%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL395+2 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 11:52:17 AM UTC 2026
% Result : Theorem 19.50s 3.99s
% Output : Refutation 20.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 5
% Syntax : Number of formulae : 93 ( 16 unt; 2 def)
% Number of atoms : 205 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 227 ( 115 ~; 108 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 300 ( 0 sgn 300 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14] : is_a_theorem(implies(implies(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5),implies(implies(implies(implies(implies(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))),implies(implies(implies(n(X9),X9),X9),X10)),X10),implies(implies(X11,implies(n(X11),X12)),X13)),X13),X14)),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f2) ).
fof(f3,conjecture,
is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(n(x),z),y)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f3) ).
fof(f4,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(n(x),z),y)))),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(n(x),z),y)))),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] : is_a_theorem(implies(implies(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5),implies(implies(implies(implies(implies(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))),implies(implies(implies(n(X9),X9),X9),X10)),X10),implies(implies(X11,implies(n(X11),X12)),X13)),X13),X14)),X14)),
inference(cnf_transformation,[],[f2]) ).
fof(f10,plain,
~ is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(n(x),z),y)))),
inference(cnf_transformation,[],[f5]) ).
fof(f11,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ is_a_theorem(implies(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6),implies(implies(implies(implies(implies(implies(implies(X7,X8),implies(implies(X8,X9),implies(X7,X9))),implies(implies(implies(n(X10),X10),X10),X11)),X11),implies(implies(X12,implies(n(X12),X13)),X14)),X14),X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f9,f8]) ).
fof(f12,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[],[f11,f9]) ).
fof(f13,plain,
! [X2,X3,X0,X1,X4,X5] : is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5)),
inference(resolution,[],[f12,f11]) ).
fof(f15,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[],[f13,f11]) ).
fof(f16,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ is_a_theorem(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f13,f8]) ).
fof(f17,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : is_a_theorem(implies(X0,implies(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X8)),X8))),
inference(resolution,[],[f15,f11]) ).
fof(f19,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( is_a_theorem(implies(implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4),implies(implies(X5,implies(n(X5),X6)),X7)),X7))
| ~ is_a_theorem(X8) ),
inference(resolution,[],[f17,f8]) ).
fof(f21,definition,
( spl0_1
<=> ! [X8] : ~ is_a_theorem(X8) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( ! [X8] : ~ is_a_theorem(X8)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,definition,
( spl0_2
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] : is_a_theorem(implies(implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4),implies(implies(X5,implies(n(X5),X6)),X7)),X7)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f25,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : is_a_theorem(implies(implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4),implies(implies(X5,implies(n(X5),X6)),X7)),X7))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f19,f24,f21]) ).
fof(f28,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ is_a_theorem(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X0)))
| is_a_theorem(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f25,f8]) ).
fof(f31,plain,
( ! [X2,X3,X0,X1,X4] : is_a_theorem(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4))
| ~ spl0_2 ),
inference(resolution,[],[f28,f12]) ).
fof(f32,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(n(X1),X2))))
| ~ spl0_2 ),
inference(resolution,[],[f28,f15]) ).
fof(f54,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f22,f13]) ).
fof(f67,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f54]) ).
fof(f81,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),implies(X3,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f16,f31]) ).
fof(f90,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f81,f28]) ).
fof(f96,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) )
| ~ spl0_2 ),
inference(resolution,[],[f90,f8]) ).
fof(f100,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f96,f8]) ).
fof(f106,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X3,X2))))
| ~ is_a_theorem(implies(X0,implies(X3,X1))) )
| ~ spl0_2 ),
inference(resolution,[],[f100,f90]) ).
fof(f108,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f100,f12]) ).
fof(f122,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2))
| is_a_theorem(X2) )
| ~ spl0_2 ),
inference(resolution,[],[f108,f16]) ).
fof(f130,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f122,f90]) ).
fof(f137,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X3,implies(X4,X3)),implies(X2,X0)))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) )
| ~ spl0_2 ),
inference(resolution,[],[f122,f106]) ).
fof(f144,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X2,X0),X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f130,f8]) ).
fof(f159,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))
| ~ spl0_2 ),
inference(resolution,[],[f137,f31]) ).
fof(f169,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(n(X0),X1),X2),implies(X0,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f137,f32]) ).
fof(f181,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(implies(implies(X1,X3),implies(X0,X3)),X2))
| is_a_theorem(implies(implies(X0,X1),X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f159,f8]) ).
fof(f190,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,X3))))
| ~ is_a_theorem(implies(X2,implies(X1,X3))) )
| ~ spl0_2 ),
inference(resolution,[],[f181,f96]) ).
fof(f240,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(n(X1),X3),X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f169,f100]) ).
fof(f280,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(implies(implies(n(X0),X0),X0),X1),X1))
| ~ spl0_2 ),
inference(resolution,[],[f144,f31]) ).
fof(f288,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,X1))))
| ~ spl0_2 ),
inference(resolution,[],[f144,f90]) ).
fof(f318,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X0,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f280,f181]) ).
fof(f330,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X1),implies(implies(X1,X0),X0)))
| ~ spl0_2 ),
inference(resolution,[],[f318,f181]) ).
fof(f333,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,implies(n(X2),X2))))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f318,f100]) ).
fof(f338,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f330,f144]) ).
fof(f342,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(n(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f330,f8]) ).
fof(f359,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f333,f15]) ).
fof(f389,plain,
( ! [X0,X1] : is_a_theorem(implies(n(X0),implies(X0,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f338,f240]) ).
fof(f398,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),X0))
| ~ spl0_2 ),
inference(resolution,[],[f342,f389]) ).
fof(f423,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1))
| ~ spl0_2 ),
inference(resolution,[],[f359,f342]) ).
fof(f447,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f398,f181]) ).
fof(f448,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X1,X2),X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f398,f100]) ).
fof(f465,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,implies(X1,X2))))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f447,f100]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f465,f190]) ).
fof(f546,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X1,implies(X0,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f527,f144]) ).
fof(f616,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))
| ~ spl0_2 ),
inference(resolution,[],[f546,f90]) ).
fof(f633,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X2,X1))))
| ~ spl0_2 ),
inference(resolution,[],[f546,f288]) ).
fof(f652,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X1,X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f616,f8]) ).
fof(f686,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X0),implies(X1,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f652,f465]) ).
fof(f701,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),X3)))
| is_a_theorem(implies(implies(X0,X2),implies(implies(X2,X1),X3))) )
| ~ spl0_2 ),
inference(resolution,[],[f686,f181]) ).
fof(f804,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),X2),X1),implies(X0,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f633,f448]) ).
fof(f823,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X3),X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f804,f100]) ).
fof(f1082,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X2,X2),X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f423,f100]) ).
fof(f1183,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(implies(implies(X2,X1),X3),X0))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) )
| ~ spl0_2 ),
inference(resolution,[],[f823,f96]) ).
fof(f1215,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),implies(X2,X0)))
| ~ spl0_2 ),
inference(resolution,[],[f1183,f130]) ).
fof(f1257,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X0),X0)))
| ~ spl0_2 ),
inference(resolution,[],[f1215,f701]) ).
fof(f1332,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f1257,f181]) ).
fof(f1364,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X0,X2),X2)))
| ~ spl0_2 ),
inference(resolution,[],[f1332,f546]) ).
fof(f1377,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f1364,f1183]) ).
fof(f1389,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X1,X3),X2)))
| is_a_theorem(implies(X0,implies(implies(X1,X2),X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f1364,f100]) ).
fof(f1399,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f1377,f181]) ).
fof(f1416,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(implies(X1,X3),X3),X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f1377,f100]) ).
fof(f1425,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(X0,implies(implies(X1,X2),X2))))
| ~ spl0_2 ),
inference(resolution,[],[f1399,f181]) ).
fof(f1458,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(implies(X1,X2),X2)))
| ~ spl0_2 ),
inference(resolution,[],[f1425,f1082]) ).
fof(f1494,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X3,X3),X1)))
| is_a_theorem(implies(X0,implies(implies(X1,X2),X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f1458,f100]) ).
fof(f1718,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X0),implies(implies(X0,X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f1494,f330]) ).
fof(f1747,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(n(X0),X0),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f1718,f546]) ).
fof(f1760,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(n(X0),X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f1747,f1389]) ).
fof(f1791,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X1),implies(implies(X0,X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f1760,f546]) ).
fof(f1812,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X1,X2),X2)))
| ~ is_a_theorem(implies(X0,implies(n(X1),X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f1791,f100]) ).
fof(f1840,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(n(X1),X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f1812,f546]) ).
fof(f2272,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(n(X1),X2)))
| is_a_theorem(implies(X3,implies(X0,X2)))
| ~ is_a_theorem(implies(X3,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f1840,f100]) ).
fof(f3058,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(X2,implies(implies(X2,X0),X1))))
| ~ spl0_2 ),
inference(resolution,[],[f1416,f616]) ).
fof(f3108,plain,
( $false
| ~ spl0_2 ),
inference(unit_resulting_resolution,[],[f2272,f633,f10,f3058]) ).
fof(f3144,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f3108]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s9,plain,
~ spl0_1,
inference(sat_conversion,[],[f67]) ).
cnf(s22,plain,
~ spl0_2,
inference(sat_conversion,[],[f3144]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s1,s22,s9]) ).
fof(f3145,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL395+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 15:42:26 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.50/3.97 % (3019324)Detected formulas, will run a generic FOF schedule.
% 19.50/3.97 % (3019333)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2021469770:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 19.50/3.97 % (3019329)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=3398432026:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 19.50/3.97 % (3019330)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=3724326543:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 19.50/3.97 % (3019333)Instruction limit reached!
% 19.50/3.97 % (3019333)------------------------------
% 19.50/3.97 % (3019333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.97 % (3019333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.97 % (3019333)CaDiCaL version: 2.1.3
% 19.50/3.97 % (3019333)Termination reason: Instruction limit
% 19.50/3.97 % (3019333)Termination phase: Saturation
% 19.50/3.97 % (3019333)Time elapsed: 0.065 s
% 19.50/3.97 % (3019333)Peak memory usage: 88 MB
% 19.50/3.97 % (3019333)Instructions burned: 120 (million)
% 19.50/3.97 % (3019334)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=609390150:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 19.50/3.97 % (3019331)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=2583704050:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 19.50/3.97 % (3019332)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2860920418:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 19.50/3.97 % (3019335)dis-21_1_sil=8000:lcm=predicate:random_seed=439418964: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)
% 19.50/3.97 % (3019332)Refutation not found, incomplete strategy
% 19.50/3.97 % (3019332)------------------------------
% 19.50/3.97 % (3019332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.97 % (3019332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.97 % (3019332)CaDiCaL version: 2.1.3
% 19.50/3.97 % (3019332)Termination reason: Refutation not found, incomplete strategy
% 19.50/3.97 % (3019332)Time elapsed: 0.002 s
% 19.50/3.97 % (3019332)Peak memory usage: 87 MB
% 19.50/3.97 % (3019335)Instruction limit reached!
% 19.50/3.97 % (3019335)------------------------------
% 19.50/3.97 % (3019335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.97 % (3019335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.97 % (3019335)CaDiCaL version: 2.1.3
% 19.50/3.97 % (3019335)Termination reason: Instruction limit
% 19.50/3.97 % (3019335)Termination phase: Saturation
% 19.50/3.97 % (3019335)Time elapsed: 0.131 s
% 19.50/3.97 % (3019335)Peak memory usage: 89 MB
% 19.50/3.97 % (3019335)Instructions burned: 129 (million)
% 19.50/3.97 % (3019334)Instruction limit reached!
% 19.50/3.97 % (3019334)------------------------------
% 19.50/3.97 % (3019334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.97 % (3019334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.97 % (3019334)CaDiCaL version: 2.1.3
% 19.50/3.97 % (3019334)Termination reason: Instruction limit
% 19.50/3.97 % (3019334)Termination phase: Saturation
% 19.50/3.97 % (3019334)Time elapsed: 0.133 s
% 19.50/3.97 % (3019334)Peak memory usage: 89 MB
% 19.50/3.97 % (3019334)Instructions burned: 139 (million)
% 19.50/3.97 % (3019339)lrs+10_1_sil=8000:sp=occurrence:random_seed=2800761898:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 19.50/3.97 % (3019344)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2362631677:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 19.50/3.97 % (3019345)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1498852093:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 19.50/3.97 % (3019332)------------------------------
% 19.50/3.97 % (3019332)------------------------------
% 19.50/3.97 % (3019344)Instruction limit reached!
% 19.50/3.97 % (3019344)------------------------------
% 19.50/3.97 % (3019344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.97 % (3019344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019344)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019344)Termination reason: Instruction limit
% 19.50/3.99 % (3019344)Termination phase: Saturation
% 19.50/3.99 % (3019344)Time elapsed: 0.072 s
% 19.50/3.99 % (3019344)Peak memory usage: 88 MB
% 19.50/3.99 % (3019344)Instructions burned: 159 (million)
% 19.50/3.99 % (3019339)Instruction limit reached!
% 19.50/3.99 % (3019339)------------------------------
% 19.50/3.99 % (3019339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019339)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019339)Termination reason: Instruction limit
% 19.50/3.99 % (3019339)Termination phase: Saturation
% 19.50/3.99 % (3019339)Time elapsed: 0.281 s
% 19.50/3.99 % (3019339)Peak memory usage: 91 MB
% 19.50/3.99 % (3019339)Instructions burned: 286 (million)
% 19.50/3.99 % (3019350)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3511290830:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 19.50/3.99 % (3019350)Refutation not found, incomplete strategy
% 19.50/3.99 % (3019350)------------------------------
% 19.50/3.99 % (3019350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019350)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019350)Termination reason: Refutation not found, incomplete strategy
% 19.50/3.99 % (3019350)Time elapsed: 0.001 s
% 19.50/3.99 % (3019350)Peak memory usage: 87 MB
% 19.50/3.99 % (3019349)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=2641789921:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 19.50/3.99 % (3019345)Instruction limit reached!
% 19.50/3.99 % (3019345)------------------------------
% 19.50/3.99 % (3019345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019345)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019345)Termination reason: Instruction limit
% 19.50/3.99 % (3019345)Termination phase: Saturation
% 19.50/3.99 % (3019345)Time elapsed: 0.310 s
% 19.50/3.99 % (3019345)Peak memory usage: 90 MB
% 19.50/3.99 % (3019345)Instructions burned: 327 (million)
% 19.50/3.99 % (3019351)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=652305217:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 19.50/3.99 % (3019349)Instruction limit reached!
% 19.50/3.99 % (3019349)------------------------------
% 19.50/3.99 % (3019349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019349)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019349)Termination reason: Instruction limit
% 19.50/3.99 % (3019349)Termination phase: Saturation
% 19.50/3.99 % (3019349)Time elapsed: 0.211 s
% 19.50/3.99 % (3019349)Peak memory usage: 88 MB
% 19.50/3.99 % (3019349)Instructions burned: 249 (million)
% 19.50/3.99 % (3019350)------------------------------
% 19.50/3.99 % (3019350)------------------------------
% 19.50/3.99 % (3019354)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=274044637:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 19.50/3.99 % (3019357)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1151097756:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2988 on theBenchmark for (2988ds/114Mi)
% 19.50/3.99 % (3019354)Instruction limit reached!
% 19.50/3.99 % (3019354)------------------------------
% 19.50/3.99 % (3019354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019354)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019354)Termination reason: Instruction limit
% 19.50/3.99 % (3019354)Termination phase: Saturation
% 19.50/3.99 % (3019354)Time elapsed: 0.102 s
% 19.50/3.99 % (3019354)Peak memory usage: 88 MB
% 19.50/3.99 % (3019354)Instructions burned: 113 (million)
% 19.50/3.99 % (3019357)Instruction limit reached!
% 19.50/3.99 % (3019357)------------------------------
% 19.50/3.99 % (3019357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019357)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019357)Termination reason: Instruction limit
% 19.50/3.99 % (3019357)Termination phase: Saturation
% 19.50/3.99 % (3019357)Time elapsed: 0.052 s
% 19.50/3.99 % (3019357)Peak memory usage: 89 MB
% 19.50/3.99 % (3019357)Instructions burned: 115 (million)
% 19.50/3.99 % (3019356)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=870402149:i=127:av=off:fsr=off:sup=off_2988 on theBenchmark for (2988ds/127Mi)
% 19.50/3.99 % (3019356)Instruction limit reached!
% 19.50/3.99 % (3019356)------------------------------
% 19.50/3.99 % (3019356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019356)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019356)Termination reason: Instruction limit
% 19.50/3.99 % (3019356)Termination phase: Saturation
% 19.50/3.99 % (3019356)Time elapsed: 0.110 s
% 19.50/3.99 % (3019356)Peak memory usage: 87 MB
% 19.50/3.99 % (3019356)Instructions burned: 128 (million)
% 19.50/3.99 % (3019361)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1370139893:i=437:sd=1:aac=none:ss=included_2985 on theBenchmark for (2985ds/437Mi)
% 19.50/3.99 % (3019361)Refutation not found, incomplete strategy
% 19.50/3.99 % (3019361)------------------------------
% 19.50/3.99 % (3019361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019361)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019361)Termination reason: Refutation not found, incomplete strategy
% 19.50/3.99 % (3019361)Time elapsed: 0.001 s
% 19.50/3.99 % (3019361)Peak memory usage: 88 MB
% 19.50/3.99 % (3019360)lrs+10_1_sil=8000:sp=occurrence:random_seed=473087462:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2986 on theBenchmark for (2986ds/907Mi)
% 19.50/3.99 % (3019363)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3817631629:i=5202:ss=axioms:sgt=16_2984 on theBenchmark for (2984ds/5202Mi)
% 19.50/3.99 % (3019361)------------------------------
% 19.50/3.99 % (3019361)------------------------------
% 19.50/3.99 % (3019367)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=308268979:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2981 on theBenchmark for (2981ds/134Mi)
% 19.50/3.99 % (3019367)Instruction limit reached!
% 19.50/3.99 % (3019367)------------------------------
% 19.50/3.99 % (3019367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019367)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019367)Termination reason: Instruction limit
% 19.50/3.99 % (3019367)Termination phase: Saturation
% 19.50/3.99 % (3019367)Time elapsed: 0.060 s
% 19.50/3.99 % (3019367)Peak memory usage: 89 MB
% 19.50/3.99 % (3019367)Instructions burned: 136 (million)
% 19.50/3.99 % (3019330)First to succeed.
% 19.50/3.99 % (3019330)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3019324"
% 19.50/3.99 % (3019369)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1025363841:st=8:i=592:sd=3:ep=RST:ss=axioms_2978 on theBenchmark for (2978ds/592Mi)
% 19.50/3.99 % (3019369)Refutation not found, incomplete strategy
% 19.50/3.99 % (3019369)------------------------------
% 19.50/3.99 % (3019369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019369)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019369)Termination reason: Refutation not found, incomplete strategy
% 19.50/3.99 % (3019369)Time elapsed: 0.001 s
% 19.50/3.99 % (3019369)Peak memory usage: 87 MB
% 19.50/3.99 % (3019360)Instruction limit reached!
% 19.50/3.99 % (3019360)------------------------------
% 19.50/3.99 % (3019360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.50/3.99 % (3019360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.50/3.99 % (3019360)CaDiCaL version: 2.1.3
% 19.50/3.99 % (3019360)Termination reason: Instruction limit
% 19.50/3.99 % (3019360)Termination phase: Saturation
% 19.50/3.99 % (3019360)Time elapsed: 0.887 s
% 19.50/3.99 % (3019360)Peak memory usage: 97 MB
% 19.50/3.99 % (3019360)Instructions burned: 907 (million)
% 19.50/3.99 % (3019369)------------------------------
% 19.50/3.99 % (3019369)------------------------------
% 19.50/3.99 % (3019371)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=178197304:st=3:i=13193:sd=3:ss=axioms_2974 on theBenchmark for (2974ds/13193Mi)
% 19.50/3.99 % (3019330)Refutation found. Thanks to Tanya!
% 19.50/3.99 % SZS status Theorem for theBenchmark
% 19.50/3.99 % SZS output start Proof for theBenchmark
% See solution above
% 20.72/4.37 % (3019330)------------------------------
% 20.72/4.37 % (3019330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.72/4.37 % (3019330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.72/4.37 % (3019330)CaDiCaL version: 2.1.3
% 20.72/4.37 % (3019330)Termination reason: Refutation
% 20.72/4.37 % (3019330)Time elapsed: 2.079 s
% 20.72/4.37 % (3019330)Peak memory usage: 138 MB
% 20.72/4.37 % (3019330)Instructions burned: 1995 (million)
% 20.72/4.37 % (3019330)------------------------------
% 20.72/4.37 % (3019330)------------------------------
% 20.72/4.37 % (3019324)Success in time 2.796 s
% 20.72/4.37 % Vampire exiting
%------------------------------------------------------------------------------