%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW317+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 : n026.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 03:10:17 PM UTC 2026
% Result : ContradictoryAxioms 2.65s 1.33s
% Output : CNFRefutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 26 unt; 0 def)
% Number of atoms : 49 ( 12 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 10 |; 2 &)
% ( 1 <=>; 2 =>; 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 : 18 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 65 ( 7 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_not__add__less2,axiom,
! [X115,X114] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X115)),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X89] : hAPP(c_Nat_OSuc,X89) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X89),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X145] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X145))
<=> ? [X146] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X145))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X146)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_finite__set,axiom,
! [X259,X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_List_Oset(X5),X259))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__set) ).
fof(fact_set__map,axiom,
! [X259,X2,X25,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(X25,X5),X2),X259)) = hAPP(c_Set_Oimage(X25,X5,X2),hAPP(c_List_Oset(X25),X259)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__map) ).
fof(fact_rangeI,axiom,
! [X25,X21,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X21)),hAPP(c_Set_Oimage(X25,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X25,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_UNIV__enum,axiom,
! [X5] :
( class_Enum_Oenum(X5)
=> c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_List_Oset(X5),c_Enum_Oenum__class_Oenum(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__enum) ).
fof(arity_HOL__Obool__Enum_Oenum,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
fof(c_0_9,plain,
! [X115,X114] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X115)),X115)),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(c_0_10,plain,
! [X2213] : hAPP(c_Nat_OSuc,X2213) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2213),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(c_0_11,plain,
! [X818,X819] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X819),X818)),X818)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[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]) ).
cnf(c_0_13,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
cnf(c_0_14,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_11]) ).
cnf(c_0_15,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X1354,X1356,X1357,X1358] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk28_2(X1357,X1358)),X1358)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1357))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk28_2(X1357,X1358)),X1357)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1356),esk27_1(X1354)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1356),X1354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1354)) ) ),
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])])])])])])]) ).
fof(c_0_17,plain,
! [X2287,X2288] : hBOOL(hAPP(c_Finite__Set_Ofinite(X2288),hAPP(c_List_Oset(X2288),X2287))),
inference(variable_rename,[status(thm)],[fact_finite__set]) ).
fof(c_0_18,plain,
! [X2605,X2606,X2607,X2608] : hAPP(c_List_Oset(X2608),hAPP(hAPP(c_List_Omap(X2607,X2608),X2606),X2605)) = hAPP(c_Set_Oimage(X2607,X2608,X2606),hAPP(c_List_Oset(X2607),X2605)),
inference(variable_rename,[status(thm)],[fact_set__map]) ).
cnf(c_0_19,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk27_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X2578,X2579,X2580,X2581] : hBOOL(hAPP(hAPP(c_member(X2581),hAPP(X2580,X2579)),hAPP(c_Set_Oimage(X2578,X2581,X2580),c_Orderings_Otop__class_Otop(tc_fun(X2578,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_22,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) = hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_List_Oset(X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X2309] :
( c_Orderings_Otop__class_Otop(tc_fun(X2309,tc_HOL_Obool)) = hAPP(c_List_Oset(X2309),c_Enum_Oenum__class_Oenum(X2309))
| ~ class_Enum_Oenum(X2309) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UNIV__enum])])]) ).
cnf(c_0_25,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_OSuc,esk27_1(X1))),X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_List_Oset(X2),X4)))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( ~ class_Enum_Oenum(X1)
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(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_25,c_0_26]) ).
cnf(c_0_30,plain,
( ~ class_Enum_Oenum(X2)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
class_Enum_Oenum(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]) ).
cnf(c_0_32,plain,
~ class_Enum_Oenum(X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
$false,
inference(sr,[status(thm)],[c_0_31,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW317+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 09:49:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 2.65/1.33 % Version: 3.5.1
% 2.65/1.33 % Preprocessing class: FMLMSMSMSSSNFFN.
% 2.65/1.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.65/1.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.65/1.33 % Starting new_bool_3 with 300s (1) cores
% 2.65/1.33 % Starting new_bool_1 with 300s (1) cores
% 2.65/1.33 % Starting sh5l with 300s (1) cores
% 2.65/1.33 % new_bool_1 with pid 1969578 completed with status 0
% 2.65/1.33 % Result found by new_bool_1
% 2.65/1.33 % Preprocessing class: FMLMSMSMSSSNFFN.
% 2.65/1.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.65/1.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.65/1.33 % Starting new_bool_3 with 300s (1) cores
% 2.65/1.33 % Starting new_bool_1 with 300s (1) cores
% 2.65/1.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.65/1.33 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.65/1.33 % Search class: FGHSM-SSLM32-DFFFFFNN
% 2.65/1.33 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 2.65/1.33 % Starting SubtermCWHack with 28s (1) cores
% 2.65/1.33 % SubtermCWHack with pid 1969580 completed with status 0
% 2.65/1.33 % Result found by SubtermCWHack
% 2.65/1.33 % Preprocessing class: FMLMSMSMSSSNFFN.
% 2.65/1.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.65/1.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.65/1.33 % Starting new_bool_3 with 300s (1) cores
% 2.65/1.33 % Starting new_bool_1 with 300s (1) cores
% 2.65/1.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.65/1.33 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.65/1.33 % Search class: FGHSM-SSLM32-DFFFFFNN
% 2.65/1.33 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 2.65/1.33 % Starting SubtermCWHack with 28s (1) cores
% 2.65/1.33 % Preprocessing time : 0.026 s
% 2.65/1.33
% 2.65/1.33 % Proof found!
% 2.65/1.33 % SZS status ContradictoryAxioms
% 2.65/1.33 % SZS output start CNFRefutation
% See solution above
% 2.65/1.33 % Parsed axioms : 5242
% 2.65/1.33 % Removed by relevancy pruning/SinE : 4515
% 2.65/1.33 % Initial clauses : 1104
% 2.65/1.33 % Removed in clause preprocessing : 54
% 2.65/1.33 % Initial clauses in saturation : 1050
% 2.65/1.33 % Processed clauses : 4710
% 2.65/1.33 % ...of these trivial : 154
% 2.65/1.33 % ...subsumed : 3152
% 2.65/1.33 % ...remaining for further processing : 1404
% 2.65/1.33 % Other redundant clauses eliminated : 351
% 2.65/1.33 % Clauses deleted for lack of memory : 0
% 2.65/1.33 % Backward-subsumed : 70
% 2.65/1.33 % Backward-rewritten : 64
% 2.65/1.33 % Generated clauses : 23596
% 2.65/1.33 % ...of the previous two non-redundant : 20468
% 2.65/1.33 % ...aggressively subsumed : 0
% 2.65/1.33 % Contextual simplify-reflections : 1
% 2.65/1.33 % Paramodulations : 23211
% 2.65/1.33 % Factorizations : 8
% 2.65/1.33 % NegExts : 0
% 2.65/1.33 % Equation resolutions : 387
% 2.65/1.33 % Disequality decompositions : 0
% 2.65/1.33 % Total rewrite steps : 6173
% 2.65/1.33 % ...of those cached : 4855
% 2.65/1.33 % Propositional unsat checks : 0
% 2.65/1.33 % Propositional check models : 0
% 2.65/1.33 % Propositional check unsatisfiable : 0
% 2.65/1.33 % Propositional clauses : 0
% 2.65/1.33 % Propositional clauses after purity: 0
% 2.65/1.33 % Propositional unsat core size : 0
% 2.65/1.33 % Propositional preprocessing time : 0.000
% 2.65/1.33 % Propositional encoding time : 0.000
% 2.65/1.33 % Propositional solver time : 0.000
% 2.65/1.33 % Success case prop preproc time : 0.000
% 2.65/1.33 % Success case prop encoding time : 0.000
% 2.65/1.33 % Success case prop solver time : 0.000
% 2.65/1.33 % Current number of processed clauses : 1187
% 2.65/1.33 % Positive orientable unit clauses : 258
% 2.65/1.33 % Positive unorientable unit clauses: 19
% 2.65/1.33 % Negative unit clauses : 132
% 2.65/1.33 % Non-unit-clauses : 778
% 2.65/1.33 % Current number of unprocessed clauses: 16683
% 2.65/1.33 % ...number of literals in the above : 42859
% 2.65/1.33 % Current number of archived formulas : 0
% 2.65/1.33 % Current number of archived clauses : 135
% 2.65/1.33 % Clause-clause subsumption calls (NU) : 163333
% 2.65/1.33 % Rec. Clause-clause subsumption calls : 107443
% 2.65/1.33 % Non-unit clause-clause subsumptions : 1534
% 2.65/1.33 % Unit Clause-clause subsumption calls : 3261
% 2.65/1.33 % Rewrite failures with RHS unbound : 163
% 2.65/1.33 % BW rewrite match attempts : 5650
% 2.65/1.33 % BW rewrite match successes : 142
% 2.65/1.33 % Condensation attempts : 0
% 2.65/1.33 % Condensation successes : 0
% 2.65/1.33 % Termbank termtop insertions : 675214
% 2.65/1.33 % Search garbage collected termcells : 57366
% 2.65/1.33
% 2.65/1.33 % -------------------------------------------------
% 2.65/1.33 % User time : 0.702 s
% 2.65/1.33 % System time : 0.066 s
% 2.65/1.33 % Total time : 0.767 s
% 2.65/1.33 % Maximum resident set size: 13708 pages
% 2.65/1.33
% 2.65/1.33 % -------------------------------------------------
% 2.65/1.33 % User time : 0.826 s
% 2.65/1.33 % System time : 0.075 s
% 2.65/1.33 % Total time : 0.902 s
% 2.65/1.33 % Maximum resident set size: 12288 pages
% 2.65/1.33 % E exiting
%------------------------------------------------------------------------------