%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM545+2 : 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 : n012.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 01:49:30 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 143 ( 17 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 165 ( 54 ~; 54 |; 43 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-1 aty)
% Number of variables : 31 ( 2 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( ( ( ! [X2] :
( aElementOf0(X2,slbdtrb0(X1))
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X1)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(slbdtrb0(X1)) )
=> ( aSubsetOf0(xS,slbdtrb0(X1))
| ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X1)) ) ) )
& aElementOf0(X1,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2035,hypothesis,
( ~ ( xS = slcrc0
& ~ ? [X1] : aElementOf0(X1,xS) )
=> ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ! [X1] :
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(szmzazxdt0(xS)))
& aElementOf0(X1,szNzAzT0) ) )
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,szmzazxdt0(xS)) )
& aElementOf0(szmzazxdt0(xS),xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2035) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( szszuzczcdt0(X1) != sz00
& aElementOf0(szszuzczcdt0(X1),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(m__1986,hypothesis,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(c_0_7,negated_conjecture,
~ ? [X1] :
( ( ( ! [X2] :
( aElementOf0(X2,slbdtrb0(X1))
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X1)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(slbdtrb0(X1)) )
=> ( aSubsetOf0(xS,slbdtrb0(X1))
| ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X1)) ) ) )
& aElementOf0(X1,szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,hypothesis,
! [X6,X7,X8,X9] :
( ( xS = slcrc0
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ( xS = slcrc0
| aElementOf0(X9,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X9,xS) )
& ( xS = slcrc0
| aElementOf0(X8,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ sdtlseqdt0(szszuzczcdt0(X8),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(X8,szNzAzT0) )
& ( xS = slcrc0
| ~ aElementOf0(X8,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| sdtlseqdt0(szszuzczcdt0(X8),szszuzczcdt0(szmzazxdt0(xS))) )
& ( xS = slcrc0
| ~ aElementOf0(X8,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| aElementOf0(X8,szNzAzT0) )
& ( xS = slcrc0
| aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ( xS = slcrc0
| sdtlseqdt0(X7,szmzazxdt0(xS))
| ~ aElementOf0(X7,xS) )
& ( xS = slcrc0
| aElementOf0(szmzazxdt0(xS),xS) )
& ( ~ aElementOf0(X6,xS)
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ( ~ aElementOf0(X6,xS)
| aElementOf0(X9,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X9,xS) )
& ( ~ aElementOf0(X6,xS)
| aElementOf0(X8,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ sdtlseqdt0(szszuzczcdt0(X8),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(X8,szNzAzT0) )
& ( ~ aElementOf0(X6,xS)
| ~ aElementOf0(X8,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| sdtlseqdt0(szszuzczcdt0(X8),szszuzczcdt0(szmzazxdt0(xS))) )
& ( ~ aElementOf0(X6,xS)
| ~ aElementOf0(X8,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| aElementOf0(X8,szNzAzT0) )
& ( ~ aElementOf0(X6,xS)
| aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ( ~ aElementOf0(X6,xS)
| sdtlseqdt0(X7,szmzazxdt0(xS))
| ~ aElementOf0(X7,xS) )
& ( ~ aElementOf0(X6,xS)
| aElementOf0(szmzazxdt0(xS),xS) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2035])])])])]) ).
fof(c_0_9,negated_conjecture,
! [X10,X11,X12] :
( ( ~ aElementOf0(X10,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(X10)) )
& ( ~ aElementOf0(X10,szNzAzT0)
| ~ aElementOf0(esk1_1(X10),slbdtrb0(X10)) )
& ( ~ aElementOf0(X10,szNzAzT0)
| aElementOf0(esk1_1(X10),xS) )
& ( ~ aElementOf0(X10,szNzAzT0)
| aElementOf0(X12,slbdtrb0(X10))
| ~ sdtlseqdt0(szszuzczcdt0(X12),X10)
| ~ aElementOf0(X12,szNzAzT0) )
& ( ~ aElementOf0(X10,szNzAzT0)
| ~ aElementOf0(X11,slbdtrb0(X10))
| sdtlseqdt0(szszuzczcdt0(X11),X10) )
& ( ~ aElementOf0(X10,szNzAzT0)
| ~ aElementOf0(X11,slbdtrb0(X10))
| aElementOf0(X11,szNzAzT0) )
& ( ~ aElementOf0(X10,szNzAzT0)
| aSet0(slbdtrb0(X10)) ) ),
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])])])])])])]) ).
cnf(c_0_10,hypothesis,
( ~ aElementOf0(X1,xS)
| aElementOf0(szmzazxdt0(xS),xS) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(esk1_1(X1),xS) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( szszuzczcdt0(X1) != sz00
& aElementOf0(szszuzczcdt0(X1),szNzAzT0) ) ),
inference(fof_simplification,[status(thm)],[mSuccNum]) ).
fof(c_0_13,hypothesis,
! [X5] :
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(X5,szNzAzT0)
| ~ aElementOf0(X5,xS) )
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1986])])])]) ).
cnf(c_0_14,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(szmzazxdt0(xS),xS) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_16,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,hypothesis,
( xS = slcrc0
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_18,plain,
! [X67] :
( ( ~ aElementOf0(X67,szNzAzT0)
| szszuzczcdt0(X67) != sz00 )
& ( ~ aElementOf0(X67,szNzAzT0)
| aElementOf0(szszuzczcdt0(X67),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_19,hypothesis,
( ~ aElementOf0(X1,xS)
| aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,hypothesis,
aElementOf0(szmzazxdt0(xS),xS),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
slbdtrb0(sz00) = slcrc0,
inference(split_conjunct,[status(thm)],[mSegZero]) ).
cnf(c_0_22,negated_conjecture,
( ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| slcrc0 = xS ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(szszuzczcdt0(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,hypothesis,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
~ aSubsetOf0(xS,slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_15])]) ).
cnf(c_0_26,negated_conjecture,
slcrc0 = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
fof(c_0_27,plain,
! [X22] :
( aSubsetOf0(X22,X22)
| ~ aSet0(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])])]) ).
cnf(c_0_28,negated_conjecture,
~ aSubsetOf0(xS,xS),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( ~ aSet0(X1)
| aSubsetOf0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM545+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 02:39:07 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 Running first-order theorem proving
% 0.08/0.34 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
% 0.08/0.38 % Version: 3.5.1
% 0.08/0.38 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.38 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.38 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.38 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.38 % Starting sh5l with 300s (1) cores
% 0.08/0.38 % new_bool_3 with pid 1393370 completed with status 0
% 0.08/0.38 % Result found by new_bool_3
% 0.08/0.38 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.38 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.38 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.38 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.38 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.38 % Search class: FGHSF-FSMM31-MFFFFFNN
% 0.08/0.38 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.38 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.38 % SubtermCWHack with pid 1393373 completed with status 0
% 0.08/0.38 % Result found by SubtermCWHack
% 0.08/0.38 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.38 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.38 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.38 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.38 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.38 % Search class: FGHSF-FSMM31-MFFFFFNN
% 0.08/0.38 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.38 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.38 % Preprocessing time : 0.002 s
% 0.08/0.38
% 0.08/0.38 % Proof found!
% 0.08/0.38 % SZS status Theorem
% 0.08/0.38 % SZS output start CNFRefutation
% See solution above
% 0.08/0.38 % Parsed axioms : 57
% 0.08/0.38 % Removed by relevancy pruning/SinE : 4
% 0.08/0.38 % Initial clauses : 117
% 0.08/0.38 % Removed in clause preprocessing : 5
% 0.08/0.38 % Initial clauses in saturation : 112
% 0.08/0.38 % Processed clauses : 74
% 0.08/0.38 % ...of these trivial : 0
% 0.08/0.38 % ...subsumed : 7
% 0.08/0.38 % ...remaining for further processing : 67
% 0.08/0.38 % Other redundant clauses eliminated : 5
% 0.08/0.38 % Clauses deleted for lack of memory : 0
% 0.08/0.38 % Backward-subsumed : 4
% 0.08/0.38 % Backward-rewritten : 18
% 0.08/0.38 % Generated clauses : 56
% 0.08/0.38 % ...of the previous two non-redundant : 48
% 0.08/0.38 % ...aggressively subsumed : 0
% 0.08/0.38 % Contextual simplify-reflections : 0
% 0.08/0.38 % Paramodulations : 51
% 0.08/0.38 % Factorizations : 0
% 0.08/0.38 % NegExts : 0
% 0.08/0.38 % Equation resolutions : 5
% 0.08/0.38 % Disequality decompositions : 0
% 0.08/0.38 % Total rewrite steps : 62
% 0.08/0.38 % ...of those cached : 50
% 0.08/0.38 % Propositional unsat checks : 0
% 0.08/0.38 % Propositional check models : 0
% 0.08/0.38 % Propositional check unsatisfiable : 0
% 0.08/0.38 % Propositional clauses : 0
% 0.08/0.38 % Propositional clauses after purity: 0
% 0.08/0.38 % Propositional unsat core size : 0
% 0.08/0.38 % Propositional preprocessing time : 0.000
% 0.08/0.38 % Propositional encoding time : 0.000
% 0.08/0.38 % Propositional solver time : 0.000
% 0.08/0.38 % Success case prop preproc time : 0.000
% 0.08/0.38 % Success case prop encoding time : 0.000
% 0.08/0.38 % Success case prop solver time : 0.000
% 0.08/0.38 % Current number of processed clauses : 40
% 0.08/0.38 % Positive orientable unit clauses : 12
% 0.08/0.38 % Positive unorientable unit clauses: 0
% 0.08/0.38 % Negative unit clauses : 3
% 0.08/0.38 % Non-unit-clauses : 25
% 0.08/0.38 % Current number of unprocessed clauses: 79
% 0.08/0.38 % ...number of literals in the above : 347
% 0.08/0.38 % Current number of archived formulas : 0
% 0.08/0.38 % Current number of archived clauses : 22
% 0.08/0.38 % Clause-clause subsumption calls (NU) : 79
% 0.08/0.38 % Rec. Clause-clause subsumption calls : 70
% 0.08/0.38 % Non-unit clause-clause subsumptions : 6
% 0.08/0.38 % Unit Clause-clause subsumption calls : 14
% 0.08/0.38 % Rewrite failures with RHS unbound : 0
% 0.08/0.38 % BW rewrite match attempts : 5
% 0.08/0.38 % BW rewrite match successes : 5
% 0.08/0.38 % Condensation attempts : 0
% 0.08/0.38 % Condensation successes : 0
% 0.08/0.38 % Termbank termtop insertions : 9643
% 0.08/0.38 % Search garbage collected termcells : 2122
% 0.08/0.38
% 0.08/0.38 % -------------------------------------------------
% 0.08/0.38 % User time : 0.011 s
% 0.08/0.38 % System time : 0.004 s
% 0.08/0.38 % Total time : 0.015 s
% 0.08/0.38 % Maximum resident set size: 3960 pages
% 0.08/0.38
% 0.08/0.38 % -------------------------------------------------
% 0.08/0.38 % User time : 0.014 s
% 0.08/0.38 % System time : 0.007 s
% 0.08/0.38 % Total time : 0.021 s
% 0.08/0.38 % Maximum resident set size: 4864 pages
% 0.08/0.38 % E exiting
%------------------------------------------------------------------------------