%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU283+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:48:09 PM UTC 2026
% Result : Theorem 6.65s 2.01s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 125 ( 14 unt; 8 def)
% Number of atoms : 546 ( 150 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 688 ( 267 ~; 273 |; 111 &)
% ( 20 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 2 con; 0-2 aty)
% Number of variables : 226 ( 0 sgn 189 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ! [X1,X2,X3] :
( ( in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
=> X2 = X3 )
& ! [X1] :
~ ( in(X1,X0)
& ! [X2] : X2 != singleton(X1) ) )
=> ? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ! [X1,X2,X3] :
( ( in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
=> X2 = X3 )
& ! [X1] :
~ ( in(X1,X0)
& ! [X2] : X2 != singleton(X1) ) )
=> ? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X3 = singleton(X1) )
=> X2 = X3 )
=> ? [X1] :
( relation(X1)
& function(X1)
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& in(X2,X0)
& X3 = singleton(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
fof(f12,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f13,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f14,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f39,plain,
~ ! [X0] :
( ( ! [X1,X2,X3] :
( ( in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
=> X2 = X3 )
& ! [X4] :
~ ( in(X4,X0)
& ! [X5] : singleton(X4) != X5 ) )
=> ? [X6] :
( relation(X6)
& function(X6)
& relation_dom(X6) = X0
& ! [X7] :
( in(X7,X0)
=> apply(X6,X7) = singleton(X7) ) ) ),
inference(rectify,[],[f2]) ).
fof(f40,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X3 = singleton(X1) )
=> X2 = X3 )
=> ? [X4] :
( relation(X4)
& function(X4)
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( in(X5,X0)
& in(X5,X0)
& singleton(X5) = X6 ) ) ) ),
inference(rectify,[],[f8]) ).
fof(f43,plain,
? [X0] :
( ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| relation_dom(X6) != X0
| ? [X7] :
( apply(X6,X7) != singleton(X7)
& in(X7,X0) ) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(X1,X0)
| singleton(X1) != X2
| singleton(X1) != X3 )
& ! [X4] :
( ~ in(X4,X0)
| ? [X5] : singleton(X4) = X5 ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f44,plain,
? [X0] :
( ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| relation_dom(X6) != X0
| ? [X7] :
( apply(X6,X7) != singleton(X7)
& in(X7,X0) ) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(X1,X0)
| singleton(X1) != X2
| singleton(X1) != X3 )
& ! [X4] :
( ~ in(X4,X0)
| ? [X5] : singleton(X4) = X5 ) ),
inference(flattening,[],[f43]) ).
fof(f46,plain,
! [X0] :
( ? [X4] :
( relation(X4)
& function(X4)
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( in(X5,X0)
& in(X5,X0)
& singleton(X5) = X6 ) ) )
| ? [X1,X2,X3] :
( X2 != X3
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X3 = singleton(X1) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f47,plain,
! [X0] :
( ? [X4] :
( relation(X4)
& function(X4)
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( in(X5,X0)
& in(X5,X0)
& singleton(X5) = X6 ) ) )
| ? [X1,X2,X3] :
( X2 != X3
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X3 = singleton(X1) ) ),
inference(flattening,[],[f46]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f51,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f63,definition,
! [X0] :
( ? [X4] :
( relation(X4)
& function(X4)
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( in(X5,X0)
& in(X5,X0)
& singleton(X5) = X6 ) ) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f64,plain,
! [X0] :
( sP0(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X3 = singleton(X1) ) ),
inference(definition_folding,[],[f47,f63]) ).
fof(f65,plain,
? [X0] :
( ! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != singleton(X2)
& in(X2,X0) ) )
& ! [X3,X4,X5] :
( X4 = X5
| ~ in(X3,X0)
| singleton(X3) != X4
| singleton(X3) != X5 )
& ! [X6] :
( ~ in(X6,X0)
| ? [X7] : singleton(X6) = X7 ) ),
inference(rectify,[],[f44]) ).
fof(f66,plain,
( ! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != sK1
| ( apply(X1,sK2(X1)) != singleton(sK2(X1))
& in(sK2(X1),sK1) ) )
& ! [X3,X4,X5] :
( X4 = X5
| ~ in(X3,sK1)
| singleton(X3) != X4
| singleton(X3) != X5 )
& ! [X6] :
( ~ in(X6,sK1)
| singleton(X6) = sK3(X6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X2,sK2(X1)),skolemize(X7,sK3(X6))],[f65]) ).
fof(f68,plain,
! [X0] :
( ? [X4] :
( relation(X4)
& function(X4)
& ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X4)
| ~ in(X5,X0)
| ~ in(X5,X0)
| singleton(X5) != X6 )
& ( ( in(X5,X0)
& in(X5,X0)
& singleton(X5) = X6 )
| ~ in(ordered_pair(X5,X6),X4) ) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f69,plain,
! [X0] :
( ? [X4] :
( relation(X4)
& function(X4)
& ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X4)
| ~ in(X5,X0)
| ~ in(X5,X0)
| singleton(X5) != X6 )
& ( ( in(X5,X0)
& in(X5,X0)
& singleton(X5) = X6 )
| ~ in(ordered_pair(X5,X6),X4) ) ) )
| ~ sP0(X0) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ? [X1] :
( relation(X1)
& function(X1)
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(X2,X0)
| ~ in(X2,X0)
| singleton(X2) != X3 )
& ( ( in(X2,X0)
& in(X2,X0)
& singleton(X2) = X3 )
| ~ in(ordered_pair(X2,X3),X1) ) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ( relation(sK5(X0))
& function(sK5(X0))
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),sK5(X0))
| ~ in(X2,X0)
| ~ in(X2,X0)
| singleton(X2) != X3 )
& ( ( in(X2,X0)
& in(X2,X0)
& singleton(X2) = X3 )
| ~ in(ordered_pair(X2,X3),sK5(X0)) ) ) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f70]) ).
fof(f72,plain,
! [X0] :
( sP0(X0)
| ( sK7(X0) != sK8(X0)
& in(sK6(X0),X0)
& sK7(X0) = singleton(sK6(X0))
& in(sK6(X0),X0)
& sK8(X0) = singleton(sK6(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0)),skolemize(X3,sK8(X0))],[f64]) ).
fof(f73,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK9(X0,X1),X3),X0)
| ~ in(sK9(X0,X1),X1) )
& ( in(ordered_pair(sK9(X0,X1),sK10(X0,X1)),X0)
| in(sK9(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK11(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X2,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X7,sK11(X0,X5))],[f75]) ).
fof(f87,plain,
! [X1] :
( relation_dom(X1) != sK1
| ~ function(X1)
| ~ relation(X1)
| in(sK2(X1),sK1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f88,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != sK1
| apply(X1,sK2(X1)) != singleton(sK2(X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f93,plain,
! [X2,X3,X0] :
( in(X2,X0)
| ~ in(ordered_pair(X2,X3),sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f95,plain,
! [X2,X3,X0] :
( in(ordered_pair(X2,X3),sK5(X0))
| ~ in(X2,X0)
| ~ in(X2,X0)
| singleton(X2) != X3
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f96,plain,
! [X0] :
( function(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f97,plain,
! [X0] :
( relation(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f98,plain,
! [X0] :
( sP0(X0)
| sK8(X0) = singleton(sK6(X0)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f100,plain,
! [X0] :
( sP0(X0)
| sK7(X0) = singleton(sK6(X0)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f102,plain,
! [X0] :
( sK7(X0) != sK8(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f109,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f111,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f112,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK9(X0,X1),sK10(X0,X1)),X0)
| in(sK9(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f113,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK9(X0,X1),X3),X0)
| ~ in(sK9(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f114,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f141,plain,
! [X2,X3,X0] :
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK5(X0))
| ~ in(X2,X0)
| ~ in(X2,X0)
| singleton(X2) != X3
| ~ sP0(X0) ),
inference(definition_unfolding,[],[f95,f114]) ).
fof(f143,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK5(X0))
| in(X2,X0)
| ~ sP0(X0) ),
inference(definition_unfolding,[],[f93,f114]) ).
fof(f145,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f109,f114]) ).
fof(f147,plain,
! [X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK9(X0,X1),X3),singleton(sK9(X0,X1))),X0)
| relation_dom(X0) = X1
| ~ in(sK9(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f113,f114]) ).
fof(f148,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK9(X0,X1),sK10(X0,X1)),singleton(sK9(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK9(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f112,f114]) ).
fof(f149,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f111,f114]) ).
fof(f154,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(X2,singleton(X2)),singleton(X2)),sK5(X0))
| ~ in(X2,X0)
| ~ in(X2,X0)
| ~ sP0(X0) ),
inference(equality_resolution,[],[f141]) ).
fof(f158,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f149]) ).
fof(f160,definition,
! [X1] : sF19(X1) = apply(X1,sK2(X1)),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f161,plain,
! [X1] : apply(X1,sK2(X1)) = sF19(X1),
inference(reorient_equations,[],[f160]) ).
fof(f162,definition,
! [X1] : sF20(X1) = singleton(sK2(X1)),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f163,plain,
! [X1] : singleton(sK2(X1)) = sF20(X1),
inference(reorient_equations,[],[f162]) ).
fof(f164,plain,
! [X1] :
( sF19(X1) != sF20(X1)
| ~ function(X1)
| relation_dom(X1) != sK1
| ~ relation(X1) ),
inference(definition_folding,[],[f88,f163,f161]) ).
fof(f165,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(X2,singleton(X2)),singleton(X2)),sK5(X0))
| ~ in(X2,X0)
| ~ sP0(X0) ),
inference(duplicate_literal_removal,[],[f154]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f145,f158]) ).
fof(f202,definition,
( spl21_5
<=> sP0(sK1) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f203,plain,
( ~ sP0(sK1)
| spl21_5 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f204,plain,
( sP0(sK1)
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f243,plain,
! [X0,X1] :
( in(sK9(sK5(X0),X1),X0)
| ~ sP0(X0)
| relation_dom(sK5(X0)) = X1
| in(sK9(sK5(X0),X1),X1)
| ~ relation(sK5(X0)) ),
inference(resolution,[],[f143,f148]) ).
fof(f249,plain,
! [X0,X1] :
( in(sK9(sK5(X0),X1),X1)
| in(sK9(sK5(X0),X1),X0)
| relation_dom(sK5(X0)) = X1
| ~ sP0(X0) ),
inference(forward_subsumption_resolution,[],[f243,f97]) ).
fof(f254,plain,
! [X0] :
( in(sK9(sK5(X0),X0),X0)
| relation_dom(sK5(X0)) = X0
| ~ sP0(X0) ),
inference(factoring,[],[f249]) ).
fof(f340,plain,
! [X0,X1] :
( ~ in(sK9(sK5(X0),X1),X0)
| ~ sP0(X0)
| relation_dom(sK5(X0)) = X1
| ~ in(sK9(sK5(X0),X1),X1)
| ~ relation(sK5(X0)) ),
inference(resolution,[],[f165,f147]) ).
fof(f341,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ sP0(X1)
| singleton(X0) = apply(sK5(X1),X0)
| ~ relation(sK5(X1))
| ~ function(sK5(X1)) ),
inference(resolution,[],[f165,f166]) ).
fof(f348,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ sP0(X1)
| singleton(X0) = apply(sK5(X1),X0)
| ~ function(sK5(X1)) ),
inference(forward_subsumption_resolution,[],[f341,f97]) ).
fof(f349,plain,
! [X0,X1] :
( ~ in(sK9(sK5(X0),X1),X1)
| ~ sP0(X0)
| relation_dom(sK5(X0)) = X1
| ~ in(sK9(sK5(X0),X1),X0) ),
inference(forward_subsumption_resolution,[],[f340,f97]) ).
fof(f350,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ sP0(X1)
| singleton(X0) = apply(sK5(X1),X0) ),
inference(forward_subsumption_resolution,[],[f348,f96]) ).
fof(f370,plain,
! [X0] :
( ~ sP0(X0)
| relation_dom(sK5(X0)) = X0
| ~ in(sK9(sK5(X0),X0),X0)
| relation_dom(sK5(X0)) = X0
| ~ sP0(X0) ),
inference(resolution,[],[f349,f254]) ).
fof(f373,plain,
! [X0] :
( ~ sP0(X0)
| relation_dom(sK5(X0)) = X0
| ~ in(sK9(sK5(X0),X0),X0) ),
inference(duplicate_literal_removal,[],[f370]) ).
fof(f375,plain,
! [X0] :
( ~ sP0(X0)
| relation_dom(sK5(X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f373,f254]) ).
fof(f383,plain,
( singleton(sK6(sK1)) = sK7(sK1)
| spl21_5 ),
inference(resolution,[],[f100,f203]) ).
fof(f474,plain,
( singleton(sK6(sK1)) = sK8(sK1)
| spl21_5 ),
inference(resolution,[],[f98,f203]) ).
fof(f478,plain,
( sK7(sK1) = sK8(sK1)
| spl21_5 ),
inference(forward_demodulation,[],[f474,f383]) ).
fof(f479,plain,
( sK7(sK1) != sK7(sK1)
| sP0(sK1)
| spl21_5 ),
inference(superposition,[],[f102,f478]) ).
fof(f480,plain,
( sP0(sK1)
| spl21_5 ),
inference(trivial_inequality_removal,[],[f479]) ).
fof(f481,plain,
( $false
| spl21_5 ),
inference(forward_subsumption_resolution,[],[f480,f203]) ).
fof(f482,plain,
spl21_5,
inference(avatar_contradiction_clause,[],[f481]) ).
fof(f489,definition,
( spl21_9
<=> in(sK2(sK5(sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl21_9])],[avatar_definition]) ).
fof(f491,plain,
( in(sK2(sK5(sK1)),sK1)
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f493,definition,
( spl21_10
<=> relation(sK5(sK1)) ),
introduced(definition,[new_symbols(definition,[spl21_10])],[avatar_definition]) ).
fof(f494,plain,
( relation(sK5(sK1))
| ~ spl21_10 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f495,plain,
( ~ relation(sK5(sK1))
| spl21_10 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f497,definition,
( spl21_11
<=> function(sK5(sK1)) ),
introduced(definition,[new_symbols(definition,[spl21_11])],[avatar_definition]) ).
fof(f498,plain,
( function(sK5(sK1))
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f499,plain,
( ~ function(sK5(sK1))
| spl21_11 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f501,plain,
( ~ sP0(sK1)
| spl21_10 ),
inference(resolution,[],[f495,f97]) ).
fof(f502,plain,
( $false
| ~ spl21_5
| spl21_10 ),
inference(forward_subsumption_resolution,[],[f501,f204]) ).
fof(f503,plain,
( ~ spl21_5
| spl21_10 ),
inference(avatar_contradiction_clause,[],[f502]) ).
fof(f504,plain,
( ~ sP0(sK1)
| spl21_11 ),
inference(resolution,[],[f499,f96]) ).
fof(f505,plain,
( $false
| ~ spl21_5
| spl21_11 ),
inference(forward_subsumption_resolution,[],[f504,f204]) ).
fof(f506,plain,
( ~ spl21_5
| spl21_11 ),
inference(avatar_contradiction_clause,[],[f505]) ).
fof(f529,definition,
( spl21_12
<=> sK1 = relation_dom(sK5(sK1)) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
fof(f530,plain,
( sK1 != relation_dom(sK5(sK1))
| spl21_12 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f531,plain,
( sK1 = relation_dom(sK5(sK1))
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f542,plain,
( sK1 != sK1
| ~ function(sK5(sK1))
| ~ relation(sK5(sK1))
| in(sK2(sK5(sK1)),sK1)
| ~ spl21_12 ),
inference(superposition,[],[f87,f531]) ).
fof(f543,plain,
( ~ function(sK5(sK1))
| ~ relation(sK5(sK1))
| in(sK2(sK5(sK1)),sK1)
| ~ spl21_12 ),
inference(trivial_inequality_removal,[],[f542]) ).
fof(f544,plain,
( ~ relation(sK5(sK1))
| in(sK2(sK5(sK1)),sK1)
| ~ spl21_11
| ~ spl21_12 ),
inference(forward_subsumption_resolution,[],[f543,f498]) ).
fof(f548,plain,
( in(sK2(sK5(sK1)),sK1)
| ~ spl21_10
| ~ spl21_11
| ~ spl21_12 ),
inference(forward_subsumption_resolution,[],[f544,f494]) ).
fof(f551,plain,
( spl21_9
| ~ spl21_10
| ~ spl21_11
| ~ spl21_12 ),
inference(avatar_split_clause,[],[f548,f529,f497,f493,f489]) ).
fof(f565,plain,
( ~ sP0(sK1)
| singleton(sK2(sK5(sK1))) = apply(sK5(sK1),sK2(sK5(sK1)))
| ~ spl21_9 ),
inference(resolution,[],[f491,f350]) ).
fof(f566,plain,
( singleton(sK2(sK5(sK1))) = apply(sK5(sK1),sK2(sK5(sK1)))
| ~ spl21_5
| ~ spl21_9 ),
inference(forward_subsumption_resolution,[],[f565,f204]) ).
fof(f568,plain,
( singleton(sK2(sK5(sK1))) = sF19(sK5(sK1))
| ~ spl21_5
| ~ spl21_9 ),
inference(forward_demodulation,[],[f566,f161]) ).
fof(f569,plain,
( sF20(sK5(sK1)) = sF19(sK5(sK1))
| ~ spl21_5
| ~ spl21_9 ),
inference(forward_demodulation,[],[f568,f163]) ).
fof(f571,plain,
( sF19(sK5(sK1)) != sF19(sK5(sK1))
| ~ function(sK5(sK1))
| sK1 != relation_dom(sK5(sK1))
| ~ relation(sK5(sK1))
| ~ spl21_5
| ~ spl21_9 ),
inference(superposition,[],[f164,f569]) ).
fof(f572,plain,
( ~ function(sK5(sK1))
| sK1 != relation_dom(sK5(sK1))
| ~ relation(sK5(sK1))
| ~ spl21_5
| ~ spl21_9 ),
inference(trivial_inequality_removal,[],[f571]) ).
fof(f573,plain,
( sK1 != relation_dom(sK5(sK1))
| ~ relation(sK5(sK1))
| ~ spl21_5
| ~ spl21_9
| ~ spl21_11 ),
inference(forward_subsumption_resolution,[],[f572,f498]) ).
fof(f575,plain,
( ~ relation(sK5(sK1))
| ~ spl21_5
| ~ spl21_9
| ~ spl21_11
| ~ spl21_12 ),
inference(forward_subsumption_resolution,[],[f573,f531]) ).
fof(f577,plain,
( $false
| ~ spl21_5
| ~ spl21_9
| ~ spl21_10
| ~ spl21_11
| ~ spl21_12 ),
inference(forward_subsumption_resolution,[],[f575,f494]) ).
fof(f578,plain,
( ~ spl21_5
| ~ spl21_9
| ~ spl21_10
| ~ spl21_11
| ~ spl21_12 ),
inference(avatar_contradiction_clause,[],[f577]) ).
fof(f617,plain,
( sK1 = relation_dom(sK5(sK1))
| ~ spl21_5 ),
inference(resolution,[],[f204,f375]) ).
fof(f619,plain,
( $false
| ~ spl21_5
| spl21_12 ),
inference(forward_subsumption_resolution,[],[f617,f530]) ).
fof(f620,plain,
( ~ spl21_5
| spl21_12 ),
inference(avatar_contradiction_clause,[],[f619]) ).
cnf(s5,plain,
spl21_5,
inference(sat_conversion,[],[f482]) ).
cnf(s7,plain,
( ~ spl21_5
| spl21_10 ),
inference(sat_conversion,[],[f503]) ).
cnf(s8,plain,
( ~ spl21_5
| spl21_11 ),
inference(sat_conversion,[],[f506]) ).
cnf(s10,plain,
( spl21_9
| ~ spl21_10
| ~ spl21_11
| ~ spl21_12 ),
inference(sat_conversion,[],[f551]) ).
cnf(s11,plain,
( ~ spl21_5
| ~ spl21_9
| ~ spl21_10
| ~ spl21_11
| ~ spl21_12 ),
inference(sat_conversion,[],[f578]) ).
cnf(s14,plain,
( ~ spl21_5
| spl21_12 ),
inference(sat_conversion,[],[f620]) ).
cnf(s15,plain,
spl21_12,
inference(rat,[],[s14,s5]) ).
cnf(s16,plain,
spl21_11,
inference(rat,[],[s8,s5]) ).
cnf(s17,plain,
spl21_10,
inference(rat,[],[s7,s5]) ).
cnf(s18,plain,
spl21_9,
inference(rat,[],[s10,s15,s16,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s11,s15,s16,s5,s17,s18]) ).
fof(f621,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU283+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:28:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.65/2.01 % (4148320)Detected formulas, will run a generic FOF schedule.
% 6.65/2.01 % (4148328)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=64637261:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.65/2.01 % (4148328)Instruction limit reached!
% 6.65/2.01 % (4148328)------------------------------
% 6.65/2.01 % (4148328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148328)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148328)Termination reason: Instruction limit
% 6.65/2.01 % (4148328)Termination phase: Saturation
% 6.65/2.01 % (4148328)Time elapsed: 0.033 s
% 6.65/2.01 % (4148328)Peak memory usage: 89 MB
% 6.65/2.01 % (4148328)Instructions burned: 114 (million)
% 6.65/2.01 % (4148326)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=2707862246:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.65/2.01 % (4148331)dis-21_1_sil=8000:lcm=predicate:random_seed=3756696447:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.65/2.01 % (4148327)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=3709015458:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.65/2.01 % (4148329)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2288102554:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.65/2.01 % (4148325)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=287641519:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.65/2.01 % (4148330)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2708973200:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.65/2.01 % (4148331)Instruction limit reached!
% 6.65/2.01 % (4148331)------------------------------
% 6.65/2.01 % (4148331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148331)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148331)Termination reason: Instruction limit
% 6.65/2.01 % (4148331)Termination phase: Saturation
% 6.65/2.01 % (4148331)Time elapsed: 0.069 s
% 6.65/2.01 % (4148331)Peak memory usage: 90 MB
% 6.65/2.01 % (4148331)Instructions burned: 130 (million)
% 6.65/2.01 % (4148329)Instruction limit reached!
% 6.65/2.01 % (4148329)------------------------------
% 6.65/2.01 % (4148329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148329)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148329)Termination reason: Instruction limit
% 6.65/2.01 % (4148329)Termination phase: Saturation
% 6.65/2.01 % (4148329)Time elapsed: 0.070 s
% 6.65/2.01 % (4148329)Peak memory usage: 88 MB
% 6.65/2.01 % (4148329)Instructions burned: 120 (million)
% 6.65/2.01 % (4148330)Instruction limit reached!
% 6.65/2.01 % (4148330)------------------------------
% 6.65/2.01 % (4148330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148330)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148330)Termination reason: Instruction limit
% 6.65/2.01 % (4148330)Termination phase: Saturation
% 6.65/2.01 % (4148330)Time elapsed: 0.083 s
% 6.65/2.01 % (4148330)Peak memory usage: 90 MB
% 6.65/2.01 % (4148330)Instructions burned: 139 (million)
% 6.65/2.01 % (4148333)lrs+10_1_sil=8000:sp=occurrence:random_seed=3783464451:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.65/2.01 % (4148333)Instruction limit reached!
% 6.65/2.01 % (4148333)------------------------------
% 6.65/2.01 % (4148333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148333)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148333)Termination reason: Instruction limit
% 6.65/2.01 % (4148333)Termination phase: Saturation
% 6.65/2.01 % (4148333)Time elapsed: 0.092 s
% 6.65/2.01 % (4148333)Peak memory usage: 91 MB
% 6.65/2.01 % (4148333)Instructions burned: 287 (million)
% 6.65/2.01 % (4148340)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3051067251:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.65/2.01 % (4148341)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1341342926:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.65/2.01 % (4148340)Refutation not found, incomplete strategy
% 6.65/2.01 % (4148340)------------------------------
% 6.65/2.01 % (4148340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148340)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148340)Termination reason: Refutation not found, incomplete strategy
% 6.65/2.01 % (4148340)Time elapsed: 0.007 s
% 6.65/2.01 % (4148340)Peak memory usage: 89 MB
% 6.65/2.01 % (4148340)Instructions burned: 7 (million)
% 6.65/2.01 % (4148343)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=1527313358:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.65/2.01 % (4148344)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=57560265:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.65/2.01 % (4148344)Refutation not found, incomplete strategy
% 6.65/2.01 % (4148344)------------------------------
% 6.65/2.01 % (4148344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148344)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148344)Termination reason: Refutation not found, incomplete strategy
% 6.65/2.01 % (4148344)Time elapsed: 0.002 s
% 6.65/2.01 % (4148344)Peak memory usage: 89 MB
% 6.65/2.01 % (4148344)Instructions burned: 3 (million)
% 6.65/2.01 % (4148343)Instruction limit reached!
% 6.65/2.01 % (4148343)------------------------------
% 6.65/2.01 % (4148343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148343)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148343)Termination reason: Instruction limit
% 6.65/2.01 % (4148343)Termination phase: Saturation
% 6.65/2.01 % (4148343)Time elapsed: 0.142 s
% 6.65/2.01 % (4148343)Peak memory usage: 90 MB
% 6.65/2.01 % (4148343)Instructions burned: 249 (million)
% 6.65/2.01 % (4148341)Instruction limit reached!
% 6.65/2.01 % (4148341)------------------------------
% 6.65/2.01 % (4148341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148341)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148341)Termination reason: Instruction limit
% 6.65/2.01 % (4148341)Termination phase: Saturation
% 6.65/2.01 % (4148341)Time elapsed: 0.201 s
% 6.65/2.01 % (4148341)Peak memory usage: 91 MB
% 6.65/2.01 % (4148341)Instructions burned: 326 (million)
% 6.65/2.01 % (4148340)------------------------------
% 6.65/2.01 % (4148340)------------------------------
% 6.65/2.01 % (4148344)------------------------------
% 6.65/2.01 % (4148344)------------------------------
% 6.65/2.01 % (4148350)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=63387394:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.65/2.01 % (4148349)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2703306110:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.65/2.01 % (4148351)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4033163248:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.65/2.01 % (4148351)Instruction limit reached!
% 6.65/2.01 % (4148351)------------------------------
% 6.65/2.01 % (4148351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148351)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148351)Termination reason: Instruction limit
% 6.65/2.01 % (4148351)Termination phase: Saturation
% 6.65/2.01 % (4148351)Time elapsed: 0.035 s
% 6.65/2.01 % (4148351)Peak memory usage: 88 MB
% 6.65/2.01 % (4148351)Instructions burned: 131 (million)
% 6.65/2.01 % (4148352)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1118587938:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.65/2.01 % (4148350)Instruction limit reached!
% 6.65/2.01 % (4148350)------------------------------
% 6.65/2.01 % (4148350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148350)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148350)Termination reason: Instruction limit
% 6.65/2.01 % (4148350)Termination phase: Saturation
% 6.65/2.01 % (4148350)Time elapsed: 0.084 s
% 6.65/2.01 % (4148350)Peak memory usage: 90 MB
% 6.65/2.01 % (4148350)Instructions burned: 114 (million)
% 6.65/2.01 % (4148352)Instruction limit reached!
% 6.65/2.01 % (4148352)------------------------------
% 6.65/2.01 % (4148352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148352)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148352)Termination reason: Instruction limit
% 6.65/2.01 % (4148352)Termination phase: Saturation
% 6.65/2.01 % (4148352)Time elapsed: 0.066 s
% 6.65/2.01 % (4148352)Peak memory usage: 89 MB
% 6.65/2.01 % (4148352)Instructions burned: 114 (million)
% 6.65/2.01 % (4148325)First to succeed.
% 6.65/2.01 % (4148325)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4148320"
% 6.65/2.01 % (4148326)Also succeeded, but the first one will report.
% 6.65/2.01 % (4148356)lrs+10_1_sil=8000:sp=occurrence:random_seed=4015733884:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.65/2.01 % (4148327)Also succeeded, but the first one will report.
% 6.65/2.01 % (4148358)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1880723220:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.65/2.01 % (4148358)Refutation not found, incomplete strategy
% 6.65/2.01 % (4148358)------------------------------
% 6.65/2.01 % (4148358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.65/2.01 % (4148358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.65/2.01 % (4148358)CaDiCaL version: 2.1.3
% 6.65/2.01 % (4148358)Termination reason: Refutation not found, incomplete strategy
% 6.65/2.01 % (4148358)Time elapsed: 0.003 s
% 6.65/2.01 % (4148358)Peak memory usage: 88 MB
% 6.65/2.01 % (4148358)Instructions burned: 3 (million)
% 6.65/2.01 % (4148359)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3379094998:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.65/2.01 % (4148325)Refutation found. Thanks to Tanya!
% 6.65/2.01 % SZS status Theorem for theBenchmark
% 6.65/2.01 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/2.20 % (4148325)------------------------------
% 0.18/2.20 % (4148325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/2.20 % (4148325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/2.20 % (4148325)CaDiCaL version: 2.1.3
% 0.18/2.20 % (4148325)Termination reason: Refutation
% 0.18/2.20 % (4148325)Time elapsed: 0.708 s
% 0.18/2.20 % (4148325)Peak memory usage: 129 MB
% 0.18/2.20 % (4148325)Instructions burned: 1059 (million)
% 0.18/2.20 % (4148325)------------------------------
% 0.18/2.20 % (4148325)------------------------------
% 0.18/2.20 % (4148320)Success in time 1.14 s
% 0.18/2.20 % Vampire exiting
%------------------------------------------------------------------------------