%------------------------------------------------------------------------------
% File : E-SAT---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 : n013.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 01:55:31 PM UTC 2026
% Result : Theorem 0.14s 5.47s
% Output : CNFRefutation 0.14s
% 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,
! [X54,X55,X56,X57,X58,X59] :
( ( ~ aElementOf0(X55,szNzAzT0)
| ~ aSet0(X54)
| X59 = slbdtsldtrb0(X54,X55)
| ~ aSet0(X59)
| aElementOf0(esk10_3(X54,X55,X59),X59)
| sbrdtbr0(esk10_3(X54,X55,X59)) = X55 )
& ( ~ aElementOf0(X55,szNzAzT0)
| ~ aSet0(X54)
| X59 = slbdtsldtrb0(X54,X55)
| ~ aSet0(X59)
| aElementOf0(esk10_3(X54,X55,X59),X59)
| aSubsetOf0(esk10_3(X54,X55,X59),X54) )
& ( ~ aElementOf0(X55,szNzAzT0)
| ~ aSet0(X54)
| X59 = slbdtsldtrb0(X54,X55)
| ~ aSet0(X59)
| sbrdtbr0(esk10_3(X54,X55,X59)) != X55
| ~ aSubsetOf0(esk10_3(X54,X55,X59),X54)
| ~ aElementOf0(esk10_3(X54,X55,X59),X59) )
& ( ~ aElementOf0(X55,szNzAzT0)
| ~ aSet0(X54)
| X56 != slbdtsldtrb0(X54,X55)
| aElementOf0(X58,X56)
| sbrdtbr0(X58) != X55
| ~ aSubsetOf0(X58,X54) )
& ( ~ aElementOf0(X55,szNzAzT0)
| ~ aSet0(X54)
| X56 != slbdtsldtrb0(X54,X55)
| ~ aElementOf0(X57,X56)
| sbrdtbr0(X57) = X55 )
& ( ~ aElementOf0(X55,szNzAzT0)
| ~ aSet0(X54)
| X56 != slbdtsldtrb0(X54,X55)
| ~ aElementOf0(X57,X56)
| aSubsetOf0(X57,X54) )
& ( ~ aElementOf0(X55,szNzAzT0)
| ~ aSet0(X54)
| X56 != slbdtsldtrb0(X54,X55)
| aSet0(X56) ) ),
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,
! [X23,X24,X25,X26] :
( ( ~ aSet0(X23)
| aSubsetOf0(X26,X23)
| ~ aSet0(X26)
| ~ aElementOf0(esk4_2(X23,X26),X23) )
& ( ~ aSet0(X23)
| aSubsetOf0(X26,X23)
| ~ aSet0(X26)
| aElementOf0(esk4_2(X23,X26),X26) )
& ( ~ aSet0(X23)
| ~ aSubsetOf0(X24,X23)
| aElementOf0(X25,X23)
| ~ aElementOf0(X25,X24) )
& ( ~ aSet0(X23)
| ~ aSubsetOf0(X24,X23)
| aSet0(X24) ) ),
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,esk3_0) != sdtlpdtrp0(xc,slcrc0)
& aElementOf0(esk3_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(esk3_0,slbdtsldtrb0(xS,sz00)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X81] :
( ( ~ aSet0(X81)
| sbrdtbr0(X81) = sz00
| X81 != slcrc0 )
& ( ~ aSet0(X81)
| X81 = slcrc0
| sbrdtbr0(X81) != 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(esk3_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(esk3_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(esk3_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,esk3_0) != sdtlpdtrp0(xc,slcrc0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,negated_conjecture,
esk3_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
% 0.00/0.03 % Problem : NUM565+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n013.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 02:39:42 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.47 % Version: 3.5.1
% 0.14/5.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.47 % Starting sh5l with 300s (1) cores
% 0.14/5.47 % new_bool_1 with pid 3968418 completed with status 0
% 0.14/5.47 % Result found by new_bool_1
% 0.14/5.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.47 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.14/5.47 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.47 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.47 % SubtermCWHack with pid 3968420 completed with status 0
% 0.14/5.47 % Result found by SubtermCWHack
% 0.14/5.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.47 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.14/5.47 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.47 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.47 % Preprocessing time : 0.003 s
% 0.14/5.47
% 0.14/5.47 % Proof found!
% 0.14/5.47 % SZS status Theorem
% 0.14/5.47 % SZS output start CNFRefutation
% See solution above
% 0.14/5.47 % Parsed axioms : 80
% 0.14/5.47 % Removed by relevancy pruning/SinE : 7
% 0.14/5.47 % Initial clauses : 136
% 0.14/5.47 % Removed in clause preprocessing : 7
% 0.14/5.47 % Initial clauses in saturation : 129
% 0.14/5.47 % Processed clauses : 415
% 0.14/5.47 % ...of these trivial : 1
% 0.14/5.47 % ...subsumed : 152
% 0.14/5.47 % ...remaining for further processing : 262
% 0.14/5.47 % Other redundant clauses eliminated : 33
% 0.14/5.47 % Clauses deleted for lack of memory : 0
% 0.14/5.47 % Backward-subsumed : 5
% 0.14/5.47 % Backward-rewritten : 27
% 0.14/5.47 % Generated clauses : 688
% 0.14/5.47 % ...of the previous two non-redundant : 590
% 0.14/5.47 % ...aggressively subsumed : 0
% 0.14/5.47 % Contextual simplify-reflections : 20
% 0.14/5.47 % Paramodulations : 658
% 0.14/5.47 % Factorizations : 0
% 0.14/5.47 % NegExts : 0
% 0.14/5.47 % Equation resolutions : 34
% 0.14/5.47 % Disequality decompositions : 0
% 0.14/5.47 % Total rewrite steps : 469
% 0.14/5.47 % ...of those cached : 438
% 0.14/5.47 % Propositional unsat checks : 0
% 0.14/5.47 % Propositional check models : 0
% 0.14/5.47 % Propositional check unsatisfiable : 0
% 0.14/5.47 % Propositional clauses : 0
% 0.14/5.47 % Propositional clauses after purity: 0
% 0.14/5.47 % Propositional unsat core size : 0
% 0.14/5.47 % Propositional preprocessing time : 0.000
% 0.14/5.47 % Propositional encoding time : 0.000
% 0.14/5.47 % Propositional solver time : 0.000
% 0.14/5.47 % Success case prop preproc time : 0.000
% 0.14/5.47 % Success case prop encoding time : 0.000
% 0.14/5.47 % Success case prop solver time : 0.000
% 0.14/5.47 % Current number of processed clauses : 205
% 0.14/5.47 % Positive orientable unit clauses : 32
% 0.14/5.47 % Positive unorientable unit clauses: 0
% 0.14/5.47 % Negative unit clauses : 7
% 0.14/5.47 % Non-unit-clauses : 166
% 0.14/5.47 % Current number of unprocessed clauses: 292
% 0.14/5.47 % ...number of literals in the above : 1593
% 0.14/5.47 % Current number of archived formulas : 0
% 0.14/5.47 % Current number of archived clauses : 32
% 0.14/5.47 % Clause-clause subsumption calls (NU) : 6261
% 0.14/5.47 % Rec. Clause-clause subsumption calls : 3192
% 0.14/5.47 % Non-unit clause-clause subsumptions : 137
% 0.14/5.47 % Unit Clause-clause subsumption calls : 625
% 0.14/5.47 % Rewrite failures with RHS unbound : 0
% 0.14/5.47 % BW rewrite match attempts : 5
% 0.14/5.47 % BW rewrite match successes : 5
% 0.14/5.47 % Condensation attempts : 0
% 0.14/5.47 % Condensation successes : 0
% 0.14/5.47 % Termbank termtop insertions : 21974
% 0.14/5.47 % Search garbage collected termcells : 2828
% 0.14/5.47
% 0.14/5.47 % -------------------------------------------------
% 0.14/5.47 % User time : 0.032 s
% 0.14/5.47 % System time : 0.005 s
% 0.14/5.47 % Total time : 0.036 s
% 0.14/5.47 % Maximum resident set size: 3988 pages
% 0.14/5.47
% 0.14/5.47 % -------------------------------------------------
% 0.14/5.47 % User time : 0.036 s
% 0.14/5.47 % System time : 0.008 s
% 0.14/5.47 % Total time : 0.044 s
% 0.14/5.47 % Maximum resident set size: 4608 pages
% 0.14/5.47 % E exiting
%------------------------------------------------------------------------------