%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM539+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 : n005.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 01:49:29 PM UTC 2026
% Result : Theorem 0.26s 10.66s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 126 ( 34 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 144 ( 57 ~; 52 |; 24 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 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__1779,hypothesis,
( xT != slcrc0
& xS != slcrc0
& aSubsetOf0(xT,szNzAzT0)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1779) ).
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__,conjecture,
szmzizndt0(xS) = szmzizndt0(xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
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__1802,hypothesis,
( aElementOf0(szmzizndt0(xT),xS)
& aElementOf0(szmzizndt0(xS),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1802) ).
fof(c_0_7,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_8,plain,
! [X92,X93,X94,X95] :
( ( X92 = slcrc0
| ~ aSubsetOf0(X92,szNzAzT0)
| X95 = szmzizndt0(X92)
| ~ aElementOf0(X95,X92)
| ~ sdtlseqdt0(X95,esk7_2(X92,X95)) )
& ( X92 = slcrc0
| ~ aSubsetOf0(X92,szNzAzT0)
| X95 = szmzizndt0(X92)
| ~ aElementOf0(X95,X92)
| aElementOf0(esk7_2(X92,X95),X92) )
& ( X92 = slcrc0
| ~ aSubsetOf0(X92,szNzAzT0)
| X93 != szmzizndt0(X92)
| sdtlseqdt0(X93,X94)
| ~ aElementOf0(X94,X92) )
& ( X92 = slcrc0
| ~ aSubsetOf0(X92,szNzAzT0)
| X93 != szmzizndt0(X92)
| aElementOf0(X93,X92) ) ),
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_7])])])])])])]) ).
fof(c_0_9,hypothesis,
( xT != slcrc0
& xS != slcrc0
& aSubsetOf0(xT,szNzAzT0)
& aSubsetOf0(xS,szNzAzT0) ),
inference(fof_simplification,[status(thm)],[m__1779]) ).
cnf(c_0_10,plain,
( ~ aSubsetOf0(X2,szNzAzT0)
| X3 != szmzizndt0(X2)
| ~ aElementOf0(X1,X2)
| X2 = slcrc0
| sdtlseqdt0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,hypothesis,
( xT != slcrc0
& xS != slcrc0
& aSubsetOf0(xT,szNzAzT0)
& aSubsetOf0(xS,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X17,X18,X19,X20] :
( ( ~ aSet0(X17)
| aSubsetOf0(X20,X17)
| ~ aSet0(X20)
| ~ aElementOf0(esk2_2(X17,X20),X17) )
& ( ~ aSet0(X17)
| aSubsetOf0(X20,X17)
| ~ aSet0(X20)
| aElementOf0(esk2_2(X17,X20),X20) )
& ( ~ aSet0(X17)
| ~ aSubsetOf0(X18,X17)
| aElementOf0(X19,X17)
| ~ aElementOf0(X19,X18) )
& ( ~ aSet0(X17)
| ~ aSubsetOf0(X18,X17)
| aSet0(X18) ) ),
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_13,plain,
( ~ aSubsetOf0(X2,szNzAzT0)
| X1 != szmzizndt0(X2)
| X2 = slcrc0
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_15,plain,
( ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| sdtlseqdt0(szmzizndt0(X1),X2)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aSubsetOf0(xT,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
xT != slcrc0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_20,plain,
( ~ aSubsetOf0(X1,szNzAzT0)
| aElementOf0(szmzizndt0(X1),X1)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_13]) ).
fof(c_0_21,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_22,plain,
! [X70,X71] :
( X70 = X71
| ~ sdtlseqdt0(X71,X70)
| ~ sdtlseqdt0(X70,X71)
| ~ aElementOf0(X71,szNzAzT0)
| ~ aElementOf0(X70,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])])]) ).
cnf(c_0_23,hypothesis,
( ~ aElementOf0(X1,xT)
| sdtlseqdt0(szmzizndt0(xT),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_24,hypothesis,
aElementOf0(szmzizndt0(xS),xT),
inference(split_conjunct,[status(thm)],[m__1802]) ).
cnf(c_0_25,hypothesis,
( ~ aElementOf0(X1,xT)
| aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_19])]) ).
cnf(c_0_26,hypothesis,
aElementOf0(szmzizndt0(xT),xT),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_17]) ).
fof(c_0_27,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(fof_nnf,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,hypothesis,
xS != slcrc0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,hypothesis,
sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,hypothesis,
aElementOf0(szmzizndt0(xT),szNzAzT0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,hypothesis,
aElementOf0(szmzizndt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_34,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,hypothesis,
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(szmzizndt0(xS),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_28]),c_0_29]) ).
cnf(c_0_36,hypothesis,
aElementOf0(szmzizndt0(xT),xS),
inference(split_conjunct,[status(thm)],[m__1802]) ).
cnf(c_0_37,hypothesis,
~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM539+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/10.49 % Computer : n005.cluster.edu
% 0.21/10.49 % Model : x86_64 x86_64
% 0.21/10.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/10.49 % Memory : 8046.5625MB
% 0.21/10.49 % OS : Linux 6.8.0-71-generic
% 0.21/10.50 % CPULimit : 300
% 0.21/10.50 % WCLimit : 300
% 0.21/10.50 % DateTime : Mon Sep 21 02:38:44 UTC 2026
% 0.25/10.50 % CPUTime :
% 0.25/10.50 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/10.57 Running first-order theorem proving
% 0.25/10.57 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
% 0.26/10.66 % Version: 3.5.1
% 0.26/10.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/10.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/10.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/10.66 % Starting new_bool_3 with 300s (1) cores
% 0.26/10.66 % Starting new_bool_1 with 300s (1) cores
% 0.26/10.66 % Starting sh5l with 300s (1) cores
% 0.26/10.66 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2371145 completed with status 0
% 0.26/10.66 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.26/10.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/10.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/10.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/10.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/10.66 % No SInE strategy applied
% 0.26/10.66 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.26/10.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/10.66 % Starting SubtermCWHack with 136s (1) cores
% 0.26/10.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/10.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.26/10.66 % Starting new_bool_3 with 136s (1) cores
% 0.26/10.66 % Starting new_bool_1 with 136s (1) cores
% 0.26/10.66 % new_bool_3 with pid 2371152 completed with status 0
% 0.26/10.66 % Result found by new_bool_3
% 0.26/10.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/10.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/10.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/10.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/10.66 % No SInE strategy applied
% 0.26/10.66 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.26/10.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/10.66 % Starting SubtermCWHack with 136s (1) cores
% 0.26/10.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/10.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.26/10.66 % Starting new_bool_3 with 136s (1) cores
% 0.26/10.66 % Preprocessing time : 0.002 s
% 0.26/10.66 % Presaturation interreduction done
% 0.26/10.66
% 0.26/10.66 % Proof found!
% 0.26/10.66 % SZS status Theorem
% 0.26/10.66 % SZS output start CNFRefutation
% See solution above
% 0.26/10.66 % Parsed axioms : 51
% 0.26/10.66 % Removed by relevancy pruning/SinE : 0
% 0.26/10.66 % Initial clauses : 89
% 0.26/10.66 % Removed in clause preprocessing : 6
% 0.26/10.66 % Initial clauses in saturation : 83
% 0.26/10.66 % Processed clauses : 267
% 0.26/10.66 % ...of these trivial : 1
% 0.26/10.66 % ...subsumed : 7
% 0.26/10.66 % ...remaining for further processing : 258
% 0.26/10.66 % Other redundant clauses eliminated : 20
% 0.26/10.66 % Clauses deleted for lack of memory : 0
% 0.26/10.66 % Backward-subsumed : 3
% 0.26/10.66 % Backward-rewritten : 0
% 0.26/10.66 % Generated clauses : 303
% 0.26/10.66 % ...of the previous two non-redundant : 251
% 0.26/10.66 % ...aggressively subsumed : 0
% 0.26/10.66 % Contextual simplify-reflections : 12
% 0.26/10.66 % Paramodulations : 284
% 0.26/10.66 % Factorizations : 0
% 0.26/10.66 % NegExts : 0
% 0.26/10.66 % Equation resolutions : 21
% 0.26/10.66 % Disequality decompositions : 0
% 0.26/10.66 % Total rewrite steps : 204
% 0.26/10.66 % ...of those cached : 172
% 0.26/10.66 % Propositional unsat checks : 0
% 0.26/10.66 % Propositional check models : 0
% 0.26/10.66 % Propositional check unsatisfiable : 0
% 0.26/10.66 % Propositional clauses : 0
% 0.26/10.66 % Propositional clauses after purity: 0
% 0.26/10.66 % Propositional unsat core size : 0
% 0.26/10.66 % Propositional preprocessing time : 0.000
% 0.26/10.66 % Propositional encoding time : 0.000
% 0.26/10.66 % Propositional solver time : 0.000
% 0.26/10.66 % Success case prop preproc time : 0.000
% 0.26/10.66 % Success case prop encoding time : 0.000
% 0.26/10.66 % Success case prop solver time : 0.000
% 0.26/10.66 % Current number of processed clauses : 154
% 0.26/10.66 % Positive orientable unit clauses : 57
% 0.26/10.66 % Positive unorientable unit clauses: 0
% 0.26/10.66 % Negative unit clauses : 7
% 0.26/10.66 % Non-unit-clauses : 90
% 0.26/10.66 % Current number of unprocessed clauses: 150
% 0.26/10.66 % ...number of literals in the above : 440
% 0.26/10.66 % Current number of archived formulas : 0
% 0.26/10.66 % Current number of archived clauses : 86
% 0.26/10.66 % Clause-clause subsumption calls (NU) : 1956
% 0.26/10.66 % Rec. Clause-clause subsumption calls : 578
% 0.26/10.66 % Non-unit clause-clause subsumptions : 19
% 0.26/10.66 % Unit Clause-clause subsumption calls : 436
% 0.26/10.66 % Rewrite failures with RHS unbound : 0
% 0.26/10.66 % BW rewrite match attempts : 3
% 0.26/10.66 % BW rewrite match successes : 0
% 0.26/10.66 % Condensation attempts : 0
% 0.26/10.66 % Condensation successes : 0
% 0.26/10.66 % Termbank termtop insertions : 12146
% 0.26/10.66 % Search garbage collected termcells : 1653
% 0.26/10.66
% 0.26/10.66 % -------------------------------------------------
% 0.26/10.66 % User time : 0.025 s
% 0.26/10.66 % System time : 0.001 s
% 0.26/10.66 % Total time : 0.026 s
% 0.26/10.66 % Maximum resident set size: 3944 pages
% 0.26/10.66
% 0.26/10.66 % -------------------------------------------------
% 0.26/10.66 % User time : 0.130 s
% 0.26/10.66 % System time : 0.022 s
% 0.26/10.66 % Total time : 0.152 s
% 0.26/10.66 % Maximum resident set size: 4864 pages
% 0.26/10.66 % E exiting
%------------------------------------------------------------------------------