%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV610+1 : TPTP v9.3.1. Released v9.3.0.
% 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 02:35:19 PM UTC 2026
% Result : Theorem 0.16s 1.39s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 106 ( 3 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 119 ( 45 ~; 45 |; 15 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('$_lam_34547',axiom,
! [X1,X2] :
( c_24__lam__34547___24a2(X1,X2)
<=> ~ p(happ(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_34547') ).
fof('$adef_$_lam_34547_$a2',axiom,
! [X2282,X2283] :
( p(happ(happ(c_24__lam__34547,X2282),X2283))
<=> c_24__lam__34547___24a2(X2282,X2283) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_34547_$a2') ).
fof('_HAMMER_GOAL',conjecture,
! [X51] :
( c_24__type__1___24t(X51)
=> ( ~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X51)
=> cDirectedSets_2efor__large_2eeventually___24a1(c_24__lam__34547___24a1(X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('$_def_DirectedSets.for_large.exists_arbitrarily_large',axiom,
! [X51] :
( cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X51)
<=> ! [X67] :
( cDirectedSets_2eDS__set___24t(cI,X67)
=> ? [X714] :
( p(happ(X51,X714))
& cDirectedSets_2eDS__ord___24a3(cI,X67,X714)
& cDirectedSets_2eDS__set___24t(cI,X714) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_DirectedSets.for_large.exists_arbitrarily_large') ).
fof('$_def_DirectedSets.for_large.eventually',axiom,
! [X51] :
( cDirectedSets_2efor__large_2eeventually___24a1(X51)
<=> ? [X67] :
( ! [X714] :
( cDirectedSets_2eDS__set___24t(cI,X714)
=> ( cDirectedSets_2eDS__ord___24a3(cI,X67,X714)
=> p(happ(X51,X714)) ) )
& cDirectedSets_2eDS__set___24t(cI,X67) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_DirectedSets.for_large.eventually') ).
fof('$adef_$_lam_34547_$a1',axiom,
! [X2282] : happ(c_24__lam__34547,X2282) = c_24__lam__34547___24a1(X2282),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_34547_$a1') ).
fof(c_0_6,plain,
! [X1,X2] :
( c_24__lam__34547___24a2(X1,X2)
<=> ~ p(happ(X1,X2)) ),
inference(fof_simplification,[status(thm)],['$_lam_34547']) ).
fof(c_0_7,plain,
! [X2336,X2337] :
( ( p(happ(happ(c_24__lam__34547,X2336),X2337))
| ~ c_24__lam__34547___24a2(X2336,X2337) )
& ( c_24__lam__34547___24a2(X2336,X2337)
| ~ p(happ(happ(c_24__lam__34547,X2336),X2337)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['$adef_$_lam_34547_$a2'])])]) ).
fof(c_0_8,plain,
! [X2374,X2375] :
( ( c_24__lam__34547___24a2(X2374,X2375)
| p(happ(X2374,X2375)) )
& ( ~ p(happ(X2374,X2375))
| ~ c_24__lam__34547___24a2(X2374,X2375) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X51] :
( c_24__type__1___24t(X51)
=> ( ~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X51)
=> cDirectedSets_2efor__large_2eeventually___24a1(c_24__lam__34547___24a1(X51)) ) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_10,plain,
! [X2316,X2317,X2319,X2321] :
( ( cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X2319)
| ~ p(happ(X2319,X2321))
| ~ cDirectedSets_2eDS__ord___24a3(cI,esk6_1(X2319),X2321)
| ~ cDirectedSets_2eDS__set___24t(cI,X2321) )
& ( cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X2319)
| cDirectedSets_2eDS__set___24t(cI,esk6_1(X2319)) )
& ( ~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X2316)
| ~ cDirectedSets_2eDS__set___24t(cI,X2317)
| p(happ(X2316,esk5_2(X2316,X2317))) )
& ( ~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X2316)
| ~ cDirectedSets_2eDS__set___24t(cI,X2317)
| cDirectedSets_2eDS__ord___24a3(cI,X2317,esk5_2(X2316,X2317)) )
& ( ~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X2316)
| ~ cDirectedSets_2eDS__set___24t(cI,X2317)
| cDirectedSets_2eDS__set___24t(cI,esk5_2(X2316,X2317)) ) ),
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)],['$_def_DirectedSets.for_large.exists_arbitrarily_large'])])])])])])]) ).
fof(c_0_11,plain,
! [X2306,X2308,X2309,X2310] :
( ( cDirectedSets_2efor__large_2eeventually___24a1(X2309)
| ~ cDirectedSets_2eDS__set___24t(cI,X2310)
| ~ p(happ(X2309,esk3_2(X2309,X2310))) )
& ( cDirectedSets_2efor__large_2eeventually___24a1(X2309)
| ~ cDirectedSets_2eDS__set___24t(cI,X2310)
| cDirectedSets_2eDS__ord___24a3(cI,X2310,esk3_2(X2309,X2310)) )
& ( cDirectedSets_2efor__large_2eeventually___24a1(X2309)
| ~ cDirectedSets_2eDS__set___24t(cI,X2310)
| cDirectedSets_2eDS__set___24t(cI,esk3_2(X2309,X2310)) )
& ( ~ cDirectedSets_2efor__large_2eeventually___24a1(X2306)
| p(happ(X2306,X2308))
| ~ cDirectedSets_2eDS__ord___24a3(cI,esk2_1(X2306),X2308)
| ~ cDirectedSets_2eDS__set___24t(cI,X2308) )
& ( ~ cDirectedSets_2efor__large_2eeventually___24a1(X2306)
| cDirectedSets_2eDS__set___24t(cI,esk2_1(X2306)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_DirectedSets.for_large.eventually'])])])])])])]) ).
cnf(c_0_12,plain,
( ~ c_24__lam__34547___24a2(X1,X2)
| p(happ(happ(c_24__lam__34547,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( c_24__lam__34547___24a2(X1,X2)
| p(happ(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,negated_conjecture,
~ ! [X51] :
( c_24__type__1___24t(X51)
=> ( ~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X51)
=> cDirectedSets_2efor__large_2eeventually___24a1(c_24__lam__34547___24a1(X51)) ) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ p(happ(X2,X1))
| ~ cDirectedSets_2eDS__ord___24a3(cI,esk6_1(X2),X1)
| ~ cDirectedSets_2eDS__set___24t(cI,X1)
| cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ cDirectedSets_2eDS__set___24t(cI,X1)
| cDirectedSets_2efor__large_2eeventually___24a1(X2)
| cDirectedSets_2eDS__ord___24a3(cI,X1,esk3_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X1)
| cDirectedSets_2eDS__set___24t(cI,esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( ~ cDirectedSets_2eDS__set___24t(cI,X2)
| ~ p(happ(X1,esk3_2(X1,X2)))
| cDirectedSets_2efor__large_2eeventually___24a1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( p(happ(X1,X2))
| p(happ(happ(c_24__lam__34547,X1),X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_20,negated_conjecture,
( ~ cDirectedSets_2efor__large_2eeventually___24a1(c_24__lam__34547___24a1(esk1_0))
& ~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(esk1_0)
& c_24__type__1___24t(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_21,plain,
! [X2315] : happ(c_24__lam__34547,X2315) = c_24__lam__34547___24a1(X2315),
inference(variable_rename,[status(thm)],['$adef_$_lam_34547_$a1']) ).
cnf(c_0_22,plain,
( ~ p(happ(X1,esk3_2(X2,esk6_1(X1))))
| ~ cDirectedSets_2eDS__set___24t(cI,esk3_2(X2,esk6_1(X1)))
| cDirectedSets_2efor__large_2eeventually___24a1(X2)
| cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
( ~ cDirectedSets_2eDS__set___24t(cI,X2)
| p(happ(X1,esk3_2(happ(c_24__lam__34547,X1),X2)))
| cDirectedSets_2efor__large_2eeventually___24a1(happ(c_24__lam__34547,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
~ cDirectedSets_2efor__large_2eeventually___24a1(c_24__lam__34547___24a1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
happ(c_24__lam__34547,X1) = c_24__lam__34547___24a1(X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ cDirectedSets_2eDS__set___24t(cI,esk3_2(happ(c_24__lam__34547,X1),esk6_1(X1)))
| cDirectedSets_2efor__large_2eeventually___24a1(happ(c_24__lam__34547,X1))
| cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17]) ).
cnf(c_0_27,plain,
( ~ cDirectedSets_2eDS__set___24t(cI,X2)
| cDirectedSets_2efor__large_2eeventually___24a1(X1)
| cDirectedSets_2eDS__set___24t(cI,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
~ cDirectedSets_2efor__large_2eeventually___24a1(happ(c_24__lam__34547,esk1_0)),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( cDirectedSets_2efor__large_2eeventually___24a1(happ(c_24__lam__34547,X1))
| cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17]) ).
cnf(c_0_30,negated_conjecture,
~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV610+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/1.07 % Computer : n006.cluster.edu
% 0.13/1.07 % Model : x86_64 x86_64
% 0.13/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/1.07 % Memory : 8046.5625MB
% 0.13/1.07 % OS : Linux 6.8.0-71-generic
% 0.13/1.07 % CPULimit : 300
% 0.13/1.07 % WCLimit : 300
% 0.13/1.07 % DateTime : Mon Sep 21 07:29:30 UTC 2026
% 0.13/1.07 % CPUTime :
% 0.13/1.07 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/1.12 Running first-order theorem proving
% 0.13/1.12 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
% 0.16/1.39 % Version: 3.5.1
% 0.16/1.39 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.16/1.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/1.39 % Starting new_bool_3 with 900s (3) cores
% 0.16/1.39 % Starting new_bool_1 with 900s (3) cores
% 0.16/1.39 % Starting sh5l with 300s (1) cores
% 0.16/1.39 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 0.16/1.39 % new_bool_1 with pid 2330027 completed with status 0
% 0.16/1.39 % Result found by new_bool_1
% 0.16/1.39 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.16/1.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/1.39 % Starting new_bool_3 with 900s (3) cores
% 0.16/1.39 % Starting new_bool_1 with 900s (3) cores
% 0.16/1.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/1.39 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/1.39 % Search class: FGHSS-FFMS31-MFFFFFNN
% 0.16/1.39 % partial match(1): FGHSM-FFMS31-MFFFFFNN
% 0.16/1.39 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 0.16/1.39 % Starting SubtermCWHack with 82s (1) cores
% 0.16/1.39 % Starting new_bool_1 with 91s (1) cores
% 0.16/1.39 % Starting G-E--_107_C37_SOS_F1_PI_AE_Q4_CS_SP_PS_S0Y with 228s (1) cores
% 0.16/1.39 % SubtermCWHack with pid 2330030 completed with status 0
% 0.16/1.39 % Result found by SubtermCWHack
% 0.16/1.39 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.16/1.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/1.39 % Starting new_bool_3 with 900s (3) cores
% 0.16/1.39 % Starting new_bool_1 with 900s (3) cores
% 0.16/1.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/1.39 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/1.39 % Search class: FGHSS-FFMS31-MFFFFFNN
% 0.16/1.39 % partial match(1): FGHSM-FFMS31-MFFFFFNN
% 0.16/1.39 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 0.16/1.39 % Starting SubtermCWHack with 82s (1) cores
% 0.16/1.39 % Preprocessing time : 0.005 s
% 0.16/1.39
% 0.16/1.39 % Proof found!
% 0.16/1.39 % SZS status Theorem
% 0.16/1.39 % SZS output start CNFRefutation
% See solution above
% 0.16/1.39 % Parsed axioms : 2778
% 0.16/1.39 % Removed by relevancy pruning/SinE : 2747
% 0.16/1.39 % Initial clauses : 72
% 0.16/1.39 % Removed in clause preprocessing : 20
% 0.16/1.39 % Initial clauses in saturation : 52
% 0.16/1.39 % Processed clauses : 87
% 0.16/1.39 % ...of these trivial : 0
% 0.16/1.39 % ...subsumed : 2
% 0.16/1.39 % ...remaining for further processing : 85
% 0.16/1.39 % Other redundant clauses eliminated : 0
% 0.16/1.39 % Clauses deleted for lack of memory : 0
% 0.16/1.39 % Backward-subsumed : 2
% 0.16/1.39 % Backward-rewritten : 1
% 0.16/1.39 % Generated clauses : 76
% 0.16/1.39 % ...of the previous two non-redundant : 63
% 0.16/1.39 % ...aggressively subsumed : 0
% 0.16/1.39 % Contextual simplify-reflections : 8
% 0.16/1.39 % Paramodulations : 76
% 0.16/1.39 % Factorizations : 0
% 0.16/1.39 % NegExts : 0
% 0.16/1.39 % Equation resolutions : 0
% 0.16/1.39 % Disequality decompositions : 0
% 0.16/1.39 % Total rewrite steps : 6
% 0.16/1.39 % ...of those cached : 3
% 0.16/1.39 % Propositional unsat checks : 0
% 0.16/1.39 % Propositional check models : 0
% 0.16/1.39 % Propositional check unsatisfiable : 0
% 0.16/1.39 % Propositional clauses : 0
% 0.16/1.39 % Propositional clauses after purity: 0
% 0.16/1.39 % Propositional unsat core size : 0
% 0.16/1.39 % Propositional preprocessing time : 0.000
% 0.16/1.39 % Propositional encoding time : 0.000
% 0.16/1.39 % Propositional solver time : 0.000
% 0.16/1.39 % Success case prop preproc time : 0.000
% 0.16/1.39 % Success case prop encoding time : 0.000
% 0.16/1.39 % Success case prop solver time : 0.000
% 0.16/1.39 % Current number of processed clauses : 82
% 0.16/1.39 % Positive orientable unit clauses : 6
% 0.16/1.39 % Positive unorientable unit clauses: 0
% 0.16/1.39 % Negative unit clauses : 3
% 0.16/1.39 % Non-unit-clauses : 73
% 0.16/1.39 % Current number of unprocessed clauses: 28
% 0.16/1.39 % ...number of literals in the above : 118
% 0.16/1.39 % Current number of archived formulas : 0
% 0.16/1.39 % Current number of archived clauses : 3
% 0.16/1.39 % Clause-clause subsumption calls (NU) : 801
% 0.16/1.39 % Rec. Clause-clause subsumption calls : 431
% 0.16/1.39 % Non-unit clause-clause subsumptions : 12
% 0.16/1.39 % Unit Clause-clause subsumption calls : 2
% 0.16/1.39 % Rewrite failures with RHS unbound : 0
% 0.16/1.39 % BW rewrite match attempts : 1
% 0.16/1.39 % BW rewrite match successes : 1
% 0.16/1.39 % Condensation attempts : 0
% 0.16/1.39 % Condensation successes : 0
% 0.16/1.39 % Termbank termtop insertions : 58060
% 0.16/1.39 % Search garbage collected termcells : 38498
% 0.16/1.39
% 0.16/1.39 % -------------------------------------------------
% 0.16/1.39 % User time : 0.023 s
% 0.16/1.39 % System time : 0.030 s
% 0.16/1.39 % Total time : 0.053 s
% 0.16/1.39 % Maximum resident set size: 14976 pages
% 0.16/1.39
% 0.16/1.39 % -------------------------------------------------
% 0.16/1.39 % User time : 0.239 s
% 0.16/1.39 % System time : 0.078 s
% 0.16/1.39 % Total time : 0.317 s
% 0.16/1.39 % Maximum resident set size: 11520 pages
% 0.16/1.39 % E exiting
%------------------------------------------------------------------------------