%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT168+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:07:59 PM UTC 2026
% Result : ContradictoryAxioms 0.57s 0.89s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 14 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 58 ( 5 sgn 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Suc__n__not__le__n,axiom,
! [X46] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X46)),X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X55] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X55)
<=> ? [X20] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X55))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_rangeI,axiom,
! [X15,X8,X2,X10] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X8)),c_Set_Oimage(X15,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_rev__finite__subset,axiom,
! [X12,X11,X10] :
( c_Finite__Set_Ofinite(X10,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> c_Finite__Set_Ofinite(X10,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_subset__UNIV,axiom,
! [X12,X10] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_finite__imageI,axiom,
! [X65,X15,X27,X10] :
( c_Finite__Set_Ofinite(X10,X27)
=> c_Finite__Set_Ofinite(X15,c_Set_Oimage(X10,X15,X65,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_finite__indi,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(c_0_7,plain,
! [X46] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X46)),X46)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(c_0_8,plain,
! [X982] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X982)),X982)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_9,plain,
! [X776,X778,X779,X780] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X779)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk24_2(X779,X780)),X780)) )
& ( c_Finite__Set_Ofinite(tc_Nat_Onat,X779)
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk24_2(X779,X780)),X779)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X778),esk23_1(X776)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X778),X776))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X776) ) ),
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)],[fact_finite__nat__set__iff__bounded__le])])])])])])]) ).
cnf(c_0_10,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk23_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X578,X579,X580,X581] : hBOOL(hAPP(hAPP(c_member(X581),hAPP(X580,X579)),c_Set_Oimage(X578,X581,X580,c_Orderings_Otop__class_Otop(tc_fun(X578,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(c_0_13,plain,
! [X764,X765,X766] :
( c_Finite__Set_Ofinite(X766,X764)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X766,tc_HOL_Obool),X764),X765))
| ~ c_Finite__Set_Ofinite(X766,X765) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])])]) ).
fof(c_0_14,plain,
! [X539,X540] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X540,tc_HOL_Obool),X539),c_Orderings_Otop__class_Otop(tc_fun(X540,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
cnf(c_0_15,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_OSuc,esk23_1(X1))),X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X715,X716,X717,X718] :
( c_Finite__Set_Ofinite(X716,c_Set_Oimage(X718,X716,X715,X717))
| ~ c_Finite__Set_Ofinite(X718,X717) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])])]) ).
cnf(c_0_18,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,c_Set_Oimage(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_finite__indi]) ).
cnf(c_0_24,plain,
~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
$false,
inference(spm,[status(thm)],[c_0_24,c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT168+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.51 % Computer : n005.cluster.edu
% 0.20/0.51 % Model : x86_64 x86_64
% 0.20/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.51 % Memory : 8046.5625MB
% 0.20/0.51 % OS : Linux 6.8.0-71-generic
% 0.20/0.51 % CPULimit : 300
% 0.20/0.51 % WCLimit : 300
% 0.20/0.51 % DateTime : Mon Sep 21 04:35:35 UTC 2026
% 0.20/0.52 % CPUTime :
% 0.20/0.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.62 Running first-order theorem proving
% 0.25/0.62 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
% 0.57/0.89 % Version: 3.5.1
% 0.57/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.57/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.57/0.89 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.89 % Starting new_bool_1 with 300s (1) cores
% 0.57/0.89 % Starting sh5l with 300s (1) cores
% 0.57/0.89 % new_bool_3 with pid 2558832 completed with status 0
% 0.57/0.89 % Result found by new_bool_3
% 0.57/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.57/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.57/0.89 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.89 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.57/0.89 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.57/0.89 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.57/0.89 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.89 % Starting SubtermCWHack with 28s (1) cores
% 0.57/0.89 % SubtermCWHack with pid 2558836 completed with status 0
% 0.57/0.89 % Result found by SubtermCWHack
% 0.57/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.57/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.57/0.89 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.89 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.57/0.89 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.57/0.89 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.57/0.89 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.89 % Starting SubtermCWHack with 28s (1) cores
% 0.57/0.89 % Preprocessing time : 0.015 s
% 0.57/0.89
% 0.57/0.89 % Proof found!
% 0.57/0.89 % SZS status ContradictoryAxioms
% 0.57/0.89 % SZS output start CNFRefutation
% See solution above
% 0.57/0.89 % Parsed axioms : 533
% 0.57/0.89 % Removed by relevancy pruning/SinE : 223
% 0.57/0.89 % Initial clauses : 549
% 0.57/0.89 % Removed in clause preprocessing : 58
% 0.57/0.89 % Initial clauses in saturation : 491
% 0.57/0.89 % Processed clauses : 1113
% 0.57/0.89 % ...of these trivial : 57
% 0.57/0.89 % ...subsumed : 635
% 0.57/0.89 % ...remaining for further processing : 421
% 0.57/0.89 % Other redundant clauses eliminated : 83
% 0.57/0.89 % Clauses deleted for lack of memory : 0
% 0.57/0.89 % Backward-subsumed : 14
% 0.57/0.89 % Backward-rewritten : 8
% 0.57/0.89 % Generated clauses : 3027
% 0.57/0.89 % ...of the previous two non-redundant : 2461
% 0.57/0.89 % ...aggressively subsumed : 0
% 0.57/0.89 % Contextual simplify-reflections : 1
% 0.57/0.89 % Paramodulations : 2937
% 0.57/0.89 % Factorizations : 4
% 0.57/0.89 % NegExts : 0
% 0.57/0.89 % Equation resolutions : 91
% 0.57/0.89 % Disequality decompositions : 0
% 0.57/0.89 % Total rewrite steps : 1044
% 0.57/0.89 % ...of those cached : 792
% 0.57/0.89 % Propositional unsat checks : 0
% 0.57/0.89 % Propositional check models : 0
% 0.57/0.89 % Propositional check unsatisfiable : 0
% 0.57/0.89 % Propositional clauses : 0
% 0.57/0.89 % Propositional clauses after purity: 0
% 0.57/0.89 % Propositional unsat core size : 0
% 0.57/0.89 % Propositional preprocessing time : 0.000
% 0.57/0.89 % Propositional encoding time : 0.000
% 0.57/0.89 % Propositional solver time : 0.000
% 0.57/0.89 % Success case prop preproc time : 0.000
% 0.57/0.89 % Success case prop encoding time : 0.000
% 0.57/0.89 % Success case prop solver time : 0.000
% 0.57/0.89 % Current number of processed clauses : 360
% 0.57/0.89 % Positive orientable unit clauses : 101
% 0.57/0.89 % Positive unorientable unit clauses: 3
% 0.57/0.89 % Negative unit clauses : 78
% 0.57/0.89 % Non-unit-clauses : 178
% 0.57/0.89 % Current number of unprocessed clauses: 1818
% 0.57/0.89 % ...number of literals in the above : 4469
% 0.57/0.89 % Current number of archived formulas : 0
% 0.57/0.89 % Current number of archived clauses : 22
% 0.57/0.89 % Clause-clause subsumption calls (NU) : 5670
% 0.57/0.89 % Rec. Clause-clause subsumption calls : 4956
% 0.57/0.89 % Non-unit clause-clause subsumptions : 239
% 0.57/0.89 % Unit Clause-clause subsumption calls : 979
% 0.57/0.89 % Rewrite failures with RHS unbound : 0
% 0.57/0.89 % BW rewrite match attempts : 215
% 0.57/0.89 % BW rewrite match successes : 19
% 0.57/0.89 % Condensation attempts : 0
% 0.57/0.89 % Condensation successes : 0
% 0.57/0.89 % Termbank termtop insertions : 125928
% 0.57/0.89 % Search garbage collected termcells : 8930
% 0.57/0.89
% 0.57/0.89 % -------------------------------------------------
% 0.57/0.89 % User time : 0.119 s
% 0.57/0.89 % System time : 0.017 s
% 0.57/0.89 % Total time : 0.136 s
% 0.57/0.89 % Maximum resident set size: 5672 pages
% 0.57/0.89
% 0.57/0.89 % -------------------------------------------------
% 0.57/0.89 % User time : 0.165 s
% 0.57/0.89 % System time : 0.025 s
% 0.57/0.89 % Total time : 0.191 s
% 0.57/0.89 % Maximum resident set size: 5120 pages
% 0.57/0.89 % E exiting
%------------------------------------------------------------------------------