%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV667+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Tue Sep 29 12:58:31 PM UTC 2026
% Result : Theorem 7.37s 2.23s
% Output : Refutation 8.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 115 ( 29 unt; 4 def)
% Number of atoms : 334 ( 28 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 391 ( 172 ~; 167 |; 23 &)
% ( 11 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 5 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 125 ( 0 sgn 117 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f243,axiom,
! [X0] : cQuotients_2eInducedFunction2_2eprojf___24a1(X0) = cQuotients_2equotient__projection___24a3(cB,cS,cf___24a1(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Quotients.InducedFunction2.projf') ).
fof(f651,axiom,
! [X0] :
( c_24__type__163663___24t(X0)
<=> ! [X1] :
( cA___24t(X1)
=> cB___24t(happ(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_163663') ).
fof(f916,axiom,
! [X0,X1,X2] :
( c_24__type__92___24t(X0,X1,X2)
<=> ! [X3] :
( t(X3,X0)
=> t(happ(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_92') ).
fof(f935,axiom,
cType___24t(cB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_B') ).
fof(f1579,axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cB,cS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_S') ).
fof(f1580,axiom,
c_24__type__163663___24t(cf),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_f') ).
fof(f1873,axiom,
! [X0] :
( cType___24t(X0)
=> ! [X1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(X0,X1)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(X0,X1)
=> ! [X2] :
( t(X2,X0)
=> ! [X3] :
( t(X3,X0)
=> ( p(happ(happ(X1,X2),X3))
=> cQuotients_2equotient__projection___24a3(X0,X1,X2) = cQuotients_2equotient__projection___24a3(X0,X1,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Quotients.quotient_projection_collapses_R') ).
fof(f1880,axiom,
cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(cB,cS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivS) ).
fof(f1881,axiom,
! [X0] :
( cA___24t(X0)
=> ! [X1] :
( cA___24t(X1)
=> ( cR___24a2(X0,X1)
=> cS___24a2(cf___24a1(X0),cf___24a1(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined2) ).
fof(f2191,axiom,
! [X0] : happ(cQuotients_2eInducedFunction2_2eprojf,X0) = cQuotients_2eInducedFunction2_2eprojf___24a1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Quotients.InducedFunction2.projf_$a1') ).
fof(f2246,axiom,
! [X0,X1] :
( p(happ(happ(cS,X0),X1))
<=> cS___24a2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_S_$a2') ).
fof(f2322,axiom,
! [X0] : happ(cf,X0) = cf___24a1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_f_$a1') ).
fof(f2657,axiom,
! [X0] :
( cB___24t(X0)
<=> t(X0,cB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_B') ).
fof(f2700,axiom,
! [X0] :
( cA___24t(X0)
<=> t(X0,cA) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_A') ).
fof(f2863,conjecture,
! [X0] :
( cA___24t(X0)
=> ! [X1] :
( cA___24t(X1)
=> ( cR___24a2(X0,X1)
=> cQuotients_2eInducedFunction2_2eprojf___24a1(X0) = cQuotients_2eInducedFunction2_2eprojf___24a1(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof(f2864,negated_conjecture,
~ ! [X0] :
( cA___24t(X0)
=> ! [X1] :
( cA___24t(X1)
=> ( cR___24a2(X0,X1)
=> cQuotients_2eInducedFunction2_2eprojf___24a1(X0) = cQuotients_2eInducedFunction2_2eprojf___24a1(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f2863]) ).
fof(f2866,plain,
! [X0,X1] :
( cS___24a2(X0,X1)
=> p(happ(happ(cS,X0),X1)) ),
inference(unused_predicate_definition_removal,[],[f2246]) ).
fof(f2872,plain,
? [X0] :
( ? [X1] :
( cQuotients_2eInducedFunction2_2eprojf___24a1(X0) != cQuotients_2eInducedFunction2_2eprojf___24a1(X1)
& cR___24a2(X0,X1)
& cA___24t(X1) )
& cA___24t(X0) ),
inference(ennf_transformation,[],[f2864]) ).
fof(f2873,plain,
? [X0] :
( ? [X1] :
( cQuotients_2eInducedFunction2_2eprojf___24a1(X0) != cQuotients_2eInducedFunction2_2eprojf___24a1(X1)
& cR___24a2(X0,X1)
& cA___24t(X1) )
& cA___24t(X0) ),
inference(flattening,[],[f2872]) ).
fof(f2874,plain,
! [X0] :
( ! [X1] :
( cS___24a2(cf___24a1(X0),cf___24a1(X1))
| ~ cR___24a2(X0,X1)
| ~ cA___24t(X1) )
| ~ cA___24t(X0) ),
inference(ennf_transformation,[],[f1881]) ).
fof(f2875,plain,
! [X0] :
( ! [X1] :
( cS___24a2(cf___24a1(X0),cf___24a1(X1))
| ~ cR___24a2(X0,X1)
| ~ cA___24t(X1) )
| ~ cA___24t(X0) ),
inference(flattening,[],[f2874]) ).
fof(f2877,plain,
! [X0] :
( c_24__type__163663___24t(X0)
<=> ! [X1] :
( cB___24t(happ(X0,X1))
| ~ cA___24t(X1) ) ),
inference(ennf_transformation,[],[f651]) ).
fof(f2878,plain,
! [X0,X1] :
( p(happ(happ(cS,X0),X1))
| ~ cS___24a2(X0,X1) ),
inference(ennf_transformation,[],[f2866]) ).
fof(f2881,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( cQuotients_2equotient__projection___24a3(X0,X1,X2) = cQuotients_2equotient__projection___24a3(X0,X1,X3)
| ~ p(happ(happ(X1,X2),X3))
| ~ t(X3,X0) )
| ~ t(X2,X0) )
| ~ cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(X0,X1)
| ~ cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(X0,X1) )
| ~ cType___24t(X0) ),
inference(ennf_transformation,[],[f1873]) ).
fof(f2882,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( cQuotients_2equotient__projection___24a3(X0,X1,X2) = cQuotients_2equotient__projection___24a3(X0,X1,X3)
| ~ p(happ(happ(X1,X2),X3))
| ~ t(X3,X0) )
| ~ t(X2,X0) )
| ~ cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(X0,X1)
| ~ cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(X0,X1) )
| ~ cType___24t(X0) ),
inference(flattening,[],[f2881]) ).
fof(f2894,plain,
! [X0,X1,X2] :
( c_24__type__92___24t(X0,X1,X2)
<=> ! [X3] :
( t(happ(X2,X3),X1)
| ~ t(X3,X0) ) ),
inference(ennf_transformation,[],[f916]) ).
fof(f2900,plain,
( cQuotients_2eInducedFunction2_2eprojf___24a1(sK1) != cQuotients_2eInducedFunction2_2eprojf___24a1(sK2)
& cR___24a2(sK1,sK2)
& cA___24t(sK2)
& cA___24t(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f2873]) ).
fof(f2901,plain,
! [X0] :
( ( cA___24t(X0)
| ~ t(X0,cA) )
& ( t(X0,cA)
| ~ cA___24t(X0) ) ),
inference(nnf_transformation,[],[f2700]) ).
fof(f2905,plain,
! [X0] :
( ( c_24__type__163663___24t(X0)
| ? [X1] :
( ~ cB___24t(happ(X0,X1))
& cA___24t(X1) ) )
& ( ! [X1] :
( cB___24t(happ(X0,X1))
| ~ cA___24t(X1) )
| ~ c_24__type__163663___24t(X0) ) ),
inference(nnf_transformation,[],[f2877]) ).
fof(f2906,plain,
! [X0] :
( ( c_24__type__163663___24t(X0)
| ? [X1] :
( ~ cB___24t(happ(X0,X1))
& cA___24t(X1) ) )
& ( ! [X2] :
( cB___24t(happ(X0,X2))
| ~ cA___24t(X2) )
| ~ c_24__type__163663___24t(X0) ) ),
inference(rectify,[],[f2905]) ).
fof(f2907,plain,
! [X0] :
( ( c_24__type__163663___24t(X0)
| ( ~ cB___24t(happ(X0,sK4(X0)))
& cA___24t(sK4(X0)) ) )
& ( ! [X2] :
( cB___24t(happ(X0,X2))
| ~ cA___24t(X2) )
| ~ c_24__type__163663___24t(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f2906]) ).
fof(f2909,plain,
! [X0] :
( ( cB___24t(X0)
| ~ t(X0,cB) )
& ( t(X0,cB)
| ~ cB___24t(X0) ) ),
inference(nnf_transformation,[],[f2657]) ).
fof(f2928,plain,
! [X0,X1,X2] :
( ( c_24__type__92___24t(X0,X1,X2)
| ? [X3] :
( ~ t(happ(X2,X3),X1)
& t(X3,X0) ) )
& ( ! [X3] :
( t(happ(X2,X3),X1)
| ~ t(X3,X0) )
| ~ c_24__type__92___24t(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f2894]) ).
fof(f2929,plain,
! [X0,X1,X2] :
( ( c_24__type__92___24t(X0,X1,X2)
| ? [X3] :
( ~ t(happ(X2,X3),X1)
& t(X3,X0) ) )
& ( ! [X4] :
( t(happ(X2,X4),X1)
| ~ t(X4,X0) )
| ~ c_24__type__92___24t(X0,X1,X2) ) ),
inference(rectify,[],[f2928]) ).
fof(f2930,plain,
! [X0,X1,X2] :
( ( c_24__type__92___24t(X0,X1,X2)
| ( ~ t(happ(X2,sK22(X0,X1,X2)),X1)
& t(sK22(X0,X1,X2),X0) ) )
& ( ! [X4] :
( t(happ(X2,X4),X1)
| ~ t(X4,X0) )
| ~ c_24__type__92___24t(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X3,sK22(X0,X1,X2))],[f2929]) ).
fof(f2937,plain,
cA___24t(sK1),
inference(cnf_transformation,[],[f2900]) ).
fof(f2938,plain,
cA___24t(sK2),
inference(cnf_transformation,[],[f2900]) ).
fof(f2939,plain,
cR___24a2(sK1,sK2),
inference(cnf_transformation,[],[f2900]) ).
fof(f2940,plain,
cQuotients_2eInducedFunction2_2eprojf___24a1(sK1) != cQuotients_2eInducedFunction2_2eprojf___24a1(sK2),
inference(cnf_transformation,[],[f2900]) ).
fof(f2941,plain,
! [X0] : cQuotients_2eInducedFunction2_2eprojf___24a1(X0) = happ(cQuotients_2eInducedFunction2_2eprojf,X0),
inference(cnf_transformation,[],[f2191]) ).
fof(f2942,plain,
! [X0] : cQuotients_2eInducedFunction2_2eprojf___24a1(X0) = cQuotients_2equotient__projection___24a3(cB,cS,cf___24a1(X0)),
inference(cnf_transformation,[],[f243]) ).
fof(f2943,plain,
! [X0] :
( t(X0,cA)
| ~ cA___24t(X0) ),
inference(cnf_transformation,[],[f2901]) ).
fof(f2944,plain,
! [X0] :
( ~ t(X0,cA)
| cA___24t(X0) ),
inference(cnf_transformation,[],[f2901]) ).
fof(f2945,plain,
! [X0,X1] :
( cS___24a2(cf___24a1(X0),cf___24a1(X1))
| ~ cR___24a2(X0,X1)
| ~ cA___24t(X1)
| ~ cA___24t(X0) ),
inference(cnf_transformation,[],[f2875]) ).
fof(f2949,plain,
! [X2,X0] :
( cB___24t(happ(X0,X2))
| ~ cA___24t(X2)
| ~ c_24__type__163663___24t(X0) ),
inference(cnf_transformation,[],[f2907]) ).
fof(f2955,plain,
! [X0] :
( t(X0,cB)
| ~ cB___24t(X0) ),
inference(cnf_transformation,[],[f2909]) ).
fof(f2957,plain,
cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(cB,cS),
inference(cnf_transformation,[],[f1880]) ).
fof(f2958,plain,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cB,cS),
inference(cnf_transformation,[],[f1579]) ).
fof(f2959,plain,
cType___24t(cB),
inference(cnf_transformation,[],[f935]) ).
fof(f2960,plain,
! [X0,X1] :
( p(happ(happ(cS,X0),X1))
| ~ cS___24a2(X0,X1) ),
inference(cnf_transformation,[],[f2878]) ).
fof(f2961,plain,
! [X0] : cf___24a1(X0) = happ(cf,X0),
inference(cnf_transformation,[],[f2322]) ).
fof(f2963,plain,
! [X2,X3,X0,X1] :
( ~ p(happ(happ(X1,X2),X3))
| cQuotients_2equotient__projection___24a3(X0,X1,X2) = cQuotients_2equotient__projection___24a3(X0,X1,X3)
| ~ t(X3,X0)
| ~ t(X2,X0)
| ~ cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(X0,X1)
| ~ cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(X0,X1)
| ~ cType___24t(X0) ),
inference(cnf_transformation,[],[f2882]) ).
fof(f3009,plain,
c_24__type__163663___24t(cf),
inference(cnf_transformation,[],[f1580]) ).
fof(f3013,plain,
! [X2,X0,X1,X4] :
( ~ c_24__type__92___24t(X0,X1,X2)
| ~ t(X4,X0)
| t(happ(X2,X4),X1) ),
inference(cnf_transformation,[],[f2930]) ).
fof(f3014,plain,
! [X2,X0,X1] :
( t(sK22(X0,X1,X2),X0)
| c_24__type__92___24t(X0,X1,X2) ),
inference(cnf_transformation,[],[f2930]) ).
fof(f3015,plain,
! [X2,X0,X1] :
( ~ t(happ(X2,sK22(X0,X1,X2)),X1)
| c_24__type__92___24t(X0,X1,X2) ),
inference(cnf_transformation,[],[f2930]) ).
fof(f3035,plain,
happ(cQuotients_2eInducedFunction2_2eprojf,sK1) != happ(cQuotients_2eInducedFunction2_2eprojf,sK2),
inference(definition_unfolding,[],[f2940,f2941,f2941]) ).
fof(f3036,plain,
! [X0] : happ(cQuotients_2eInducedFunction2_2eprojf,X0) = cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,X0)),
inference(definition_unfolding,[],[f2942,f2941,f2961]) ).
fof(f3037,plain,
! [X0,X1] :
( cS___24a2(happ(cf,X0),happ(cf,X1))
| ~ cR___24a2(X0,X1)
| ~ cA___24t(X1)
| ~ cA___24t(X0) ),
inference(definition_unfolding,[],[f2945,f2961,f2961]) ).
fof(f3074,plain,
! [X0,X1] :
( cA___24t(sK22(cA,X0,X1))
| c_24__type__92___24t(cA,X0,X1) ),
inference(resolution,[],[f3014,f2944]) ).
fof(f3087,plain,
! [X0,X1] :
( ~ cB___24t(happ(X1,sK22(X0,cB,X1)))
| c_24__type__92___24t(X0,cB,X1) ),
inference(resolution,[],[f3015,f2955]) ).
fof(f3095,plain,
! [X0,X1] :
( ~ cA___24t(sK22(X0,cB,X1))
| c_24__type__92___24t(X0,cB,X1)
| ~ c_24__type__163663___24t(X1) ),
inference(resolution,[],[f3087,f2949]) ).
fof(f3160,plain,
! [X0] :
( c_24__type__92___24t(cA,cB,X0)
| ~ c_24__type__163663___24t(X0)
| c_24__type__92___24t(cA,cB,X0) ),
inference(resolution,[],[f3095,f3074]) ).
fof(f3161,plain,
! [X0] :
( c_24__type__92___24t(cA,cB,X0)
| ~ c_24__type__163663___24t(X0) ),
inference(duplicate_literal_removal,[],[f3160]) ).
fof(f3172,plain,
! [X0,X1] :
( t(happ(X0,X1),cB)
| ~ t(X1,cA)
| ~ c_24__type__163663___24t(X0) ),
inference(resolution,[],[f3161,f3013]) ).
fof(f3174,plain,
! [X2,X0,X1] :
( ~ cS___24a2(X1,X2)
| ~ t(X2,X0)
| ~ t(X1,X0)
| ~ cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(X0,cS)
| ~ cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(X0,cS)
| ~ cType___24t(X0)
| cQuotients_2equotient__projection___24a3(X0,cS,X1) = cQuotients_2equotient__projection___24a3(X0,cS,X2) ),
inference(resolution,[],[f2963,f2960]) ).
fof(f3374,plain,
! [X2,X0,X1] :
( ~ t(happ(cf,X2),X1)
| ~ t(happ(cf,X0),X1)
| ~ cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(X1,cS)
| ~ cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(X1,cS)
| ~ cType___24t(X1)
| cQuotients_2equotient__projection___24a3(X1,cS,happ(cf,X2)) = cQuotients_2equotient__projection___24a3(X1,cS,happ(cf,X0))
| ~ cR___24a2(X2,X0)
| ~ cA___24t(X0)
| ~ cA___24t(X2) ),
inference(resolution,[],[f3174,f3037]) ).
fof(f3390,definition,
( spl25_16
<=> t(sK2,cA) ),
introduced(definition,[new_symbols(definition,[spl25_16])],[avatar_definition]) ).
fof(f3391,plain,
( t(sK2,cA)
| ~ spl25_16 ),
inference(avatar_component_clause,[],[f3390]) ).
fof(f3392,plain,
( ~ t(sK2,cA)
| spl25_16 ),
inference(avatar_component_clause,[],[f3390]) ).
fof(f3394,definition,
( spl25_17
<=> t(sK1,cA) ),
introduced(definition,[new_symbols(definition,[spl25_17])],[avatar_definition]) ).
fof(f3395,plain,
( t(sK1,cA)
| ~ spl25_17 ),
inference(avatar_component_clause,[],[f3394]) ).
fof(f3396,plain,
( ~ t(sK1,cA)
| spl25_17 ),
inference(avatar_component_clause,[],[f3394]) ).
fof(f3407,plain,
( ~ cA___24t(sK2)
| spl25_16 ),
inference(resolution,[],[f3392,f2943]) ).
fof(f3408,plain,
( $false
| spl25_16 ),
inference(forward_subsumption_resolution,[],[f3407,f2938]) ).
fof(f3409,plain,
spl25_16,
inference(avatar_contradiction_clause,[],[f3408]) ).
fof(f3421,plain,
( ~ cA___24t(sK1)
| spl25_17 ),
inference(resolution,[],[f3396,f2943]) ).
fof(f3422,plain,
( $false
| spl25_17 ),
inference(forward_subsumption_resolution,[],[f3421,f2937]) ).
fof(f3423,plain,
spl25_17,
inference(avatar_contradiction_clause,[],[f3422]) ).
fof(f3499,definition,
( spl25_18
<=> t(happ(cf,sK2),cB) ),
introduced(definition,[new_symbols(definition,[spl25_18])],[avatar_definition]) ).
fof(f3500,plain,
( t(happ(cf,sK2),cB)
| ~ spl25_18 ),
inference(avatar_component_clause,[],[f3499]) ).
fof(f3501,plain,
( ~ t(happ(cf,sK2),cB)
| spl25_18 ),
inference(avatar_component_clause,[],[f3499]) ).
fof(f3513,plain,
( ~ t(sK2,cA)
| ~ c_24__type__163663___24t(cf)
| spl25_18 ),
inference(resolution,[],[f3501,f3172]) ).
fof(f3515,plain,
( ~ c_24__type__163663___24t(cf)
| ~ spl25_16
| spl25_18 ),
inference(forward_subsumption_resolution,[],[f3513,f3391]) ).
fof(f3516,plain,
( $false
| ~ spl25_16
| spl25_18 ),
inference(forward_subsumption_resolution,[],[f3515,f3009]) ).
fof(f3517,plain,
( ~ spl25_16
| spl25_18 ),
inference(avatar_contradiction_clause,[],[f3516]) ).
fof(f3552,definition,
( spl25_20
<=> t(happ(cf,sK1),cB) ),
introduced(definition,[new_symbols(definition,[spl25_20])],[avatar_definition]) ).
fof(f3553,plain,
( t(happ(cf,sK1),cB)
| ~ spl25_20 ),
inference(avatar_component_clause,[],[f3552]) ).
fof(f3554,plain,
( ~ t(happ(cf,sK1),cB)
| spl25_20 ),
inference(avatar_component_clause,[],[f3552]) ).
fof(f3569,plain,
( ~ t(sK1,cA)
| ~ c_24__type__163663___24t(cf)
| spl25_20 ),
inference(resolution,[],[f3554,f3172]) ).
fof(f3571,plain,
( ~ c_24__type__163663___24t(cf)
| ~ spl25_17
| spl25_20 ),
inference(forward_subsumption_resolution,[],[f3569,f3395]) ).
fof(f3572,plain,
( $false
| ~ spl25_17
| spl25_20 ),
inference(forward_subsumption_resolution,[],[f3571,f3009]) ).
fof(f3573,plain,
( ~ spl25_17
| spl25_20 ),
inference(avatar_contradiction_clause,[],[f3572]) ).
fof(f4265,plain,
( ! [X0] :
( ~ t(happ(cf,X0),cB)
| ~ cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(cB,cS)
| ~ cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cB,cS)
| ~ cType___24t(cB)
| cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,X0)) = cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,sK1))
| ~ cR___24a2(sK1,X0)
| ~ cA___24t(X0)
| ~ cA___24t(sK1) )
| ~ spl25_20 ),
inference(resolution,[],[f3374,f3553]) ).
fof(f4278,plain,
( ! [X0] :
( ~ t(happ(cf,X0),cB)
| ~ cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cB,cS)
| ~ cType___24t(cB)
| cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,X0)) = cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,sK1))
| ~ cR___24a2(sK1,X0)
| ~ cA___24t(X0)
| ~ cA___24t(sK1) )
| ~ spl25_20 ),
inference(forward_subsumption_resolution,[],[f4265,f2957]) ).
fof(f4282,plain,
( ! [X0] :
( ~ t(happ(cf,X0),cB)
| ~ cType___24t(cB)
| cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,X0)) = cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,sK1))
| ~ cR___24a2(sK1,X0)
| ~ cA___24t(X0)
| ~ cA___24t(sK1) )
| ~ spl25_20 ),
inference(forward_subsumption_resolution,[],[f4278,f2958]) ).
fof(f4286,plain,
( ! [X0] :
( ~ t(happ(cf,X0),cB)
| cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,X0)) = cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,sK1))
| ~ cR___24a2(sK1,X0)
| ~ cA___24t(X0)
| ~ cA___24t(sK1) )
| ~ spl25_20 ),
inference(forward_subsumption_resolution,[],[f4282,f2959]) ).
fof(f4290,plain,
( ! [X0] :
( ~ t(happ(cf,X0),cB)
| cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,X0)) = cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,sK1))
| ~ cR___24a2(sK1,X0)
| ~ cA___24t(X0) )
| ~ spl25_20 ),
inference(forward_subsumption_resolution,[],[f4286,f2937]) ).
fof(f4294,plain,
( ! [X0] :
( happ(cQuotients_2eInducedFunction2_2eprojf,sK1) = cQuotients_2equotient__projection___24a3(cB,cS,happ(cf,X0))
| ~ t(happ(cf,X0),cB)
| ~ cR___24a2(sK1,X0)
| ~ cA___24t(X0) )
| ~ spl25_20 ),
inference(forward_demodulation,[],[f4290,f3036]) ).
fof(f4297,plain,
( ! [X0] :
( ~ t(happ(cf,X0),cB)
| happ(cQuotients_2eInducedFunction2_2eprojf,X0) = happ(cQuotients_2eInducedFunction2_2eprojf,sK1)
| ~ cR___24a2(sK1,X0)
| ~ cA___24t(X0) )
| ~ spl25_20 ),
inference(forward_demodulation,[],[f4294,f3036]) ).
fof(f4399,plain,
( happ(cQuotients_2eInducedFunction2_2eprojf,sK1) = happ(cQuotients_2eInducedFunction2_2eprojf,sK2)
| ~ cR___24a2(sK1,sK2)
| ~ cA___24t(sK2)
| ~ spl25_18
| ~ spl25_20 ),
inference(resolution,[],[f4297,f3500]) ).
fof(f4404,plain,
( ~ cR___24a2(sK1,sK2)
| ~ cA___24t(sK2)
| ~ spl25_18
| ~ spl25_20 ),
inference(forward_subsumption_resolution,[],[f4399,f3035]) ).
fof(f4406,plain,
( ~ cA___24t(sK2)
| ~ spl25_18
| ~ spl25_20 ),
inference(forward_subsumption_resolution,[],[f4404,f2939]) ).
fof(f4407,plain,
( $false
| ~ spl25_18
| ~ spl25_20 ),
inference(forward_subsumption_resolution,[],[f4406,f2938]) ).
fof(f4408,plain,
( ~ spl25_18
| ~ spl25_20 ),
inference(avatar_contradiction_clause,[],[f4407]) ).
cnf(s12,plain,
spl25_16,
inference(sat_conversion,[],[f3409]) ).
cnf(s13,plain,
spl25_17,
inference(sat_conversion,[],[f3423]) ).
cnf(s15,plain,
( ~ spl25_16
| spl25_18 ),
inference(sat_conversion,[],[f3517]) ).
cnf(s17,plain,
( ~ spl25_17
| spl25_20 ),
inference(sat_conversion,[],[f3573]) ).
cnf(s31,plain,
( ~ spl25_18
| ~ spl25_20 ),
inference(sat_conversion,[],[f4408]) ).
cnf(s33,plain,
spl25_20,
inference(rat,[],[s17,s13]) ).
cnf(s36,plain,
~ spl25_18,
inference(rat,[],[s31,s33]) ).
cnf(s37,plain,
~ spl25_16,
inference(rat,[],[s15,s36]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s12,s37]) ).
fof(f4409,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV667+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 06:52:10 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.37/2.23 % (2055802)Detected formulas, will run a generic FOF schedule.
% 7.37/2.23 % (2055850)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3340898085:i=141193_2997 on theBenchmark for (2997ds/141193Mi)
% 7.37/2.23 % (2055856)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3265625087:s2a=on:i=139:gtg=position_2997 on theBenchmark for (2997ds/139Mi)
% 7.37/2.23 % (2055855)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3046865902:i=119:av=off:ss=axioms_2997 on theBenchmark for (2997ds/119Mi)
% 7.37/2.23 % (2055854)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=52096388:i=109:sd=1:ins=1:gsp=on:ss=axioms_2997 on theBenchmark for (2997ds/109Mi)
% 7.37/2.23 % (2055852)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2788353342:i=141695:sd=1:nm=32:gsp=on:ss=included_2997 on theBenchmark for (2997ds/141695Mi)
% 7.37/2.23 % (2055851)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2511139931:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2997 on theBenchmark for (2997ds/134677Mi)
% 7.37/2.23 % (2055856)Instruction limit reached!
% 7.37/2.23 % (2055856)------------------------------
% 7.37/2.23 % (2055856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.23 % (2055856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.23 % (2055856)CaDiCaL version: 2.1.3
% 7.37/2.23 % (2055856)Termination reason: Instruction limit
% 7.37/2.23 % (2055856)Termination phase: Preprocessing 3
% 7.37/2.23 % (2055856)Time elapsed: 0.069 s
% 7.37/2.23 % (2055856)Peak memory usage: 93 MB
% 7.37/2.23 % (2055856)Instructions burned: 139 (million)
% 7.37/2.23 % (2055854)Refutation not found, incomplete strategy
% 7.37/2.23 % (2055854)------------------------------
% 7.37/2.23 % (2055854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.23 % (2055854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.23 % (2055854)CaDiCaL version: 2.1.3
% 7.37/2.23 % (2055854)Termination reason: Refutation not found, incomplete strategy
% 7.37/2.23 % (2055854)Time elapsed: 0.022 s
% 7.37/2.23 % (2055854)Peak memory usage: 91 MB
% 7.37/2.23 % (2055854)Instructions burned: 29 (million)
% 7.37/2.23 % (2055858)dis-21_1_sil=8000:lcm=predicate:random_seed=1948411187:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2997 on theBenchmark for (2997ds/129Mi)
% 7.37/2.23 % (2055855)Instruction limit reached!
% 7.37/2.23 % (2055855)------------------------------
% 7.37/2.23 % (2055855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.23 % (2055855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.23 % (2055855)CaDiCaL version: 2.1.3
% 7.37/2.23 % (2055855)Termination reason: Instruction limit
% 7.37/2.23 % (2055855)Termination phase: Saturation
% 7.37/2.23 % (2055855)Time elapsed: 0.090 s
% 7.37/2.23 % (2055855)Peak memory usage: 91 MB
% 7.37/2.23 % (2055855)Instructions burned: 120 (million)
% 7.37/2.23 % (2055858)Instruction limit reached!
% 7.37/2.23 % (2055858)------------------------------
% 7.37/2.23 % (2055858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.23 % (2055858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.23 % (2055858)CaDiCaL version: 2.1.3
% 7.37/2.23 % (2055858)Termination reason: Instruction limit
% 7.37/2.23 % (2055858)Termination phase: Clausification
% 7.37/2.23 % (2055858)Time elapsed: 0.121 s
% 7.37/2.23 % (2055858)Peak memory usage: 94 MB
% 7.37/2.23 % (2055858)Instructions burned: 129 (million)
% 7.37/2.23 % (2055865)lrs+10_1_sil=8000:sp=occurrence:random_seed=3404121771:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 7.37/2.23 % (2055867)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1080475893:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/157Mi)
% 7.37/2.23 % (2055867)Refutation not found, incomplete strategy
% 7.37/2.23 % (2055867)------------------------------
% 7.37/2.23 % (2055867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.23 % (2055867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.23 % (2055867)CaDiCaL version: 2.1.3
% 7.37/2.23 % (2055867)Termination reason: Refutation not found, incomplete strategy
% 7.37/2.23 % (2055867)Time elapsed: 0.024 s
% 7.37/2.23 % (2055867)Peak memory usage: 92 MB
% 7.37/2.23 % (2055867)Instructions burned: 61 (million)
% 7.37/2.23 % (2055865)First to succeed.
% 7.37/2.23 % (2055854)------------------------------
% 7.37/2.23 % (2055854)------------------------------
% 7.37/2.23 % (2055865)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2055802"
% 7.37/2.23 % (2055868)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3009128708:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 7.37/2.23 % (2055868)Refutation not found, incomplete strategy
% 7.37/2.23 % (2055868)------------------------------
% 7.37/2.23 % (2055868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.23 % (2055868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.23 % (2055868)CaDiCaL version: 2.1.3
% 7.37/2.23 % (2055868)Termination reason: Refutation not found, incomplete strategy
% 7.37/2.23 % (2055868)Time elapsed: 0.021 s
% 7.37/2.23 % (2055868)Peak memory usage: 92 MB
% 7.37/2.23 % (2055868)Instructions burned: 27 (million)
% 7.37/2.23 % (2055867)------------------------------
% 7.37/2.23 % (2055867)------------------------------
% 7.37/2.23 % (2055876)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3972463838:s2a=on:i=248:s2at=1.23:gtg=position_2991 on theBenchmark for (2991ds/248Mi)
% 7.37/2.23 % (2055879)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=902161661:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2989 on theBenchmark for (2989ds/294Mi)
% 7.37/2.23 % (2055865)Refutation found. Thanks to Tanya!
% 7.37/2.23 % SZS status Theorem for theBenchmark
% 7.37/2.23 % SZS output start Proof for theBenchmark
% See solution above
% 8.66/2.58 % (2055865)------------------------------
% 8.66/2.58 % (2055865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.58 % (2055865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.58 % (2055865)CaDiCaL version: 2.1.3
% 8.66/2.58 % (2055865)Termination reason: Refutation
% 8.66/2.58 % (2055865)Time elapsed: 0.162 s
% 8.66/2.58 % (2055865)Peak memory usage: 95 MB
% 8.66/2.58 % (2055865)Instructions burned: 162 (million)
% 8.66/2.58 % (2055865)------------------------------
% 8.66/2.58 % (2055865)------------------------------
% 8.66/2.58 % (2055802)Success in time 1.285 s
% 8.66/2.58 % Vampire exiting
%------------------------------------------------------------------------------