%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT159+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 : n006.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 02:07:58 PM UTC 2026
% Result : ContradictoryAxioms 0.16s 5.69s
% Output : CNFRefutation 0.16s
% 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 : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 47 ( 4 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Suc__n__not__le__n,axiom,
! [X25] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X38] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X38)
<=> ? [X30] :
! [X3] :
( c_member(tc_Nat_Onat,X3,X38)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_rangeI,axiom,
! [X5,X8,X2,X6] : c_member(X6,hAPP(X2,X8),c_Set_Oimage(X5,X6,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_finite__imageI,axiom,
! [X11,X5,X12,X6] :
( c_Finite__Set_Ofinite(X6,X12)
=> c_Finite__Set_Ofinite(X5,c_Set_Oimage(X6,X5,X11,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_finite,axiom,
! [X4,X6] :
( class_Finite__Set_Ofinite(X6)
=> c_Finite__Set_Ofinite(X6,X4) ),
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,
! [X25] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25),X25),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(c_0_7,plain,
! [X890] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X890),X890),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_8,plain,
! [X638,X640,X641,X642] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X641)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk15_2(X641,X642),X642) )
& ( c_Finite__Set_Ofinite(tc_Nat_Onat,X641)
| c_member(tc_Nat_Onat,esk15_2(X641,X642),X641) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X640,esk14_1(X638))
| ~ c_member(tc_Nat_Onat,X640,X638)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X638) ) ),
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,
~ 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,
( ~ c_member(tc_Nat_Onat,X2,X1)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk14_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X771,X772,X773,X774] : c_member(X774,hAPP(X773,X772),c_Set_Oimage(X771,X774,X773,c_Orderings_Otop__class_Otop(tc_fun(X771,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_12,plain,
( ~ c_member(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk14_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,
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,
! [X110,X111,X112,X113] :
( c_Finite__Set_Ofinite(X111,c_Set_Oimage(X113,X111,X110,X112))
| ~ c_Finite__Set_Ofinite(X113,X112) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])])]) ).
fof(c_0_15,plain,
! [X114,X115] :
( c_Finite__Set_Ofinite(X115,X114)
| ~ class_Finite__Set_Ofinite(X115) ),
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
% 0.00/0.04 % Problem : SCT159+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n006.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Mon Sep 21 04:35:34 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 0.16/5.69 % Version: 3.5.1
% 0.16/5.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.69 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.69 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.69 % Starting sh5l with 300s (1) cores
% 0.16/5.69 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2012868 completed with status 0
% 0.16/5.69 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.16/5.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.69 % No SInE strategy applied
% 0.16/5.69 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.16/5.69 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.69 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.16/5.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 0.16/5.69 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 0.16/5.69 % Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 0.16/5.69 % SubtermCWHack with pid 2012875 completed with status 0
% 0.16/5.69 % Result found by SubtermCWHack
% 0.16/5.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.69 % No SInE strategy applied
% 0.16/5.69 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.16/5.69 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.69 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.69 % Preprocessing time : 0.007 s
% 0.16/5.69
% 0.16/5.69 % Proof found!
% 0.16/5.69 % SZS status ContradictoryAxioms
% 0.16/5.69 % SZS output start CNFRefutation
% See solution above
% 0.16/5.69 % Parsed axioms : 533
% 0.16/5.69 % Removed by relevancy pruning/SinE : 0
% 0.16/5.69 % Initial clauses : 777
% 0.16/5.69 % Removed in clause preprocessing : 42
% 0.16/5.69 % Initial clauses in saturation : 735
% 0.16/5.69 % Processed clauses : 4256
% 0.16/5.69 % ...of these trivial : 181
% 0.16/5.69 % ...subsumed : 2897
% 0.16/5.69 % ...remaining for further processing : 1178
% 0.16/5.69 % Other redundant clauses eliminated : 199
% 0.16/5.69 % Clauses deleted for lack of memory : 0
% 0.16/5.69 % Backward-subsumed : 40
% 0.16/5.69 % Backward-rewritten : 50
% 0.16/5.69 % Generated clauses : 18464
% 0.16/5.69 % ...of the previous two non-redundant : 15211
% 0.16/5.69 % ...aggressively subsumed : 0
% 0.16/5.69 % Contextual simplify-reflections : 8
% 0.16/5.69 % Paramodulations : 18246
% 0.16/5.69 % Factorizations : 18
% 0.16/5.69 % NegExts : 0
% 0.16/5.69 % Equation resolutions : 212
% 0.16/5.69 % Disequality decompositions : 0
% 0.16/5.69 % Total rewrite steps : 9956
% 0.16/5.69 % ...of those cached : 9031
% 0.16/5.69 % Propositional unsat checks : 0
% 0.16/5.69 % Propositional check models : 0
% 0.16/5.69 % Propositional check unsatisfiable : 0
% 0.16/5.69 % Propositional clauses : 0
% 0.16/5.69 % Propositional clauses after purity: 0
% 0.16/5.69 % Propositional unsat core size : 0
% 0.16/5.69 % Propositional preprocessing time : 0.000
% 0.16/5.69 % Propositional encoding time : 0.000
% 0.16/5.69 % Propositional solver time : 0.000
% 0.16/5.69 % Success case prop preproc time : 0.000
% 0.16/5.69 % Success case prop encoding time : 0.000
% 0.16/5.69 % Success case prop solver time : 0.000
% 0.16/5.69 % Current number of processed clauses : 1011
% 0.16/5.69 % Positive orientable unit clauses : 261
% 0.16/5.69 % Positive unorientable unit clauses: 5
% 0.16/5.69 % Negative unit clauses : 72
% 0.16/5.69 % Non-unit-clauses : 673
% 0.16/5.69 % Current number of unprocessed clauses: 11199
% 0.16/5.69 % ...number of literals in the above : 28596
% 0.16/5.69 % Current number of archived formulas : 0
% 0.16/5.69 % Current number of archived clauses : 90
% 0.16/5.69 % Clause-clause subsumption calls (NU) : 62493
% 0.16/5.69 % Rec. Clause-clause subsumption calls : 54290
% 0.16/5.69 % Non-unit clause-clause subsumptions : 1600
% 0.16/5.69 % Unit Clause-clause subsumption calls : 6112
% 0.16/5.69 % Rewrite failures with RHS unbound : 53
% 0.16/5.69 % BW rewrite match attempts : 6236
% 0.16/5.69 % BW rewrite match successes : 62
% 0.16/5.69 % Condensation attempts : 0
% 0.16/5.69 % Condensation successes : 0
% 0.16/5.69 % Termbank termtop insertions : 278039
% 0.16/5.69 % Search garbage collected termcells : 11337
% 0.16/5.69
% 0.16/5.69 % -------------------------------------------------
% 0.16/5.69 % User time : 0.204 s
% 0.16/5.69 % System time : 0.020 s
% 0.16/5.69 % Total time : 0.224 s
% 0.16/5.69 % Maximum resident set size: 6836 pages
% 0.16/5.69
% 0.16/5.69 % -------------------------------------------------
% 0.16/5.69 % User time : 0.890 s
% 0.16/5.69 % System time : 0.072 s
% 0.16/5.69 % Total time : 0.962 s
% 0.16/5.69 % Maximum resident set size: 5376 pages
% 0.16/5.69 % E exiting
%------------------------------------------------------------------------------