%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:15:52 PM UTC 2026
% Result : Theorem 0.25s 0.56s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 4 unt; 0 def)
% Number of atoms : 93 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 104 ( 44 ~; 41 |; 14 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 6 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t117_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( ~ subset(X2,X3)
& ( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| subset(cartesian_product2(X2,X1),cartesian_product2(X3,X1)) )
& X1 != empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(l55_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X2,X4)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ~ subset(X2,X3)
& ( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| subset(cartesian_product2(X2,X1),cartesian_product2(X3,X1)) )
& X1 != empty_set ),
inference(assume_negation,[status(cth)],[t117_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ~ subset(X2,X3)
& ( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| subset(cartesian_product2(X2,X1),cartesian_product2(X3,X1)) )
& X1 != empty_set ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,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_7,negated_conjecture,
( ~ subset(esk2_0,esk3_0)
& ( subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk1_0,esk3_0))
| subset(cartesian_product2(esk2_0,esk1_0),cartesian_product2(esk3_0,esk1_0)) )
& esk1_0 != empty_set ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_8,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk1_0,esk3_0))
| subset(cartesian_product2(esk2_0,esk1_0),cartesian_product2(esk3_0,esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X34,X35,X36,X37] :
( ( in(ordered_pair(X34,X35),cartesian_product2(X36,X37))
| ~ in(X35,X37)
| ~ in(X34,X36) )
& ( ~ in(ordered_pair(X34,X35),cartesian_product2(X36,X37))
| in(X35,X37) )
& ( ~ in(ordered_pair(X34,X35),cartesian_product2(X36,X37))
| in(X34,X36) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])])]) ).
fof(c_0_11,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_12,negated_conjecture,
( ~ in(X1,cartesian_product2(esk2_0,esk1_0))
| in(X1,cartesian_product2(esk3_0,esk1_0))
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( ~ in(X3,X4)
| ~ in(X1,X2)
| in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X38,X39,X40] :
( ( X40 = empty_set
| in(esk10_1(X40),X40) )
& ( ~ in(X39,X38)
| X38 != empty_set ) ),
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)],[c_0_11])])])])])]) ).
cnf(c_0_15,negated_conjecture,
( ~ in(X1,esk2_0)
| ~ in(X2,esk1_0)
| in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk1_0))
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( X1 = empty_set
| in(esk10_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
( ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(X1,esk2_0)
| in(ordered_pair(X1,esk10_1(esk1_0)),cartesian_product2(esk3_0,esk1_0))
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk1_0,esk3_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(X1,esk2_0)
| in(X1,esk3_0)
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,plain,
( ~ in(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
( in(esk4_2(esk2_0,X1),esk3_0)
| subset(esk2_0,X1)
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
~ subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk1_0,esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,plain,
( ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(X1,cartesian_product2(esk1_0,esk2_0))
| in(X1,cartesian_product2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_8,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(ordered_pair(X2,X1),cartesian_product2(esk1_0,esk2_0))
| in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(X2,esk1_0)
| ~ in(X1,esk2_0)
| in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_13]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(X1,esk2_0)
| in(X1,esk3_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( ~ in(esk4_2(X1,esk3_0),esk2_0)
| subset(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_21]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n004.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:45:19 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 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
% 0.25/0.56 % Version: 3.5.1
% 0.25/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.56 % Starting sh5l with 300s (1) cores
% 0.25/0.56 % new_bool_3 with pid 2370381 completed with status 0
% 0.25/0.56 % Result found by new_bool_3
% 0.25/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.56 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.25/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.56 % SubtermCWHack with pid 2370388 completed with status 0
% 0.25/0.56 % Result found by SubtermCWHack
% 0.25/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.56 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.25/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.56 % Preprocessing time : 0.002 s
% 0.25/0.56
% 0.25/0.56 % Proof found!
% 0.25/0.56 % SZS status Theorem
% 0.25/0.56 % SZS output start CNFRefutation
% See solution above
% 0.25/0.56 % Parsed axioms : 13
% 0.25/0.56 % Removed by relevancy pruning/SinE : 2
% 0.25/0.56 % Initial clauses : 25
% 0.25/0.56 % Removed in clause preprocessing : 0
% 0.25/0.56 % Initial clauses in saturation : 25
% 0.25/0.56 % Processed clauses : 94
% 0.25/0.56 % ...of these trivial : 0
% 0.25/0.56 % ...subsumed : 25
% 0.25/0.56 % ...remaining for further processing : 69
% 0.25/0.56 % Other redundant clauses eliminated : 6
% 0.25/0.56 % Clauses deleted for lack of memory : 0
% 0.25/0.56 % Backward-subsumed : 1
% 0.25/0.56 % Backward-rewritten : 16
% 0.25/0.56 % Generated clauses : 147
% 0.25/0.56 % ...of the previous two non-redundant : 144
% 0.25/0.56 % ...aggressively subsumed : 0
% 0.25/0.56 % Contextual simplify-reflections : 0
% 0.25/0.56 % Paramodulations : 142
% 0.25/0.56 % Factorizations : 0
% 0.25/0.56 % NegExts : 0
% 0.25/0.56 % Equation resolutions : 6
% 0.25/0.56 % Disequality decompositions : 0
% 0.25/0.56 % Total rewrite steps : 21
% 0.25/0.56 % ...of those cached : 15
% 0.25/0.56 % Propositional unsat checks : 0
% 0.25/0.56 % Propositional check models : 0
% 0.25/0.56 % Propositional check unsatisfiable : 0
% 0.25/0.56 % Propositional clauses : 0
% 0.25/0.56 % Propositional clauses after purity: 0
% 0.25/0.56 % Propositional unsat core size : 0
% 0.25/0.56 % Propositional preprocessing time : 0.000
% 0.25/0.56 % Propositional encoding time : 0.000
% 0.25/0.56 % Propositional solver time : 0.000
% 0.25/0.56 % Success case prop preproc time : 0.000
% 0.25/0.56 % Success case prop encoding time : 0.000
% 0.25/0.56 % Success case prop solver time : 0.000
% 0.25/0.56 % Current number of processed clauses : 47
% 0.25/0.56 % Positive orientable unit clauses : 7
% 0.25/0.56 % Positive unorientable unit clauses: 0
% 0.25/0.56 % Negative unit clauses : 6
% 0.25/0.56 % Non-unit-clauses : 34
% 0.25/0.56 % Current number of unprocessed clauses: 61
% 0.25/0.56 % ...number of literals in the above : 240
% 0.25/0.56 % Current number of archived formulas : 0
% 0.25/0.56 % Current number of archived clauses : 17
% 0.25/0.56 % Clause-clause subsumption calls (NU) : 382
% 0.25/0.56 % Rec. Clause-clause subsumption calls : 251
% 0.25/0.56 % Non-unit clause-clause subsumptions : 4
% 0.25/0.56 % Unit Clause-clause subsumption calls : 38
% 0.25/0.56 % Rewrite failures with RHS unbound : 0
% 0.25/0.56 % BW rewrite match attempts : 3
% 0.25/0.56 % BW rewrite match successes : 3
% 0.25/0.56 % Condensation attempts : 0
% 0.25/0.56 % Condensation successes : 0
% 0.25/0.56 % Termbank termtop insertions : 3684
% 0.25/0.56 % Search garbage collected termcells : 462
% 0.25/0.56
% 0.25/0.56 % -------------------------------------------------
% 0.25/0.56 % User time : 0.014 s
% 0.25/0.56 % System time : 0.007 s
% 0.25/0.56 % Total time : 0.021 s
% 0.25/0.56 % Maximum resident set size: 3644 pages
% 0.25/0.56
% 0.25/0.56 % -------------------------------------------------
% 0.25/0.56 % User time : 0.019 s
% 0.25/0.56 % System time : 0.011 s
% 0.25/0.56 % Total time : 0.030 s
% 0.25/0.56 % Maximum resident set size: 4864 pages
% 0.25/0.56 % E exiting
%------------------------------------------------------------------------------