%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM565+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 : n006.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 01:49:35 PM UTC 2026
% Result : Theorem 0.21s 0.84s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 16 unt; 0 def)
% Number of atoms : 135 ( 37 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 165 ( 67 ~; 69 |; 19 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSel,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aSet0(X1) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sbrdtbr0(X4) = X2
& aSubsetOf0(X4,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
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,
! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__3453,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(m__3462,hypothesis,
xK = sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(c_0_9,plain,
! [X120,X121,X122,X123,X124,X125] :
( ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| aElementOf0(esk11_3(X120,X121,X125),X125)
| sbrdtbr0(esk11_3(X120,X121,X125)) = X121 )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| aElementOf0(esk11_3(X120,X121,X125),X125)
| aSubsetOf0(esk11_3(X120,X121,X125),X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| sbrdtbr0(esk11_3(X120,X121,X125)) != X121
| ~ aSubsetOf0(esk11_3(X120,X121,X125),X120)
| ~ aElementOf0(esk11_3(X120,X121,X125),X125) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| aElementOf0(X124,X122)
| sbrdtbr0(X124) != X121
| ~ aSubsetOf0(X124,X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| ~ aElementOf0(X123,X122)
| sbrdtbr0(X123) = X121 )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| ~ aElementOf0(X123,X122)
| aSubsetOf0(X123,X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| aSet0(X122) ) ),
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)],[mDefSel])])])])])])]) ).
fof(c_0_10,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_11,negated_conjecture,
~ ! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_12,plain,
( ~ aElementOf0(X4,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aElementOf0(X1,X3)
| aSubsetOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_14,hypothesis,
xK = sz00,
inference(split_conjunct,[status(thm)],[m__3462]) ).
cnf(c_0_15,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_17,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_18,negated_conjecture,
( sdtlpdtrp0(xc,esk22_0) != sdtlpdtrp0(xc,slcrc0)
& aElementOf0(esk22_0,slbdtsldtrb0(xS,sz00)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_19,plain,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X4)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aElementOf0(X1,X3)
| sbrdtbr0(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| aSubsetOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_23,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_24,negated_conjecture,
aElementOf0(esk22_0,slbdtsldtrb0(xS,sz00)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X84] :
( ( ~ aSet0(X84)
| sbrdtbr0(X84) = sz00
| X84 != slcrc0 )
& ( ~ aSet0(X84)
| X84 = slcrc0
| sbrdtbr0(X84) != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])])]) ).
cnf(c_0_26,plain,
( ~ aSet0(X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| sbrdtbr0(X1) = X2 ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aSubsetOf0(X1,xS) ),
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,
aElementOf0(esk22_0,szDzozmdt0(xc)),
inference(rw,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_29,plain,
( ~ aSet0(X1)
| sbrdtbr0(X1) != sz00
| X1 = slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| sbrdtbr0(X1) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_31,negated_conjecture,
aSubsetOf0(esk22_0,xS),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,hypothesis,
( ~ aSet0(X1)
| ~ aElementOf0(X1,szDzozmdt0(xc))
| X1 = slcrc0 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
aSet0(esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_31]),c_0_23])]) ).
cnf(c_0_34,negated_conjecture,
sdtlpdtrp0(xc,esk22_0) != sdtlpdtrp0(xc,slcrc0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,negated_conjecture,
esk22_0 = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM565+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.64 % Computer : n006.cluster.edu
% 0.17/0.64 % Model : x86_64 x86_64
% 0.17/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.64 % Memory : 8046.5625MB
% 0.17/0.64 % OS : Linux 6.8.0-71-generic
% 0.17/0.64 % CPULimit : 300
% 0.17/0.64 % WCLimit : 300
% 0.17/0.64 % DateTime : Mon Sep 21 02:39:59 UTC 2026
% 0.17/0.65 % CPUTime :
% 0.17/0.65 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.72 Running first-order theorem proving
% 0.21/0.72 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
% 0.21/0.84 % Version: 3.5.1
% 0.21/0.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.84 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.84 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.84 % Starting sh5l with 300s (1) cores
% 0.21/0.84 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1828309 completed with status 0
% 0.21/0.84 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.21/0.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.84 % No SInE strategy applied
% 0.21/0.84 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.21/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.84 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.21/0.84 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.21/0.84 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 0.21/0.84 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 0.21/0.84 % SubtermCWHack with pid 1828316 completed with status 0
% 0.21/0.84 % Result found by SubtermCWHack
% 0.21/0.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.84 % No SInE strategy applied
% 0.21/0.84 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.21/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.84 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.84 % Preprocessing time : 0.003 s
% 0.21/0.84
% 0.21/0.84 % Proof found!
% 0.21/0.84 % SZS status Theorem
% 0.21/0.84 % SZS output start CNFRefutation
% See solution above
% 0.21/0.84 % Parsed axioms : 80
% 0.21/0.84 % Removed by relevancy pruning/SinE : 0
% 0.21/0.84 % Initial clauses : 160
% 0.21/0.84 % Removed in clause preprocessing : 7
% 0.21/0.84 % Initial clauses in saturation : 153
% 0.21/0.84 % Processed clauses : 483
% 0.21/0.84 % ...of these trivial : 1
% 0.21/0.84 % ...subsumed : 172
% 0.21/0.84 % ...remaining for further processing : 310
% 0.21/0.84 % Other redundant clauses eliminated : 43
% 0.21/0.84 % Clauses deleted for lack of memory : 0
% 0.21/0.84 % Backward-subsumed : 5
% 0.21/0.84 % Backward-rewritten : 34
% 0.21/0.84 % Generated clauses : 875
% 0.21/0.84 % ...of the previous two non-redundant : 765
% 0.21/0.84 % ...aggressively subsumed : 0
% 0.21/0.84 % Contextual simplify-reflections : 21
% 0.21/0.84 % Paramodulations : 835
% 0.21/0.84 % Factorizations : 0
% 0.21/0.84 % NegExts : 0
% 0.21/0.84 % Equation resolutions : 44
% 0.21/0.84 % Disequality decompositions : 0
% 0.21/0.84 % Total rewrite steps : 568
% 0.21/0.84 % ...of those cached : 535
% 0.21/0.84 % Propositional unsat checks : 0
% 0.21/0.84 % Propositional check models : 0
% 0.21/0.84 % Propositional check unsatisfiable : 0
% 0.21/0.84 % Propositional clauses : 0
% 0.21/0.84 % Propositional clauses after purity: 0
% 0.21/0.84 % Propositional unsat core size : 0
% 0.21/0.84 % Propositional preprocessing time : 0.000
% 0.21/0.84 % Propositional encoding time : 0.000
% 0.21/0.84 % Propositional solver time : 0.000
% 0.21/0.84 % Success case prop preproc time : 0.000
% 0.21/0.84 % Success case prop encoding time : 0.000
% 0.21/0.84 % Success case prop solver time : 0.000
% 0.21/0.84 % Current number of processed clauses : 236
% 0.21/0.84 % Positive orientable unit clauses : 31
% 0.21/0.84 % Positive unorientable unit clauses: 0
% 0.21/0.84 % Negative unit clauses : 9
% 0.21/0.84 % Non-unit-clauses : 196
% 0.21/0.84 % Current number of unprocessed clauses: 423
% 0.21/0.84 % ...number of literals in the above : 2315
% 0.21/0.84 % Current number of archived formulas : 0
% 0.21/0.84 % Current number of archived clauses : 39
% 0.21/0.84 % Clause-clause subsumption calls (NU) : 10180
% 0.21/0.84 % Rec. Clause-clause subsumption calls : 5077
% 0.21/0.84 % Non-unit clause-clause subsumptions : 147
% 0.21/0.84 % Unit Clause-clause subsumption calls : 614
% 0.21/0.84 % Rewrite failures with RHS unbound : 0
% 0.21/0.84 % BW rewrite match attempts : 7
% 0.21/0.84 % BW rewrite match successes : 7
% 0.21/0.84 % Condensation attempts : 0
% 0.21/0.84 % Condensation successes : 0
% 0.21/0.84 % Termbank termtop insertions : 26914
% 0.21/0.84 % Search garbage collected termcells : 3393
% 0.21/0.84
% 0.21/0.84 % -------------------------------------------------
% 0.21/0.84 % User time : 0.048 s
% 0.21/0.84 % System time : 0.010 s
% 0.21/0.84 % Total time : 0.058 s
% 0.21/0.84 % Maximum resident set size: 4244 pages
% 0.21/0.84
% 0.21/0.84 % -------------------------------------------------
% 0.21/0.84 % User time : 0.152 s
% 0.21/0.84 % System time : 0.035 s
% 0.21/0.84 % Total time : 0.187 s
% 0.21/0.84 % Maximum resident set size: 4864 pages
% 0.21/0.84 % E exiting
%------------------------------------------------------------------------------