43 % ...of these trivial : 0
% 0.15/0.43 % ...subsumed : 0
% 0.15/0.43 % ...remaining for further processing : 26
% 0.15/0.43 % Other redundant clauses eliminated : 6
% 0.15/0.43 % Clauses deleted for lack of memory : 0
% 0.15/0.43 % Backward-subsumed : 0
% 0.15/0.43 % Backward-rewritten : 0
% 0.15/0.43 % Generated clauses : 20
% 0.15/0.43 % ...of the previous two non-redundant : 18
% 0.15/0.43 % ...aggressively subsumed : 0
% 0.15/0.43 % Contextual simplify-reflections : 0
% 0.15/0.43 % Paramodulations : 14
% 0.15/0.43 % Factorizations : 0
% 0.15/0.43 % NegExts : 0
% 0.15/0.43 % Equation resolutions : 6
% 0.15/0.43 % Disequality decompositions : 0
% 0.15/0.43 % Total rewrite steps : 0
% 0.15/0.43 % ...of those cached : 0
% 0.15/0.43 % Propositional unsat checks : 0
% 0.15/0.43 % Propositional check models : 0
% 0.15/0.43 % Propositional check unsatisfiable : 0
% 0.15/0.43 % Propositional clauses : 0
% 0.15/0.43 % Propositional clauses after purity: 0
% 0.15/0.43 % Propositional unsat core size : 0
% 0.15/0.43 % Propositional preprocessing time : 0.000
% 0.15/0.43 % Propositional encoding time : 0.000
% 0.15/0.43 % Propositional solver time : 0.000
% 0.15/0.43 % Success case prop preproc time : 0.000
% 0.15/0.43 % Success case prop encoding time : 0.000
% 0.15/0.43 % Success case prop solver time : 0.000
% 0.15/0.43 % Current number of processed clauses : 21
% 0.15/0.43 % Positive orientable unit clauses : 1
% 0.15/0.43 % Positive unorientable unit clauses: 0
% 0.15/0.43 % Negative unit clauses : 5
% 0.15/0.43 % Non-unit-clauses : 15
% 0.15/0.43 % Current number of unprocessed clauses: 6
% 0.15/0.43 % ...number of literals in the above : 23
% 0.15/0.43 % Current number of archived formulas : 0
% 0.15/0.43 % Current number of archived clauses : 1
% 0.15/0.43 % Clause-clause subsumption calls (NU) : 39
% 0.15/0.43 % Rec. Clause-clause subsumption calls : 33
% 0.15/0.43 % Non-unit clause-clause subsumptions : 0
% 0.15/0.43 % Unit Clause-clause subsumption calls : 8
% 0.15/0.43 % Rewrite failures with RHS unbound : 0
% 0.15/0.43 % BW rewrite match attempts : 0
% 0.15/0.43 % BW rewrite match successes : 0
% 0.15/0.43 % Condensation attempts : 0
% 0.15/0.43 % Condensation successes : 0
% 0.15/0.43 % Termbank termtop insertions : 1254
% 0.15/0.43 % Search garbage collected termcells : 307
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.008 s
% 0.15/0.43 % System time : 0.000 s
% 0.15/0.43 % Total time : 0.008 s
% 0.15/0.43 % Maximum resident set size: 3584 pages
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.009 s
% 0.15/0.43 % System time : 0.005 s
% 0.15/0.43 % Total time : 0.014 s
% 0.15/0.43 % Maximum resident set size: 4864 pages
% 0.15/0.43 % E exiting
%------------------------------------------------------------------------------