%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:14:51 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 73 ( 26 ~; 23 |; 5 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 1 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X3))
=> ( subset(X1,X4)
=> subset(X1,cross_product(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(prove_relset_1_4,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X3))
=> ( subset(X1,X4)
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_4) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( subset(X1,cross_product(X2,X3))
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(c_0_4,plain,
! [X10,X11,X12,X13] :
( subset(X10,cross_product(X11,X12))
| ~ subset(X10,X13)
| ~ ilf_type(X13,relation_type(X11,X12))
| ~ ilf_type(X12,set_type)
| ~ ilf_type(X11,set_type)
| ~ ilf_type(X10,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
fof(c_0_5,plain,
! [X9] : ilf_type(X9,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X3))
=> ( subset(X1,X4)
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_4]) ).
fof(c_0_7,plain,
! [X14,X15,X16] :
( ilf_type(X14,relation_type(X15,X16))
| ~ subset(X14,cross_product(X15,X16))
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X14,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_8,plain,
( ~ subset(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| subset(X1,cross_product(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,negated_conjecture,
( ~ ilf_type(esk1_0,relation_type(esk2_0,esk3_0))
& subset(esk1_0,esk4_0)
& ilf_type(esk4_0,relation_type(esk2_0,esk3_0))
& ilf_type(esk3_0,set_type)
& ilf_type(esk2_0,set_type)
& ilf_type(esk1_0,set_type) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_11,plain,
( ~ subset(X1,cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,relation_type(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ ilf_type(X4,relation_type(X2,X3))
| ~ subset(X1,X4)
| subset(X1,cross_product(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]),c_0_9])]) ).
cnf(c_0_13,negated_conjecture,
ilf_type(esk4_0,relation_type(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ subset(X1,cross_product(X2,X3))
| ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_9]),c_0_9]),c_0_9])]) ).
cnf(c_0_15,negated_conjecture,
( ~ subset(X1,esk4_0)
| subset(X1,cross_product(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
~ ilf_type(esk1_0,relation_type(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( ~ subset(X1,esk4_0)
| ilf_type(X1,relation_type(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
subset(esk1_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:35:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % new_bool_3 with pid 1660412 completed with status 0
% 0.11/0.45 % Result found by new_bool_3
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % SubtermCWHack with pid 1660434 completed with status 0
% 0.11/0.45 % Result found by SubtermCWHack
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % Preprocessing time : 0.002 s
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 20
% 0.11/0.45 % Removed by relevancy pruning/SinE : 1
% 0.11/0.45 % Initial clauses : 41
% 0.11/0.45 % Removed in clause preprocessing : 0
% 0.11/0.45 % Initial clauses in saturation : 41
% 0.11/0.45 % Processed clauses : 112
% 0.11/0.45 % ...of these trivial : 8
% 0.11/0.45 % ...subsumed : 17
% 0.11/0.45 % ...remaining for further processing : 87
% 0.11/0.45 % Other redundant clauses eliminated : 1
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 0
% 0.11/0.45 % Backward-rewritten : 3
% 0.11/0.45 % Generated clauses : 140
% 0.11/0.45 % ...of the previous two non-redundant : 120
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 1
% 0.11/0.45 % Paramodulations : 139
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 1
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 80
% 0.11/0.45 % ...of those cached : 59
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 84
% 0.11/0.45 % Positive orientable unit clauses : 21
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 2
% 0.11/0.45 % Non-unit-clauses : 61
% 0.11/0.45 % Current number of unprocessed clauses: 49
% 0.11/0.45 % ...number of literals in the above : 121
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 3
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 229
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 201
% 0.11/0.45 % Non-unit clause-clause subsumptions : 13
% 0.11/0.45 % Unit Clause-clause subsumption calls : 50
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 16
% 0.11/0.45 % BW rewrite match successes : 3
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 5521
% 0.11/0.45 % Search garbage collected termcells : 901
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.013 s
% 0.11/0.45 % System time : 0.004 s
% 0.11/0.45 % Total time : 0.017 s
% 0.11/0.45 % Maximum resident set size: 3656 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.016 s
% 0.11/0.45 % System time : 0.008 s
% 0.11/0.45 % Total time : 0.025 s
% 0.11/0.45 % Maximum resident set size: 4864 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------