%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU278+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 : n012.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 12:48:08 PM UTC 2026
% Result : Theorem 10.21s 2.16s
% Output : Refutation 10.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 11
% Syntax : Number of formulae : 162 ( 20 unt; 4 def)
% Number of atoms : 562 ( 73 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 660 ( 260 ~; 310 |; 72 &)
% ( 12 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 368 ( 0 sgn 320 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( relation(X1)
& relation(X2)
& function(X2) )
=> ? [X3] :
( relation(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X0)
& in(X5,X0)
& in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relat_1__e6_21__wellord2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X1)
& relation(X2)
& function(X2) )
=> ? [X3] :
( relation(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X0)
& in(X5,X0)
& in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f20,axiom,
! [X0,X1,X2] :
( ( relation(X1)
& relation(X2)
& function(X2) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(f21,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f22,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f23,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(f35,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f38,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X0 = X2
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f42,plain,
? [X0,X1,X2] :
( ! [X3] :
( ~ relation(X3)
| ? [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<~> ( in(X4,X0)
& in(X5,X0)
& in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1) ) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ! [X3] :
( ~ relation(X3)
| ? [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<~> ( in(X4,X0)
& in(X5,X0)
& in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1) ) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f42]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) ) )
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) ) )
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ( X0 = X2
& X1 = X3 )
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f38]) ).
fof(f64,plain,
? [X0,X1,X2] :
( ! [X3] :
( ~ relation(X3)
| ? [X4,X5] :
( ( ~ in(X4,X0)
| ~ in(X5,X0)
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(ordered_pair(X4,X5),X3) )
& ( ( in(X4,X0)
& in(X5,X0)
& in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1) )
| in(ordered_pair(X4,X5),X3) ) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(nnf_transformation,[],[f43]) ).
fof(f65,plain,
? [X0,X1,X2] :
( ! [X3] :
( ~ relation(X3)
| ? [X4,X5] :
( ( ~ in(X4,X0)
| ~ in(X5,X0)
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(ordered_pair(X4,X5),X3) )
& ( ( in(X4,X0)
& in(X5,X0)
& in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1) )
| in(ordered_pair(X4,X5),X3) ) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
( ! [X3] :
( ~ relation(X3)
| ( ( ~ in(sK3(X3),sK0)
| ~ in(sK4(X3),sK0)
| ~ in(ordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),sK1)
| ~ in(ordered_pair(sK3(X3),sK4(X3)),X3) )
& ( ( in(sK3(X3),sK0)
& in(sK4(X3),sK0)
& in(ordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),sK1) )
| in(ordered_pair(sK3(X3),sK4(X3)),X3) ) ) )
& relation(sK1)
& relation(sK2)
& function(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3(X3)),skolemize(X5,sK4(X3))],[f65]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ~ in(X4,cartesian_product2(X0,X0))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) )
& ( ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) )
| ~ in(X4,X3) ) )
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(nnf_transformation,[],[f53]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ~ in(X4,cartesian_product2(X0,X0))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) )
& ( ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) )
| ~ in(X4,X3) ) )
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ~ in(X4,cartesian_product2(X0,X0))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) )
& ( ( in(X4,cartesian_product2(X0,X0))
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1) ) )
| ~ in(X4,X3) ) )
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK13(X0,X1,X2))
| ~ in(X4,cartesian_product2(X0,X0))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) )
& ( ( in(X4,cartesian_product2(X0,X0))
& ordered_pair(sK14(X1,X2,X4),sK15(X1,X2,X4)) = X4
& in(ordered_pair(apply(X2,sK14(X1,X2,X4)),apply(X2,sK15(X1,X2,X4))),X1) )
| ~ in(X4,sK13(X0,X1,X2)) ) )
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X3,sK13(X0,X1,X2)),skolemize(X7,sK14(X1,X2,X4)),skolemize(X8,sK15(X1,X2,X4))],[f77]) ).
fof(f79,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f80,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ? [X5,X6] : ordered_pair(X5,X6) = X4 )
| ~ relation(X0) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ( relation(X0)
| ( in(sK16(X0),X0)
& ! [X2,X3] : ordered_pair(X2,X3) != sK16(X0) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ordered_pair(sK17(X4),sK18(X4)) = X4 )
| ~ relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X1,sK16(X0)),skolemize(X5,sK17(X4)),skolemize(X6,sK18(X4))],[f80]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
function(sK2),
inference(cnf_transformation,[],[f66]) ).
fof(f87,plain,
relation(sK2),
inference(cnf_transformation,[],[f66]) ).
fof(f88,plain,
relation(sK1),
inference(cnf_transformation,[],[f66]) ).
fof(f89,plain,
! [X3] :
( ~ relation(X3)
| in(ordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),sK1)
| in(ordered_pair(sK3(X3),sK4(X3)),X3) ),
inference(cnf_transformation,[],[f66]) ).
fof(f90,plain,
! [X3] :
( ~ relation(X3)
| in(sK4(X3),sK0)
| in(ordered_pair(sK3(X3),sK4(X3)),X3) ),
inference(cnf_transformation,[],[f66]) ).
fof(f91,plain,
! [X3] :
( ~ relation(X3)
| in(sK3(X3),sK0)
| in(ordered_pair(sK3(X3),sK4(X3)),X3) ),
inference(cnf_transformation,[],[f66]) ).
fof(f92,plain,
! [X3] :
( ~ relation(X3)
| ~ in(sK3(X3),sK0)
| ~ in(sK4(X3),sK0)
| ~ in(ordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),sK1)
| ~ in(ordered_pair(sK3(X3),sK4(X3)),X3) ),
inference(cnf_transformation,[],[f66]) ).
fof(f129,plain,
! [X2,X0,X1,X4] :
( in(ordered_pair(apply(X2,sK14(X1,X2,X4)),apply(X2,sK15(X1,X2,X4))),X1)
| ~ in(X4,sK13(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f130,plain,
! [X2,X0,X1,X4] :
( ordered_pair(sK14(X1,X2,X4),sK15(X1,X2,X4)) = X4
| ~ in(X4,sK13(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f131,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK13(X0,X1,X2))
| in(X4,cartesian_product2(X0,X0))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f132,plain,
! [X2,X0,X1,X6,X4,X5] :
( in(X4,sK13(X0,X1,X2))
| ~ in(X4,cartesian_product2(X0,X0))
| ordered_pair(X5,X6) != X4
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f133,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f21]) ).
fof(f134,plain,
! [X0,X4] :
( ~ in(X4,X0)
| ordered_pair(sK17(X4),sK18(X4)) = X4
| ~ relation(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f135,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK16(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f136,plain,
! [X0] :
( in(sK16(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f137,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f150,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f60]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f60]) ).
fof(f155,plain,
! [X3] :
( ~ relation(X3)
| ~ in(sK3(X3),sK0)
| ~ in(sK4(X3),sK0)
| ~ in(unordered_pair(unordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),singleton(apply(sK2,sK3(X3)))),sK1)
| ~ in(unordered_pair(unordered_pair(sK3(X3),sK4(X3)),singleton(sK3(X3))),X3) ),
inference(definition_unfolding,[],[f92,f137,f137]) ).
fof(f156,plain,
! [X3] :
( ~ relation(X3)
| in(sK3(X3),sK0)
| in(unordered_pair(unordered_pair(sK3(X3),sK4(X3)),singleton(sK3(X3))),X3) ),
inference(definition_unfolding,[],[f91,f137]) ).
fof(f157,plain,
! [X3] :
( ~ relation(X3)
| in(sK4(X3),sK0)
| in(unordered_pair(unordered_pair(sK3(X3),sK4(X3)),singleton(sK3(X3))),X3) ),
inference(definition_unfolding,[],[f90,f137]) ).
fof(f158,plain,
! [X3] :
( ~ relation(X3)
| in(unordered_pair(unordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3))),singleton(apply(sK2,sK3(X3)))),sK1)
| in(unordered_pair(unordered_pair(sK3(X3),sK4(X3)),singleton(sK3(X3))),X3) ),
inference(definition_unfolding,[],[f89,f137,f137]) ).
fof(f160,plain,
! [X2,X0,X1,X6,X4,X5] :
( in(X4,sK13(X0,X1,X2))
| ~ in(X4,cartesian_product2(X0,X0))
| unordered_pair(unordered_pair(X5,X6),singleton(X5)) != X4
| ~ in(unordered_pair(unordered_pair(apply(X2,X5),apply(X2,X6)),singleton(apply(X2,X5))),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(definition_unfolding,[],[f132,f137,f137]) ).
fof(f161,plain,
! [X2,X0,X1,X4] :
( unordered_pair(unordered_pair(sK14(X1,X2,X4),sK15(X1,X2,X4)),singleton(sK14(X1,X2,X4))) = X4
| ~ in(X4,sK13(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(definition_unfolding,[],[f130,f137]) ).
fof(f162,plain,
! [X2,X0,X1,X4] :
( in(unordered_pair(unordered_pair(apply(X2,sK14(X1,X2,X4)),apply(X2,sK15(X1,X2,X4))),singleton(apply(X2,sK14(X1,X2,X4)))),X1)
| ~ in(X4,sK13(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(definition_unfolding,[],[f129,f137]) ).
fof(f163,plain,
! [X2,X3,X0] :
( sK16(X0) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| relation(X0) ),
inference(definition_unfolding,[],[f135,f137]) ).
fof(f164,plain,
! [X0,X4] :
( ~ relation(X0)
| unordered_pair(unordered_pair(sK17(X4),sK18(X4)),singleton(sK17(X4))) = X4
| ~ in(X4,X0) ),
inference(definition_unfolding,[],[f134,f137]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f147,f137]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f146,f137]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f145,f137]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X0 = X2 ),
inference(definition_unfolding,[],[f151,f137,f137]) ).
fof(f169,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X1 = X3 ),
inference(definition_unfolding,[],[f150,f137,f137]) ).
fof(f170,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK13(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),cartesian_product2(X0,X0))
| ~ in(unordered_pair(unordered_pair(apply(X2,X5),apply(X2,X6)),singleton(apply(X2,X5))),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(equality_resolution,[],[f160]) ).
fof(f171,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK13(X0,X1,X2))
| in(unordered_pair(singleton(apply(X2,sK14(X1,X2,X4))),unordered_pair(apply(X2,sK14(X1,X2,X4)),apply(X2,sK15(X1,X2,X4)))),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_demodulation,[],[f162,f133]) ).
fof(f172,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK13(X0,X1,X2))
| unordered_pair(singleton(sK14(X1,X2,X4)),unordered_pair(sK14(X1,X2,X4),sK15(X1,X2,X4))) = X4
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_demodulation,[],[f161,f133]) ).
fof(f173,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),sK13(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),cartesian_product2(X0,X0))
| ~ in(unordered_pair(unordered_pair(apply(X2,X5),apply(X2,X6)),singleton(apply(X2,X5))),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_demodulation,[],[f170,f133]) ).
fof(f174,plain,
! [X3] :
( in(unordered_pair(singleton(apply(sK2,sK3(X3))),unordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3)))),sK1)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(sK3(X3),sK4(X3)),singleton(sK3(X3))),X3) ),
inference(forward_demodulation,[],[f158,f133]) ).
fof(f175,plain,
! [X3] :
( ~ relation(X3)
| in(unordered_pair(singleton(sK3(X3)),unordered_pair(sK3(X3),sK4(X3))),X3)
| in(sK4(X3),sK0) ),
inference(forward_demodulation,[],[f157,f133]) ).
fof(f176,plain,
! [X3] :
( ~ relation(X3)
| in(unordered_pair(singleton(sK3(X3)),unordered_pair(sK3(X3),sK4(X3))),X3)
| in(sK3(X3),sK0) ),
inference(forward_demodulation,[],[f156,f133]) ).
fof(f177,plain,
! [X3] :
( ~ in(unordered_pair(singleton(apply(sK2,sK3(X3))),unordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3)))),sK1)
| ~ relation(X3)
| ~ in(sK3(X3),sK0)
| ~ in(sK4(X3),sK0)
| ~ in(unordered_pair(unordered_pair(sK3(X3),sK4(X3)),singleton(sK3(X3))),X3) ),
inference(forward_demodulation,[],[f155,f133]) ).
fof(f178,plain,
! [X2,X0,X1,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),cartesian_product2(X0,X0))
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),sK13(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(apply(X2,X5),apply(X2,X6)),singleton(apply(X2,X5))),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_demodulation,[],[f173,f133]) ).
fof(f179,plain,
! [X3] :
( ~ relation(X3)
| in(unordered_pair(singleton(apply(sK2,sK3(X3))),unordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3)))),sK1)
| in(unordered_pair(singleton(sK3(X3)),unordered_pair(sK3(X3),sK4(X3))),X3) ),
inference(forward_demodulation,[],[f174,f133]) ).
fof(f180,plain,
! [X3] :
( ~ in(sK4(X3),sK0)
| ~ in(unordered_pair(singleton(apply(sK2,sK3(X3))),unordered_pair(apply(sK2,sK3(X3)),apply(sK2,sK4(X3)))),sK1)
| ~ relation(X3)
| ~ in(sK3(X3),sK0)
| ~ in(unordered_pair(singleton(sK3(X3)),unordered_pair(sK3(X3),sK4(X3))),X3) ),
inference(forward_demodulation,[],[f177,f133]) ).
fof(f181,plain,
! [X2,X0,X1,X6,X5] :
( ~ function(X2)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),cartesian_product2(X0,X0))
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),sK13(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(apply(X2,X5)),unordered_pair(apply(X2,X5),apply(X2,X6))),X1) ),
inference(forward_demodulation,[],[f178,f133]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK13(X2,X3,sK2))
| ~ relation(X3)
| ~ relation(sK2)
| ~ in(unordered_pair(singleton(apply(sK2,X0)),unordered_pair(apply(sK2,X0),apply(sK2,X1))),X3) ),
inference(resolution,[],[f181,f86]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK13(X2,X3,sK2))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X2))
| ~ in(unordered_pair(singleton(apply(sK2,X0)),unordered_pair(apply(sK2,X0),apply(sK2,X1))),X3) ),
inference(forward_subsumption_resolution,[],[f214,f87]) ).
fof(f226,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(superposition,[],[f166,f133]) ).
fof(f232,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(superposition,[],[f167,f133]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ function(X2)
| sK16(sK13(X0,X1,X2)) = unordered_pair(singleton(sK14(X1,X2,sK16(sK13(X0,X1,X2)))),unordered_pair(sK14(X1,X2,sK16(sK13(X0,X1,X2))),sK15(X1,X2,sK16(sK13(X0,X1,X2)))))
| ~ relation(X1)
| ~ relation(X2)
| relation(sK13(X0,X1,X2)) ),
inference(resolution,[],[f136,f172]) ).
fof(f248,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK13(X2,sK1,sK2))
| ~ in(unordered_pair(singleton(apply(sK2,X0)),unordered_pair(apply(sK2,X0),apply(sK2,X1))),sK1) ),
inference(resolution,[],[f215,f88]) ).
fof(f253,plain,
! [X2,X0,X1] :
( relation(X2)
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2) ),
inference(superposition,[],[f163,f133]) ).
fof(f263,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X2,X3),singleton(X2)) != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| X0 = X2 ),
inference(superposition,[],[f168,f133]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
| X0 = X2 ),
inference(forward_demodulation,[],[f263,f133]) ).
fof(f291,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X2,X3),singleton(X2)) != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| X1 = X3 ),
inference(superposition,[],[f169,f133]) ).
fof(f293,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
| X1 = X3 ),
inference(forward_demodulation,[],[f291,f133]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(apply(sK2,X1)),unordered_pair(apply(sK2,X1),apply(sK2,X0))),sK1)
| in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK13(X2,sK1,sK2))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),cartesian_product2(X2,X2)) ),
inference(superposition,[],[f248,f133]) ).
fof(f1426,plain,
! [X0,X1] :
( sK16(sK13(X0,X1,sK2)) = unordered_pair(singleton(sK14(X1,sK2,sK16(sK13(X0,X1,sK2)))),unordered_pair(sK14(X1,sK2,sK16(sK13(X0,X1,sK2))),sK15(X1,sK2,sK16(sK13(X0,X1,sK2)))))
| ~ relation(X1)
| ~ relation(sK2)
| relation(sK13(X0,X1,sK2)) ),
inference(resolution,[],[f246,f86]) ).
fof(f1427,plain,
! [X0,X1] :
( sK16(sK13(X0,X1,sK2)) = unordered_pair(singleton(sK14(X1,sK2,sK16(sK13(X0,X1,sK2)))),unordered_pair(sK14(X1,sK2,sK16(sK13(X0,X1,sK2))),sK15(X1,sK2,sK16(sK13(X0,X1,sK2)))))
| ~ relation(X1)
| relation(sK13(X0,X1,sK2)) ),
inference(forward_subsumption_resolution,[],[f1426,f87]) ).
fof(f1428,plain,
! [X0,X1] :
( relation(sK13(X0,X1,sK2))
| ~ relation(X1) ),
inference(forward_subsumption_resolution,[],[f1427,f253]) ).
fof(f1430,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| unordered_pair(unordered_pair(sK17(X1),sK18(X1)),singleton(sK17(X1))) = X1
| ~ in(X1,sK13(X2,X0,sK2)) ),
inference(resolution,[],[f1428,f164]) ).
fof(f1431,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(singleton(sK3(sK13(X1,X0,sK2))),unordered_pair(sK3(sK13(X1,X0,sK2)),sK4(sK13(X1,X0,sK2)))),sK13(X1,X0,sK2))
| in(sK4(sK13(X1,X0,sK2)),sK0) ),
inference(resolution,[],[f1428,f175]) ).
fof(f1432,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(singleton(sK3(sK13(X1,X0,sK2))),unordered_pair(sK3(sK13(X1,X0,sK2)),sK4(sK13(X1,X0,sK2)))),sK13(X1,X0,sK2))
| in(sK3(sK13(X1,X0,sK2)),sK0) ),
inference(resolution,[],[f1428,f176]) ).
fof(f1433,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(singleton(apply(sK2,sK3(sK13(X1,X0,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X1,X0,sK2))),apply(sK2,sK4(sK13(X1,X0,sK2))))),sK1)
| in(unordered_pair(singleton(sK3(sK13(X1,X0,sK2))),unordered_pair(sK3(sK13(X1,X0,sK2)),sK4(sK13(X1,X0,sK2)))),sK13(X1,X0,sK2)) ),
inference(resolution,[],[f1428,f179]) ).
fof(f1434,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| unordered_pair(singleton(sK17(X1)),unordered_pair(sK17(X1),sK18(X1))) = X1
| ~ in(X1,sK13(X2,X0,sK2)) ),
inference(forward_demodulation,[],[f1430,f133]) ).
fof(f1438,plain,
! [X0] :
( in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),sK13(X0,sK1,sK2))
| in(sK4(sK13(X0,sK1,sK2)),sK0) ),
inference(resolution,[],[f1431,f88]) ).
fof(f1449,plain,
! [X0] :
( in(sK4(sK13(X0,sK1,sK2)),sK0)
| in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),cartesian_product2(X0,X0))
| ~ relation(sK1)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f1438,f131]) ).
fof(f1462,plain,
! [X0] :
( in(sK4(sK13(X0,sK1,sK2)),sK0)
| in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),cartesian_product2(X0,X0))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f1449,f88]) ).
fof(f1465,plain,
! [X0] :
( in(sK4(sK13(X0,sK1,sK2)),sK0)
| in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),cartesian_product2(X0,X0))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f1462,f87]) ).
fof(f1468,plain,
! [X0] :
( in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),cartesian_product2(X0,X0))
| in(sK4(sK13(X0,sK1,sK2)),sK0) ),
inference(forward_subsumption_resolution,[],[f1465,f86]) ).
fof(f1471,plain,
! [X0] :
( in(sK4(sK13(X0,sK1,sK2)),sK0)
| in(sK4(sK13(X0,sK1,sK2)),X0) ),
inference(resolution,[],[f1468,f232]) ).
fof(f1506,plain,
in(sK4(sK13(sK0,sK1,sK2)),sK0),
inference(factoring,[],[f1471]) ).
fof(f1545,plain,
( ~ in(unordered_pair(singleton(apply(sK2,sK3(sK13(sK0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(sK0,sK1,sK2))),apply(sK2,sK4(sK13(sK0,sK1,sK2))))),sK1)
| ~ relation(sK13(sK0,sK1,sK2))
| ~ in(sK3(sK13(sK0,sK1,sK2)),sK0)
| ~ in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))),sK13(sK0,sK1,sK2)) ),
inference(resolution,[],[f1506,f180]) ).
fof(f1551,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(unordered_pair(unordered_pair(X0,sK4(sK13(sK0,sK1,sK2))),singleton(X0)),cartesian_product2(X1,sK0)) ),
inference(resolution,[],[f1506,f165]) ).
fof(f1552,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK4(sK13(sK0,sK1,sK2)))),cartesian_product2(X1,sK0))
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f1551,f133]) ).
fof(f1554,definition,
( spl21_58
<=> in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))),sK13(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl21_58])],[avatar_definition]) ).
fof(f1555,plain,
( ~ in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))),sK13(sK0,sK1,sK2))
| spl21_58 ),
inference(avatar_component_clause,[],[f1554]) ).
fof(f1557,definition,
( spl21_59
<=> in(sK3(sK13(sK0,sK1,sK2)),sK0) ),
introduced(definition,[new_symbols(definition,[spl21_59])],[avatar_definition]) ).
fof(f1558,plain,
( ~ in(sK3(sK13(sK0,sK1,sK2)),sK0)
| spl21_59 ),
inference(avatar_component_clause,[],[f1557]) ).
fof(f1560,definition,
( spl21_60
<=> relation(sK13(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl21_60])],[avatar_definition]) ).
fof(f1561,plain,
( ~ relation(sK13(sK0,sK1,sK2))
| spl21_60 ),
inference(avatar_component_clause,[],[f1560]) ).
fof(f1563,definition,
( spl21_61
<=> in(unordered_pair(singleton(apply(sK2,sK3(sK13(sK0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(sK0,sK1,sK2))),apply(sK2,sK4(sK13(sK0,sK1,sK2))))),sK1) ),
introduced(definition,[new_symbols(definition,[spl21_61])],[avatar_definition]) ).
fof(f1564,plain,
( ~ in(unordered_pair(singleton(apply(sK2,sK3(sK13(sK0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(sK0,sK1,sK2))),apply(sK2,sK4(sK13(sK0,sK1,sK2))))),sK1)
| spl21_61 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f1565,plain,
( ~ spl21_58
| ~ spl21_59
| ~ spl21_60
| ~ spl21_61 ),
inference(avatar_split_clause,[],[f1545,f1563,f1560,f1557,f1554]) ).
fof(f1987,plain,
! [X0] :
( in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),sK13(X0,sK1,sK2))
| in(sK3(sK13(X0,sK1,sK2)),sK0) ),
inference(resolution,[],[f1432,f88]) ).
fof(f2001,plain,
! [X0] :
( in(sK3(sK13(X0,sK1,sK2)),sK0)
| in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),cartesian_product2(X0,X0))
| ~ relation(sK1)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f1987,f131]) ).
fof(f2014,plain,
! [X0] :
( in(sK3(sK13(X0,sK1,sK2)),sK0)
| in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),cartesian_product2(X0,X0))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f2001,f88]) ).
fof(f2017,plain,
! [X0] :
( in(sK3(sK13(X0,sK1,sK2)),sK0)
| in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),cartesian_product2(X0,X0))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f2014,f87]) ).
fof(f2020,plain,
! [X0] :
( in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),cartesian_product2(X0,X0))
| in(sK3(sK13(X0,sK1,sK2)),sK0) ),
inference(forward_subsumption_resolution,[],[f2017,f86]) ).
fof(f2091,plain,
! [X0] :
( in(sK3(sK13(X0,sK1,sK2)),sK0)
| in(sK3(sK13(X0,sK1,sK2)),X0) ),
inference(resolution,[],[f2020,f226]) ).
fof(f2140,plain,
in(sK3(sK13(sK0,sK1,sK2)),sK0),
inference(factoring,[],[f2091]) ).
fof(f2590,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1)
| in(unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))),sK13(X0,sK1,sK2)) ),
inference(resolution,[],[f1433,f88]) ).
fof(f2608,plain,
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(sK0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(sK0,sK1,sK2))),apply(sK2,sK4(sK13(sK0,sK1,sK2))))),sK1)
| spl21_58 ),
inference(resolution,[],[f2590,f1555]) ).
fof(f2611,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1)
| in(unordered_pair(singleton(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))))),unordered_pair(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))),apply(sK2,sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))))),sK1)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f2590,f171]) ).
fof(f2613,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1)
| unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))) = unordered_pair(singleton(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))),unordered_pair(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))),sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))))
| ~ relation(sK1)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f2590,f172]) ).
fof(f2624,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1)
| unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))) = unordered_pair(singleton(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))),unordered_pair(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))),sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f2613,f88]) ).
fof(f2626,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1)
| in(unordered_pair(singleton(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))))),unordered_pair(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))),apply(sK2,sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))))),sK1)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f2611,f88]) ).
fof(f2632,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1)
| unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))) = unordered_pair(singleton(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))),unordered_pair(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))),sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f2624,f87]) ).
fof(f2634,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1)
| in(unordered_pair(singleton(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))))),unordered_pair(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))),apply(sK2,sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))))),sK1)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f2626,f87]) ).
fof(f2636,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1)
| unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))) = unordered_pair(singleton(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))),unordered_pair(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))),sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))))) ),
inference(forward_subsumption_resolution,[],[f2632,f86]) ).
fof(f2638,plain,
! [X0] :
( in(unordered_pair(singleton(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2))))))),unordered_pair(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))),apply(sK2,sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(X0,sK1,sK2))),unordered_pair(sK3(sK13(X0,sK1,sK2)),sK4(sK13(X0,sK1,sK2)))))))),sK1)
| in(unordered_pair(singleton(apply(sK2,sK3(sK13(X0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(X0,sK1,sK2))),apply(sK2,sK4(sK13(X0,sK1,sK2))))),sK1) ),
inference(forward_subsumption_resolution,[],[f2634,f86]) ).
fof(f2667,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK4(sK13(sK0,sK1,sK2)),sK3(sK13(sK0,sK1,sK2)))),sK13(X0,sK1,sK2))
| ~ in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK4(sK13(sK0,sK1,sK2)),sK3(sK13(sK0,sK1,sK2)))),cartesian_product2(X0,X0)) )
| spl21_58 ),
inference(resolution,[],[f2608,f311]) ).
fof(f2679,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))),sK13(X0,sK1,sK2))
| ~ in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK4(sK13(sK0,sK1,sK2)),sK3(sK13(sK0,sK1,sK2)))),cartesian_product2(X0,X0)) )
| spl21_58 ),
inference(forward_demodulation,[],[f2667,f133]) ).
fof(f2680,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))),cartesian_product2(X0,X0))
| in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))),sK13(X0,sK1,sK2)) )
| spl21_58 ),
inference(forward_demodulation,[],[f2679,f133]) ).
fof(f2866,plain,
! [X0,X1] :
( ~ in(X0,sK13(X1,sK1,sK2))
| unordered_pair(singleton(sK17(X0)),unordered_pair(sK17(X0),sK18(X0))) = X0 ),
inference(resolution,[],[f1434,f88]) ).
fof(f2927,plain,
! [X0] :
( sK16(sK13(X0,sK1,sK2)) = unordered_pair(singleton(sK17(sK16(sK13(X0,sK1,sK2)))),unordered_pair(sK17(sK16(sK13(X0,sK1,sK2))),sK18(sK16(sK13(X0,sK1,sK2)))))
| relation(sK13(X0,sK1,sK2)) ),
inference(resolution,[],[f2866,f136]) ).
fof(f2928,plain,
! [X0] : relation(sK13(X0,sK1,sK2)),
inference(forward_subsumption_resolution,[],[f2927,f253]) ).
fof(f3100,plain,
( in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))),sK13(sK0,sK1,sK2))
| ~ in(sK3(sK13(sK0,sK1,sK2)),sK0)
| spl21_58 ),
inference(resolution,[],[f2680,f1552]) ).
fof(f3101,plain,
( in(unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))),sK13(sK0,sK1,sK2))
| spl21_58 ),
inference(forward_subsumption_resolution,[],[f3100,f1987]) ).
fof(f3102,plain,
( $false
| spl21_58 ),
inference(forward_subsumption_resolution,[],[f3101,f1555]) ).
fof(f3103,plain,
spl21_58,
inference(avatar_contradiction_clause,[],[f3102]) ).
fof(f3104,plain,
( $false
| spl21_59 ),
inference(forward_subsumption_resolution,[],[f2140,f1558]) ).
fof(f3105,plain,
spl21_59,
inference(avatar_contradiction_clause,[],[f3104]) ).
fof(f3106,plain,
( $false
| spl21_60 ),
inference(forward_subsumption_resolution,[],[f1561,f2928]) ).
fof(f3107,plain,
spl21_60,
inference(avatar_contradiction_clause,[],[f3106]) ).
fof(f3108,plain,
( unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))) = unordered_pair(singleton(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))))),unordered_pair(sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2))))),sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))))))
| spl21_61 ),
inference(resolution,[],[f1564,f2636]) ).
fof(f3176,plain,
( ! [X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2))))
| sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2))))) = X0 )
| spl21_61 ),
inference(superposition,[],[f265,f3108]) ).
fof(f3179,plain,
( ! [X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2))))
| sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2))))) = X1 )
| spl21_61 ),
inference(superposition,[],[f293,f3108]) ).
fof(f4143,plain,
( sK3(sK13(sK0,sK1,sK2)) = sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))))
| spl21_61 ),
inference(equality_resolution,[],[f3176]) ).
fof(f4613,plain,
( sK4(sK13(sK0,sK1,sK2)) = sK15(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))))
| spl21_61 ),
inference(equality_resolution,[],[f3179]) ).
fof(f4661,plain,
( in(unordered_pair(singleton(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2))))))),unordered_pair(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))))),apply(sK2,sK4(sK13(sK0,sK1,sK2))))),sK1)
| in(unordered_pair(singleton(apply(sK2,sK3(sK13(sK0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(sK0,sK1,sK2))),apply(sK2,sK4(sK13(sK0,sK1,sK2))))),sK1)
| spl21_61 ),
inference(superposition,[],[f2638,f4613]) ).
fof(f4662,plain,
( in(unordered_pair(singleton(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2))))))),unordered_pair(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))))),apply(sK2,sK4(sK13(sK0,sK1,sK2))))),sK1)
| spl21_61 ),
inference(forward_subsumption_resolution,[],[f4661,f1564]) ).
fof(f4667,plain,
( in(unordered_pair(singleton(apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2))))))),unordered_pair(apply(sK2,sK4(sK13(sK0,sK1,sK2))),apply(sK2,sK14(sK1,sK2,unordered_pair(singleton(sK3(sK13(sK0,sK1,sK2))),unordered_pair(sK3(sK13(sK0,sK1,sK2)),sK4(sK13(sK0,sK1,sK2)))))))),sK1)
| spl21_61 ),
inference(forward_demodulation,[],[f4662,f133]) ).
fof(f4670,plain,
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(sK0,sK1,sK2)))),unordered_pair(apply(sK2,sK4(sK13(sK0,sK1,sK2))),apply(sK2,sK3(sK13(sK0,sK1,sK2))))),sK1)
| spl21_61 ),
inference(forward_demodulation,[],[f4667,f4143]) ).
fof(f4672,plain,
( in(unordered_pair(singleton(apply(sK2,sK3(sK13(sK0,sK1,sK2)))),unordered_pair(apply(sK2,sK3(sK13(sK0,sK1,sK2))),apply(sK2,sK4(sK13(sK0,sK1,sK2))))),sK1)
| spl21_61 ),
inference(forward_demodulation,[],[f4670,f133]) ).
fof(f4675,plain,
( $false
| spl21_61 ),
inference(forward_subsumption_resolution,[],[f4672,f1564]) ).
fof(f4676,plain,
spl21_61,
inference(avatar_contradiction_clause,[],[f4675]) ).
cnf(s35,plain,
( ~ spl21_58
| ~ spl21_59
| ~ spl21_60
| ~ spl21_61 ),
inference(sat_conversion,[],[f1565]) ).
cnf(s78,plain,
spl21_58,
inference(sat_conversion,[],[f3103]) ).
cnf(s79,plain,
spl21_59,
inference(sat_conversion,[],[f3105]) ).
cnf(s80,plain,
spl21_60,
inference(sat_conversion,[],[f3107]) ).
cnf(s131,plain,
spl21_61,
inference(sat_conversion,[],[f4676]) ).
cnf(s132,plain,
$false,
inference(rat,[],[s35,s131,s80,s79,s78]) ).
fof(f4677,plain,
$false,
inference(avatar_sat_refutation,[],[s132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU278+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.34 % Computer : n012.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 28 04:27:19 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.37 Running first-order theorem proving
% 0.07/0.37 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
% 10.21/2.16 % (3014176)Detected formulas, will run a generic FOF schedule.
% 10.21/2.16 % (3014184)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=599871622:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.21/2.16 % (3014186)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=253599572:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.21/2.16 % (3014185)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1939551210:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.21/2.16 % (3014183)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=330806742:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.21/2.16 % (3014181)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=566618443:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.21/2.16 % (3014182)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=2759657171:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.21/2.16 % (3014187)dis-21_1_sil=8000:lcm=predicate:random_seed=1966143197: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)
% 10.21/2.16 % (3014184)Refutation not found, incomplete strategy
% 10.21/2.16 % (3014184)------------------------------
% 10.21/2.16 % (3014184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014184)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014184)Termination reason: Refutation not found, incomplete strategy
% 10.21/2.16 % (3014184)Time elapsed: 0.003 s
% 10.21/2.16 % (3014184)Peak memory usage: 88 MB
% 10.21/2.16 % (3014184)Instructions burned: 4 (million)
% 10.21/2.16 % (3014185)Instruction limit reached!
% 10.21/2.16 % (3014185)------------------------------
% 10.21/2.16 % (3014185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014185)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014185)Termination reason: Instruction limit
% 10.21/2.16 % (3014185)Termination phase: Saturation
% 10.21/2.16 % (3014185)Time elapsed: 0.057 s
% 10.21/2.16 % (3014185)Peak memory usage: 88 MB
% 10.21/2.16 % (3014185)Instructions burned: 121 (million)
% 10.21/2.16 % (3014187)Instruction limit reached!
% 10.21/2.16 % (3014187)------------------------------
% 10.21/2.16 % (3014187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014187)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014187)Termination reason: Instruction limit
% 10.21/2.16 % (3014187)Termination phase: Saturation
% 10.21/2.16 % (3014187)Time elapsed: 0.063 s
% 10.21/2.16 % (3014187)Peak memory usage: 89 MB
% 10.21/2.16 % (3014187)Instructions burned: 132 (million)
% 10.21/2.16 % (3014186)Instruction limit reached!
% 10.21/2.16 % (3014186)------------------------------
% 10.21/2.16 % (3014186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014186)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014186)Termination reason: Instruction limit
% 10.21/2.16 % (3014186)Termination phase: Saturation
% 10.21/2.16 % (3014186)Time elapsed: 0.067 s
% 10.21/2.16 % (3014186)Peak memory usage: 90 MB
% 10.21/2.16 % (3014186)Instructions burned: 141 (million)
% 10.21/2.16 % (3014184)------------------------------
% 10.21/2.16 % (3014184)------------------------------
% 10.21/2.16 % (3014197)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3259212562:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.21/2.16 % (3014195)lrs+10_1_sil=8000:sp=occurrence:random_seed=3884440400:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.21/2.16 % (3014196)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2612204631:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.21/2.16 % (3014198)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=3853426735:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 10.21/2.16 % (3014196)Instruction limit reached!
% 10.21/2.16 % (3014196)------------------------------
% 10.21/2.16 % (3014196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014196)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014196)Termination reason: Instruction limit
% 10.21/2.16 % (3014196)Termination phase: Saturation
% 10.21/2.16 % (3014196)Time elapsed: 0.073 s
% 10.21/2.16 % (3014196)Peak memory usage: 90 MB
% 10.21/2.16 % (3014196)Instructions burned: 159 (million)
% 10.21/2.16 % (3014197)Instruction limit reached!
% 10.21/2.16 % (3014197)------------------------------
% 10.21/2.16 % (3014197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014197)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014197)Termination reason: Instruction limit
% 10.21/2.16 % (3014197)Termination phase: Saturation
% 10.21/2.16 % (3014197)Time elapsed: 0.133 s
% 10.21/2.16 % (3014197)Peak memory usage: 90 MB
% 10.21/2.16 % (3014197)Instructions burned: 326 (million)
% 10.21/2.16 % (3014198)Instruction limit reached!
% 10.21/2.16 % (3014198)------------------------------
% 10.21/2.16 % (3014198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014198)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014198)Termination reason: Instruction limit
% 10.21/2.16 % (3014198)Termination phase: Saturation
% 10.21/2.16 % (3014198)Time elapsed: 0.100 s
% 10.21/2.16 % (3014198)Peak memory usage: 92 MB
% 10.21/2.16 % (3014198)Instructions burned: 249 (million)
% 10.21/2.16 % (3014195)Instruction limit reached!
% 10.21/2.16 % (3014195)------------------------------
% 10.21/2.16 % (3014195)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014195)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014195)Termination reason: Instruction limit
% 10.21/2.16 % (3014195)Termination phase: Saturation
% 10.21/2.16 % (3014195)Time elapsed: 0.140 s
% 10.21/2.16 % (3014195)Peak memory usage: 91 MB
% 10.21/2.16 % (3014195)Instructions burned: 286 (million)
% 10.21/2.16 % (3014203)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4008193731:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.21/2.16 % (3014203)Refutation not found, incomplete strategy
% 10.21/2.16 % (3014203)------------------------------
% 10.21/2.16 % (3014203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014203)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014203)Termination reason: Refutation not found, incomplete strategy
% 10.21/2.16 % (3014203)Time elapsed: 0.005 s
% 10.21/2.16 % (3014203)Peak memory usage: 89 MB
% 10.21/2.16 % (3014203)Instructions burned: 6 (million)
% 10.21/2.16 % (3014206)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4161392541:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 10.21/2.16 % (3014205)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1896646978:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 10.21/2.16 % (3014204)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3859583811:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.21/2.16 % (3014206)Instruction limit reached!
% 10.21/2.16 % (3014206)------------------------------
% 10.21/2.16 % (3014206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014206)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014206)Termination reason: Instruction limit
% 10.21/2.16 % (3014206)Termination phase: Saturation
% 10.21/2.16 % (3014206)Time elapsed: 0.040 s
% 10.21/2.16 % (3014206)Peak memory usage: 89 MB
% 10.21/2.16 % (3014206)Instructions burned: 130 (million)
% 10.21/2.16 % (3014205)Instruction limit reached!
% 10.21/2.16 % (3014205)------------------------------
% 10.21/2.16 % (3014205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014205)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014205)Termination reason: Instruction limit
% 10.21/2.16 % (3014205)Termination phase: Saturation
% 10.21/2.16 % (3014205)Time elapsed: 0.061 s
% 10.21/2.16 % (3014205)Peak memory usage: 89 MB
% 10.21/2.16 % (3014205)Instructions burned: 114 (million)
% 10.21/2.16 % (3014211)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1647472522:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 10.21/2.16 % (3014203)------------------------------
% 10.21/2.16 % (3014203)------------------------------
% 10.21/2.16 % (3014211)Instruction limit reached!
% 10.21/2.16 % (3014211)------------------------------
% 10.21/2.16 % (3014211)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014211)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014211)Termination reason: Instruction limit
% 10.21/2.16 % (3014211)Termination phase: Saturation
% 10.21/2.16 % (3014211)Time elapsed: 0.039 s
% 10.21/2.16 % (3014211)Peak memory usage: 89 MB
% 10.21/2.16 % (3014211)Instructions burned: 118 (million)
% 10.21/2.16 % (3014212)lrs+10_1_sil=8000:sp=occurrence:random_seed=2477717157:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.21/2.16 % (3014214)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3315043861:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 10.21/2.16 % (3014214)Refutation not found, incomplete strategy
% 10.21/2.16 % (3014214)------------------------------
% 10.21/2.16 % (3014214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014214)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014214)Termination reason: Refutation not found, incomplete strategy
% 10.21/2.16 % (3014214)Time elapsed: 0.019 s
% 10.21/2.16 % (3014214)Peak memory usage: 89 MB
% 10.21/2.16 % (3014214)Instructions burned: 53 (million)
% 10.21/2.16 % (3014215)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1056097248:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 10.21/2.16 % (3014182)First to succeed.
% 10.21/2.16 % (3014182)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3014176"
% 10.21/2.16 % (3014214)------------------------------
% 10.21/2.16 % (3014214)------------------------------
% 10.21/2.16 % (3014204)Also succeeded, but the first one will report.
% 10.21/2.16 % (3014212)Instruction limit reached!
% 10.21/2.16 % (3014212)------------------------------
% 10.21/2.16 % (3014212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.16 % (3014212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.16 % (3014212)CaDiCaL version: 2.1.3
% 10.21/2.16 % (3014212)Termination reason: Instruction limit
% 10.21/2.16 % (3014212)Termination phase: Saturation
% 10.21/2.16 % (3014212)Time elapsed: 0.440 s
% 10.21/2.16 % (3014212)Peak memory usage: 97 MB
% 10.21/2.16 % (3014212)Instructions burned: 908 (million)
% 10.21/2.16 % (3014182)Refutation found. Thanks to Tanya!
% 10.21/2.16 % SZS status Theorem for theBenchmark
% 10.21/2.16 % SZS output start Proof for theBenchmark
% See solution above
% 10.70/2.31 % (3014182)------------------------------
% 10.70/2.31 % (3014182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.70/2.31 % (3014182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.70/2.31 % (3014182)CaDiCaL version: 2.1.3
% 10.70/2.31 % (3014182)Termination reason: Refutation
% 10.70/2.31 % (3014182)Time elapsed: 1.043 s
% 10.70/2.31 % (3014182)Peak memory usage: 135 MB
% 10.70/2.31 % (3014182)Instructions burned: 1801 (million)
% 10.70/2.31 % (3014182)------------------------------
% 10.70/2.31 % (3014182)------------------------------
% 10.70/2.31 % (3014176)Success in time 1.456 s
% 10.70/2.31 % Vampire exiting
%------------------------------------------------------------------------------