%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET983+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 02:15:53 PM UTC 2026
% Result : Theorem 0.15s 0.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 50 ( 11 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 55 ( 20 ~; 21 |; 10 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 46 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t137_zfmisc_1,conjecture,
! [X1,X2,X3,X4,X5] :
( ( in(X1,cartesian_product2(X4,X5))
& in(X1,cartesian_product2(X2,X3)) )
=> in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
fof(t123_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(c_0_3,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( X20 = set_intersection2(X18,X19)
| in(esk6_3(X18,X19,X20),X20)
| in(esk6_3(X18,X19,X20),X19) )
& ( X20 = set_intersection2(X18,X19)
| in(esk6_3(X18,X19,X20),X20)
| in(esk6_3(X18,X19,X20),X18) )
& ( X20 = set_intersection2(X18,X19)
| ~ in(esk6_3(X18,X19,X20),X19)
| ~ in(esk6_3(X18,X19,X20),X18)
| ~ in(esk6_3(X18,X19,X20),X20) )
& ( X15 != set_intersection2(X13,X14)
| in(X17,X15)
| ~ in(X17,X14)
| ~ in(X17,X13) )
& ( X15 != set_intersection2(X13,X14)
| ~ in(X16,X15)
| in(X16,X14) )
& ( X15 != set_intersection2(X13,X14)
| ~ in(X16,X15)
| in(X16,X13) ) ),
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_xboole_0])])])])])])]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4,X5] :
( ( in(X1,cartesian_product2(X4,X5))
& in(X1,cartesian_product2(X2,X3)) )
=> in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
inference(assume_negation,[status(cth)],[t137_zfmisc_1]) ).
cnf(c_0_5,plain,
( X4 != set_intersection2(X2,X3)
| ~ in(X1,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [X22,X23,X24,X25] : cartesian_product2(set_intersection2(X22,X23),set_intersection2(X24,X25)) = set_intersection2(cartesian_product2(X22,X24),cartesian_product2(X23,X25)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( ~ in(esk1_0,cartesian_product2(set_intersection2(esk2_0,esk4_0),set_intersection2(esk3_0,esk5_0)))
& in(esk1_0,cartesian_product2(esk4_0,esk5_0))
& in(esk1_0,cartesian_product2(esk2_0,esk3_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_8,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ in(esk1_0,cartesian_product2(set_intersection2(esk2_0,esk4_0),set_intersection2(esk3_0,esk5_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ in(X1,cartesian_product2(X2,X4))
| ~ in(X1,cartesian_product2(X3,X5))
| in(X1,cartesian_product2(set_intersection2(X2,X3),set_intersection2(X4,X5))) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
in(esk1_0,cartesian_product2(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
in(esk1_0,cartesian_product2(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.54 % Computer : n004.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Mon Sep 21 05:46:05 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.55 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.58 Running first-order theorem proving
% 0.15/0.58 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
% 0.15/0.61 % Version: 3.5.1
% 0.15/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.61 % Starting sh5l with 300s (1) cores
% 0.15/0.61 % new_bool_3 with pid 2372770 completed with status 0
% 0.15/0.61 % Result found by new_bool_3
% 0.15/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.61 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.15/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.61 % SubtermCWHack with pid 2372777 completed with status 0
% 0.15/0.61 % Result found by SubtermCWHack
% 0.15/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.61 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.15/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.61 % Preprocessing time : 0.001 s
% 0.15/0.61
% 0.15/0.61 % Proof found!
% 0.15/0.61 % SZS status Theorem
% 0.15/0.61 % SZS output start CNFRefutation
% See solution above
% 0.15/0.61 % Parsed axioms : 8
% 0.15/0.61 % Removed by relevancy pruning/SinE : 2
% 0.15/0.61 % Initial clauses : 13
% 0.15/0.61 % Removed in clause preprocessing : 0
% 0.15/0.61 % Initial clauses in saturation : 13
% 0.15/0.61 % Processed clauses : 88
% 0.15/0.61 % ...of these trivial : 2
% 0.15/0.61 % ...subsumed : 44
% 0.15/0.61 % ...remaining for further processing : 42
% 0.15/0.61 % Other redundant clauses eliminated : 3
% 0.15/0.61 % Clauses deleted for lack of memory : 0
% 0.15/0.61 % Backward-subsumed : 0
% 0.15/0.61 % Backward-rewritten : 0
% 0.15/0.61 % Generated clauses : 211
% 0.15/0.61 % ...of the previous two non-redundant : 170
% 0.15/0.61 % ...aggressively subsumed : 0
% 0.15/0.61 % Contextual simplify-reflections : 2
% 0.15/0.61 % Paramodulations : 204
% 0.15/0.61 % Factorizations : 4
% 0.15/0.61 % NegExts : 0
% 0.15/0.61 % Equation resolutions : 3
% 0.15/0.61 % Disequality decompositions : 0
% 0.15/0.61 % Total rewrite steps : 12
% 0.15/0.61 % ...of those cached : 6
% 0.15/0.61 % Propositional unsat checks : 0
% 0.15/0.61 % Propositional check models : 0
% 0.15/0.61 % Propositional check unsatisfiable : 0
% 0.15/0.61 % Propositional clauses : 0
% 0.15/0.61 % Propositional clauses after purity: 0
% 0.15/0.61 % Propositional unsat core size : 0
% 0.15/0.61 % Propositional preprocessing time : 0.000
% 0.15/0.61 % Propositional encoding time : 0.000
% 0.15/0.61 % Propositional solver time : 0.000
% 0.15/0.61 % Success case prop preproc time : 0.000
% 0.15/0.61 % Success case prop encoding time : 0.000
% 0.15/0.61 % Success case prop solver time : 0.000
% 0.15/0.61 % Current number of processed clauses : 39
% 0.15/0.61 % Positive orientable unit clauses : 4
% 0.15/0.61 % Positive unorientable unit clauses: 1
% 0.15/0.61 % Negative unit clauses : 3
% 0.15/0.61 % Non-unit-clauses : 31
% 0.15/0.61 % Current number of unprocessed clauses: 92
% 0.15/0.61 % ...number of literals in the above : 254
% 0.15/0.61 % Current number of archived formulas : 0
% 0.15/0.61 % Current number of archived clauses : 0
% 0.15/0.61 % Clause-clause subsumption calls (NU) : 532
% 0.15/0.61 % Rec. Clause-clause subsumption calls : 478
% 0.15/0.61 % Non-unit clause-clause subsumptions : 46
% 0.15/0.61 % Unit Clause-clause subsumption calls : 1
% 0.15/0.61 % Rewrite failures with RHS unbound : 0
% 0.15/0.61 % BW rewrite match attempts : 2
% 0.15/0.61 % BW rewrite match successes : 2
% 0.15/0.61 % Condensation attempts : 0
% 0.15/0.61 % Condensation successes : 0
% 0.15/0.61 % Termbank termtop insertions : 3528
% 0.15/0.61 % Search garbage collected termcells : 231
% 0.15/0.61
% 0.15/0.61 % -------------------------------------------------
% 0.15/0.61 % User time : 0.007 s
% 0.15/0.61 % System time : 0.001 s
% 0.15/0.61 % Total time : 0.008 s
% 0.15/0.61 % Maximum resident set size: 3636 pages
% 0.15/0.61
% 0.15/0.61 % -------------------------------------------------
% 0.15/0.61 % User time : 0.009 s
% 0.15/0.61 % System time : 0.005 s
% 0.15/0.61 % Total time : 0.014 s
% 0.15/0.61 % Maximum resident set size: 4864 pages
% 0.15/0.61 % E exiting
%------------------------------------------------------------------------------