%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT165+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 : n020.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 02:08:35 PM UTC 2026
% Result : ContradictoryAxioms 0.22s 10.85s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 20 unt; 0 def)
% Number of atoms : 52 ( 3 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 42 ( 21 ~; 14 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 66 ( 6 sgn 40 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_not__add__less2,axiom,
! [X20,X19] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X20)),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X24] : hAPP(c_Nat_OSuc,X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X51] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X51)
<=> ? [X5] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X51))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_rangeI,axiom,
! [X18,X9,X2,X12] : hBOOL(hAPP(hAPP(c_member(X12),hAPP(X2,X9)),c_Set_Oimage(X18,X12,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,X12] :
( c_Finite__Set_Ofinite(X12,X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
=> c_Finite__Set_Ofinite(X12,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_subset__UNIV,axiom,
! [X15,X12] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_finite__imageI,axiom,
! [X65,X18,X46,X12] :
( c_Finite__Set_Ofinite(X12,X46)
=> c_Finite__Set_Ofinite(X18,c_Set_Oimage(X12,X18,X65,X46)) ),
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_8,plain,
! [X20,X19] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X20)),X20)),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(c_0_9,plain,
! [X103,X104] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X104),X103)),X103)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
fof(c_0_10,plain,
! [X96] : hAPP(c_Nat_OSuc,X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X96),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
cnf(c_0_11,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X679,X681,X682,X683] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X682)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk17_2(X682,X683)),X683)) )
& ( c_Finite__Set_Ofinite(tc_Nat_Onat,X682)
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk17_2(X682,X683)),X682)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X681),esk16_1(X679)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X681),X679))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X679) ) ),
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])])])])])])]) ).
cnf(c_0_14,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk16_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,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_17,plain,
! [X654,X655,X656] :
( c_Finite__Set_Ofinite(X656,X654)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X656,tc_HOL_Obool),X654),X655))
| ~ c_Finite__Set_Ofinite(X656,X655) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])])]) ).
fof(c_0_18,plain,
! [X530,X531] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X531,tc_HOL_Obool),X530),c_Orderings_Otop__class_Otop(tc_fun(X531,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
cnf(c_0_19,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_OSuc,esk16_1(X1))),X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,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_16]) ).
fof(c_0_21,plain,
! [X660,X661,X662,X663] :
( c_Finite__Set_Ofinite(X661,c_Set_Oimage(X663,X661,X660,X662))
| ~ c_Finite__Set_Ofinite(X663,X662) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])])]) ).
cnf(c_0_22,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_17]) ).
cnf(c_0_23,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_18]) ).
cnf(c_0_24,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_19,c_0_20]) ).
cnf(c_0_25,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_21]) ).
cnf(c_0_26,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_22,c_0_23]) ).
cnf(c_0_27,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_28,plain,
~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
$false,
inference(spm,[status(thm)],[c_0_28,c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT165+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/10.43 % Computer : n020.cluster.edu
% 0.18/10.43 % Model : x86_64 x86_64
% 0.18/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.43 % Memory : 8046.5625MB
% 0.18/10.43 % OS : Linux 6.8.0-71-generic
% 0.18/10.43 % CPULimit : 300
% 0.18/10.43 % WCLimit : 300
% 0.18/10.43 % DateTime : Mon Sep 21 04:36:13 UTC 2026
% 0.18/10.44 % CPUTime :
% 0.18/10.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/10.51 Running first-order theorem proving
% 0.22/10.51 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
% 0.22/10.85 % Version: 3.5.1
% 0.22/10.85 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.22/10.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.85 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.22/10.85 % Starting new_bool_3 with 300s (1) cores
% 0.22/10.85 % Starting new_bool_1 with 300s (1) cores
% 0.22/10.85 % Starting sh5l with 300s (1) cores
% 0.22/10.85 % new_bool_3 with pid 2008969 completed with status 0
% 0.22/10.85 % Result found by new_bool_3
% 0.22/10.85 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.22/10.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.85 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.22/10.85 % Starting new_bool_3 with 300s (1) cores
% 0.22/10.85 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/10.85 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/10.85 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.22/10.85 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.22/10.85 % Starting SubtermCWHack with 28s (1) cores
% 0.22/10.85 % SubtermCWHack with pid 2008972 completed with status 0
% 0.22/10.85 % Result found by SubtermCWHack
% 0.22/10.85 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.22/10.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.85 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.22/10.85 % Starting new_bool_3 with 300s (1) cores
% 0.22/10.85 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/10.85 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/10.85 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.22/10.85 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.22/10.85 % Starting SubtermCWHack with 28s (1) cores
% 0.22/10.85 % Preprocessing time : 0.013 s
% 0.22/10.85
% 0.22/10.85 % Proof found!
% 0.22/10.85 % SZS status ContradictoryAxioms
% 0.22/10.85 % SZS output start CNFRefutation
% See solution above
% 0.22/10.85 % Parsed axioms : 533
% 0.22/10.85 % Removed by relevancy pruning/SinE : 200
% 0.22/10.85 % Initial clauses : 645
% 0.22/10.85 % Removed in clause preprocessing : 82
% 0.22/10.85 % Initial clauses in saturation : 563
% 0.22/10.85 % Processed clauses : 2257
% 0.22/10.85 % ...of these trivial : 44
% 0.22/10.85 % ...subsumed : 1547
% 0.22/10.85 % ...remaining for further processing : 666
% 0.22/10.85 % Other redundant clauses eliminated : 269
% 0.22/10.85 % Clauses deleted for lack of memory : 0
% 0.22/10.85 % Backward-subsumed : 27
% 0.22/10.85 % Backward-rewritten : 14
% 0.22/10.85 % Generated clauses : 11140
% 0.22/10.85 % ...of the previous two non-redundant : 9081
% 0.22/10.85 % ...aggressively subsumed : 0
% 0.22/10.85 % Contextual simplify-reflections : 2
% 0.22/10.85 % Paramodulations : 10858
% 0.22/10.85 % Factorizations : 6
% 0.22/10.85 % NegExts : 0
% 0.22/10.85 % Equation resolutions : 281
% 0.22/10.85 % Disequality decompositions : 0
% 0.22/10.85 % Total rewrite steps : 3408
% 0.22/10.85 % ...of those cached : 2869
% 0.22/10.85 % Propositional unsat checks : 0
% 0.22/10.85 % Propositional check models : 0
% 0.22/10.85 % Propositional check unsatisfiable : 0
% 0.22/10.85 % Propositional clauses : 0
% 0.22/10.85 % Propositional clauses after purity: 0
% 0.22/10.85 % Propositional unsat core size : 0
% 0.22/10.85 % Propositional preprocessing time : 0.000
% 0.22/10.85 % Propositional encoding time : 0.000
% 0.22/10.85 % Propositional solver time : 0.000
% 0.22/10.85 % Success case prop preproc time : 0.000
% 0.22/10.85 % Success case prop encoding time : 0.000
% 0.22/10.85 % Success case prop solver time : 0.000
% 0.22/10.85 % Current number of processed clauses : 573
% 0.22/10.85 % Positive orientable unit clauses : 112
% 0.22/10.85 % Positive unorientable unit clauses: 5
% 0.22/10.85 % Negative unit clauses : 78
% 0.22/10.85 % Non-unit-clauses : 378
% 0.22/10.85 % Current number of unprocessed clauses: 7314
% 0.22/10.85 % ...number of literals in the above : 21440
% 0.22/10.85 % Current number of archived formulas : 0
% 0.22/10.85 % Current number of archived clauses : 41
% 0.22/10.85 % Clause-clause subsumption calls (NU) : 8863
% 0.22/10.85 % Rec. Clause-clause subsumption calls : 7020
% 0.22/10.85 % Non-unit clause-clause subsumptions : 759
% 0.22/10.85 % Unit Clause-clause subsumption calls : 908
% 0.22/10.85 % Rewrite failures with RHS unbound : 0
% 0.22/10.85 % BW rewrite match attempts : 288
% 0.22/10.85 % BW rewrite match successes : 23
% 0.22/10.85 % Condensation attempts : 0
% 0.22/10.85 % Condensation successes : 0
% 0.22/10.85 % Termbank termtop insertions : 309654
% 0.22/10.85 % Search garbage collected termcells : 9966
% 0.22/10.85
% 0.22/10.85 % -------------------------------------------------
% 0.22/10.85 % User time : 0.246 s
% 0.22/10.85 % System time : 0.018 s
% 0.22/10.85 % Total time : 0.264 s
% 0.22/10.85 % Maximum resident set size: 6392 pages
% 0.22/10.85
% 0.22/10.85 % -------------------------------------------------
% 0.22/10.85 % User time : 0.290 s
% 0.22/10.85 % System time : 0.026 s
% 0.22/10.85 % Total time : 0.316 s
% 0.22/10.85 % Maximum resident set size: 5376 pages
% 0.22/10.85 % E exiting
%------------------------------------------------------------------------------