%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM624+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 01:55:45 PM UTC 2026
% Result : Theorem 0.21s 0.48s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 24 unt; 0 def)
% Number of atoms : 133 ( 38 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 143 ( 57 ~; 47 |; 28 &)
% ( 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 : 34 ( 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/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
fof(m__5518,hypothesis,
( sdtlpdtrp0(xN,xm) != slcrc0
& xQ != slcrc0
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& aSubsetOf0(xQ,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5518) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(m__,conjecture,
xp = xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__5401,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5401) ).
fof(m__5106,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(m__5093,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(m__5481,hypothesis,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5481) ).
fof(m__5173,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).
fof(m__5365,hypothesis,
( aElementOf0(xx,xO)
& aElementOf0(xx,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(c_0_13,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_14,plain,
! [X94,X95,X96,X97] :
( ( X94 = slcrc0
| ~ aSubsetOf0(X94,szNzAzT0)
| X97 = szmzizndt0(X94)
| ~ aElementOf0(X97,X94)
| ~ sdtlseqdt0(X97,esk7_2(X94,X97)) )
& ( X94 = slcrc0
| ~ aSubsetOf0(X94,szNzAzT0)
| X97 = szmzizndt0(X94)
| ~ aElementOf0(X97,X94)
| aElementOf0(esk7_2(X94,X97),X94) )
& ( X94 = slcrc0
| ~ aSubsetOf0(X94,szNzAzT0)
| X95 != szmzizndt0(X94)
| sdtlseqdt0(X95,X96)
| ~ aElementOf0(X96,X94) )
& ( X94 = slcrc0
| ~ aSubsetOf0(X94,szNzAzT0)
| X95 != szmzizndt0(X94)
| aElementOf0(X95,X94) ) ),
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_13])])])])])])]) ).
fof(c_0_15,hypothesis,
( sdtlpdtrp0(xN,xm) != slcrc0
& xQ != slcrc0
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& aSubsetOf0(xQ,szNzAzT0) ),
inference(fof_simplification,[status(thm)],[m__5518]) ).
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_14]) ).
fof(c_0_17,hypothesis,
( sdtlpdtrp0(xN,xm) != slcrc0
& xQ != slcrc0
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& aSubsetOf0(xQ,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X19,X20,X21,X22] :
( ( ~ aSet0(X19)
| aSubsetOf0(X22,X19)
| ~ aSet0(X22)
| ~ aElementOf0(esk2_2(X19,X22),X19) )
& ( ~ aSet0(X19)
| aSubsetOf0(X22,X19)
| ~ aSet0(X22)
| aElementOf0(esk2_2(X19,X22),X22) )
& ( ~ aSet0(X19)
| ~ aSubsetOf0(X20,X19)
| aElementOf0(X21,X19)
| ~ aElementOf0(X21,X20) )
& ( ~ aSet0(X19)
| ~ aSubsetOf0(X20,X19)
| aSet0(X20) ) ),
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_19,negated_conjecture,
xp != xx,
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_20,plain,
( ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| sdtlseqdt0(szmzizndt0(X1),X2)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[m__5401]) ).
cnf(c_0_22,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
sdtlpdtrp0(xN,xm) != slcrc0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5106]) ).
cnf(c_0_26,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_27,negated_conjecture,
xp != xx,
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_28,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_simplification,[status(thm)],[m__5093]) ).
fof(c_0_29,plain,
! [X72,X73] :
( X72 = X73
| ~ sdtlseqdt0(X73,X72)
| ~ sdtlseqdt0(X72,X73)
| ~ aElementOf0(X73,szNzAzT0)
| ~ aElementOf0(X72,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])])]) ).
cnf(c_0_30,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_20,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_31,hypothesis,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[m__5481]) ).
cnf(c_0_32,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_33,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[m__5173]) ).
fof(c_0_34,negated_conjecture,
xp != xx,
inference(fof_nnf,[status(thm)],[c_0_27]) ).
fof(c_0_35,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_nnf,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,hypothesis,
sdtlseqdt0(xx,xp),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,hypothesis,
aElementOf0(xx,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5365]) ).
cnf(c_0_39,hypothesis,
aElementOf0(xp,szNzAzT0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
xp != xx,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
cnf(c_0_42,hypothesis,
xQ != slcrc0,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,hypothesis,
~ sdtlseqdt0(xp,xx),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]),c_0_40]) ).
cnf(c_0_44,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_20,c_0_41]),c_0_25])]),c_0_42]) ).
cnf(c_0_45,hypothesis,
aElementOf0(xx,xQ),
inference(split_conjunct,[status(thm)],[m__5481]) ).
cnf(c_0_46,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]),
[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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:45:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.21/0.48 % Version: 3.5.1
% 0.21/0.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.48 % Starting sh5l with 300s (1) cores
% 0.21/0.48 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2086460 completed with status 0
% 0.21/0.48 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.21/0.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.48 % No SInE strategy applied
% 0.21/0.48 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.21/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.21/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.21/0.48 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.21/0.48 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.21/0.48 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2086473 completed with status 0
% 0.21/0.48 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.21/0.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.48 % No SInE strategy applied
% 0.21/0.48 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.21/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.21/0.48 % Preprocessing time : 0.003 s
% 0.21/0.48 % Presaturation interreduction done
% 0.21/0.48
% 0.21/0.48 % Proof found!
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 % SZS output start CNFRefutation
% See solution above
% 0.21/0.48 % Parsed axioms : 121
% 0.21/0.48 % Removed by relevancy pruning/SinE : 0
% 0.21/0.48 % Initial clauses : 233
% 0.21/0.48 % Removed in clause preprocessing : 7
% 0.21/0.48 % Initial clauses in saturation : 226
% 0.21/0.48 % Processed clauses : 731
% 0.21/0.48 % ...of these trivial : 12
% 0.21/0.48 % ...subsumed : 61
% 0.21/0.48 % ...remaining for further processing : 658
% 0.21/0.48 % Other redundant clauses eliminated : 53
% 0.21/0.48 % Clauses deleted for lack of memory : 0
% 0.21/0.48 % Backward-subsumed : 11
% 0.21/0.48 % Backward-rewritten : 6
% 0.21/0.48 % Generated clauses : 1461
% 0.21/0.48 % ...of the previous two non-redundant : 1273
% 0.21/0.48 % ...aggressively subsumed : 0
% 0.21/0.48 % Contextual simplify-reflections : 19
% 0.21/0.48 % Paramodulations : 1410
% 0.21/0.48 % Factorizations : 0
% 0.21/0.48 % NegExts : 0
% 0.21/0.48 % Equation resolutions : 56
% 0.21/0.48 % Disequality decompositions : 0
% 0.21/0.48 % Total rewrite steps : 1024
% 0.21/0.48 % ...of those cached : 942
% 0.21/0.48 % Propositional unsat checks : 0
% 0.21/0.48 % Propositional check models : 0
% 0.21/0.48 % Propositional check unsatisfiable : 0
% 0.21/0.48 % Propositional clauses : 0
% 0.21/0.48 % Propositional clauses after purity: 0
% 0.21/0.48 % Propositional unsat core size : 0
% 0.21/0.48 % Propositional preprocessing time : 0.000
% 0.21/0.48 % Propositional encoding time : 0.000
% 0.21/0.48 % Propositional solver time : 0.000
% 0.21/0.48 % Success case prop preproc time : 0.000
% 0.21/0.48 % Success case prop encoding time : 0.000
% 0.21/0.48 % Success case prop solver time : 0.000
% 0.21/0.48 % Current number of processed clauses : 379
% 0.21/0.48 % Positive orientable unit clauses : 118
% 0.21/0.48 % Positive unorientable unit clauses: 0
% 0.21/0.48 % Negative unit clauses : 23
% 0.21/0.48 % Non-unit-clauses : 238
% 0.21/0.48 % Current number of unprocessed clauses: 983
% 0.21/0.48 % ...number of literals in the above : 5083
% 0.21/0.48 % Current number of archived formulas : 0
% 0.21/0.48 % Current number of archived clauses : 239
% 0.21/0.48 % Clause-clause subsumption calls (NU) : 13970
% 0.21/0.48 % Rec. Clause-clause subsumption calls : 3114
% 0.21/0.48 % Non-unit clause-clause subsumptions : 59
% 0.21/0.48 % Unit Clause-clause subsumption calls : 1293
% 0.21/0.48 % Rewrite failures with RHS unbound : 0
% 0.21/0.48 % BW rewrite match attempts : 7
% 0.21/0.48 % BW rewrite match successes : 7
% 0.21/0.48 % Condensation attempts : 0
% 0.21/0.48 % Condensation successes : 0
% 0.21/0.48 % Termbank termtop insertions : 44469
% 0.21/0.48 % Search garbage collected termcells : 3750
% 0.21/0.48
% 0.21/0.48 % -------------------------------------------------
% 0.21/0.48 % User time : 0.052 s
% 0.21/0.48 % System time : 0.004 s
% 0.21/0.48 % Total time : 0.056 s
% 0.21/0.48 % Maximum resident set size: 4292 pages
% 0.21/0.48
% 0.21/0.48 % -------------------------------------------------
% 0.21/0.48 % User time : 0.167 s
% 0.21/0.48 % System time : 0.021 s
% 0.21/0.48 % Total time : 0.188 s
% 0.21/0.48 % Maximum resident set size: 4608 pages
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------