%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV629+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:15:27 PM UTC 2026
% Result : Theorem 49.72s 50.12s
% Output : CNFRefutation 49.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 50 ( 3 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 45 ( 16 ~; 17 |; 6 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 3 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [X42,X134] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X42,X134)
<=> ! [X131] :
( t(X131,X42)
=> p(happ(happ(X134,X131),X131)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Relations.Relation_Definitions.reflexive') ).
fof('$adef_HahnSets.set_subset_$a3',axiom,
! [X2813,X2814,X2815] :
( p(happ(happ(happ(cHahnSets_2eset__subset,X2813),X2814),X2815))
<=> cHahnSets_2eset__subset___24a3(X2813,X2814,X2815) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HahnSets.set_subset_$a3') ).
fof('$_def_HahnSets.set_subset',axiom,
! [X42,X452,X453] :
( cHahnSets_2eset__subset___24a3(X42,X452,X453)
<=> ! [X24] :
( t(X24,X42)
=> ( p(happ(X452,X24))
=> p(happ(X453,X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_HahnSets.set_subset') ).
fof('_HAMMER_GOAL',conjecture,
cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,cHahnSets_2eset__subset___24a1(cA)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('$adef_HahnSets.set_subset_$a1',axiom,
! [X2813] : happ(cHahnSets_2eset__subset,X2813) = cHahnSets_2eset__subset___24a1(X2813),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HahnSets.set_subset_$a1') ).
fof(c_0_5,plain,
! [X2886,X2887,X2888,X2889,X2890] :
( ( ~ cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X2886,X2887)
| ~ t(X2888,X2886)
| p(happ(happ(X2887,X2888),X2888)) )
& ( t(esk1_2(X2889,X2890),X2889)
| cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X2889,X2890) )
& ( ~ p(happ(happ(X2890,esk1_2(X2889,X2890)),esk1_2(X2889,X2890)))
| cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X2889,X2890) ) ),
inference(distribute,[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)],['$_def_Coq.Relations.Relation_Definitions.reflexive'])])])])])]) ).
fof(c_0_6,plain,
! [X2894,X2895,X2896] :
( ( ~ p(happ(happ(happ(cHahnSets_2eset__subset,X2894),X2895),X2896))
| cHahnSets_2eset__subset___24a3(X2894,X2895,X2896) )
& ( ~ cHahnSets_2eset__subset___24a3(X2894,X2895,X2896)
| p(happ(happ(happ(cHahnSets_2eset__subset,X2894),X2895),X2896)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['$adef_HahnSets.set_subset_$a3'])]) ).
fof(c_0_7,plain,
! [X2905,X2906,X2907,X2908,X2909,X2910,X2911] :
( ( ~ cHahnSets_2eset__subset___24a3(X2905,X2906,X2907)
| ~ t(X2908,X2905)
| ~ p(happ(X2906,X2908))
| p(happ(X2907,X2908)) )
& ( t(esk5_3(X2909,X2910,X2911),X2909)
| cHahnSets_2eset__subset___24a3(X2909,X2910,X2911) )
& ( p(happ(X2910,esk5_3(X2909,X2910,X2911)))
| cHahnSets_2eset__subset___24a3(X2909,X2910,X2911) )
& ( ~ p(happ(X2911,esk5_3(X2909,X2910,X2911)))
| cHahnSets_2eset__subset___24a3(X2909,X2910,X2911) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_HahnSets.set_subset'])])])])])]) ).
fof(c_0_8,negated_conjecture,
~ cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,cHahnSets_2eset__subset___24a1(cA)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['_HAMMER_GOAL'])]) ).
fof(c_0_9,plain,
! [X2892] : happ(cHahnSets_2eset__subset,X2892) = cHahnSets_2eset__subset___24a1(X2892),
inference(variable_rename,[status(thm)],['$adef_HahnSets.set_subset_$a1']) ).
cnf(c_0_10,plain,
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X2,X1)
| ~ p(happ(happ(X1,esk1_2(X2,X1)),esk1_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( p(happ(happ(happ(cHahnSets_2eset__subset,X1),X2),X3))
| ~ cHahnSets_2eset__subset___24a3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( cHahnSets_2eset__subset___24a3(X2,X3,X1)
| ~ p(happ(X1,esk5_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( p(happ(X1,esk5_3(X2,X1,X3)))
| cHahnSets_2eset__subset___24a3(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
~ cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,cHahnSets_2eset__subset___24a1(cA)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
happ(cHahnSets_2eset__subset,X1) = cHahnSets_2eset__subset___24a1(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X1,happ(cHahnSets_2eset__subset,X2))
| ~ cHahnSets_2eset__subset___24a3(X2,esk1_2(X1,happ(cHahnSets_2eset__subset,X2)),esk1_2(X1,happ(cHahnSets_2eset__subset,X2))) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
cHahnSets_2eset__subset___24a3(X1,X2,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
~ cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,happ(cHahnSets_2eset__subset,cA)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X1,happ(cHahnSets_2eset__subset,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV629+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 23:03:56 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 49.72/50.12 % Version : CSE_E---1.7
% 49.72/50.12 % Problem : theBenchmark.p
% 49.72/50.12 % SZS status Theorem for theBenchmark.p
% 49.72/50.12 % SZS output start CNFRefutation
% See solution above
% 49.72/50.12 % Total time : 49.862s
%------------------------------------------------------------------------------