%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET598+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 : n006.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 02:14:39 PM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 106 ( 29 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 116 ( 46 ~; 49 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th57,conjecture,
! [X1,X2,X3] :
( X1 = intersection(X2,X3)
<=> ( ! [X4] :
( ( subset(X4,X3)
& subset(X4,X2) )
=> subset(X4,X1) )
& subset(X1,X3)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th57) ).
fof(intersection_is_subset,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(intersection_of_subsets,axiom,
! [X1,X2,X3] :
( ( subset(X1,X3)
& subset(X1,X2) )
=> subset(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_subsets) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( X1 = intersection(X2,X3)
<=> ( ! [X4] :
( ( subset(X4,X3)
& subset(X4,X2) )
=> subset(X4,X1) )
& subset(X1,X3)
& subset(X1,X2) ) ),
inference(assume_negation,[status(cth)],[prove_th57]) ).
fof(c_0_6,negated_conjecture,
! [X9] :
( ( esk1_0 = intersection(esk2_0,esk3_0)
| subset(X9,esk1_0)
| ~ subset(X9,esk3_0)
| ~ subset(X9,esk2_0) )
& ( esk1_0 = intersection(esk2_0,esk3_0)
| subset(esk1_0,esk3_0) )
& ( esk1_0 = intersection(esk2_0,esk3_0)
| subset(esk1_0,esk2_0) )
& ( esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0)
| ~ subset(esk4_0,esk1_0) )
& ( esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0)
| subset(esk4_0,esk3_0) )
& ( esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0)
| subset(esk4_0,esk2_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
fof(c_0_7,plain,
! [X10,X11] : subset(intersection(X10,X11),X10),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
fof(c_0_8,plain,
! [X18,X19] : intersection(X18,X19) = intersection(X19,X18),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_9,plain,
! [X15,X16] :
( ( X15 = X16
| ~ subset(X16,X15)
| ~ subset(X15,X16) )
& ( X15 != X16
| subset(X16,X15) )
& ( X15 != X16
| subset(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
fof(c_0_10,plain,
! [X12,X13,X14] :
( subset(X12,intersection(X13,X14))
| ~ subset(X12,X14)
| ~ subset(X12,X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_of_subsets])])]) ).
cnf(c_0_11,negated_conjecture,
( ~ subset(X1,esk3_0)
| ~ subset(X1,esk2_0)
| esk1_0 = intersection(esk2_0,esk3_0)
| subset(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ subset(X1,X3)
| ~ subset(X1,X2)
| subset(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ subset(intersection(esk3_0,X1),esk2_0)
| subset(intersection(esk3_0,X1),esk1_0)
| intersection(esk2_0,esk3_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( esk1_0 = intersection(esk2_0,esk3_0)
| subset(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( esk1_0 = intersection(esk2_0,esk3_0)
| subset(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
( ~ subset(X3,X1)
| ~ subset(X3,X2)
| ~ subset(intersection(X1,X2),X3)
| intersection(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( subset(intersection(esk2_0,esk3_0),esk1_0)
| intersection(esk2_0,esk3_0) = esk1_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_13]) ).
cnf(c_0_22,negated_conjecture,
subset(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
subset(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0)
| subset(esk4_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
( esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0)
| subset(esk4_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
( esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0)
| ~ subset(esk4_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
intersection(esk2_0,esk3_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
( intersection(esk2_0,esk3_0) != esk1_0
| subset(esk4_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_23]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
( intersection(esk2_0,esk3_0) != esk1_0
| subset(esk4_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_23]),c_0_22])]) ).
cnf(c_0_30,negated_conjecture,
( ~ subset(esk4_0,esk1_0)
| intersection(esk2_0,esk3_0) != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_23]),c_0_22])]) ).
cnf(c_0_31,negated_conjecture,
( ~ subset(X1,esk2_0)
| ~ subset(X1,esk3_0)
| subset(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
subset(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
subset(esk4_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_27])]) ).
cnf(c_0_34,negated_conjecture,
~ subset(esk4_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_27])]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET598+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:27:57 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43 % Version: 3.5.1
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.43 % Starting sh5l with 300s (1) cores
% 0.12/0.43 % new_bool_3 with pid 2086875 completed with status 0
% 0.12/0.43 % Result found by new_bool_3
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.43 % Search class: FGHSS-FFSF22-SFFFFFNN
% 0.12/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.43 % SubtermCWHack with pid 2086878 completed with status 0
% 0.12/0.43 % Result found by SubtermCWHack
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.43 % Search class: FGHSS-FFSF22-SFFFFFNN
% 0.12/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.43 % Preprocessing time : 0.001 s
% 0.12/0.43
% 0.12/0.43 % Proof found!
% 0.12/0.43 % SZS status Theorem
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.43 % Parsed axioms : 9
% 0.12/0.43 % Removed by relevancy pruning/SinE : 3
% 0.12/0.43 % Initial clauses : 13
% 0.12/0.43 % Removed in clause preprocessing : 0
% 0.12/0.43 % Initial clauses in saturation : 13
% 0.12/0.43 % Processed clauses : 79
% 0.12/0.43 % ...of these trivial : 1
% 0.12/0.43 % ...subsumed : 28
% 0.12/0.43 % ...remaining for further processing : 50
% 0.12/0.43 % Other redundant clauses eliminated : 2
% 0.12/0.43 % Clauses deleted for lack of memory : 0
% 0.12/0.43 % Backward-subsumed : 16
% 0.12/0.43 % Backward-rewritten : 8
% 0.12/0.43 % Generated clauses : 109
% 0.12/0.43 % ...of the previous two non-redundant : 86
% 0.12/0.43 % ...aggressively subsumed : 0
% 0.12/0.43 % Contextual simplify-reflections : 6
% 0.12/0.43 % Paramodulations : 107
% 0.12/0.43 % Factorizations : 0
% 0.12/0.43 % NegExts : 0
% 0.12/0.43 % Equation resolutions : 2
% 0.12/0.43 % Disequality decompositions : 0
% 0.12/0.43 % Total rewrite steps : 40
% 0.12/0.43 % ...of those cached : 29
% 0.12/0.43 % Propositional unsat checks : 0
% 0.12/0.43 % Propositional check models : 0
% 0.12/0.43 % Propositional check unsatisfiable : 0
% 0.12/0.43 % Propositional clauses : 0
% 0.12/0.43 % Propositional clauses after purity: 0
% 0.12/0.43 % Propositional unsat core size : 0
% 0.12/0.43 % Propositional preprocessing time : 0.000
% 0.12/0.43 % Propositional encoding time : 0.000
% 0.12/0.43 % Propositional solver time : 0.000
% 0.12/0.43 % Success case prop preproc time : 0.000
% 0.12/0.43 % Success case prop encoding time : 0.000
% 0.12/0.43 % Success case prop solver time : 0.000
% 0.12/0.43 % Current number of processed clauses : 24
% 0.12/0.43 % Positive orientable unit clauses : 8
% 0.12/0.43 % Positive unorientable unit clauses: 1
% 0.12/0.43 % Negative unit clauses : 1
% 0.12/0.43 % Non-unit-clauses : 14
% 0.12/0.43 % Current number of unprocessed clauses: 13
% 0.12/0.43 % ...number of literals in the above : 54
% 0.12/0.43 % Current number of archived formulas : 0
% 0.12/0.43 % Current number of archived clauses : 24
% 0.12/0.43 % Clause-clause subsumption calls (NU) : 232
% 0.12/0.43 % Rec. Clause-clause subsumption calls : 195
% 0.12/0.43 % Non-unit clause-clause subsumptions : 41
% 0.12/0.43 % Unit Clause-clause subsumption calls : 12
% 0.12/0.43 % Rewrite failures with RHS unbound : 0
% 0.12/0.43 % BW rewrite match attempts : 8
% 0.12/0.43 % BW rewrite match successes : 7
% 0.12/0.43 % Condensation attempts : 0
% 0.12/0.43 % Condensation successes : 0
% 0.12/0.43 % Termbank termtop insertions : 1804
% 0.12/0.43 % Search garbage collected termcells : 227
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.005 s
% 0.12/0.43 % System time : 0.001 s
% 0.12/0.43 % Total time : 0.007 s
% 0.12/0.43 % Maximum resident set size: 3636 pages
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.007 s
% 0.12/0.43 % System time : 0.005 s
% 0.12/0.43 % Total time : 0.012 s
% 0.12/0.43 % Maximum resident set size: 4864 pages
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------