%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM545+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 : n014.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 01:55:26 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 12 unt; 0 def)
% Number of atoms : 138 ( 32 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 155 ( 60 ~; 57 |; 23 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aSubsetOf0(xS,slbdtrb0(X1))
& aElementOf0(X1,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2035,hypothesis,
( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2035) ).
fof(mDefMax,axiom,
! [X1] :
( ( X1 != slcrc0
& isFinite0(X1)
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzazxdt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X3,X2) )
& aElementOf0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMax) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( szszuzczcdt0(X1) != sz00
& aElementOf0(szszuzczcdt0(X1),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
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__1986,hypothesis,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(c_0_11,negated_conjecture,
~ ? [X1] :
( aSubsetOf0(xS,slbdtrb0(X1))
& aElementOf0(X1,szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,hypothesis,
( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(fof_simplification,[status(thm)],[m__2035]) ).
fof(c_0_13,plain,
! [X1] :
( ( X1 != slcrc0
& isFinite0(X1)
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzazxdt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X3,X2) )
& aElementOf0(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDefMax]) ).
fof(c_0_14,negated_conjecture,
! [X115] :
( ~ aSubsetOf0(xS,slbdtrb0(X115))
| ~ aElementOf0(X115,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_15,hypothesis,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( szszuzczcdt0(X1) != sz00
& aElementOf0(szszuzczcdt0(X1),szNzAzT0) ) ),
inference(fof_simplification,[status(thm)],[mSuccNum]) ).
fof(c_0_17,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])])])])])])]) ).
fof(c_0_18,plain,
! [X97,X98,X99,X100] :
( ( X97 = slcrc0
| ~ isFinite0(X97)
| ~ aSubsetOf0(X97,szNzAzT0)
| X100 = szmzazxdt0(X97)
| ~ aElementOf0(X100,X97)
| ~ sdtlseqdt0(esk8_2(X97,X100),X100) )
& ( X97 = slcrc0
| ~ isFinite0(X97)
| ~ aSubsetOf0(X97,szNzAzT0)
| X100 = szmzazxdt0(X97)
| ~ aElementOf0(X100,X97)
| aElementOf0(esk8_2(X97,X100),X97) )
& ( X97 = slcrc0
| ~ isFinite0(X97)
| ~ aSubsetOf0(X97,szNzAzT0)
| X98 != szmzazxdt0(X97)
| sdtlseqdt0(X99,X98)
| ~ aElementOf0(X99,X97) )
& ( X97 = slcrc0
| ~ isFinite0(X97)
| ~ aSubsetOf0(X97,szNzAzT0)
| X98 != szmzazxdt0(X97)
| aElementOf0(X98,X97) ) ),
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])])])])])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ aSubsetOf0(xS,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,hypothesis,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X56] :
( ( ~ aElementOf0(X56,szNzAzT0)
| szszuzczcdt0(X56) != sz00 )
& ( ~ aElementOf0(X56,szNzAzT0)
| aElementOf0(szszuzczcdt0(X56),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_22,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1986]) ).
cnf(c_0_24,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_25,plain,
( ~ isFinite0(X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| X1 != szmzazxdt0(X2)
| X2 = slcrc0
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| xS = slcrc0 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(szszuzczcdt0(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
slbdtrb0(sz00) = slcrc0,
inference(split_conjunct,[status(thm)],[mSegZero]) ).
cnf(c_0_29,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_30,hypothesis,
( ~ aElementOf0(X1,xS)
| aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_31,plain,
( ~ isFinite0(X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| aElementOf0(szmzazxdt0(X1),X1)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__1986]) ).
cnf(c_0_33,negated_conjecture,
( ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| xS = slcrc0 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_34,plain,
! [X10,X11,X12] :
( ( X12 = slcrc0
| aElementOf0(esk1_1(X12),X12)
| ~ aSet0(X12) )
& ( X10 != slcrc0
| ~ aElementOf0(X11,X10) )
& ( X10 != slcrc0
| aSet0(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)],[mDefEmp])])])])])])]) ).
cnf(c_0_35,negated_conjecture,
~ aSubsetOf0(xS,slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_28]),c_0_29])]) ).
cnf(c_0_36,hypothesis,
xS = slcrc0,
inference(csr,[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_23]),c_0_32])]),c_0_33]) ).
fof(c_0_37,plain,
! [X24] :
( aSubsetOf0(X24,X24)
| ~ aSet0(X24) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])])]) ).
cnf(c_0_38,plain,
( X1 != slcrc0
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
~ aSubsetOf0(slcrc0,slcrc0),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( ~ aSet0(X1)
| aSubsetOf0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM545+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n014.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 02:39:04 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.44 % Version: 3.5.1
% 0.15/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2968546 completed with status 0
% 0.15/0.44 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.44 % No SInE strategy applied
% 0.15/0.44 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.15/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.44 % SubtermCWHack with pid 2968550 completed with status 0
% 0.15/0.44 % Result found by SubtermCWHack
% 0.15/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.44 % No SInE strategy applied
% 0.15/0.44 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.15/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.44 % Preprocessing time : 0.003 s
% 0.15/0.44
% 0.15/0.44 % Proof found!
% 0.15/0.44 % SZS status Theorem
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
% 0.15/0.44 % Parsed axioms : 57
% 0.15/0.44 % Removed by relevancy pruning/SinE : 0
% 0.15/0.44 % Initial clauses : 101
% 0.15/0.44 % Removed in clause preprocessing : 6
% 0.15/0.44 % Initial clauses in saturation : 95
% 0.15/0.44 % Processed clauses : 86
% 0.15/0.44 % ...of these trivial : 0
% 0.15/0.44 % ...subsumed : 4
% 0.15/0.44 % ...remaining for further processing : 82
% 0.15/0.44 % Other redundant clauses eliminated : 9
% 0.15/0.44 % Clauses deleted for lack of memory : 0
% 0.15/0.44 % Backward-subsumed : 1
% 0.15/0.44 % Backward-rewritten : 15
% 0.15/0.44 % Generated clauses : 67
% 0.15/0.44 % ...of the previous two non-redundant : 53
% 0.15/0.44 % ...aggressively subsumed : 0
% 0.15/0.44 % Contextual simplify-reflections : 2
% 0.15/0.44 % Paramodulations : 58
% 0.15/0.44 % Factorizations : 0
% 0.15/0.44 % NegExts : 0
% 0.15/0.44 % Equation resolutions : 9
% 0.15/0.44 % Disequality decompositions : 0
% 0.15/0.44 % Total rewrite steps : 72
% 0.15/0.44 % ...of those cached : 63
% 0.15/0.44 % Propositional unsat checks : 0
% 0.15/0.44 % Propositional check models : 0
% 0.15/0.44 % Propositional check unsatisfiable : 0
% 0.15/0.44 % Propositional clauses : 0
% 0.15/0.44 % Propositional clauses after purity: 0
% 0.15/0.44 % Propositional unsat core size : 0
% 0.15/0.44 % Propositional preprocessing time : 0.000
% 0.15/0.44 % Propositional encoding time : 0.000
% 0.15/0.44 % Propositional solver time : 0.000
% 0.15/0.44 % Success case prop preproc time : 0.000
% 0.15/0.44 % Success case prop encoding time : 0.000
% 0.15/0.44 % Success case prop solver time : 0.000
% 0.15/0.44 % Current number of processed clauses : 57
% 0.15/0.44 % Positive orientable unit clauses : 9
% 0.15/0.44 % Positive unorientable unit clauses: 0
% 0.15/0.44 % Negative unit clauses : 4
% 0.15/0.44 % Non-unit-clauses : 44
% 0.15/0.44 % Current number of unprocessed clauses: 62
% 0.15/0.44 % ...number of literals in the above : 307
% 0.15/0.44 % Current number of archived formulas : 0
% 0.15/0.44 % Current number of archived clauses : 16
% 0.15/0.44 % Clause-clause subsumption calls (NU) : 234
% 0.15/0.44 % Rec. Clause-clause subsumption calls : 158
% 0.15/0.44 % Non-unit clause-clause subsumptions : 5
% 0.15/0.44 % Unit Clause-clause subsumption calls : 4
% 0.15/0.44 % Rewrite failures with RHS unbound : 0
% 0.15/0.44 % BW rewrite match attempts : 1
% 0.15/0.44 % BW rewrite match successes : 1
% 0.15/0.44 % Condensation attempts : 0
% 0.15/0.44 % Condensation successes : 0
% 0.15/0.44 % Termbank termtop insertions : 9379
% 0.15/0.44 % Search garbage collected termcells : 1997
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.011 s
% 0.15/0.44 % System time : 0.003 s
% 0.15/0.44 % Total time : 0.014 s
% 0.15/0.44 % Maximum resident set size: 3952 pages
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.043 s
% 0.15/0.44 % System time : 0.013 s
% 0.15/0.44 % Total time : 0.056 s
% 0.15/0.44 % Maximum resident set size: 4608 pages
% 0.15/0.44 % E exiting
%------------------------------------------------------------------------------