%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:14:29 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% 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_th56,conjecture,
! [X1,X2,X3] :
( X1 = union(X2,X3)
<=> ( ! [X4] :
( ( subset(X3,X4)
& subset(X2,X4) )
=> subset(X1,X4) )
& subset(X3,X1)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th56) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(union_subset,axiom,
! [X1,X2,X3] :
( ( subset(X3,X2)
& subset(X1,X2) )
=> subset(union(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_subset) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( X1 = union(X2,X3)
<=> ( ! [X4] :
( ( subset(X3,X4)
& subset(X2,X4) )
=> subset(X1,X4) )
& subset(X3,X1)
& subset(X2,X1) ) ),
inference(assume_negation,[status(cth)],[prove_th56]) ).
fof(c_0_6,negated_conjecture,
! [X9] :
( ( esk1_0 = union(esk2_0,esk3_0)
| subset(esk1_0,X9)
| ~ subset(esk3_0,X9)
| ~ subset(esk2_0,X9) )
& ( esk1_0 = union(esk2_0,esk3_0)
| subset(esk3_0,esk1_0) )
& ( esk1_0 = union(esk2_0,esk3_0)
| subset(esk2_0,esk1_0) )
& ( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk1_0,esk4_0) )
& ( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0)
| subset(esk3_0,esk4_0) )
& ( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0)
| subset(esk2_0,esk4_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(X10,union(X10,X11)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
fof(c_0_8,plain,
! [X18,X19] : union(X18,X19) = union(X19,X18),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
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(union(X12,X14),X13)
| ~ subset(X14,X13)
| ~ subset(X12,X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_subset])])]) ).
cnf(c_0_11,negated_conjecture,
( ~ subset(esk3_0,X1)
| ~ subset(esk2_0,X1)
| esk1_0 = union(esk2_0,esk3_0)
| subset(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
union(X1,X2) = union(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(X3,X2)
| ~ subset(X1,X2)
| subset(union(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ subset(esk2_0,union(esk3_0,X1))
| subset(esk1_0,union(esk3_0,X1))
| union(esk2_0,esk3_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( esk1_0 = union(esk2_0,esk3_0)
| subset(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( esk1_0 = union(esk2_0,esk3_0)
| subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
( ~ subset(X2,X1)
| ~ subset(X3,X1)
| ~ subset(X1,union(X2,X3))
| X1 = union(X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( subset(esk1_0,union(esk2_0,esk3_0))
| union(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(esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
subset(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0)
| subset(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0)
| subset(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
union(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,
( union(esk2_0,esk3_0) != esk1_0
| subset(esk3_0,esk4_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,
( union(esk2_0,esk3_0) != esk1_0
| subset(esk2_0,esk4_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(esk1_0,esk4_0)
| union(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(esk2_0,X1)
| ~ subset(esk3_0,X1)
| subset(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
subset(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
subset(esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_27])]) ).
cnf(c_0_34,negated_conjecture,
~ subset(esk1_0,esk4_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 : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:32:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.42 % Version: 3.5.1
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % new_bool_1 with pid 1651195 completed with status 0
% 0.14/0.42 % Result found by new_bool_1
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 % Search class: FGHSS-FFSF22-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % SubtermCWHack with pid 1651198 completed with status 0
% 0.14/0.42 % Result found by SubtermCWHack
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 % Search class: FGHSS-FFSF22-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % Preprocessing time : 0.001 s
% 0.14/0.42
% 0.14/0.42 % Proof found!
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start CNFRefutation
% See solution above
% 0.14/0.42 % Parsed axioms : 9
% 0.14/0.42 % Removed by relevancy pruning/SinE : 3
% 0.14/0.42 % Initial clauses : 13
% 0.14/0.42 % Removed in clause preprocessing : 0
% 0.14/0.42 % Initial clauses in saturation : 13
% 0.14/0.42 % Processed clauses : 78
% 0.14/0.42 % ...of these trivial : 1
% 0.14/0.42 % ...subsumed : 28
% 0.14/0.42 % ...remaining for further processing : 49
% 0.14/0.42 % Other redundant clauses eliminated : 2
% 0.14/0.42 % Clauses deleted for lack of memory : 0
% 0.14/0.42 % Backward-subsumed : 12
% 0.14/0.42 % Backward-rewritten : 11
% 0.14/0.42 % Generated clauses : 112
% 0.14/0.42 % ...of the previous two non-redundant : 92
% 0.14/0.42 % ...aggressively subsumed : 0
% 0.14/0.42 % Contextual simplify-reflections : 5
% 0.14/0.42 % Paramodulations : 110
% 0.14/0.42 % Factorizations : 0
% 0.14/0.42 % NegExts : 0
% 0.14/0.42 % Equation resolutions : 2
% 0.14/0.42 % Disequality decompositions : 0
% 0.14/0.42 % Total rewrite steps : 47
% 0.14/0.42 % ...of those cached : 36
% 0.14/0.42 % Propositional unsat checks : 0
% 0.14/0.42 % Propositional check models : 0
% 0.14/0.42 % Propositional check unsatisfiable : 0
% 0.14/0.42 % Propositional clauses : 0
% 0.14/0.42 % Propositional clauses after purity: 0
% 0.14/0.42 % Propositional unsat core size : 0
% 0.14/0.42 % Propositional preprocessing time : 0.000
% 0.14/0.42 % Propositional encoding time : 0.000
% 0.14/0.42 % Propositional solver time : 0.000
% 0.14/0.42 % Success case prop preproc time : 0.000
% 0.14/0.42 % Success case prop encoding time : 0.000
% 0.14/0.42 % Success case prop solver time : 0.000
% 0.14/0.42 % Current number of processed clauses : 24
% 0.14/0.42 % Positive orientable unit clauses : 8
% 0.14/0.42 % Positive unorientable unit clauses: 1
% 0.14/0.42 % Negative unit clauses : 1
% 0.14/0.42 % Non-unit-clauses : 14
% 0.14/0.42 % Current number of unprocessed clauses: 16
% 0.14/0.42 % ...number of literals in the above : 58
% 0.14/0.42 % Current number of archived formulas : 0
% 0.14/0.42 % Current number of archived clauses : 23
% 0.14/0.42 % Clause-clause subsumption calls (NU) : 233
% 0.14/0.42 % Rec. Clause-clause subsumption calls : 198
% 0.14/0.42 % Non-unit clause-clause subsumptions : 37
% 0.14/0.42 % Unit Clause-clause subsumption calls : 10
% 0.14/0.42 % Rewrite failures with RHS unbound : 0
% 0.14/0.42 % BW rewrite match attempts : 8
% 0.14/0.42 % BW rewrite match successes : 7
% 0.14/0.42 % Condensation attempts : 0
% 0.14/0.42 % Condensation successes : 0
% 0.14/0.42 % Termbank termtop insertions : 1859
% 0.14/0.42 % Search garbage collected termcells : 227
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.004 s
% 0.14/0.42 % System time : 0.003 s
% 0.14/0.42 % Total time : 0.007 s
% 0.14/0.42 % Maximum resident set size: 3636 pages
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.006 s
% 0.14/0.42 % System time : 0.007 s
% 0.14/0.42 % Total time : 0.013 s
% 0.14/0.42 % Maximum resident set size: 4608 pages
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------