%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT165+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 : n008.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 0.14s 5.74s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 17 unt; 0 def)
% Number of atoms : 44 ( 3 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 11 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 55 ( 5 sgn 34 !; 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
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/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_finite,axiom,
! [X15,X12] :
( class_Finite__Set_Ofinite(X12)
=> c_Finite__Set_Ofinite(X12,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(c_0_7,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_8,plain,
! [X89,X90] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X89)),X89)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_9,plain,
! [X340] : hAPP(c_Nat_OSuc,X340) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X340),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
cnf(c_0_10,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_8]) ).
cnf(c_0_11,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_9]) ).
fof(c_0_12,plain,
! [X444,X446,X447,X448] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X447)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk10_2(X447,X448)),X448)) )
& ( c_Finite__Set_Ofinite(tc_Nat_Onat,X447)
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk10_2(X447,X448)),X447)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X446),esk9_1(X444)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X446),X444))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X444) ) ),
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_13,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,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),esk9_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X646,X647,X648,X649] : hBOOL(hAPP(hAPP(c_member(X649),hAPP(X648,X647)),c_Set_Oimage(X646,X649,X648,c_Orderings_Otop__class_Otop(tc_fun(X646,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_16,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_OSuc,esk9_1(X1))),X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,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_15]) ).
fof(c_0_18,plain,
! [X950,X951,X952,X953] :
( c_Finite__Set_Ofinite(X951,c_Set_Oimage(X953,X951,X950,X952))
| ~ c_Finite__Set_Ofinite(X953,X952) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])])]) ).
fof(c_0_19,plain,
! [X1164,X1165] :
( c_Finite__Set_Ofinite(X1165,X1164)
| ~ class_Finite__Set_Ofinite(X1165) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])])]) ).
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_16,c_0_17]) ).
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_18]) ).
cnf(c_0_22,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).
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_Product__Type_Ounit,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
% 0.00/0.03 % Problem : SCT165+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n008.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 04:36:01 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.43 Running first-order theorem proving
% 0.14/5.43 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
% 0.14/5.74 % Version: 3.5.1
% 0.14/5.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.74 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.74 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.74 % Starting sh5l with 300s (1) cores
% 0.14/5.74 % sh5l with pid 146536 completed with status 0
% 0.14/5.74 % Result found by sh5l
% 0.14/5.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.74 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.74 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.74 % Starting sh5l with 300s (1) cores
% 0.14/5.74 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.74 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.74 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.14/5.74 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.74 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.74 % SubtermCWHack with pid 146537 completed with status 0
% 0.14/5.74 % Result found by SubtermCWHack
% 0.14/5.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.74 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.74 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.74 % Starting sh5l with 300s (1) cores
% 0.14/5.74 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.74 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.74 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.14/5.74 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.74 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.74 % Preprocessing time : 0.016 s
% 0.14/5.74
% 0.14/5.74 % Proof found!
% 0.14/5.74 % SZS status ContradictoryAxioms
% 0.14/5.74 % SZS output start CNFRefutation
% See solution above
% 0.14/5.74 % Parsed axioms : 533
% 0.14/5.74 % Removed by relevancy pruning/SinE : 167
% 0.14/5.74 % Initial clauses : 685
% 0.14/5.74 % Removed in clause preprocessing : 82
% 0.14/5.74 % Initial clauses in saturation : 603
% 0.14/5.74 % Processed clauses : 2752
% 0.14/5.74 % ...of these trivial : 44
% 0.14/5.74 % ...subsumed : 1560
% 0.14/5.74 % ...remaining for further processing : 1148
% 0.14/5.74 % Other redundant clauses eliminated : 138
% 0.14/5.74 % Clauses deleted for lack of memory : 0
% 0.14/5.74 % Backward-subsumed : 32
% 0.14/5.74 % Backward-rewritten : 13
% 0.14/5.74 % Generated clauses : 9634
% 0.14/5.74 % ...of the previous two non-redundant : 6720
% 0.14/5.74 % ...aggressively subsumed : 0
% 0.14/5.74 % Contextual simplify-reflections : 2
% 0.14/5.74 % Paramodulations : 9486
% 0.14/5.74 % Factorizations : 4
% 0.14/5.74 % NegExts : 0
% 0.14/5.74 % Equation resolutions : 149
% 0.14/5.74 % Disequality decompositions : 0
% 0.14/5.74 % Total rewrite steps : 4017
% 0.14/5.74 % ...of those cached : 3358
% 0.14/5.74 % Propositional unsat checks : 0
% 0.14/5.74 % Propositional check models : 0
% 0.14/5.74 % Propositional check unsatisfiable : 0
% 0.14/5.74 % Propositional clauses : 0
% 0.14/5.74 % Propositional clauses after purity: 0
% 0.14/5.74 % Propositional unsat core size : 0
% 0.14/5.74 % Propositional preprocessing time : 0.000
% 0.14/5.74 % Propositional encoding time : 0.000
% 0.14/5.74 % Propositional solver time : 0.000
% 0.14/5.74 % Success case prop preproc time : 0.000
% 0.14/5.74 % Success case prop encoding time : 0.000
% 0.14/5.74 % Success case prop solver time : 0.000
% 0.14/5.74 % Current number of processed clauses : 1051
% 0.14/5.74 % Positive orientable unit clauses : 229
% 0.14/5.74 % Positive unorientable unit clauses: 7
% 0.14/5.74 % Negative unit clauses : 51
% 0.14/5.74 % Non-unit-clauses : 764
% 0.14/5.74 % Current number of unprocessed clauses: 4505
% 0.14/5.74 % ...number of literals in the above : 13070
% 0.14/5.74 % Current number of archived formulas : 0
% 0.14/5.74 % Current number of archived clauses : 45
% 0.14/5.74 % Clause-clause subsumption calls (NU) : 41977
% 0.14/5.74 % Rec. Clause-clause subsumption calls : 38793
% 0.14/5.74 % Non-unit clause-clause subsumptions : 1102
% 0.14/5.74 % Unit Clause-clause subsumption calls : 1675
% 0.14/5.74 % Rewrite failures with RHS unbound : 23
% 0.14/5.74 % BW rewrite match attempts : 2082
% 0.14/5.74 % BW rewrite match successes : 30
% 0.14/5.74 % Condensation attempts : 0
% 0.14/5.74 % Condensation successes : 0
% 0.14/5.74 % Termbank termtop insertions : 289002
% 0.14/5.74 % Search garbage collected termcells : 10063
% 0.14/5.74
% 0.14/5.74 % -------------------------------------------------
% 0.14/5.74 % User time : 0.231 s
% 0.14/5.74 % System time : 0.024 s
% 0.14/5.74 % Total time : 0.255 s
% 0.14/5.74 % Maximum resident set size: 6392 pages
% 0.14/5.74
% 0.14/5.74 % -------------------------------------------------
% 0.14/5.74 % User time : 0.256 s
% 0.14/5.74 % System time : 0.030 s
% 0.14/5.74 % Total time : 0.286 s
% 0.14/5.74 % Maximum resident set size: 5376 pages
% 0.14/5.74 % E exiting
%------------------------------------------------------------------------------