%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEV612+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 02:36:53 PM UTC 2026
% Result : Theorem 10.82s 10.55s
% Output : CNFRefutation 10.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 35 |; 8 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ZornsLemma.InfiniteTypes.infinite_nat_inj',axiom,
! [X419] :
( cType___24t(X419)
=> ( ~ p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(X419))
=> ? [X100] :
( cZornsLemma_2eFunctionProperties_2einjective___24a3(cCoq_2eInit_2eDatatypes_2enat,X419,X100)
& c_24__type__1386___24t(X419,X100) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ZornsLemma.InfiniteTypes.infinite_nat_inj') ).
fof('$_type_1386',axiom,
! [X1,X2039] :
( c_24__type__1386___24t(X1,X2039)
<=> ! [X2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X2)
=> t(happ(X2039,X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_1386') ).
fof('ZornsLemma.InfiniteTypes.nat_infinite',axiom,
~ p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(cCoq_2eInit_2eDatatypes_2enat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ZornsLemma.InfiniteTypes.nat_infinite') ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [X2431] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X2431)
<=> t(X2431,cCoq_2eInit_2eDatatypes_2enat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$tdef_Coq.Init.Datatypes.nat') ).
fof('$_type_102',axiom,
! [X1,X2009] :
( c_24__type__102___24t(X1,X2009)
<=> ! [X2] :
( t(X2,X1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(X2009,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_102') ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.nat') ).
fof('_HAMMER_GOAL',conjecture,
cZornsLemma_2eCountableTypes_2eCountableT___24a1(cCoq_2eInit_2eDatatypes_2enat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('ZornsLemma.CountableTypes.intro_nat_injection',axiom,
! [X419] :
( cType___24t(X419)
=> ! [X61] :
( c_24__type__102___24t(X419,X61)
=> ( cZornsLemma_2eFunctionProperties_2einjective___24a3(X419,cCoq_2eInit_2eDatatypes_2enat,X61)
=> cZornsLemma_2eCountableTypes_2eCountableT___24a1(X419) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ZornsLemma.CountableTypes.intro_nat_injection') ).
fof(c_0_8,plain,
! [X419] :
( cType___24t(X419)
=> ( ~ p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(X419))
=> ? [X100] :
( cZornsLemma_2eFunctionProperties_2einjective___24a3(cCoq_2eInit_2eDatatypes_2enat,X419,X100)
& c_24__type__1386___24t(X419,X100) ) ) ),
inference(fof_simplification,[status(thm)],['ZornsLemma.InfiniteTypes.infinite_nat_inj']) ).
fof(c_0_9,plain,
! [X2786,X2787,X2788,X2789,X2790] :
( ( c_24__type__1386___24t(X2789,X2790)
| ~ t(happ(X2790,esk87_2(X2789,X2790)),X2789) )
& ( c_24__type__1386___24t(X2789,X2790)
| cCoq_2eInit_2eDatatypes_2enat___24t(esk87_2(X2789,X2790)) )
& ( t(happ(X2787,X2788),X2786)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2788)
| ~ c_24__type__1386___24t(X2786,X2787) ) ),
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)],['$_type_1386'])])])])])])]) ).
fof(c_0_10,plain,
! [X2470] :
( ( ~ cType___24t(X2470)
| p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(X2470))
| cZornsLemma_2eFunctionProperties_2einjective___24a3(cCoq_2eInit_2eDatatypes_2enat,X2470,esk6_1(X2470)) )
& ( ~ cType___24t(X2470)
| p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(X2470))
| c_24__type__1386___24t(X2470,esk6_1(X2470)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
fof(c_0_11,plain,
~ p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(cCoq_2eInit_2eDatatypes_2enat)),
inference(fof_simplification,[status(thm)],['ZornsLemma.InfiniteTypes.nat_infinite']) ).
fof(c_0_12,plain,
! [X2448] :
( ( cCoq_2eInit_2eDatatypes_2enat___24t(X2448)
| ~ t(X2448,cCoq_2eInit_2eDatatypes_2enat) )
& ( t(X2448,cCoq_2eInit_2eDatatypes_2enat)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2448) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['$tdef_Coq.Init.Datatypes.nat'])])]) ).
cnf(c_0_13,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X3)
| ~ c_24__type__1386___24t(X1,X2)
| t(happ(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ cType___24t(X1)
| p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(X1))
| c_24__type__1386___24t(X1,esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
~ p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(cCoq_2eInit_2eDatatypes_2enat)),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X2479,X2480,X2481,X2482,X2483] :
( ( c_24__type__102___24t(X2482,X2483)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(happ(X2483,esk8_2(X2482,X2483))) )
& ( c_24__type__102___24t(X2482,X2483)
| t(esk8_2(X2482,X2483),X2482) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(happ(X2480,X2481))
| ~ t(X2481,X2479)
| ~ c_24__type__102___24t(X2479,X2480) ) ),
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)],['$_type_102'])])])])])])]) ).
cnf(c_0_17,plain,
( ~ t(X1,cCoq_2eInit_2eDatatypes_2enat)
| cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ cType___24t(X1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2)
| p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(X1))
| t(happ(esk6_1(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
cType___24t(cCoq_2eInit_2eDatatypes_2enat),
inference(split_conjunct,[status(thm)],['$_typeof_Coq.Init.Datatypes.nat']) ).
cnf(c_0_20,plain,
~ p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(cCoq_2eInit_2eDatatypes_2enat)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,negated_conjecture,
~ cZornsLemma_2eCountableTypes_2eCountableT___24a1(cCoq_2eInit_2eDatatypes_2enat),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
cnf(c_0_22,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(happ(X1,esk8_2(X2,X1)))
| c_24__type__102___24t(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| cCoq_2eInit_2eDatatypes_2enat___24t(happ(esk6_1(cCoq_2eInit_2eDatatypes_2enat),X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_24,plain,
( c_24__type__102___24t(X1,X2)
| t(esk8_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,negated_conjecture,
~ cZornsLemma_2eCountableTypes_2eCountableT___24a1(cCoq_2eInit_2eDatatypes_2enat),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X2443,X2444] :
( cZornsLemma_2eCountableTypes_2eCountableT___24a1(X2443)
| ~ cZornsLemma_2eFunctionProperties_2einjective___24a3(X2443,cCoq_2eInit_2eDatatypes_2enat,X2444)
| ~ c_24__type__102___24t(X2443,X2444)
| ~ cType___24t(X2443) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ZornsLemma.CountableTypes.intro_nat_injection'])])])]) ).
cnf(c_0_27,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk8_2(X1,esk6_1(cCoq_2eInit_2eDatatypes_2enat)))
| c_24__type__102___24t(X1,esk6_1(cCoq_2eInit_2eDatatypes_2enat)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( cCoq_2eInit_2eDatatypes_2enat___24t(esk8_2(cCoq_2eInit_2eDatatypes_2enat,X1))
| c_24__type__102___24t(cCoq_2eInit_2eDatatypes_2enat,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
fof(c_0_29,negated_conjecture,
~ cZornsLemma_2eCountableTypes_2eCountableT___24a1(cCoq_2eInit_2eDatatypes_2enat),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( ~ cZornsLemma_2eFunctionProperties_2einjective___24a3(X1,cCoq_2eInit_2eDatatypes_2enat,X2)
| ~ c_24__type__102___24t(X1,X2)
| ~ cType___24t(X1)
| cZornsLemma_2eCountableTypes_2eCountableT___24a1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
c_24__type__102___24t(cCoq_2eInit_2eDatatypes_2enat,esk6_1(cCoq_2eInit_2eDatatypes_2enat)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
~ cZornsLemma_2eCountableTypes_2eCountableT___24a1(cCoq_2eInit_2eDatatypes_2enat),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
~ cZornsLemma_2eFunctionProperties_2einjective___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,esk6_1(cCoq_2eInit_2eDatatypes_2enat)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_19])]),c_0_32]) ).
cnf(c_0_34,plain,
( ~ cType___24t(X1)
| p(cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(X1))
| cZornsLemma_2eFunctionProperties_2einjective___24a3(cCoq_2eInit_2eDatatypes_2enat,X1,esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_19])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV612+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n009.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Mon Sep 21 07:29:28 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.45 Running first-order theorem proving
% 0.10/0.46 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
% 10.82/10.55 % Version: 3.5.1
% 10.82/10.55 % Preprocessing class: FMLLSMLLSSSNFFN.
% 10.82/10.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.82/10.55 % Starting new_bool_3 with 900s (3) cores
% 10.82/10.55 % Starting new_bool_1 with 900s (3) cores
% 10.82/10.55 % Starting sh5l with 300s (1) cores
% 10.82/10.55 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 10.82/10.55 % new_bool_1 with pid 1220440 completed with status 9
% 10.82/10.55 % new_bool_3 with pid 1220439 completed with status 9
% 10.82/10.55 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with pid 1220442 completed with status 9
% 10.82/10.55 % sh5l with pid 1220441 completed with status 0
% 10.82/10.55 % Result found by sh5l
% 10.82/10.55 % Preprocessing class: FMLLSMLLSSSNFFN.
% 10.82/10.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.82/10.55 % Starting new_bool_3 with 900s (3) cores
% 10.82/10.55 % Starting new_bool_1 with 900s (3) cores
% 10.82/10.55 % Starting sh5l with 300s (1) cores
% 10.82/10.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 10.82/10.55 % SinE strategy is gf500_gu_R04_F100_L20000
% 10.82/10.55 % Search class: FGHSM-SMLM32-DFFFFFNN
% 10.82/10.55 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 10.82/10.55 % Starting SubtermCWHack with 28s (1) cores
% 10.82/10.55 % SubtermCWHack with pid 1220484 completed with status 0
% 10.82/10.55 % Result found by SubtermCWHack
% 10.82/10.55 % Preprocessing class: FMLLSMLLSSSNFFN.
% 10.82/10.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.82/10.55 % Starting new_bool_3 with 900s (3) cores
% 10.82/10.55 % Starting new_bool_1 with 900s (3) cores
% 10.82/10.55 % Starting sh5l with 300s (1) cores
% 10.82/10.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 10.82/10.55 % SinE strategy is gf500_gu_R04_F100_L20000
% 10.82/10.55 % Search class: FGHSM-SMLM32-DFFFFFNN
% 10.82/10.55 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 10.82/10.55 % Starting SubtermCWHack with 28s (1) cores
% 10.82/10.55 % Preprocessing time : 0.074 s
% 10.82/10.55
% 10.82/10.55 % Proof found!
% 10.82/10.55 % SZS status Theorem
% 10.82/10.55 % SZS output start CNFRefutation
% See solution above
% 10.82/10.55 % Parsed axioms : 2853
% 10.82/10.55 % Removed by relevancy pruning/SinE : 2159
% 10.82/10.55 % Initial clauses : 3092
% 10.82/10.55 % Removed in clause preprocessing : 142
% 10.82/10.55 % Initial clauses in saturation : 2950
% 10.82/10.55 % Processed clauses : 29456
% 10.82/10.55 % ...of these trivial : 210
% 10.82/10.55 % ...subsumed : 23100
% 10.82/10.55 % ...remaining for further processing : 6146
% 10.82/10.55 % Other redundant clauses eliminated : 2161
% 10.82/10.55 % Clauses deleted for lack of memory : 0
% 10.82/10.55 % Backward-subsumed : 156
% 10.82/10.55 % Backward-rewritten : 189
% 10.82/10.55 % Generated clauses : 180767
% 10.82/10.55 % ...of the previous two non-redundant : 172249
% 10.82/10.55 % ...aggressively subsumed : 0
% 10.82/10.55 % Contextual simplify-reflections : 176
% 10.82/10.55 % Paramodulations : 178486
% 10.82/10.55 % Factorizations : 11
% 10.82/10.55 % NegExts : 0
% 10.82/10.55 % Equation resolutions : 2269
% 10.82/10.55 % Disequality decompositions : 0
% 10.82/10.55 % Total rewrite steps : 76604
% 10.82/10.55 % ...of those cached : 75932
% 10.82/10.55 % Propositional unsat checks : 0
% 10.82/10.55 % Propositional check models : 0
% 10.82/10.55 % Propositional check unsatisfiable : 0
% 10.82/10.55 % Propositional clauses : 0
% 10.82/10.55 % Propositional clauses after purity: 0
% 10.82/10.55 % Propositional unsat core size : 0
% 10.82/10.55 % Propositional preprocessing time : 0.000
% 10.82/10.55 % Propositional encoding time : 0.000
% 10.82/10.55 % Propositional solver time : 0.000
% 10.82/10.55 % Success case prop preproc time : 0.000
% 10.82/10.55 % Success case prop encoding time : 0.000
% 10.82/10.55 % Success case prop solver time : 0.000
% 10.82/10.55 % Current number of processed clauses : 5790
% 10.82/10.55 % Positive orientable unit clauses : 368
% 10.82/10.55 % Positive unorientable unit clauses: 0
% 10.82/10.55 % Negative unit clauses : 61
% 10.82/10.55 % Non-unit-clauses : 5361
% 10.82/10.55 % Current number of unprocessed clauses: 145317
% 10.82/10.55 % ...number of literals in the above : 662387
% 10.82/10.55 % Current number of archived formulas : 0
% 10.82/10.55 % Current number of archived clauses : 346
% 10.82/10.55 % Clause-clause subsumption calls (NU) : 5935209
% 10.82/10.55 % Rec. Clause-clause subsumption calls : 2056094
% 10.82/10.55 % Non-unit clause-clause subsumptions : 20988
% 10.82/10.55 % Unit Clause-clause subsumption calls : 87061
% 10.82/10.55 % Rewrite failures with RHS unbound : 0
% 10.82/10.55 % BW rewrite match attempts : 869
% 10.82/10.55 % BW rewrite match successes : 109
% 10.82/10.55 % Condensation attempts : 0
% 10.82/10.55 % Condensation successes : 0
% 10.82/10.55 % Termbank termtop insertions : 3350952
% 10.82/10.55 % Search garbage collected termcells : 63059
% 10.82/10.55
% 10.82/10.55 % -------------------------------------------------
% 10.82/10.55 % User time : 9.571 s
% 10.82/10.55 % System time : 0.267 s
% 10.82/10.55 % Total time : 9.838 s
% 10.82/10.55 % Maximum resident set size: 20076 pages
% 10.82/10.55
% 10.82/10.55 % -------------------------------------------------
% 10.82/10.55 % User time : 10.181 s
% 10.82/10.55 % System time : 0.525 s
% 10.82/10.55 % Total time : 10.706 s
% 10.82/10.55 % Maximum resident set size: 11008 pages
% 10.82/10.55 % E exiting
%------------------------------------------------------------------------------