%------------------------------------------------------------------------------
% File : E---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 : n019.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 2.61s 0.80s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 11 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 47 ( 4 sgn 29 !; 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_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,axiom,
! [X14,X12] :
( class_Finite__Set_Ofinite(X12)
=> c_Finite__Set_Ofinite(X12,X14) ),
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_6,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_7,plain,
! [X470] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X470)),X470)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_8,plain,
! [X488,X490,X491,X492] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X491)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk11_2(X491,X492)),X492)) )
& ( c_Finite__Set_Ofinite(tc_Nat_Onat,X491)
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk11_2(X491,X492)),X491)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X490),esk10_1(X488)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X490),X488))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X488) ) ),
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_9,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_7]) ).
cnf(c_0_10,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),esk10_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X631,X632,X633,X634] : hBOOL(hAPP(hAPP(c_member(X634),hAPP(X633,X632)),c_Set_Oimage(X631,X634,X633,c_Orderings_Otop__class_Otop(tc_fun(X631,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_12,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_OSuc,esk10_1(X1))),X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,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_11]) ).
fof(c_0_14,plain,
! [X993,X994,X995,X996] :
( c_Finite__Set_Ofinite(X994,c_Set_Oimage(X996,X994,X993,X995))
| ~ c_Finite__Set_Ofinite(X996,X995) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])])]) ).
fof(c_0_15,plain,
! [X1173,X1174] :
( c_Finite__Set_Ofinite(X1174,X1173)
| ~ class_Finite__Set_Ofinite(X1174) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])])]) ).
cnf(c_0_16,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_12,c_0_13]) ).
cnf(c_0_17,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_14]) ).
cnf(c_0_18,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).
cnf(c_0_20,plain,
~ c_Finite__Set_Ofinite(X1,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(tc_Product__Type_Ounit,X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
$false,
inference(spm,[status(thm)],[c_0_20,c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT167+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:35:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 2.61/0.80 % Version: 3.5.1
% 2.61/0.80 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.61/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/0.80 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.61/0.80 % Starting new_bool_3 with 300s (1) cores
% 2.61/0.80 % Starting new_bool_1 with 300s (1) cores
% 2.61/0.80 % Starting sh5l with 300s (1) cores
% 2.61/0.80 % sh5l with pid 1692010 completed with status 0
% 2.61/0.80 % Result found by sh5l
% 2.61/0.80 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.61/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/0.80 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.61/0.80 % Starting new_bool_3 with 300s (1) cores
% 2.61/0.80 % Starting new_bool_1 with 300s (1) cores
% 2.61/0.80 % Starting sh5l with 300s (1) cores
% 2.61/0.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 2.61/0.80 % SinE strategy is gf500_gu_R04_F100_L20000
% 2.61/0.80 % Search class: FGHSM-FSLM32-DFFFFFNN
% 2.61/0.80 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 2.61/0.80 % Starting SubtermCWHack with 28s (1) cores
% 2.61/0.80 % SubtermCWHack with pid 1692011 completed with status 0
% 2.61/0.80 % Result found by SubtermCWHack
% 2.61/0.80 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.61/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/0.80 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.61/0.80 % Starting new_bool_3 with 300s (1) cores
% 2.61/0.80 % Starting new_bool_1 with 300s (1) cores
% 2.61/0.80 % Starting sh5l with 300s (1) cores
% 2.61/0.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 2.61/0.80 % SinE strategy is gf500_gu_R04_F100_L20000
% 2.61/0.80 % Search class: FGHSM-FSLM32-DFFFFFNN
% 2.61/0.80 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 2.61/0.80 % Starting SubtermCWHack with 28s (1) cores
% 2.61/0.80 % Preprocessing time : 0.016 s
% 2.61/0.80
% 2.61/0.80 % Proof found!
% 2.61/0.80 % SZS status ContradictoryAxioms
% 2.61/0.80 % SZS output start CNFRefutation
% See solution above
% 2.61/0.80 % Parsed axioms : 533
% 2.61/0.80 % Removed by relevancy pruning/SinE : 163
% 2.61/0.80 % Initial clauses : 724
% 2.61/0.80 % Removed in clause preprocessing : 112
% 2.61/0.80 % Initial clauses in saturation : 612
% 2.61/0.80 % Processed clauses : 2785
% 2.61/0.80 % ...of these trivial : 38
% 2.61/0.80 % ...subsumed : 1228
% 2.61/0.80 % ...remaining for further processing : 1519
% 2.61/0.80 % Other redundant clauses eliminated : 92
% 2.61/0.80 % Clauses deleted for lack of memory : 0
% 2.61/0.80 % Backward-subsumed : 23
% 2.61/0.80 % Backward-rewritten : 13
% 2.61/0.80 % Generated clauses : 9913
% 2.61/0.80 % ...of the previous two non-redundant : 6277
% 2.61/0.80 % ...aggressively subsumed : 0
% 2.61/0.80 % Contextual simplify-reflections : 2
% 2.61/0.80 % Paramodulations : 9810
% 2.61/0.80 % Factorizations : 4
% 2.61/0.80 % NegExts : 0
% 2.61/0.80 % Equation resolutions : 104
% 2.61/0.80 % Disequality decompositions : 0
% 2.61/0.80 % Total rewrite steps : 4105
% 2.61/0.80 % ...of those cached : 3243
% 2.61/0.80 % Propositional unsat checks : 0
% 2.61/0.80 % Propositional check models : 0
% 2.61/0.80 % Propositional check unsatisfiable : 0
% 2.61/0.80 % Propositional clauses : 0
% 2.61/0.80 % Propositional clauses after purity: 0
% 2.61/0.80 % Propositional unsat core size : 0
% 2.61/0.80 % Propositional preprocessing time : 0.000
% 2.61/0.80 % Propositional encoding time : 0.000
% 2.61/0.80 % Propositional solver time : 0.000
% 2.61/0.80 % Success case prop preproc time : 0.000
% 2.61/0.80 % Success case prop encoding time : 0.000
% 2.61/0.80 % Success case prop solver time : 0.000
% 2.61/0.80 % Current number of processed clauses : 1431
% 2.61/0.80 % Positive orientable unit clauses : 364
% 2.61/0.80 % Positive unorientable unit clauses: 7
% 2.61/0.80 % Negative unit clauses : 45
% 2.61/0.80 % Non-unit-clauses : 1015
% 2.61/0.80 % Current number of unprocessed clauses: 4078
% 2.61/0.80 % ...number of literals in the above : 11952
% 2.61/0.80 % Current number of archived formulas : 0
% 2.61/0.80 % Current number of archived clauses : 36
% 2.61/0.80 % Clause-clause subsumption calls (NU) : 224320
% 2.61/0.80 % Rec. Clause-clause subsumption calls : 216868
% 2.61/0.80 % Non-unit clause-clause subsumptions : 935
% 2.61/0.80 % Unit Clause-clause subsumption calls : 16699
% 2.61/0.80 % Rewrite failures with RHS unbound : 23
% 2.61/0.80 % BW rewrite match attempts : 7929
% 2.61/0.80 % BW rewrite match successes : 30
% 2.61/0.80 % Condensation attempts : 0
% 2.61/0.80 % Condensation successes : 0
% 2.61/0.80 % Termbank termtop insertions : 301666
% 2.61/0.80 % Search garbage collected termcells : 10311
% 2.61/0.80
% 2.61/0.80 % -------------------------------------------------
% 2.61/0.80 % User time : 0.312 s
% 2.61/0.80 % System time : 0.015 s
% 2.61/0.80 % Total time : 0.327 s
% 2.61/0.80 % Maximum resident set size: 6700 pages
% 2.61/0.80
% 2.61/0.80 % -------------------------------------------------
% 2.61/0.80 % User time : 0.337 s
% 2.61/0.80 % System time : 0.021 s
% 2.61/0.80 % Total time : 0.358 s
% 2.61/0.80 % Maximum resident set size: 5376 pages
% 2.61/0.80 % E exiting
%------------------------------------------------------------------------------