%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT164+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 0.29s 0.84s
% Output : CNFRefutation 0.29s
% 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,
! [X43] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X43)),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X47] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X47)
<=> ? [X38] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X47))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_rangeI,axiom,
! [X18,X11,X2,X13] : hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X11)),c_Set_Oimage(X18,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_rev__finite__subset,axiom,
! [X15,X14,X13] :
( c_Finite__Set_Ofinite(X13,X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> c_Finite__Set_Ofinite(X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_subset__UNIV,axiom,
! [X15,X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_finite__imageI,axiom,
! [X66,X18,X28,X13] :
( c_Finite__Set_Ofinite(X13,X28)
=> c_Finite__Set_Ofinite(X18,c_Set_Oimage(X13,X18,X66,X28)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(c_0_7,plain,
! [X43] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X43)),X43)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(c_0_8,plain,
! [X945] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X945)),X945)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_9,plain,
! [X751,X753,X754,X755] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X754)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk22_2(X754,X755)),X755)) )
& ( c_Finite__Set_Ofinite(tc_Nat_Onat,X754)
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk22_2(X754,X755)),X754)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X753),esk21_1(X751)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X753),X751))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X751) ) ),
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),esk21_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X516,X517,X518,X519] : hBOOL(hAPP(hAPP(c_member(X519),hAPP(X518,X517)),c_Set_Oimage(X516,X519,X518,c_Orderings_Otop__class_Otop(tc_fun(X516,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(c_0_13,plain,
! [X739,X740,X741] :
( c_Finite__Set_Ofinite(X741,X739)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X741,tc_HOL_Obool),X739),X740))
| ~ c_Finite__Set_Ofinite(X741,X740) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])])]) ).
fof(c_0_14,plain,
! [X485,X486] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X486,tc_HOL_Obool),X485),c_Orderings_Otop__class_Otop(tc_fun(X486,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,esk21_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,
! [X690,X691,X692,X693] :
( c_Finite__Set_Ofinite(X691,c_Set_Oimage(X693,X691,X690,X692))
| ~ c_Finite__Set_Ofinite(X693,X692) ),
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 : SCT164+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 % Computer : n005.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Mon Sep 21 04:35:18 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.56 Running first-order theorem proving
% 0.24/0.56 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
% 0.29/0.84 % Version: 3.5.1
% 0.29/0.84 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.29/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.84 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.29/0.84 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.84 % Starting new_bool_1 with 300s (1) cores
% 0.29/0.84 % Starting sh5l with 300s (1) cores
% 0.29/0.84 % new_bool_3 with pid 2558024 completed with status 0
% 0.29/0.84 % Result found by new_bool_3
% 0.29/0.84 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.29/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.84 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.29/0.84 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.84 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.29/0.84 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.29/0.84 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.29/0.84 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.84 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.84 % SubtermCWHack with pid 2558033 completed with status 0
% 0.29/0.84 % Result found by SubtermCWHack
% 0.29/0.84 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.29/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.84 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.29/0.84 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.84 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.29/0.84 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.29/0.84 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.29/0.84 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.84 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.84 % Preprocessing time : 0.015 s
% 0.29/0.84
% 0.29/0.84 % Proof found!
% 0.29/0.84 % SZS status ContradictoryAxioms
% 0.29/0.84 % SZS output start CNFRefutation
% See solution above
% 0.29/0.84 % Parsed axioms : 533
% 0.29/0.84 % Removed by relevancy pruning/SinE : 202
% 0.29/0.84 % Initial clauses : 522
% 0.29/0.84 % Removed in clause preprocessing : 35
% 0.29/0.84 % Initial clauses in saturation : 487
% 0.29/0.84 % Processed clauses : 1219
% 0.29/0.84 % ...of these trivial : 55
% 0.29/0.84 % ...subsumed : 715
% 0.29/0.84 % ...remaining for further processing : 449
% 0.29/0.84 % Other redundant clauses eliminated : 91
% 0.29/0.84 % Clauses deleted for lack of memory : 0
% 0.29/0.84 % Backward-subsumed : 16
% 0.29/0.84 % Backward-rewritten : 8
% 0.29/0.84 % Generated clauses : 3302
% 0.29/0.84 % ...of the previous two non-redundant : 2631
% 0.29/0.84 % ...aggressively subsumed : 0
% 0.29/0.84 % Contextual simplify-reflections : 1
% 0.29/0.84 % Paramodulations : 3205
% 0.29/0.84 % Factorizations : 4
% 0.29/0.84 % NegExts : 0
% 0.29/0.84 % Equation resolutions : 98
% 0.29/0.84 % Disequality decompositions : 0
% 0.29/0.84 % Total rewrite steps : 1315
% 0.29/0.84 % ...of those cached : 1038
% 0.29/0.84 % Propositional unsat checks : 0
% 0.29/0.84 % Propositional check models : 0
% 0.29/0.84 % Propositional check unsatisfiable : 0
% 0.29/0.84 % Propositional clauses : 0
% 0.29/0.84 % Propositional clauses after purity: 0
% 0.29/0.84 % Propositional unsat core size : 0
% 0.29/0.84 % Propositional preprocessing time : 0.000
% 0.29/0.84 % Propositional encoding time : 0.000
% 0.29/0.84 % Propositional solver time : 0.000
% 0.29/0.84 % Success case prop preproc time : 0.000
% 0.29/0.84 % Success case prop encoding time : 0.000
% 0.29/0.84 % Success case prop solver time : 0.000
% 0.29/0.84 % Current number of processed clauses : 381
% 0.29/0.84 % Positive orientable unit clauses : 117
% 0.29/0.84 % Positive unorientable unit clauses: 3
% 0.29/0.84 % Negative unit clauses : 78
% 0.29/0.84 % Non-unit-clauses : 183
% 0.29/0.84 % Current number of unprocessed clauses: 1875
% 0.29/0.84 % ...number of literals in the above : 4491
% 0.29/0.84 % Current number of archived formulas : 0
% 0.29/0.84 % Current number of archived clauses : 24
% 0.29/0.84 % Clause-clause subsumption calls (NU) : 7812
% 0.29/0.84 % Rec. Clause-clause subsumption calls : 5830
% 0.29/0.84 % Non-unit clause-clause subsumptions : 283
% 0.29/0.84 % Unit Clause-clause subsumption calls : 489
% 0.29/0.84 % Rewrite failures with RHS unbound : 0
% 0.29/0.84 % BW rewrite match attempts : 358
% 0.29/0.84 % BW rewrite match successes : 19
% 0.29/0.84 % Condensation attempts : 0
% 0.29/0.84 % Condensation successes : 0
% 0.29/0.84 % Termbank termtop insertions : 117602
% 0.29/0.84 % Search garbage collected termcells : 9086
% 0.29/0.84
% 0.29/0.84 % -------------------------------------------------
% 0.29/0.84 % User time : 0.122 s
% 0.29/0.84 % System time : 0.024 s
% 0.29/0.84 % Total time : 0.146 s
% 0.29/0.84 % Maximum resident set size: 5676 pages
% 0.29/0.84
% 0.29/0.84 % -------------------------------------------------
% 0.29/0.84 % User time : 0.168 s
% 0.29/0.84 % System time : 0.034 s
% 0.29/0.84 % Total time : 0.203 s
% 0.29/0.84 % Maximum resident set size: 5376 pages
% 0.29/0.84 % E exiting
%------------------------------------------------------------------------------