%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET971+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 : n003.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 0.14s 0.52s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 27 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 5 ~; 2 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t124_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X3,X4)
& subset(X1,X2) )
=> set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
fof(t28_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_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(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X3,X4)
& subset(X1,X2) )
=> set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
inference(assume_negation,[status(cth)],[t124_zfmisc_1]) ).
fof(c_0_5,plain,
! [X17,X18] :
( set_intersection2(X17,X18) = X17
| ~ subset(X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])]) ).
fof(c_0_6,negated_conjecture,
( set_intersection2(cartesian_product2(esk1_0,esk4_0),cartesian_product2(esk2_0,esk3_0)) != cartesian_product2(esk1_0,esk3_0)
& subset(esk3_0,esk4_0)
& subset(esk1_0,esk2_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,
! [X9,X10,X11,X12] : cartesian_product2(set_intersection2(X9,X10),set_intersection2(X11,X12)) = set_intersection2(cartesian_product2(X9,X11),cartesian_product2(X10,X12)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
cnf(c_0_8,plain,
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X13,X14] : set_intersection2(X13,X14) = set_intersection2(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_11,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
set_intersection2(cartesian_product2(esk1_0,esk4_0),cartesian_product2(esk2_0,esk3_0)) != cartesian_product2(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,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_7]) ).
cnf(c_0_14,negated_conjecture,
set_intersection2(esk1_0,esk2_0) = esk1_0,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
set_intersection2(esk3_0,esk4_0) = esk3_0,
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.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 05:46:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 0.14/0.52 % Version: 3.5.1
% 0.14/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.52 % Starting sh5l with 300s (1) cores
% 0.14/0.52 % new_bool_1 with pid 3536014 completed with status 0
% 0.14/0.52 % Result found by new_bool_1
% 0.14/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.52 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.14/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.52 % SubtermCWHack with pid 3536017 completed with status 0
% 0.14/0.52 % Result found by SubtermCWHack
% 0.14/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.52 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.14/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.52 % Preprocessing time : 0.002 s
% 0.14/0.52
% 0.14/0.52 % Proof found!
% 0.14/0.52 % SZS status Theorem
% 0.14/0.52 % SZS output start CNFRefutation
% See solution above
% 0.14/0.52 % Parsed axioms : 8
% 0.14/0.52 % Removed by relevancy pruning/SinE : 2
% 0.14/0.52 % Initial clauses : 8
% 0.14/0.52 % Removed in clause preprocessing : 0
% 0.14/0.52 % Initial clauses in saturation : 8
% 0.14/0.52 % Processed clauses : 10
% 0.14/0.52 % ...of these trivial : 0
% 0.14/0.52 % ...subsumed : 0
% 0.14/0.52 % ...remaining for further processing : 10
% 0.14/0.52 % Other redundant clauses eliminated : 0
% 0.14/0.52 % Clauses deleted for lack of memory : 0
% 0.14/0.52 % Backward-subsumed : 0
% 0.14/0.52 % Backward-rewritten : 1
% 0.14/0.52 % Generated clauses : 8
% 0.14/0.52 % ...of the previous two non-redundant : 2
% 0.14/0.52 % ...aggressively subsumed : 0
% 0.14/0.52 % Contextual simplify-reflections : 0
% 0.14/0.52 % Paramodulations : 8
% 0.14/0.52 % Factorizations : 0
% 0.14/0.52 % NegExts : 0
% 0.14/0.52 % Equation resolutions : 0
% 0.14/0.52 % Disequality decompositions : 0
% 0.14/0.52 % Total rewrite steps : 7
% 0.14/0.52 % ...of those cached : 2
% 0.14/0.52 % Propositional unsat checks : 0
% 0.14/0.52 % Propositional check models : 0
% 0.14/0.52 % Propositional check unsatisfiable : 0
% 0.14/0.52 % Propositional clauses : 0
% 0.14/0.52 % Propositional clauses after purity: 0
% 0.14/0.52 % Propositional unsat core size : 0
% 0.14/0.52 % Propositional preprocessing time : 0.000
% 0.14/0.52 % Propositional encoding time : 0.000
% 0.14/0.52 % Propositional solver time : 0.000
% 0.14/0.52 % Success case prop preproc time : 0.000
% 0.14/0.52 % Success case prop encoding time : 0.000
% 0.14/0.52 % Success case prop solver time : 0.000
% 0.14/0.52 % Current number of processed clauses : 9
% 0.14/0.52 % Positive orientable unit clauses : 7
% 0.14/0.52 % Positive unorientable unit clauses: 1
% 0.14/0.52 % Negative unit clauses : 0
% 0.14/0.52 % Non-unit-clauses : 1
% 0.14/0.52 % Current number of unprocessed clauses: 0
% 0.14/0.52 % ...number of literals in the above : 0
% 0.14/0.52 % Current number of archived formulas : 0
% 0.14/0.52 % Current number of archived clauses : 1
% 0.14/0.52 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.52 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.52 % Non-unit clause-clause subsumptions : 0
% 0.14/0.52 % Unit Clause-clause subsumption calls : 0
% 0.14/0.52 % Rewrite failures with RHS unbound : 0
% 0.14/0.52 % BW rewrite match attempts : 5
% 0.14/0.52 % BW rewrite match successes : 3
% 0.14/0.52 % Condensation attempts : 0
% 0.14/0.52 % Condensation successes : 0
% 0.14/0.52 % Termbank termtop insertions : 421
% 0.14/0.52 % Search garbage collected termcells : 66
% 0.14/0.52
% 0.14/0.52 % -------------------------------------------------
% 0.14/0.52 % User time : 0.004 s
% 0.14/0.52 % System time : 0.003 s
% 0.14/0.52 % Total time : 0.007 s
% 0.14/0.52 % Maximum resident set size: 3632 pages
% 0.14/0.52
% 0.14/0.52 % -------------------------------------------------
% 0.14/0.52 % User time : 0.005 s
% 0.14/0.52 % System time : 0.011 s
% 0.14/0.52 % Total time : 0.015 s
% 0.14/0.52 % Maximum resident set size: 4608 pages
% 0.14/0.52 % E exiting
%------------------------------------------------------------------------------