%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET976+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 : 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 02:15:53 PM UTC 2026
% Result : Theorem 0.22s 0.55s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 65 ( 22 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 71 ( 27 ~; 29 |; 10 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 4 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t129_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( X2 = X4
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_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(c_0_3,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( X2 = X4
& in(X1,X3) ) ),
inference(assume_negation,[status(cth)],[t129_zfmisc_1]) ).
fof(c_0_4,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( X16 = singleton(X15)
| esk5_2(X15,X16) = X15
| in(esk5_2(X15,X16),X16) )
& ( X16 = singleton(X15)
| esk5_2(X15,X16) != X15
| ~ in(esk5_2(X15,X16),X16) )
& ( X12 != singleton(X11)
| in(X14,X12)
| X14 != X11 )
& ( X12 != singleton(X11)
| X13 = X11
| ~ in(X13,X12) ) ),
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)],[d1_tarski])])])])])])]) ).
fof(c_0_5,plain,
! [X18,X19,X20,X21] :
( ( in(ordered_pair(X18,X19),cartesian_product2(X20,X21))
| ~ in(X19,X21)
| ~ in(X18,X20) )
& ( ~ in(ordered_pair(X18,X19),cartesian_product2(X20,X21))
| in(X19,X21) )
& ( ~ in(ordered_pair(X18,X19),cartesian_product2(X20,X21))
| in(X18,X20) ) ),
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_6,negated_conjecture,
( ( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| esk2_0 = esk4_0 )
& ( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| in(esk1_0,esk3_0) )
& ( esk2_0 != esk4_0
| ~ in(esk1_0,esk3_0)
| ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
cnf(c_0_7,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| esk2_0 = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0)))
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
esk2_0 = esk4_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_13,plain,
( ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( esk2_0 != esk4_0
| ~ in(esk1_0,esk3_0)
| ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,singleton(esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
in(esk1_0,esk3_0),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_16,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
~ in(ordered_pair(esk1_0,esk4_0),cartesian_product2(esk3_0,singleton(esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12]),c_0_15]),c_0_12])]) ).
cnf(c_0_18,plain,
( ~ in(X3,X4)
| ~ in(X1,X2)
| in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_16])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET976+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:43:50 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 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
% 0.22/0.55 % Version: 3.5.1
% 0.22/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.55 % Starting sh5l with 300s (1) cores
% 0.22/0.55 % sh5l with pid 300537 completed with status 0
% 0.22/0.55 % Result found by sh5l
% 0.22/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.55 % Starting sh5l with 300s (1) cores
% 0.22/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.22/0.55 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.22/0.55 % Search class: FGHSS-FFSS21-SFFFFFNN
% 0.22/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.55 % SubtermCWHack with pid 300539 completed with status 0
% 0.22/0.55 % Result found by SubtermCWHack
% 0.22/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.55 % Starting sh5l with 300s (1) cores
% 0.22/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.22/0.55 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.22/0.55 % Search class: FGHSS-FFSS21-SFFFFFNN
% 0.22/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.55 % Preprocessing time : 0.001 s
% 0.22/0.55
% 0.22/0.55 % Proof found!
% 0.22/0.55 % SZS status Theorem
% 0.22/0.55 % SZS output start CNFRefutation
% See solution above
% 0.22/0.55 % Parsed axioms : 9
% 0.22/0.55 % Removed by relevancy pruning/SinE : 0
% 0.22/0.55 % Initial clauses : 16
% 0.22/0.55 % Removed in clause preprocessing : 0
% 0.22/0.55 % Initial clauses in saturation : 16
% 0.22/0.55 % Processed clauses : 26
% 0.22/0.55 % ...of these trivial : 1
% 0.22/0.55 % ...subsumed : 0
% 0.22/0.55 % ...remaining for further processing : 25
% 0.22/0.55 % Other redundant clauses eliminated : 3
% 0.22/0.55 % Clauses deleted for lack of memory : 0
% 0.22/0.55 % Backward-subsumed : 0
% 0.22/0.55 % Backward-rewritten : 3
% 0.22/0.55 % Generated clauses : 23
% 0.22/0.55 % ...of the previous two non-redundant : 17
% 0.22/0.55 % ...aggressively subsumed : 0
% 0.22/0.55 % Contextual simplify-reflections : 2
% 0.22/0.55 % Paramodulations : 21
% 0.22/0.55 % Factorizations : 0
% 0.22/0.55 % NegExts : 0
% 0.22/0.55 % Equation resolutions : 3
% 0.22/0.55 % Disequality decompositions : 0
% 0.22/0.55 % Total rewrite steps : 14
% 0.22/0.55 % ...of those cached : 8
% 0.22/0.55 % Propositional unsat checks : 0
% 0.22/0.55 % Propositional check models : 0
% 0.22/0.55 % Propositional check unsatisfiable : 0
% 0.22/0.55 % Propositional clauses : 0
% 0.22/0.55 % Propositional clauses after purity: 0
% 0.22/0.55 % Propositional unsat core size : 0
% 0.22/0.55 % Propositional preprocessing time : 0.000
% 0.22/0.55 % Propositional encoding time : 0.000
% 0.22/0.55 % Propositional solver time : 0.000
% 0.22/0.55 % Success case prop preproc time : 0.000
% 0.22/0.55 % Success case prop encoding time : 0.000
% 0.22/0.55 % Success case prop solver time : 0.000
% 0.22/0.55 % Current number of processed clauses : 20
% 0.22/0.55 % Positive orientable unit clauses : 6
% 0.22/0.55 % Positive unorientable unit clauses: 1
% 0.22/0.55 % Negative unit clauses : 5
% 0.22/0.55 % Non-unit-clauses : 8
% 0.22/0.55 % Current number of unprocessed clauses: 6
% 0.22/0.55 % ...number of literals in the above : 10
% 0.22/0.55 % Current number of archived formulas : 0
% 0.22/0.55 % Current number of archived clauses : 3
% 0.22/0.55 % Clause-clause subsumption calls (NU) : 47
% 0.22/0.55 % Rec. Clause-clause subsumption calls : 47
% 0.22/0.55 % Non-unit clause-clause subsumptions : 2
% 0.22/0.55 % Unit Clause-clause subsumption calls : 2
% 0.22/0.55 % Rewrite failures with RHS unbound : 0
% 0.22/0.55 % BW rewrite match attempts : 2
% 0.22/0.55 % BW rewrite match successes : 1
% 0.22/0.55 % Condensation attempts : 0
% 0.22/0.55 % Condensation successes : 0
% 0.22/0.55 % Termbank termtop insertions : 1194
% 0.22/0.55 % Search garbage collected termcells : 246
% 0.22/0.55
% 0.22/0.55 % -------------------------------------------------
% 0.22/0.55 % User time : 0.005 s
% 0.22/0.55 % System time : 0.002 s
% 0.22/0.55 % Total time : 0.007 s
% 0.22/0.55 % Maximum resident set size: 3636 pages
% 0.22/0.55
% 0.22/0.55 % -------------------------------------------------
% 0.22/0.55 % User time : 0.006 s
% 0.22/0.55 % System time : 0.006 s
% 0.22/0.55 % Total time : 0.013 s
% 0.22/0.55 % Maximum resident set size: 4864 pages
% 0.22/0.55 % E exiting
%------------------------------------------------------------------------------