%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT167+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 : n001.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 02:08:36 PM UTC 2026
% Result : ContradictoryAxioms 1.34s 0.68s
% Output : CNFRefutation 1.34s
% 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,
! [X44] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44)),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X54] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X54)
<=> ? [X5] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X54))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_rangeI,axiom,
! [X17,X9,X2,X12] : hBOOL(hAPP(hAPP(c_member(X12),hAPP(X2,X9)),c_Set_Oimage(X17,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_rev__finite__subset,axiom,
! [X14,X13,X12] :
( c_Finite__Set_Ofinite(X12,X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
=> c_Finite__Set_Ofinite(X12,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_subset__UNIV,axiom,
! [X14,X12] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_finite__imageI,axiom,
! [X65,X17,X40,X12] :
( c_Finite__Set_Ofinite(X12,X40)
=> c_Finite__Set_Ofinite(X17,c_Set_Oimage(X12,X17,X65,X40)) ),
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,
! [X44] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44)),X44)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(c_0_8,plain,
! [X960] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X960)),X960)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_9,plain,
! [X684,X686,X687,X688] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X687)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk21_2(X687,X688)),X688)) )
& ( c_Finite__Set_Ofinite(tc_Nat_Onat,X687)
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk21_2(X687,X688)),X687)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X686),esk20_1(X684)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X686),X684))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X684) ) ),
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),esk20_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X579,X580,X581,X582] : hBOOL(hAPP(hAPP(c_member(X582),hAPP(X581,X580)),c_Set_Oimage(X579,X582,X581,c_Orderings_Otop__class_Otop(tc_fun(X579,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(c_0_13,plain,
! [X663,X664,X665] :
( c_Finite__Set_Ofinite(X665,X663)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X665,tc_HOL_Obool),X663),X664))
| ~ c_Finite__Set_Ofinite(X665,X664) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])])]) ).
fof(c_0_14,plain,
! [X531,X532] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X532,tc_HOL_Obool),X531),c_Orderings_Otop__class_Otop(tc_fun(X532,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,esk20_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,
! [X669,X670,X671,X672] :
( c_Finite__Set_Ofinite(X670,c_Set_Oimage(X672,X670,X669,X671))
| ~ c_Finite__Set_Ofinite(X672,X671) ),
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
% 0.00/0.02 % Problem : SCT167+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:41:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 1.34/0.68 % Version: 3.5.1
% 1.34/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.34/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.34/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.34/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.34/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.34/0.68 % Starting sh5l with 300s (1) cores
% 1.34/0.68 % new_bool_3 with pid 2199812 completed with status 0
% 1.34/0.68 % Result found by new_bool_3
% 1.34/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.34/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.34/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.34/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.34/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.34/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.34/0.68 % Search class: FGHSM-FSLM32-DFFFFFNN
% 1.34/0.68 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 1.34/0.68 % Starting SubtermCWHack with 28s (1) cores
% 1.34/0.68 % SubtermCWHack with pid 2199831 completed with status 0
% 1.34/0.68 % Result found by SubtermCWHack
% 1.34/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.34/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.34/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.34/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.34/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.34/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.34/0.68 % Search class: FGHSM-FSLM32-DFFFFFNN
% 1.34/0.68 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 1.34/0.68 % Starting SubtermCWHack with 28s (1) cores
% 1.34/0.68 % Preprocessing time : 0.008 s
% 1.34/0.68
% 1.34/0.68 % Proof found!
% 1.34/0.68 % SZS status ContradictoryAxioms
% 1.34/0.68 % SZS output start CNFRefutation
% See solution above
% 1.34/0.68 % Parsed axioms : 533
% 1.34/0.68 % Removed by relevancy pruning/SinE : 224
% 1.34/0.68 % Initial clauses : 640
% 1.34/0.68 % Removed in clause preprocessing : 110
% 1.34/0.68 % Initial clauses in saturation : 530
% 1.34/0.68 % Processed clauses : 1971
% 1.34/0.68 % ...of these trivial : 58
% 1.34/0.68 % ...subsumed : 1175
% 1.34/0.68 % ...remaining for further processing : 738
% 1.34/0.68 % Other redundant clauses eliminated : 442
% 1.34/0.68 % Clauses deleted for lack of memory : 0
% 1.34/0.68 % Backward-subsumed : 27
% 1.34/0.68 % Backward-rewritten : 17
% 1.34/0.68 % Generated clauses : 16618
% 1.34/0.68 % ...of the previous two non-redundant : 13502
% 1.34/0.68 % ...aggressively subsumed : 0
% 1.34/0.68 % Contextual simplify-reflections : 2
% 1.34/0.68 % Paramodulations : 16157
% 1.34/0.68 % Factorizations : 11
% 1.34/0.68 % NegExts : 0
% 1.34/0.68 % Equation resolutions : 455
% 1.34/0.68 % Disequality decompositions : 0
% 1.34/0.68 % Total rewrite steps : 4243
% 1.34/0.68 % ...of those cached : 3593
% 1.34/0.68 % Propositional unsat checks : 0
% 1.34/0.68 % Propositional check models : 0
% 1.34/0.68 % Propositional check unsatisfiable : 0
% 1.34/0.68 % Propositional clauses : 0
% 1.34/0.68 % Propositional clauses after purity: 0
% 1.34/0.68 % Propositional unsat core size : 0
% 1.34/0.68 % Propositional preprocessing time : 0.000
% 1.34/0.68 % Propositional encoding time : 0.000
% 1.34/0.68 % Propositional solver time : 0.000
% 1.34/0.68 % Success case prop preproc time : 0.000
% 1.34/0.68 % Success case prop encoding time : 0.000
% 1.34/0.68 % Success case prop solver time : 0.000
% 1.34/0.68 % Current number of processed clauses : 647
% 1.34/0.68 % Positive orientable unit clauses : 101
% 1.34/0.68 % Positive unorientable unit clauses: 4
% 1.34/0.68 % Negative unit clauses : 67
% 1.34/0.68 % Non-unit-clauses : 475
% 1.34/0.68 % Current number of unprocessed clauses: 12010
% 1.34/0.68 % ...number of literals in the above : 40011
% 1.34/0.68 % Current number of archived formulas : 0
% 1.34/0.68 % Current number of archived clauses : 44
% 1.34/0.68 % Clause-clause subsumption calls (NU) : 29482
% 1.34/0.68 % Rec. Clause-clause subsumption calls : 22030
% 1.34/0.68 % Non-unit clause-clause subsumptions : 662
% 1.34/0.68 % Unit Clause-clause subsumption calls : 1171
% 1.34/0.68 % Rewrite failures with RHS unbound : 0
% 1.34/0.68 % BW rewrite match attempts : 334
% 1.34/0.68 % BW rewrite match successes : 27
% 1.34/0.68 % Condensation attempts : 0
% 1.34/0.68 % Condensation successes : 0
% 1.34/0.68 % Termbank termtop insertions : 399824
% 1.34/0.68 % Search garbage collected termcells : 9711
% 1.34/0.68
% 1.34/0.68 % -------------------------------------------------
% 1.34/0.68 % User time : 0.207 s
% 1.34/0.68 % System time : 0.012 s
% 1.34/0.68 % Total time : 0.218 s
% 1.34/0.68 % Maximum resident set size: 6444 pages
% 1.34/0.68
% 1.34/0.68 % -------------------------------------------------
% 1.34/0.68 % User time : 0.232 s
% 1.34/0.68 % System time : 0.018 s
% 1.34/0.68 % Total time : 0.250 s
% 1.34/0.68 % Maximum resident set size: 5376 pages
% 1.34/0.68 % E exiting
%------------------------------------------------------------------------------