%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM624+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 : n020.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 01:49:49 PM UTC 2026
% Result : Theorem 0.15s 5.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 21 unt; 0 def)
% Number of atoms : 131 ( 39 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 145 ( 58 ~; 49 |; 27 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefMin,axiom,
! [X1] :
( ( X1 != slcrc0
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aElementOf0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
fof(m__5093,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
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(m__5106,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(m__5518,hypothesis,
( sdtlpdtrp0(xN,xm) != slcrc0
& xQ != slcrc0
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& aSubsetOf0(xQ,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5518) ).
fof(m__,conjecture,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
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__5401,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(m__5481,hypothesis,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5481) ).
fof(c_0_12,plain,
! [X1] :
( ( X1 != slcrc0
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aElementOf0(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDefMin]) ).
fof(c_0_13,plain,
! [X126,X127,X128,X129] :
( ( X126 = slcrc0
| ~ aSubsetOf0(X126,szNzAzT0)
| X129 = szmzizndt0(X126)
| ~ aElementOf0(X129,X126)
| ~ sdtlseqdt0(X129,esk16_2(X126,X129)) )
& ( X126 = slcrc0
| ~ aSubsetOf0(X126,szNzAzT0)
| X129 = szmzizndt0(X126)
| ~ aElementOf0(X129,X126)
| aElementOf0(esk16_2(X126,X129),X126) )
& ( X126 = slcrc0
| ~ aSubsetOf0(X126,szNzAzT0)
| X127 != szmzizndt0(X126)
| sdtlseqdt0(X127,X128)
| ~ aElementOf0(X128,X126) )
& ( X126 = slcrc0
| ~ aSubsetOf0(X126,szNzAzT0)
| X127 != szmzizndt0(X126)
| aElementOf0(X127,X126) ) ),
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_12])])])])])])]) ).
fof(c_0_14,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_simplification,[status(thm)],[m__5093]) ).
fof(c_0_15,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])])])])])])]) ).
cnf(c_0_16,plain,
( ~ aSubsetOf0(X2,szNzAzT0)
| X3 != szmzizndt0(X2)
| ~ aElementOf0(X1,X2)
| X2 = slcrc0
| sdtlseqdt0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5106]) ).
cnf(c_0_20,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_21,hypothesis,
( sdtlpdtrp0(xN,xm) != slcrc0
& xQ != slcrc0
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& aSubsetOf0(xQ,szNzAzT0) ),
inference(fof_simplification,[status(thm)],[m__5518]) ).
fof(c_0_22,negated_conjecture,
xp != xx,
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_23,plain,
! [X136,X137] :
( X136 = X137
| ~ sdtlseqdt0(X137,X136)
| ~ sdtlseqdt0(X136,X137)
| ~ aElementOf0(X137,szNzAzT0)
| ~ aElementOf0(X136,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])])]) ).
cnf(c_0_24,plain,
( ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| sdtlseqdt0(szmzizndt0(X1),X2)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_25,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
cnf(c_0_26,hypothesis,
xQ != slcrc0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_28,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[m__5173]) ).
fof(c_0_29,hypothesis,
( sdtlpdtrp0(xN,xm) != slcrc0
& xQ != slcrc0
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& aSubsetOf0(xQ,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[c_0_21]) ).
fof(c_0_30,negated_conjecture,
xp != xx,
inference(fof_simplification,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
( ~ aElementOf0(X1,xQ)
| sdtlseqdt0(xp,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19])]),c_0_26]) ).
cnf(c_0_33,hypothesis,
aElementOf0(xp,szNzAzT0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[m__5401]) ).
cnf(c_0_35,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,hypothesis,
sdtlpdtrp0(xN,xm) != slcrc0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_37,negated_conjecture,
xp != xx,
inference(fof_nnf,[status(thm)],[c_0_30]) ).
cnf(c_0_38,hypothesis,
( ~ aElementOf0(X1,xQ)
| ~ sdtlseqdt0(X1,xp)
| X1 = xp ),
inference(csr,[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_27]) ).
cnf(c_0_39,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_40,hypothesis,
aElementOf0(xx,xQ),
inference(split_conjunct,[status(thm)],[m__5481]) ).
cnf(c_0_41,hypothesis,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[m__5481]) ).
cnf(c_0_42,negated_conjecture,
xp != xx,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM624+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.37 % Computer : n020.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Mon Sep 21 02:46:22 UTC 2026
% 0.12/5.37 % CPUTime :
% 0.12/5.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.51 % Version: 3.5.1
% 0.15/5.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.51 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.51 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.51 % Starting sh5l with 300s (1) cores
% 0.15/5.51 % new_bool_3 with pid 1829286 completed with status 0
% 0.15/5.51 % Result found by new_bool_3
% 0.15/5.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.51 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.51 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.15/5.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.51 % Starting SubtermCWHack with 28s (1) cores
% 0.15/5.51 % SubtermCWHack with pid 1829289 completed with status 0
% 0.15/5.51 % Result found by SubtermCWHack
% 0.15/5.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.51 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.51 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.15/5.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.51 % Starting SubtermCWHack with 28s (1) cores
% 0.15/5.51 % Preprocessing time : 0.003 s
% 0.15/5.51
% 0.15/5.51 % Proof found!
% 0.15/5.51 % SZS status Theorem
% 0.15/5.51 % SZS output start CNFRefutation
% See solution above
% 0.15/5.51 % Parsed axioms : 121
% 0.15/5.51 % Removed by relevancy pruning/SinE : 2
% 0.15/5.51 % Initial clauses : 224
% 0.15/5.51 % Removed in clause preprocessing : 7
% 0.15/5.51 % Initial clauses in saturation : 217
% 0.15/5.51 % Processed clauses : 1187
% 0.15/5.51 % ...of these trivial : 16
% 0.15/5.51 % ...subsumed : 451
% 0.15/5.51 % ...remaining for further processing : 720
% 0.15/5.51 % Other redundant clauses eliminated : 44
% 0.15/5.51 % Clauses deleted for lack of memory : 0
% 0.15/5.51 % Backward-subsumed : 24
% 0.15/5.51 % Backward-rewritten : 18
% 0.15/5.51 % Generated clauses : 2472
% 0.15/5.51 % ...of the previous two non-redundant : 2179
% 0.15/5.51 % ...aggressively subsumed : 0
% 0.15/5.51 % Contextual simplify-reflections : 37
% 0.15/5.51 % Paramodulations : 2430
% 0.15/5.51 % Factorizations : 0
% 0.15/5.51 % NegExts : 0
% 0.15/5.51 % Equation resolutions : 46
% 0.15/5.51 % Disequality decompositions : 0
% 0.15/5.51 % Total rewrite steps : 1908
% 0.15/5.51 % ...of those cached : 1795
% 0.15/5.51 % Propositional unsat checks : 0
% 0.15/5.51 % Propositional check models : 0
% 0.15/5.51 % Propositional check unsatisfiable : 0
% 0.15/5.51 % Propositional clauses : 0
% 0.15/5.51 % Propositional clauses after purity: 0
% 0.15/5.51 % Propositional unsat core size : 0
% 0.15/5.51 % Propositional preprocessing time : 0.000
% 0.15/5.51 % Propositional encoding time : 0.000
% 0.15/5.51 % Propositional solver time : 0.000
% 0.15/5.51 % Success case prop preproc time : 0.000
% 0.15/5.51 % Success case prop encoding time : 0.000
% 0.15/5.51 % Success case prop solver time : 0.000
% 0.15/5.51 % Current number of processed clauses : 644
% 0.15/5.51 % Positive orientable unit clauses : 140
% 0.15/5.51 % Positive unorientable unit clauses: 0
% 0.15/5.51 % Negative unit clauses : 33
% 0.15/5.51 % Non-unit-clauses : 471
% 0.15/5.51 % Current number of unprocessed clauses: 1199
% 0.15/5.51 % ...number of literals in the above : 6272
% 0.15/5.51 % Current number of archived formulas : 0
% 0.15/5.51 % Current number of archived clauses : 43
% 0.15/5.51 % Clause-clause subsumption calls (NU) : 40621
% 0.15/5.51 % Rec. Clause-clause subsumption calls : 21958
% 0.15/5.51 % Non-unit clause-clause subsumptions : 320
% 0.15/5.51 % Unit Clause-clause subsumption calls : 2724
% 0.15/5.51 % Rewrite failures with RHS unbound : 0
% 0.15/5.51 % BW rewrite match attempts : 19
% 0.15/5.51 % BW rewrite match successes : 17
% 0.15/5.51 % Condensation attempts : 0
% 0.15/5.51 % Condensation successes : 0
% 0.15/5.51 % Termbank termtop insertions : 55165
% 0.15/5.51 % Search garbage collected termcells : 3552
% 0.15/5.51
% 0.15/5.51 % -------------------------------------------------
% 0.15/5.51 % User time : 0.065 s
% 0.15/5.51 % System time : 0.004 s
% 0.15/5.51 % Total time : 0.069 s
% 0.15/5.51 % Maximum resident set size: 4240 pages
% 0.15/5.51
% 0.15/5.51 % -------------------------------------------------
% 0.15/5.51 % User time : 0.071 s
% 0.15/5.51 % System time : 0.007 s
% 0.15/5.51 % Total time : 0.078 s
% 0.15/5.51 % Maximum resident set size: 4864 pages
% 0.15/5.51 % E exiting
%------------------------------------------------------------------------------