%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM538+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 : n011.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 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 153 ( 33 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 198 ( 81 ~; 79 |; 20 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mCardCons,axiom,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(mConsDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1522_02,hypothesis,
( aElementOf0(xx,xS)
& isFinite0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1522_02) ).
fof(m__1522,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1522) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( isFinite0(X2)
& aSet0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
fof(c_0_8,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,plain,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[mCardCons]) ).
fof(c_0_10,plain,
! [X44,X45] :
( sdtpldt0(sdtmndt0(X44,X45),X45) = X44
| ~ aElementOf0(X45,X44)
| ~ aSet0(X44) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])])]) ).
fof(c_0_11,plain,
! [X7,X8] :
( aElement0(X8)
| ~ aElementOf0(X8,X7)
| ~ aSet0(X7) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_12,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X83,X84] :
( sbrdtbr0(sdtpldt0(X83,X84)) = szszuzczcdt0(sbrdtbr0(X83))
| aElementOf0(X84,X83)
| ~ aElement0(X84)
| ~ isFinite0(X83)
| ~ aSet0(X83) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_14,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__1522_02]) ).
cnf(c_0_16,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__1522]) ).
cnf(c_0_17,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mDefDiff]) ).
cnf(c_0_20,plain,
( ~ aElement0(X2)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,hypothesis,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_22,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_16])]) ).
cnf(c_0_23,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X54,X55] :
( isFinite0(sdtmndt0(X55,X54))
| ~ isFinite0(X55)
| ~ aSet0(X55)
| ~ aElement0(X54) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])])]) ).
fof(c_0_25,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| esk4_3(X37,X38,X42) != X38 )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| aElementOf0(esk4_3(X37,X38,X42),X37) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| aElement0(esk4_3(X37,X38,X42)) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| esk4_3(X37,X38,X42) = X38
| ~ aElementOf0(esk4_3(X37,X38,X42),X37)
| ~ aElement0(esk4_3(X37,X38,X42))
| ~ aElementOf0(esk4_3(X37,X38,X42),X42) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| aElementOf0(X41,X39)
| X41 = X38
| ~ aElementOf0(X41,X37)
| ~ aElement0(X41) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| X40 != X38 )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| aElementOf0(X40,X37) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| aElement0(X40) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| aSet0(X39) ) ),
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_19])])])])])])]) ).
cnf(c_0_26,hypothesis,
( ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx))
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(sr,[status(thm)],[inference(cn,[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_27,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtmndt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__1522_02]) ).
cnf(c_0_29,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtmndt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( ~ aElement0(X2)
| ~ aSet0(X4)
| X3 != sdtmndt0(X4,X2)
| ~ aElementOf0(X1,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,hypothesis,
( ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_22]),c_0_16])]) ).
cnf(c_0_32,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtmndt0(X2,X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_30])]) ).
cnf(c_0_34,hypothesis,
aElementOf0(xx,sdtmndt0(xS,xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]),c_0_16])]) ).
cnf(c_0_35,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_22]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM538+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:38:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 787371 completed with status 0
% 0.11/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.11/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.45 % new_bool_3 with pid 787378 completed with status 0
% 0.11/0.45 % Result found by new_bool_3
% 0.11/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.45 % Preprocessing time : 0.001 s
% 0.11/0.45 % Presaturation interreduction done
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 46
% 0.11/0.45 % Removed by relevancy pruning/SinE : 0
% 0.11/0.45 % Initial clauses : 74
% 0.11/0.45 % Removed in clause preprocessing : 6
% 0.11/0.45 % Initial clauses in saturation : 68
% 0.11/0.45 % Processed clauses : 211
% 0.11/0.45 % ...of these trivial : 1
% 0.11/0.45 % ...subsumed : 12
% 0.11/0.45 % ...remaining for further processing : 198
% 0.11/0.45 % Other redundant clauses eliminated : 16
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 2
% 0.11/0.45 % Backward-rewritten : 2
% 0.11/0.45 % Generated clauses : 225
% 0.11/0.45 % ...of the previous two non-redundant : 187
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 13
% 0.11/0.45 % Paramodulations : 210
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 17
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 157
% 0.11/0.45 % ...of those cached : 132
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 112
% 0.11/0.45 % Positive orientable unit clauses : 42
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 4
% 0.11/0.45 % Non-unit-clauses : 66
% 0.11/0.45 % Current number of unprocessed clauses: 111
% 0.11/0.45 % ...number of literals in the above : 371
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 72
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 1988
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 528
% 0.11/0.45 % Non-unit clause-clause subsumptions : 24
% 0.11/0.45 % Unit Clause-clause subsumption calls : 107
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 34
% 0.11/0.45 % BW rewrite match successes : 2
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 10280
% 0.11/0.45 % Search garbage collected termcells : 1322
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.012 s
% 0.11/0.45 % System time : 0.002 s
% 0.11/0.45 % Total time : 0.014 s
% 0.11/0.45 % Maximum resident set size: 3676 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.066 s
% 0.11/0.45 % System time : 0.013 s
% 0.11/0.45 % Total time : 0.080 s
% 0.11/0.45 % Maximum resident set size: 4608 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------