%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:15:51 PM UTC 2026
% Result : Theorem 0.23s 0.64s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 83 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 86 ( 35 ~; 36 |; 8 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 11 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t114_zfmisc_1,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = X2
| X2 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
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(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = X2
| X2 = empty_set
| X1 = empty_set ) ),
inference(assume_negation,[status(cth)],[t114_zfmisc_1]) ).
fof(c_0_5,plain,
! [X11,X12,X13,X14] :
( ( in(ordered_pair(X11,X12),cartesian_product2(X13,X14))
| ~ in(X12,X14)
| ~ in(X11,X13) )
& ( ~ in(ordered_pair(X11,X12),cartesian_product2(X13,X14))
| in(X12,X14) )
& ( ~ in(ordered_pair(X11,X12),cartesian_product2(X13,X14))
| in(X11,X13) ) ),
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,
( esk1_0 != esk2_0
& esk2_0 != empty_set
& esk1_0 != empty_set
& cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk2_0,esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
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,
cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X7,X8,X9] :
( ( X9 = empty_set
| in(esk3_1(X9),X9) )
& ( ~ in(X8,X7)
| X7 != 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_7])])])])])]) ).
cnf(c_0_11,negated_conjecture,
( ~ in(ordered_pair(X2,X1),cartesian_product2(esk2_0,esk1_0))
| in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( ~ in(X3,X4)
| ~ in(X1,X2)
| in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_13,plain,
! [X17,X18] :
( ( X17 = X18
| in(esk4_2(X17,X18),X18)
| in(esk4_2(X17,X18),X17) )
& ( X17 = X18
| ~ in(esk4_2(X17,X18),X18)
| ~ in(esk4_2(X17,X18),X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])]) ).
cnf(c_0_14,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( ~ in(X2,esk2_0)
| ~ in(X1,esk1_0)
| in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( X1 = X2
| in(esk4_2(X1,X2),X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(X2,esk2_0)
| in(esk4_2(esk1_0,X1),X1)
| in(esk4_2(esk1_0,X1),esk2_0)
| esk1_0 = X1 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( in(esk4_2(empty_set,X1),X1)
| empty_set = X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,plain,
( ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
( in(esk4_2(esk1_0,X1),X1)
| in(esk4_2(esk1_0,X1),esk2_0)
| esk1_0 = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(ordered_pair(X1,X2),cartesian_product2(esk2_0,esk1_0))
| in(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_25,plain,
( ~ in(esk4_2(X1,X2),X2)
| ~ in(esk4_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
in(esk4_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_22]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(X1,esk2_0)
| ~ in(X2,esk1_0)
| in(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_28,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk4_2(esk1_0,esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(X1,esk2_0)
| in(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.48 % Computer : n011.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 05:45:25 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.57 Running first-order theorem proving
% 0.23/0.57 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
% 0.23/0.64 % Version: 3.5.1
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.64 % Starting sh5l with 300s (1) cores
% 0.23/0.64 % new_bool_3 with pid 1096200 completed with status 0
% 0.23/0.64 % Result found by new_bool_3
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.64 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.23/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.64 % SubtermCWHack with pid 1096205 completed with status 0
% 0.23/0.64 % Result found by SubtermCWHack
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.64 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.23/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.64 % Preprocessing time : 0.002 s
% 0.23/0.64
% 0.23/0.64 % Proof found!
% 0.23/0.64 % SZS status Theorem
% 0.23/0.64 % SZS output start CNFRefutation
% See solution above
% 0.23/0.64 % Parsed axioms : 11
% 0.23/0.64 % Removed by relevancy pruning/SinE : 2
% 0.23/0.64 % Initial clauses : 16
% 0.23/0.64 % Removed in clause preprocessing : 0
% 0.23/0.64 % Initial clauses in saturation : 16
% 0.23/0.64 % Processed clauses : 56
% 0.23/0.64 % ...of these trivial : 1
% 0.23/0.64 % ...subsumed : 5
% 0.23/0.64 % ...remaining for further processing : 50
% 0.23/0.64 % Other redundant clauses eliminated : 1
% 0.23/0.64 % Clauses deleted for lack of memory : 0
% 0.23/0.64 % Backward-subsumed : 2
% 0.23/0.64 % Backward-rewritten : 3
% 0.23/0.64 % Generated clauses : 89
% 0.23/0.64 % ...of the previous two non-redundant : 79
% 0.23/0.64 % ...aggressively subsumed : 0
% 0.23/0.64 % Contextual simplify-reflections : 0
% 0.23/0.64 % Paramodulations : 84
% 0.23/0.64 % Factorizations : 4
% 0.23/0.64 % NegExts : 0
% 0.23/0.64 % Equation resolutions : 1
% 0.23/0.64 % Disequality decompositions : 0
% 0.23/0.64 % Total rewrite steps : 5
% 0.23/0.64 % ...of those cached : 1
% 0.23/0.64 % Propositional unsat checks : 0
% 0.23/0.64 % Propositional check models : 0
% 0.23/0.64 % Propositional check unsatisfiable : 0
% 0.23/0.64 % Propositional clauses : 0
% 0.23/0.64 % Propositional clauses after purity: 0
% 0.23/0.64 % Propositional unsat core size : 0
% 0.23/0.64 % Propositional preprocessing time : 0.000
% 0.23/0.64 % Propositional encoding time : 0.000
% 0.23/0.64 % Propositional solver time : 0.000
% 0.23/0.64 % Success case prop preproc time : 0.000
% 0.23/0.64 % Success case prop encoding time : 0.000
% 0.23/0.64 % Success case prop solver time : 0.000
% 0.23/0.64 % Current number of processed clauses : 44
% 0.23/0.64 % Positive orientable unit clauses : 7
% 0.23/0.64 % Positive unorientable unit clauses: 0
% 0.23/0.64 % Negative unit clauses : 12
% 0.23/0.64 % Non-unit-clauses : 25
% 0.23/0.64 % Current number of unprocessed clauses: 20
% 0.23/0.64 % ...number of literals in the above : 70
% 0.23/0.64 % Current number of archived formulas : 0
% 0.23/0.64 % Current number of archived clauses : 5
% 0.23/0.64 % Clause-clause subsumption calls (NU) : 175
% 0.23/0.64 % Rec. Clause-clause subsumption calls : 154
% 0.23/0.64 % Non-unit clause-clause subsumptions : 5
% 0.23/0.64 % Unit Clause-clause subsumption calls : 52
% 0.23/0.64 % Rewrite failures with RHS unbound : 0
% 0.23/0.64 % BW rewrite match attempts : 3
% 0.23/0.64 % BW rewrite match successes : 3
% 0.23/0.64 % Condensation attempts : 0
% 0.23/0.64 % Condensation successes : 0
% 0.23/0.64 % Termbank termtop insertions : 1899
% 0.23/0.64 % Search garbage collected termcells : 210
% 0.23/0.64
% 0.23/0.64 % -------------------------------------------------
% 0.23/0.64 % User time : 0.012 s
% 0.23/0.64 % System time : 0.004 s
% 0.23/0.64 % Total time : 0.016 s
% 0.23/0.64 % Maximum resident set size: 3380 pages
% 0.23/0.64
% 0.23/0.64 % -------------------------------------------------
% 0.23/0.64 % User time : 0.014 s
% 0.23/0.64 % System time : 0.010 s
% 0.23/0.64 % Total time : 0.025 s
% 0.23/0.64 % Maximum resident set size: 4608 pages
% 0.23/0.64 % E exiting
%------------------------------------------------------------------------------