%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET201+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 : n026.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 02:13:54 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 74 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 25 ~; 27 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 6 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th41,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X3,X4)
& subset(X1,X2) )
=> subset(intersection(X1,X3),intersection(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th41) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X3,X4)
& subset(X1,X2) )
=> subset(intersection(X1,X3),intersection(X2,X4)) ),
inference(assume_negation,[status(cth)],[prove_th41]) ).
fof(c_0_5,plain,
! [X9,X10,X11,X12,X13] :
( ( subset(X12,X13)
| ~ member(esk5_2(X12,X13),X13) )
& ( subset(X12,X13)
| member(esk5_2(X12,X13),X12) )
& ( member(X11,X10)
| ~ member(X11,X9)
| ~ subset(X9,X10) ) ),
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)],[subset_defn])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( ~ subset(intersection(esk1_0,esk3_0),intersection(esk2_0,esk4_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])])])]) ).
cnf(c_0_7,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X16,X17,X18] :
( ( member(X18,intersection(X16,X17))
| ~ member(X18,X17)
| ~ member(X18,X16) )
& ( ~ member(X18,intersection(X16,X17))
| member(X18,X17) )
& ( ~ member(X18,intersection(X16,X17))
| member(X18,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_10,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ member(esk5_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(esk5_2(X1,esk4_0),esk3_0)
| subset(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( member(esk5_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ member(esk5_2(X1,esk2_0),esk1_0)
| subset(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
fof(c_0_19,plain,
! [X19,X20] : intersection(X19,X20) = intersection(X20,X19),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_20,negated_conjecture,
subset(intersection(X1,esk3_0),esk4_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
subset(intersection(X1,esk1_0),esk2_0),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(X1,intersection(X2,esk3_0))
| member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
subset(intersection(esk1_0,X1),esk2_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ member(esk5_2(X1,intersection(X2,X3)),X2)
| ~ member(esk5_2(X1,intersection(X2,X3)),X3)
| subset(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( member(esk5_2(intersection(X1,esk3_0),X2),esk4_0)
| subset(intersection(X1,esk3_0),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(X1,intersection(esk1_0,X2))
| member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( ~ member(esk5_2(intersection(X1,esk3_0),intersection(X2,esk4_0)),X2)
| subset(intersection(X1,esk3_0),intersection(X2,esk4_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( member(esk5_2(intersection(esk1_0,X1),X2),esk2_0)
| subset(intersection(esk1_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_31,negated_conjecture,
~ subset(intersection(esk1_0,esk3_0),intersection(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET201+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:03:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.45 % Version: 3.5.1
% 0.09/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.45 % Starting sh5l with 300s (1) cores
% 0.09/0.45 % new_bool_3 with pid 1426451 completed with status 0
% 0.09/0.45 % Result found by new_bool_3
% 0.09/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.45 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.09/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.45 % SubtermCWHack with pid 1426454 completed with status 0
% 0.09/0.45 % Result found by SubtermCWHack
% 0.09/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.45 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.09/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.45 % Preprocessing time : 0.001 s
% 0.09/0.45
% 0.09/0.45 % Proof found!
% 0.09/0.45 % SZS status Theorem
% 0.09/0.45 % SZS output start CNFRefutation
% See solution above
% 0.09/0.45 % Parsed axioms : 6
% 0.09/0.45 % Removed by relevancy pruning/SinE : 0
% 0.09/0.45 % Initial clauses : 15
% 0.09/0.45 % Removed in clause preprocessing : 2
% 0.09/0.45 % Initial clauses in saturation : 13
% 0.09/0.45 % Processed clauses : 440
% 0.09/0.45 % ...of these trivial : 68
% 0.09/0.45 % ...subsumed : 218
% 0.09/0.45 % ...remaining for further processing : 154
% 0.09/0.45 % Other redundant clauses eliminated : 0
% 0.09/0.45 % Clauses deleted for lack of memory : 0
% 0.09/0.45 % Backward-subsumed : 0
% 0.09/0.45 % Backward-rewritten : 0
% 0.09/0.45 % Generated clauses : 1714
% 0.09/0.45 % ...of the previous two non-redundant : 1507
% 0.09/0.45 % ...aggressively subsumed : 0
% 0.09/0.45 % Contextual simplify-reflections : 0
% 0.09/0.45 % Paramodulations : 1688
% 0.09/0.45 % Factorizations : 26
% 0.09/0.45 % NegExts : 0
% 0.09/0.45 % Equation resolutions : 0
% 0.09/0.45 % Disequality decompositions : 0
% 0.09/0.45 % Total rewrite steps : 265
% 0.09/0.45 % ...of those cached : 158
% 0.09/0.45 % Propositional unsat checks : 0
% 0.09/0.45 % Propositional check models : 0
% 0.09/0.45 % Propositional check unsatisfiable : 0
% 0.09/0.45 % Propositional clauses : 0
% 0.09/0.45 % Propositional clauses after purity: 0
% 0.09/0.45 % Propositional unsat core size : 0
% 0.09/0.45 % Propositional preprocessing time : 0.000
% 0.09/0.45 % Propositional encoding time : 0.000
% 0.09/0.45 % Propositional solver time : 0.000
% 0.09/0.45 % Success case prop preproc time : 0.000
% 0.09/0.45 % Success case prop encoding time : 0.000
% 0.09/0.45 % Success case prop solver time : 0.000
% 0.09/0.45 % Current number of processed clauses : 154
% 0.09/0.45 % Positive orientable unit clauses : 60
% 0.09/0.45 % Positive unorientable unit clauses: 1
% 0.09/0.45 % Negative unit clauses : 1
% 0.09/0.45 % Non-unit-clauses : 92
% 0.09/0.45 % Current number of unprocessed clauses: 1063
% 0.09/0.45 % ...number of literals in the above : 2621
% 0.09/0.45 % Current number of archived formulas : 0
% 0.09/0.45 % Current number of archived clauses : 0
% 0.09/0.45 % Clause-clause subsumption calls (NU) : 2084
% 0.09/0.45 % Rec. Clause-clause subsumption calls : 1972
% 0.09/0.45 % Non-unit clause-clause subsumptions : 218
% 0.09/0.45 % Unit Clause-clause subsumption calls : 188
% 0.09/0.45 % Rewrite failures with RHS unbound : 0
% 0.09/0.45 % BW rewrite match attempts : 126
% 0.09/0.45 % BW rewrite match successes : 0
% 0.09/0.45 % Condensation attempts : 0
% 0.09/0.45 % Condensation successes : 0
% 0.09/0.45 % Termbank termtop insertions : 23899
% 0.09/0.45 % Search garbage collected termcells : 270
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.027 s
% 0.09/0.45 % System time : 0.002 s
% 0.09/0.45 % Total time : 0.029 s
% 0.09/0.45 % Maximum resident set size: 3580 pages
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.028 s
% 0.09/0.45 % System time : 0.006 s
% 0.09/0.45 % Total time : 0.035 s
% 0.09/0.45 % Maximum resident set size: 4608 pages
% 0.09/0.45 % E exiting
%------------------------------------------------------------------------------