%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 11:54:19 AM UTC 2026
% Result : Theorem 3.13s 1.35s
% Output : Refutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 70 ( 13 unt; 4 def)
% Number of atoms : 475 ( 0 equ)
% Maximal formula atoms : 29 ( 6 avg)
% Number of connectives : 857 ( 452 ~; 350 |; 51 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-1 aty)
% Number of variables : 255 ( 0 sgn 232 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| ~ p1(X3) ) )
& p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ~ ( ~ ! [X6] :
( ~ r1(X5,X6)
| ~ ! [X7] :
( ~ r1(X6,X7)
| p1(X7) ) )
& ~ ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) ) )
| ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ ! [X10] :
( ~ r1(X9,X10)
| ~ ! [X11] :
( ~ r1(X10,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
& ~ ! [X13] :
( ~ r1(X9,X13)
| ~ ! [X14] :
( ~ r1(X13,X14)
| p1(X14) ) ) ) )
| ~ ! [X15] :
( ~ r1(X0,X15)
| ~ ! [X16] :
( ~ r1(X15,X16)
| $false ) )
| ! [X17] :
( ~ r1(X0,X17)
| ! [X18] :
( ~ r1(X17,X18)
| ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) )
| ~ ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| ~ p1(X3) ) )
& p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ~ ( ~ ! [X6] :
( ~ r1(X5,X6)
| ~ ! [X7] :
( ~ r1(X6,X7)
| p1(X7) ) )
& ~ ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) ) )
| ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ ! [X10] :
( ~ r1(X9,X10)
| ~ ! [X11] :
( ~ r1(X10,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
& ~ ! [X13] :
( ~ r1(X9,X13)
| ~ ! [X14] :
( ~ r1(X13,X14)
| p1(X14) ) ) ) )
| ~ ! [X15] :
( ~ r1(X0,X15)
| ~ ! [X16] : ~ r1(X15,X16) )
| ! [X17] :
( ~ r1(X0,X17)
| ! [X18] :
( ~ r1(X17,X18)
| ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) )
| ~ ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(true_and_false_elimination,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| ~ p1(X3) ) )
& p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ~ ( ~ ! [X6] :
( ~ r1(X5,X6)
| ~ ! [X7] :
( ~ r1(X6,X7)
| p1(X7) ) )
& ~ ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) ) )
| ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ ! [X10] :
( ~ r1(X9,X10)
| ~ ! [X11] :
( ~ r1(X10,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
& ~ ! [X13] :
( ~ r1(X9,X13)
| ~ ! [X14] :
( ~ r1(X13,X14)
| p1(X14) ) ) ) )
| ~ ! [X15] :
( ~ r1(X0,X15)
| ~ ! [X16] : ~ r1(X15,X16) )
| ! [X17] :
( ~ r1(X0,X17)
| ! [X18] :
( ~ r1(X17,X18)
| ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) )
| ~ ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ? [X3] :
( r1(X2,X3)
& p1(X3) ) )
| ~ p1(X1) )
& ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ! [X6] :
( ~ r1(X5,X6)
| ? [X7] :
( r1(X6,X7)
& ~ p1(X7) ) )
| ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) )
& ! [X9] :
( ~ r1(X0,X9)
| ! [X10] :
( ~ r1(X9,X10)
| ? [X11] :
( r1(X10,X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
| ! [X13] :
( ~ r1(X9,X13)
| ? [X14] :
( r1(X13,X14)
& ~ p1(X14) ) ) )
& ! [X15] :
( ~ r1(X0,X15)
| ? [X16] : r1(X15,X16) )
& ? [X17] :
( r1(X0,X17)
& ? [X18] :
( r1(X17,X18)
& ? [X19] :
( r1(X18,X19)
& ~ p1(X19) ) )
& ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ? [X3] :
( r1(X2,X3)
& p1(X3) ) )
| ~ p1(X1) )
& ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ! [X6] :
( ~ r1(X5,X6)
| ? [X7] :
( r1(X6,X7)
& ~ p1(X7) ) )
| ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) )
& ! [X9] :
( ~ r1(X0,X9)
| ! [X10] :
( ~ r1(X9,X10)
| ? [X11] :
( r1(X10,X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
| ! [X13] :
( ~ r1(X9,X13)
| ? [X14] :
( r1(X13,X14)
& ~ p1(X14) ) ) )
& ! [X15] :
( ~ r1(X0,X15)
| ? [X16] : r1(X15,X16) )
& ? [X17] :
( r1(X0,X17)
& ? [X18] :
( r1(X17,X18)
& ? [X19] :
( r1(X18,X19)
& ~ p1(X19) ) )
& ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
( ! [X1] :
( ~ r1(sK0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ( r1(X2,sK1(X2))
& p1(sK1(X2)) ) )
| ~ p1(X1) )
& ! [X4] :
( ~ r1(sK0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ! [X6] :
( ~ r1(X5,X6)
| ( r1(X6,sK2(X6))
& ~ p1(sK2(X6)) ) )
| ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) )
& ! [X9] :
( ~ r1(sK0,X9)
| ! [X10] :
( ~ r1(X9,X10)
| ( r1(X10,sK3(X10))
& ! [X12] :
( ~ r1(sK3(X10),X12)
| p1(X12) ) ) )
| ! [X13] :
( ~ r1(X9,X13)
| ( r1(X13,sK4(X13))
& ~ p1(sK4(X13)) ) ) )
& ! [X15] :
( ~ r1(sK0,X15)
| r1(X15,sK5(X15)) )
& r1(sK0,sK6)
& r1(sK6,sK7)
& r1(sK7,sK8)
& ~ p1(sK8)
& ! [X20] :
( ~ r1(sK6,X20)
| p1(X20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X3,sK1(X2)),skolemize(X7,sK2(X6)),skolemize(X11,sK3(X10)),skolemize(X14,sK4(X13)),skolemize(X16,sK5(X15)),skolemize(X17,sK6),skolemize(X18,sK7),skolemize(X19,sK8)],[f8]) ).
fof(f10,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X20] :
( p1(X20)
| ~ r1(sK6,X20) ),
inference(cnf_transformation,[],[f9]) ).
fof(f12,plain,
~ p1(sK8),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
r1(sK7,sK8),
inference(cnf_transformation,[],[f9]) ).
fof(f14,plain,
r1(sK6,sK7),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
r1(sK0,sK6),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X10,X9,X12,X13] :
( ~ p1(sK4(X13))
| ~ r1(X9,X10)
| ~ r1(sK3(X10),X12)
| p1(X12)
| ~ r1(X9,X13)
| ~ r1(sK0,X9) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
! [X10,X9,X12,X13] :
( r1(X13,sK4(X13))
| ~ r1(X9,X10)
| ~ r1(sK3(X10),X12)
| p1(X12)
| ~ r1(X9,X13)
| ~ r1(sK0,X9) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X10,X9,X13] :
( r1(X10,sK3(X10))
| ~ r1(X9,X10)
| ~ r1(sK0,X9)
| ~ r1(X9,X13)
| ~ p1(sK4(X13)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
! [X10,X9,X13] :
( r1(X13,sK4(X13))
| ~ r1(X9,X10)
| r1(X10,sK3(X10))
| ~ r1(X9,X13)
| ~ r1(sK0,X9) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X8,X6,X4,X5] :
( ~ p1(sK2(X6))
| ~ r1(X4,X5)
| ~ r1(X5,X6)
| ~ r1(sK0,X4)
| ~ r1(X5,X8)
| p1(X8) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X8,X6,X4,X5] :
( r1(X6,sK2(X6))
| ~ r1(X4,X5)
| ~ r1(X5,X6)
| ~ r1(sK0,X4)
| ~ r1(X5,X8)
| p1(X8) ),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( ~ r1(sK6,sK4(X3))
| ~ r1(sK3(X1),X2)
| p1(X2)
| ~ r1(X0,X3)
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(resolution,[],[f17,f11]) ).
fof(f37,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r1(sK3(X0),X1)
| p1(X1)
| ~ r1(X2,sK6)
| ~ r1(sK0,X2)
| ~ r1(X2,X0)
| ~ r1(X3,X4)
| ~ r1(sK3(X4),X5)
| p1(X5)
| ~ r1(X3,sK6)
| ~ r1(sK0,X3) ),
inference(resolution,[],[f27,f18]) ).
fof(f42,definition,
( spl9_2
<=> ! [X4,X3] :
( ~ r1(X3,X4)
| ~ r1(sK0,X3)
| ~ r1(X3,sK6)
| r1(X4,sK3(X4)) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f43,plain,
( ! [X3,X4] :
( r1(X4,sK3(X4))
| ~ r1(sK0,X3)
| ~ r1(X3,sK6)
| ~ r1(X3,X4) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,definition,
( spl9_3
<=> ! [X2,X0,X1] :
( ~ r1(sK3(X0),X1)
| ~ r1(X2,sK6)
| ~ r1(X2,X0)
| ~ r1(sK0,X2)
| p1(X1) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f46,plain,
( ! [X2,X0,X1] :
( ~ r1(X2,sK6)
| ~ r1(sK3(X0),X1)
| ~ r1(X2,X0)
| ~ r1(sK0,X2)
| p1(X1) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( spl9_3
| spl9_3 ),
inference(avatar_split_clause,[],[f37,f45,f45]) ).
fof(f84,plain,
( ! [X0,X1] :
( ~ r1(sK3(X0),X1)
| ~ r1(sK6,X0)
| ~ r1(sK0,sK6)
| p1(X1) )
| ~ spl9_3 ),
inference(resolution,[],[f46,f10]) ).
fof(f96,plain,
( ! [X0,X1] :
( p1(X1)
| ~ r1(sK6,X0)
| ~ r1(sK3(X0),X1) )
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f84,f15]) ).
fof(f113,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ r1(sK3(X0),sK2(X1))
| ~ r1(sK6,X0)
| ~ r1(X2,X3)
| ~ r1(X3,X1)
| ~ r1(sK0,X2)
| ~ r1(X3,X4)
| p1(X4) )
| ~ spl9_3 ),
inference(resolution,[],[f96,f21]) ).
fof(f202,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( p1(X6)
| ~ r1(X1,X2)
| ~ r1(X2,sK3(X0))
| ~ r1(sK0,X1)
| ~ r1(X2,X3)
| p1(X3)
| ~ r1(X4,X5)
| ~ r1(X5,sK3(X0))
| ~ r1(sK0,X4)
| ~ r1(X5,X6)
| ~ r1(sK6,X0) )
| ~ spl9_3 ),
inference(resolution,[],[f113,f22]) ).
fof(f230,definition,
( spl9_24
<=> ! [X0] :
( ~ r1(X0,sK7)
| ~ r1(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition]) ).
fof(f231,plain,
( ! [X0] :
( ~ r1(X0,sK7)
| ~ r1(sK0,X0) )
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f324,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ r1(X5,sK8)
| ~ r1(X1,sK3(X2))
| ~ r1(sK0,X0)
| ~ r1(X1,X3)
| p1(X3)
| ~ r1(X4,X5)
| ~ r1(X5,sK3(X2))
| ~ r1(sK0,X4)
| ~ r1(X0,X1)
| ~ r1(sK6,X2) )
| ~ spl9_3 ),
inference(resolution,[],[f202,f12]) ).
fof(f487,plain,
( ! [X2,X3,X0,X1] :
( ~ r1(X0,sK8)
| ~ r1(X0,sK3(X1))
| ~ r1(sK0,X2)
| p1(sK8)
| ~ r1(X3,X0)
| ~ r1(X0,sK3(X1))
| ~ r1(sK0,X3)
| ~ r1(X2,X0)
| ~ r1(sK6,X1) )
| ~ spl9_3 ),
inference(factoring,[],[f324]) ).
fof(f492,plain,
( ! [X2,X3,X0,X1] :
( ~ r1(X0,sK8)
| ~ r1(X0,sK3(X1))
| ~ r1(sK0,X2)
| p1(sK8)
| ~ r1(X3,X0)
| ~ r1(sK0,X3)
| ~ r1(X2,X0)
| ~ r1(sK6,X1) )
| ~ spl9_3 ),
inference(duplicate_literal_removal,[],[f487]) ).
fof(f497,plain,
( ! [X2,X3,X0,X1] :
( ~ r1(X0,sK8)
| ~ r1(X0,sK3(X1))
| ~ r1(sK0,X2)
| ~ r1(X3,X0)
| ~ r1(sK0,X3)
| ~ r1(X2,X0)
| ~ r1(sK6,X1) )
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f492,f12]) ).
fof(f523,plain,
( ~ r1(sK0,sK6)
| ~ spl9_24 ),
inference(resolution,[],[f231,f14]) ).
fof(f524,plain,
( $false
| ~ spl9_24 ),
inference(forward_subsumption_resolution,[],[f523,f15]) ).
fof(f525,plain,
~ spl9_24,
inference(avatar_contradiction_clause,[],[f524]) ).
fof(f658,plain,
( ! [X2,X0,X1] :
( ~ r1(sK7,sK3(X0))
| ~ r1(sK0,X1)
| ~ r1(X2,sK7)
| ~ r1(sK0,X2)
| ~ r1(X1,sK7)
| ~ r1(sK6,X0) )
| ~ spl9_3 ),
inference(resolution,[],[f497,f13]) ).
fof(f665,definition,
( spl9_62
<=> ! [X0] :
( ~ r1(sK7,sK3(X0))
| ~ r1(sK6,X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_62])],[avatar_definition]) ).
fof(f666,plain,
( ! [X0] :
( ~ r1(sK7,sK3(X0))
| ~ r1(sK6,X0) )
| ~ spl9_62 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f667,plain,
( spl9_24
| spl9_24
| spl9_62
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f658,f45,f665,f230,f230]) ).
fof(f671,plain,
( ! [X0] :
( ~ r1(sK6,sK7)
| ~ r1(sK0,X0)
| ~ r1(X0,sK6)
| ~ r1(X0,sK7) )
| ~ spl9_2
| ~ spl9_62 ),
inference(resolution,[],[f666,f43]) ).
fof(f672,plain,
( ! [X0,X1] :
( ~ r1(sK6,sK7)
| ~ r1(X0,sK7)
| ~ r1(sK0,X0)
| ~ r1(X0,X1)
| ~ p1(sK4(X1)) )
| ~ spl9_62 ),
inference(resolution,[],[f666,f19]) ).
fof(f673,plain,
( ! [X0,X1] :
( ~ r1(X0,sK7)
| ~ r1(sK0,X0)
| ~ r1(X0,X1)
| ~ p1(sK4(X1)) )
| ~ spl9_62 ),
inference(forward_subsumption_resolution,[],[f672,f14]) ).
fof(f674,plain,
( ! [X0] :
( ~ r1(X0,sK7)
| ~ r1(X0,sK6)
| ~ r1(sK0,X0) )
| ~ spl9_2
| ~ spl9_62 ),
inference(forward_subsumption_resolution,[],[f671,f14]) ).
fof(f679,plain,
( ~ r1(sK6,sK6)
| ~ r1(sK0,sK6)
| ~ spl9_2
| ~ spl9_62 ),
inference(resolution,[],[f674,f14]) ).
fof(f680,plain,
( ~ r1(sK0,sK6)
| ~ spl9_2
| ~ spl9_62 ),
inference(forward_subsumption_resolution,[],[f679,f10]) ).
fof(f681,plain,
( $false
| ~ spl9_2
| ~ spl9_62 ),
inference(forward_subsumption_resolution,[],[f680,f15]) ).
fof(f682,plain,
( ~ spl9_2
| ~ spl9_62 ),
inference(avatar_contradiction_clause,[],[f681]) ).
fof(f709,plain,
( ! [X0] :
( ~ r1(sK0,sK6)
| ~ r1(sK6,X0)
| ~ p1(sK4(X0)) )
| ~ spl9_62 ),
inference(resolution,[],[f673,f14]) ).
fof(f716,plain,
( ! [X0] :
( ~ r1(sK6,X0)
| ~ p1(sK4(X0)) )
| ~ spl9_62 ),
inference(forward_subsumption_resolution,[],[f709,f15]) ).
fof(f776,plain,
( ~ p1(sK4(sK6))
| ~ spl9_62 ),
inference(resolution,[],[f716,f10]) ).
fof(f818,plain,
( ~ r1(sK6,sK4(sK6))
| ~ spl9_62 ),
inference(resolution,[],[f776,f11]) ).
fof(f945,plain,
( ! [X0,X1] :
( ~ r1(X0,X1)
| r1(X1,sK3(X1))
| ~ r1(X0,sK6)
| ~ r1(sK0,X0) )
| ~ spl9_62 ),
inference(resolution,[],[f818,f20]) ).
fof(f946,plain,
( spl9_2
| ~ spl9_62 ),
inference(avatar_split_clause,[],[f945,f665,f42]) ).
cnf(s4,plain,
( spl9_3
| spl9_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
spl9_3,
inference(rat,[],[s4]) ).
cnf(s68,plain,
~ spl9_24,
inference(sat_conversion,[],[f525]) ).
cnf(s82,plain,
( spl9_24
| ~ spl9_3
| spl9_24
| spl9_62 ),
inference(sat_conversion,[],[f667]) ).
cnf(s83,plain,
( ~ spl9_3
| spl9_24
| spl9_62 ),
inference(rat,[],[s82]) ).
cnf(s84,plain,
( ~ spl9_2
| ~ spl9_62 ),
inference(sat_conversion,[],[f682]) ).
cnf(s99,plain,
( spl9_2
| ~ spl9_62 ),
inference(sat_conversion,[],[f946]) ).
cnf(s110,plain,
spl9_62,
inference(rat,[],[s83,s68,s5]) ).
cnf(s117,plain,
spl9_2,
inference(rat,[],[s99,s110]) ).
cnf(s119,plain,
$false,
inference(rat,[],[s84,s110,s117]) ).
fof(f947,plain,
$false,
inference(avatar_sat_refutation,[],[s119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 16:20:08 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.13/1.35 % (2559822)Detected formulas, will run a generic FOF schedule.
% 3.13/1.35 % (2559827)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=1638975916:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.13/1.35 % (2559833)dis-21_1_sil=8000:lcm=predicate:random_seed=3714739062: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)
% 3.13/1.35 % (2559830)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2846961296:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.13/1.35 % (2559828)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=303852119:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.13/1.35 % (2559829)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=618734045:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.13/1.35 % (2559831)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=292733328:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.13/1.35 % (2559832)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=548030827:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.13/1.35 % (2559832)First to succeed.
% 3.13/1.35 % (2559832)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2559822"
% 3.13/1.35 % (2559830)Also succeeded, but the first one will report.
% 3.13/1.35 % (2559833)Instruction limit reached!
% 3.13/1.35 % (2559833)------------------------------
% 3.13/1.35 % (2559833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2559833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2559833)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2559833)Termination reason: Instruction limit
% 3.13/1.35 % (2559833)Termination phase: Saturation
% 3.13/1.35 % (2559833)Time elapsed: 0.062 s
% 3.13/1.35 % (2559833)Peak memory usage: 88 MB
% 3.13/1.35 % (2559833)Instructions burned: 131 (million)
% 3.13/1.35 % (2559831)Instruction limit reached!
% 3.13/1.35 % (2559831)------------------------------
% 3.13/1.35 % (2559831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2559831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2559831)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2559831)Termination reason: Instruction limit
% 3.13/1.35 % (2559831)Termination phase: Saturation
% 3.13/1.35 % (2559831)Time elapsed: 0.063 s
% 3.13/1.35 % (2559831)Peak memory usage: 87 MB
% 3.13/1.35 % (2559831)Instructions burned: 121 (million)
% 3.13/1.35 % (2559841)lrs+10_1_sil=8000:sp=occurrence:random_seed=1663088338:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.13/1.35 % (2559842)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1743762:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.13/1.35 % (2559842)Refutation not found, incomplete strategy
% 3.13/1.35 % (2559842)------------------------------
% 3.13/1.35 % (2559842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2559842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2559842)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2559842)Termination reason: Refutation not found, incomplete strategy
% 3.13/1.35 % (2559842)Time elapsed: 0.007 s
% 3.13/1.35 % (2559842)Peak memory usage: 88 MB
% 3.13/1.35 % (2559842)Instructions burned: 11 (million)
% 3.13/1.35 % (2559841)Also succeeded, but the first one will report.
% 3.13/1.35 % (2559832)Refutation found. Thanks to Tanya!
% 3.13/1.35 % SZS status Theorem for theBenchmark
% 3.13/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.06/1.55 % (2559832)------------------------------
% 4.06/1.55 % (2559832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.55 % (2559832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.55 % (2559832)CaDiCaL version: 2.1.3
% 4.06/1.55 % (2559832)Termination reason: Refutation
% 4.06/1.55 % (2559832)Time elapsed: 0.058 s
% 4.06/1.55 % (2559832)Peak memory usage: 90 MB
% 4.06/1.55 % (2559832)Instructions burned: 103 (million)
% 4.06/1.55 % (2559832)------------------------------
% 4.06/1.55 % (2559832)------------------------------
% 4.06/1.55 % (2559822)Success in time 0.484 s
% 4.06/1.55 % Vampire exiting
%------------------------------------------------------------------------------