%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM548+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 : 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 01:49:31 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 122 ( 21 equ)
% Maximal formula atoms : 39 ( 4 avg)
% Number of connectives : 161 ( 68 ~; 65 |; 20 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 19 !; 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/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(m__2202_02,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(m__,conjecture,
isFinite0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(m__2270,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(m__2202,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
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(c_0_7,plain,
! [X19,X20,X21,X22,X23,X24] :
( ( ~ aElementOf0(X20,szNzAzT0)
| ~ aSet0(X19)
| X24 = slbdtsldtrb0(X19,X20)
| ~ aSet0(X24)
| aElementOf0(esk3_3(X19,X20,X24),X24)
| sbrdtbr0(esk3_3(X19,X20,X24)) = X20 )
& ( ~ aElementOf0(X20,szNzAzT0)
| ~ aSet0(X19)
| X24 = slbdtsldtrb0(X19,X20)
| ~ aSet0(X24)
| aElementOf0(esk3_3(X19,X20,X24),X24)
| aSubsetOf0(esk3_3(X19,X20,X24),X19) )
& ( ~ aElementOf0(X20,szNzAzT0)
| ~ aSet0(X19)
| X24 = slbdtsldtrb0(X19,X20)
| ~ aSet0(X24)
| sbrdtbr0(esk3_3(X19,X20,X24)) != X20
| ~ aSubsetOf0(esk3_3(X19,X20,X24),X19)
| ~ aElementOf0(esk3_3(X19,X20,X24),X24) )
& ( ~ aElementOf0(X20,szNzAzT0)
| ~ aSet0(X19)
| X21 != slbdtsldtrb0(X19,X20)
| aElementOf0(X23,X21)
| sbrdtbr0(X23) != X20
| ~ aSubsetOf0(X23,X19) )
& ( ~ aElementOf0(X20,szNzAzT0)
| ~ aSet0(X19)
| X21 != slbdtsldtrb0(X19,X20)
| ~ aElementOf0(X22,X21)
| sbrdtbr0(X22) = X20 )
& ( ~ aElementOf0(X20,szNzAzT0)
| ~ aSet0(X19)
| X21 != slbdtsldtrb0(X19,X20)
| ~ aElementOf0(X22,X21)
| aSubsetOf0(X22,X19) )
& ( ~ aElementOf0(X20,szNzAzT0)
| ~ aSet0(X19)
| X21 != slbdtsldtrb0(X19,X20)
| aSet0(X21) ) ),
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_8,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_simplification,[status(thm)],[m__2202_02]) ).
fof(c_0_9,negated_conjecture,
~ isFinite0(xQ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_10,plain,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X4)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aElementOf0(X1,X3)
| sbrdtbr0(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
~ isFinite0(xQ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( ~ aElementOf0(X4,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aElementOf0(X1,X3)
| aSubsetOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_14,plain,
! [X61] :
( ( ~ aSet0(X61)
| aElementOf0(sbrdtbr0(X61),szNzAzT0)
| ~ isFinite0(X61) )
& ( ~ aSet0(X61)
| isFinite0(X61)
| ~ aElementOf0(sbrdtbr0(X61),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])])]) ).
cnf(c_0_15,plain,
( ~ aSet0(X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| sbrdtbr0(X1) = X2 ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[m__2270]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__2202]) ).
cnf(c_0_18,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_19,negated_conjecture,
~ isFinite0(xQ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X30,X31,X32,X33] :
( ( ~ aSet0(X30)
| aSubsetOf0(X33,X30)
| ~ aSet0(X33)
| ~ aElementOf0(esk4_2(X30,X33),X30) )
& ( ~ aSet0(X30)
| aSubsetOf0(X33,X30)
| ~ aSet0(X33)
| aElementOf0(esk4_2(X30,X33),X33) )
& ( ~ aSet0(X30)
| ~ aSubsetOf0(X31,X30)
| aElementOf0(X32,X30)
| ~ aElementOf0(X32,X31) )
& ( ~ aSet0(X30)
| ~ aSubsetOf0(X31,X30)
| aSet0(X31) ) ),
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])])])])])])]) ).
cnf(c_0_21,plain,
( ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| aSubsetOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( ~ aSet0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
sbrdtbr0(xQ) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_24,negated_conjecture,
~ isFinite0(xQ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
aSubsetOf0(xQ,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_27,hypothesis,
~ aSet0(xQ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17])]),c_0_24]) ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM548+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:39:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.45 % Version: 3.5.1
% 0.09/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.45 % Starting sh5l with 300s (1) cores
% 0.09/0.45 % new_bool_3 with pid 1826643 completed with status 0
% 0.09/0.45 % Result found by new_bool_3
% 0.09/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.45 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.09/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.45 % SubtermCWHack with pid 1826646 completed with status 0
% 0.09/0.45 % Result found by SubtermCWHack
% 0.09/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.45 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.09/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.45 % Preprocessing time : 0.003 s
% 0.09/0.45
% 0.09/0.45 % Proof found!
% 0.09/0.45 % SZS status Theorem
% 0.09/0.45 % SZS output start CNFRefutation
% See solution above
% 0.09/0.45 % Parsed axioms : 66
% 0.09/0.45 % Removed by relevancy pruning/SinE : 5
% 0.09/0.45 % Initial clauses : 108
% 0.09/0.45 % Removed in clause preprocessing : 5
% 0.09/0.45 % Initial clauses in saturation : 103
% 0.09/0.45 % Processed clauses : 219
% 0.09/0.45 % ...of these trivial : 0
% 0.09/0.45 % ...subsumed : 58
% 0.09/0.45 % ...remaining for further processing : 161
% 0.09/0.45 % Other redundant clauses eliminated : 26
% 0.09/0.45 % Clauses deleted for lack of memory : 0
% 0.09/0.45 % Backward-subsumed : 4
% 0.09/0.45 % Backward-rewritten : 3
% 0.09/0.45 % Generated clauses : 324
% 0.09/0.45 % ...of the previous two non-redundant : 246
% 0.09/0.45 % ...aggressively subsumed : 0
% 0.09/0.45 % Contextual simplify-reflections : 12
% 0.09/0.45 % Paramodulations : 299
% 0.09/0.45 % Factorizations : 0
% 0.09/0.45 % NegExts : 0
% 0.09/0.45 % Equation resolutions : 27
% 0.09/0.45 % Disequality decompositions : 0
% 0.09/0.45 % Total rewrite steps : 165
% 0.09/0.45 % ...of those cached : 149
% 0.09/0.45 % Propositional unsat checks : 0
% 0.09/0.45 % Propositional check models : 0
% 0.09/0.45 % Propositional check unsatisfiable : 0
% 0.09/0.45 % Propositional clauses : 0
% 0.09/0.45 % Propositional clauses after purity: 0
% 0.09/0.45 % Propositional unsat core size : 0
% 0.09/0.45 % Propositional preprocessing time : 0.000
% 0.09/0.45 % Propositional encoding time : 0.000
% 0.09/0.45 % Propositional solver time : 0.000
% 0.09/0.45 % Success case prop preproc time : 0.000
% 0.09/0.45 % Success case prop encoding time : 0.000
% 0.09/0.45 % Success case prop solver time : 0.000
% 0.09/0.45 % Current number of processed clauses : 133
% 0.09/0.45 % Positive orientable unit clauses : 24
% 0.09/0.45 % Positive unorientable unit clauses: 0
% 0.09/0.45 % Negative unit clauses : 9
% 0.09/0.45 % Non-unit-clauses : 100
% 0.09/0.45 % Current number of unprocessed clauses: 129
% 0.09/0.45 % ...number of literals in the above : 709
% 0.09/0.45 % Current number of archived formulas : 0
% 0.09/0.45 % Current number of archived clauses : 7
% 0.09/0.45 % Clause-clause subsumption calls (NU) : 2294
% 0.09/0.45 % Rec. Clause-clause subsumption calls : 989
% 0.09/0.45 % Non-unit clause-clause subsumptions : 58
% 0.09/0.45 % Unit Clause-clause subsumption calls : 179
% 0.09/0.45 % Rewrite failures with RHS unbound : 0
% 0.09/0.45 % BW rewrite match attempts : 3
% 0.09/0.45 % BW rewrite match successes : 3
% 0.09/0.45 % Condensation attempts : 0
% 0.09/0.45 % Condensation successes : 0
% 0.09/0.45 % Termbank termtop insertions : 13672
% 0.09/0.45 % Search garbage collected termcells : 2067
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.016 s
% 0.09/0.45 % System time : 0.007 s
% 0.09/0.45 % Total time : 0.022 s
% 0.09/0.45 % Maximum resident set size: 3960 pages
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.018 s
% 0.09/0.45 % System time : 0.012 s
% 0.09/0.45 % Total time : 0.030 s
% 0.09/0.45 % Maximum resident set size: 4864 pages
% 0.09/0.45 % E exiting
%------------------------------------------------------------------------------