%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM609+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:49:45 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 17 unt; 0 def)
% Number of atoms : 149 ( 27 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 188 ( 76 ~; 76 |; 25 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5093,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__4891,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(m__5164,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(m__5173,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(m__,conjecture,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_9,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_simplification,[status(thm)],[m__5093]) ).
fof(c_0_10,plain,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mDefDiff]) ).
fof(c_0_11,plain,
! [X50,X51,X52,X53] :
( ( ~ aSet0(X50)
| aSubsetOf0(X53,X50)
| ~ aSet0(X53)
| ~ aElementOf0(esk8_2(X50,X53),X50) )
& ( ~ aSet0(X50)
| aSubsetOf0(X53,X50)
| ~ aSet0(X53)
| aElementOf0(esk8_2(X50,X53),X53) )
& ( ~ aSet0(X50)
| ~ aSubsetOf0(X51,X50)
| aElementOf0(X52,X50)
| ~ aElementOf0(X52,X51) )
& ( ~ aSet0(X50)
| ~ aSubsetOf0(X51,X50)
| aSet0(X51) ) ),
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)],[mDefSub])])])])])])]) ).
fof(c_0_12,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X109,X110,X111,X112,X113,X114] :
( ( ~ aElement0(X110)
| ~ aSet0(X109)
| X114 = sdtmndt0(X109,X110)
| ~ aSet0(X114)
| aElementOf0(esk15_3(X109,X110,X114),X114)
| esk15_3(X109,X110,X114) != X110 )
& ( ~ aElement0(X110)
| ~ aSet0(X109)
| X114 = sdtmndt0(X109,X110)
| ~ aSet0(X114)
| aElementOf0(esk15_3(X109,X110,X114),X114)
| aElementOf0(esk15_3(X109,X110,X114),X109) )
& ( ~ aElement0(X110)
| ~ aSet0(X109)
| X114 = sdtmndt0(X109,X110)
| ~ aSet0(X114)
| aElementOf0(esk15_3(X109,X110,X114),X114)
| aElement0(esk15_3(X109,X110,X114)) )
& ( ~ aElement0(X110)
| ~ aSet0(X109)
| X114 = sdtmndt0(X109,X110)
| ~ aSet0(X114)
| esk15_3(X109,X110,X114) = X110
| ~ aElementOf0(esk15_3(X109,X110,X114),X109)
| ~ aElement0(esk15_3(X109,X110,X114))
| ~ aElementOf0(esk15_3(X109,X110,X114),X114) )
& ( ~ aElement0(X110)
| ~ aSet0(X109)
| X111 != sdtmndt0(X109,X110)
| aElementOf0(X113,X111)
| X113 = X110
| ~ aElementOf0(X113,X109)
| ~ aElement0(X113) )
& ( ~ aElement0(X110)
| ~ aSet0(X109)
| X111 != sdtmndt0(X109,X110)
| ~ aElementOf0(X112,X111)
| X112 != X110 )
& ( ~ aElement0(X110)
| ~ aSet0(X109)
| X111 != sdtmndt0(X109,X110)
| ~ aElementOf0(X112,X111)
| aElementOf0(X112,X109) )
& ( ~ aElement0(X110)
| ~ aSet0(X109)
| X111 != sdtmndt0(X109,X110)
| ~ aElementOf0(X112,X111)
| aElement0(X112) )
& ( ~ aElement0(X110)
| ~ aSet0(X109)
| X111 != sdtmndt0(X109,X110)
| aSet0(X111) ) ),
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)],[c_0_10])])])])])])]) ).
fof(c_0_14,plain,
! [X168,X169] :
( aElement0(X169)
| ~ aElementOf0(X169,X168)
| ~ aSet0(X168) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_15,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,hypothesis,
aSubsetOf0(xQ,xO),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
aSet0(xO),
inference(split_conjunct,[status(thm)],[m__4891]) ).
cnf(c_0_18,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_20,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
cnf(c_0_21,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[m__5173]) ).
cnf(c_0_23,hypothesis,
aSet0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
fof(c_0_24,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_25,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_26,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,hypothesis,
aElement0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_28,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_23])]) ).
cnf(c_0_30,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk8_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[m__5164]) ).
fof(c_0_32,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(fof_nnf,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk8_2(X1,X2),X1)
| aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk8_2(X1,xP),xQ)
| aSubsetOf0(xP,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_31]),c_0_23])]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM609+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:44:34 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.45 % Version: 3.5.1
% 0.13/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.45 % Starting sh5l with 300s (1) cores
% 0.13/0.45 % new_bool_3 with pid 1522191 completed with status 0
% 0.13/0.45 % Result found by new_bool_3
% 0.13/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.45 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.45 % SubtermCWHack with pid 1522201 completed with status 0
% 0.13/0.45 % Result found by SubtermCWHack
% 0.13/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.45 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.45 % Preprocessing time : 0.004 s
% 0.13/0.45
% 0.13/0.45 % Proof found!
% 0.13/0.45 % SZS status Theorem
% 0.13/0.45 % SZS output start CNFRefutation
% See solution above
% 0.13/0.45 % Parsed axioms : 107
% 0.13/0.45 % Removed by relevancy pruning/SinE : 2
% 0.13/0.45 % Initial clauses : 202
% 0.13/0.45 % Removed in clause preprocessing : 7
% 0.13/0.45 % Initial clauses in saturation : 195
% 0.13/0.45 % Processed clauses : 349
% 0.13/0.45 % ...of these trivial : 5
% 0.13/0.45 % ...subsumed : 44
% 0.13/0.45 % ...remaining for further processing : 300
% 0.13/0.45 % Other redundant clauses eliminated : 26
% 0.13/0.45 % Clauses deleted for lack of memory : 0
% 0.13/0.45 % Backward-subsumed : 7
% 0.13/0.45 % Backward-rewritten : 6
% 0.13/0.45 % Generated clauses : 405
% 0.13/0.45 % ...of the previous two non-redundant : 331
% 0.13/0.45 % ...aggressively subsumed : 0
% 0.13/0.45 % Contextual simplify-reflections : 6
% 0.13/0.45 % Paramodulations : 380
% 0.13/0.45 % Factorizations : 0
% 0.13/0.45 % NegExts : 0
% 0.13/0.45 % Equation resolutions : 27
% 0.13/0.45 % Disequality decompositions : 0
% 0.13/0.45 % Total rewrite steps : 334
% 0.13/0.45 % ...of those cached : 282
% 0.13/0.45 % Propositional unsat checks : 0
% 0.13/0.45 % Propositional check models : 0
% 0.13/0.45 % Propositional check unsatisfiable : 0
% 0.13/0.45 % Propositional clauses : 0
% 0.13/0.45 % Propositional clauses after purity: 0
% 0.13/0.45 % Propositional unsat core size : 0
% 0.13/0.45 % Propositional preprocessing time : 0.000
% 0.13/0.45 % Propositional encoding time : 0.000
% 0.13/0.45 % Propositional solver time : 0.000
% 0.13/0.45 % Success case prop preproc time : 0.000
% 0.13/0.45 % Success case prop encoding time : 0.000
% 0.13/0.45 % Success case prop solver time : 0.000
% 0.13/0.45 % Current number of processed clauses : 267
% 0.13/0.45 % Positive orientable unit clauses : 70
% 0.13/0.45 % Positive unorientable unit clauses: 0
% 0.13/0.45 % Negative unit clauses : 14
% 0.13/0.45 % Non-unit-clauses : 183
% 0.13/0.45 % Current number of unprocessed clauses: 171
% 0.13/0.45 % ...number of literals in the above : 841
% 0.13/0.45 % Current number of archived formulas : 0
% 0.13/0.45 % Current number of archived clauses : 13
% 0.13/0.45 % Clause-clause subsumption calls (NU) : 3734
% 0.13/0.45 % Rec. Clause-clause subsumption calls : 2677
% 0.13/0.45 % Non-unit clause-clause subsumptions : 36
% 0.13/0.45 % Unit Clause-clause subsumption calls : 469
% 0.13/0.45 % Rewrite failures with RHS unbound : 0
% 0.13/0.45 % BW rewrite match attempts : 5
% 0.13/0.45 % BW rewrite match successes : 5
% 0.13/0.45 % Condensation attempts : 0
% 0.13/0.45 % Condensation successes : 0
% 0.13/0.45 % Termbank termtop insertions : 21471
% 0.13/0.45 % Search garbage collected termcells : 3548
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.038 s
% 0.13/0.45 % System time : 0.003 s
% 0.13/0.45 % Total time : 0.041 s
% 0.13/0.45 % Maximum resident set size: 4280 pages
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.041 s
% 0.13/0.45 % System time : 0.009 s
% 0.13/0.45 % Total time : 0.050 s
% 0.13/0.45 % Maximum resident set size: 4608 pages
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------