%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL391+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 : n007.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 11:52:15 AM UTC 2026
% Result : Theorem 20.82s 3.99s
% Output : Refutation 22.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 5
% Syntax : Number of formulae : 95 ( 16 unt; 2 def)
% Number of atoms : 206 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 225 ( 114 ~; 107 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 304 ( 0 sgn 304 !; 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(x,n(y)),n(x)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f3) ).
fof(f4,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(x,n(y)),n(x)))),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ is_a_theorem(implies(implies(x,y),implies(implies(x,n(y)),n(x)))),
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(x,n(y)),n(x)))),
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(f83,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(implies(n(X1),X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f16,f25]) ).
fof(f96,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(f102,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) )
| ~ spl0_2 ),
inference(resolution,[],[f96,f8]) ).
fof(f106,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,[],[f102,f8]) ).
fof(f112,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,[],[f106,f96]) ).
fof(f114,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f106,f12]) ).
fof(f128,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2))
| is_a_theorem(X2) )
| ~ spl0_2 ),
inference(resolution,[],[f114,f16]) ).
fof(f136,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f128,f96]) ).
fof(f144,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,[],[f128,f112]) ).
fof(f150,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X3,X1),X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f136,f106]) ).
fof(f151,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X2,X0),X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f136,f8]) ).
fof(f185,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,[],[f144,f31]) ).
fof(f197,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(n(X0),X1),X2),implies(X0,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f144,f32]) ).
fof(f199,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(n(X0),X0),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f144,f83]) ).
fof(f216,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,[],[f185,f8]) ).
fof(f221,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,[],[f197,f106]) ).
fof(f252,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,[],[f216,f102]) ).
fof(f317,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(implies(implies(n(X0),X0),X0),X1),X1))
| ~ spl0_2 ),
inference(resolution,[],[f151,f31]) ).
fof(f358,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X0,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f317,f216]) ).
fof(f369,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X1),implies(implies(X1,X0),X0)))
| ~ spl0_2 ),
inference(resolution,[],[f358,f216]) ).
fof(f377,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f369,f151]) ).
fof(f380,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X1,X2),X2)))
| ~ is_a_theorem(implies(X0,implies(n(X2),X1))) )
| ~ spl0_2 ),
inference(resolution,[],[f369,f106]) ).
fof(f381,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(n(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f369,f8]) ).
fof(f428,plain,
( ! [X0,X1] : is_a_theorem(implies(n(X0),implies(X0,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f377,f221]) ).
fof(f433,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),X0))
| ~ spl0_2 ),
inference(resolution,[],[f428,f381]) ).
fof(f536,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f433,f216]) ).
fof(f557,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,[],[f536,f106]) ).
fof(f626,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,[],[f557,f252]) ).
fof(f644,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X1,implies(X0,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f626,f151]) ).
fof(f786,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))
| ~ spl0_2 ),
inference(resolution,[],[f644,f96]) ).
fof(f787,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X0),implies(implies(X0,X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f644,f199]) ).
fof(f804,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(n(X1),X0)))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) )
| ~ spl0_2 ),
inference(resolution,[],[f644,f380]) ).
fof(f843,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X1,X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f786,f8]) ).
fof(f864,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,[],[f843,f557]) ).
fof(f881,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,[],[f864,f216]) ).
fof(f936,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(n(X1),X1)))
| is_a_theorem(implies(X0,implies(implies(X1,X2),X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f787,f106]) ).
fof(f973,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(n(X1),X0))
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f936,f102]) ).
fof(f1075,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),implies(implies(X0,X2),X2)))
| ~ spl0_2 ),
inference(resolution,[],[f973,f428]) ).
fof(f1125,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X0),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f1075,f644]) ).
fof(f1133,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),implies(X2,X0)))
| ~ spl0_2 ),
inference(resolution,[],[f1125,f128]) ).
fof(f1188,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X0),X0)))
| ~ spl0_2 ),
inference(resolution,[],[f1133,f881]) ).
fof(f1211,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X2,X3),X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f1133,f106]) ).
fof(f1229,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,n(X0)),implies(X1,n(X0))))
| ~ spl0_2 ),
inference(resolution,[],[f1211,f199]) ).
fof(f1254,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,n(X0)),n(X0))))
| ~ spl0_2 ),
inference(resolution,[],[f1229,f881]) ).
fof(f1289,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,n(X1)),implies(implies(X1,X0),n(X1))))
| ~ spl0_2 ),
inference(resolution,[],[f1254,f644]) ).
fof(f1353,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f1188,f216]) ).
fof(f1381,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X0,X2),X2)))
| ~ spl0_2 ),
inference(resolution,[],[f1353,f644]) ).
fof(f1393,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,implies(X0,X2)),implies(X0,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f1381,f216]) ).
fof(f1743,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X1,X0),implies(X1,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f1393,f644]) ).
fof(f1753,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X0,implies(X1,X2)),implies(X0,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f1743,f216]) ).
fof(f1806,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f1753,f644]) ).
fof(f1818,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f1806,f150]) ).
fof(f1887,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(X0,implies(implies(X1,X2),X2))))
| ~ spl0_2 ),
inference(resolution,[],[f1818,f216]) ).
fof(f4002,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(implies(n(X2),X0),X2)))
| ~ spl0_2 ),
inference(resolution,[],[f804,f1887]) ).
fof(f4064,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f4002,f150]) ).
fof(f4122,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,[],[f4064,f106]) ).
fof(f4167,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(implies(implies(X2,X3),X3),X0))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) )
| ~ spl0_2 ),
inference(resolution,[],[f4122,f102]) ).
fof(f4228,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(n(X0),X2)))
| ~ spl0_2 ),
inference(resolution,[],[f4167,f197]) ).
fof(f4317,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X1,X3),X2)))
| is_a_theorem(implies(X0,implies(n(X1),X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f4228,f106]) ).
fof(f4828,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(n(X1),n(X0))))
| ~ spl0_2 ),
inference(resolution,[],[f4317,f1254]) ).
fof(f4886,plain,
( $false
| ~ spl0_2 ),
inference(unit_resulting_resolution,[],[f106,f10,f1289,f4828]) ).
fof(f4910,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f4886]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s9,plain,
~ spl0_1,
inference(sat_conversion,[],[f67]) ).
cnf(s27,plain,
~ spl0_2,
inference(sat_conversion,[],[f4910]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s1,s27,s9]) ).
fof(f4911,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL391+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:36:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 20.82/3.99 % (1604168)Detected formulas, will run a generic FOF schedule.
% 20.82/3.99 % (1604248)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=716999948:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 20.82/3.99 % (1604250)dis-21_1_sil=8000:lcm=predicate:random_seed=2628349637: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)
% 20.82/3.99 % (1604249)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2289708013:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 20.82/3.99 % (1604244)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=1165047069:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 20.82/3.99 % (1604246)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=3074022350:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 20.82/3.99 % (1604245)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=817710788:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 20.82/3.99 % (1604248)Instruction limit reached!
% 20.82/3.99 % (1604248)------------------------------
% 20.82/3.99 % (1604248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604248)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604248)Termination reason: Instruction limit
% 20.82/3.99 % (1604248)Termination phase: Saturation
% 20.82/3.99 % (1604248)Time elapsed: 0.065 s
% 20.82/3.99 % (1604248)Peak memory usage: 88 MB
% 20.82/3.99 % (1604248)Instructions burned: 121 (million)
% 20.82/3.99 % (1604247)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2129619614:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 20.82/3.99 % (1604247)Refutation not found, incomplete strategy
% 20.82/3.99 % (1604247)------------------------------
% 20.82/3.99 % (1604247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604247)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604247)Termination reason: Refutation not found, incomplete strategy
% 20.82/3.99 % (1604247)Time elapsed: 0.002 s
% 20.82/3.99 % (1604247)Peak memory usage: 87 MB
% 20.82/3.99 % (1604250)Instruction limit reached!
% 20.82/3.99 % (1604250)------------------------------
% 20.82/3.99 % (1604250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604250)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604250)Termination reason: Instruction limit
% 20.82/3.99 % (1604250)Termination phase: Saturation
% 20.82/3.99 % (1604250)Time elapsed: 0.124 s
% 20.82/3.99 % (1604250)Peak memory usage: 89 MB
% 20.82/3.99 % (1604250)Instructions burned: 129 (million)
% 20.82/3.99 % (1604249)Instruction limit reached!
% 20.82/3.99 % (1604249)------------------------------
% 20.82/3.99 % (1604249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604249)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604249)Termination reason: Instruction limit
% 20.82/3.99 % (1604249)Termination phase: Saturation
% 20.82/3.99 % (1604249)Time elapsed: 0.136 s
% 20.82/3.99 % (1604249)Peak memory usage: 89 MB
% 20.82/3.99 % (1604249)Instructions burned: 139 (million)
% 20.82/3.99 % (1604271)lrs+10_1_sil=8000:sp=occurrence:random_seed=4244556350:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 20.82/3.99 % (1604277)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4003528277:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 20.82/3.99 % (1604276)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1252528794:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 20.82/3.99 % (1604271)Instruction limit reached!
% 20.82/3.99 % (1604271)------------------------------
% 20.82/3.99 % (1604271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604271)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604271)Termination reason: Instruction limit
% 20.82/3.99 % (1604271)Termination phase: Saturation
% 20.82/3.99 % (1604271)Time elapsed: 0.153 s
% 20.82/3.99 % (1604271)Peak memory usage: 91 MB
% 20.82/3.99 % (1604271)Instructions burned: 286 (million)
% 20.82/3.99 % (1604276)Instruction limit reached!
% 20.82/3.99 % (1604276)------------------------------
% 20.82/3.99 % (1604276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604276)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604276)Termination reason: Instruction limit
% 20.82/3.99 % (1604276)Termination phase: Saturation
% 20.82/3.99 % (1604276)Time elapsed: 0.115 s
% 20.82/3.99 % (1604276)Peak memory usage: 89 MB
% 20.82/3.99 % (1604276)Instructions burned: 157 (million)
% 20.82/3.99 % (1604247)------------------------------
% 20.82/3.99 % (1604247)------------------------------
% 20.82/3.99 % (1604277)Instruction limit reached!
% 20.82/3.99 % (1604277)------------------------------
% 20.82/3.99 % (1604277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604277)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604277)Termination reason: Instruction limit
% 20.82/3.99 % (1604277)Termination phase: Saturation
% 20.82/3.99 % (1604277)Time elapsed: 0.304 s
% 20.82/3.99 % (1604277)Peak memory usage: 90 MB
% 20.82/3.99 % (1604277)Instructions burned: 325 (million)
% 20.82/3.99 % (1604283)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=1527600481:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 20.82/3.99 % (1604284)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=901838139:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 20.82/3.99 % (1604284)Refutation not found, incomplete strategy
% 20.82/3.99 % (1604284)------------------------------
% 20.82/3.99 % (1604284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604284)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604284)Termination reason: Refutation not found, incomplete strategy
% 20.82/3.99 % (1604284)Time elapsed: 0.002 s
% 20.82/3.99 % (1604284)Peak memory usage: 87 MB
% 20.82/3.99 % (1604283)Instruction limit reached!
% 20.82/3.99 % (1604283)------------------------------
% 20.82/3.99 % (1604283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604283)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604283)Termination reason: Instruction limit
% 20.82/3.99 % (1604283)Termination phase: Saturation
% 20.82/3.99 % (1604283)Time elapsed: 0.118 s
% 20.82/3.99 % (1604283)Peak memory usage: 88 MB
% 20.82/3.99 % (1604283)Instructions burned: 250 (million)
% 20.82/3.99 % (1604285)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1238026690:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 20.82/3.99 % (1604291)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2274663522:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 20.82/3.99 % (1604295)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2394470176:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 20.82/3.99 % (1604291)Instruction limit reached!
% 20.82/3.99 % (1604291)------------------------------
% 20.82/3.99 % (1604291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604291)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604291)Termination reason: Instruction limit
% 20.82/3.99 % (1604291)Termination phase: Saturation
% 20.82/3.99 % (1604291)Time elapsed: 0.103 s
% 20.82/3.99 % (1604291)Peak memory usage: 88 MB
% 20.82/3.99 % (1604291)Instructions burned: 114 (million)
% 20.82/3.99 % (1604295)Instruction limit reached!
% 20.82/3.99 % (1604295)------------------------------
% 20.82/3.99 % (1604295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604295)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604295)Termination reason: Instruction limit
% 20.82/3.99 % (1604295)Termination phase: Saturation
% 20.82/3.99 % (1604295)Time elapsed: 0.106 s
% 20.82/3.99 % (1604295)Peak memory usage: 87 MB
% 20.82/3.99 % (1604295)Instructions burned: 128 (million)
% 20.82/3.99 % (1604284)------------------------------
% 20.82/3.99 % (1604284)------------------------------
% 20.82/3.99 % (1604301)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=840147297:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2987 on theBenchmark for (2987ds/114Mi)
% 20.82/3.99 % (1604301)Instruction limit reached!
% 20.82/3.99 % (1604301)------------------------------
% 20.82/3.99 % (1604301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604301)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604301)Termination reason: Instruction limit
% 20.82/3.99 % (1604301)Termination phase: Saturation
% 20.82/3.99 % (1604301)Time elapsed: 0.057 s
% 20.82/3.99 % (1604301)Peak memory usage: 88 MB
% 20.82/3.99 % (1604301)Instructions burned: 116 (million)
% 20.82/3.99 % (1604302)lrs+10_1_sil=8000:sp=occurrence:random_seed=3024159297:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2986 on theBenchmark for (2986ds/907Mi)
% 20.82/3.99 % (1604303)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3156922124:i=437:sd=1:aac=none:ss=included_2986 on theBenchmark for (2986ds/437Mi)
% 20.82/3.99 % (1604303)Refutation not found, incomplete strategy
% 20.82/3.99 % (1604303)------------------------------
% 20.82/3.99 % (1604303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604303)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604303)Termination reason: Refutation not found, incomplete strategy
% 20.82/3.99 % (1604303)Time elapsed: 0.002 s
% 20.82/3.99 % (1604303)Peak memory usage: 87 MB
% 20.82/3.99 % (1604307)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2243841129:i=5202:ss=axioms:sgt=16_2984 on theBenchmark for (2984ds/5202Mi)
% 20.82/3.99 % (1604303)------------------------------
% 20.82/3.99 % (1604303)------------------------------
% 20.82/3.99 % (1604317)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=28207668:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2979 on theBenchmark for (2979ds/134Mi)
% 20.82/3.99 % (1604302)Instruction limit reached!
% 20.82/3.99 % (1604302)------------------------------
% 20.82/3.99 % (1604302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604302)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604302)Termination reason: Instruction limit
% 20.82/3.99 % (1604302)Termination phase: Saturation
% 20.82/3.99 % (1604302)Time elapsed: 0.892 s
% 20.82/3.99 % (1604302)Peak memory usage: 97 MB
% 20.82/3.99 % (1604302)Instructions burned: 907 (million)
% 20.82/3.99 % (1604317)Instruction limit reached!
% 20.82/3.99 % (1604317)------------------------------
% 20.82/3.99 % (1604317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604317)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604317)Termination reason: Instruction limit
% 20.82/3.99 % (1604317)Termination phase: Saturation
% 20.82/3.99 % (1604317)Time elapsed: 0.116 s
% 20.82/3.99 % (1604317)Peak memory usage: 89 MB
% 20.82/3.99 % (1604317)Instructions burned: 134 (million)
% 20.82/3.99 % (1604245)First to succeed.
% 20.82/3.99 % (1604245)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1604168"
% 20.82/3.99 % (1604319)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3578425591:st=8:i=592:sd=3:ep=RST:ss=axioms_2975 on theBenchmark for (2975ds/592Mi)
% 20.82/3.99 % (1604319)Refutation not found, incomplete strategy
% 20.82/3.99 % (1604319)------------------------------
% 20.82/3.99 % (1604319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.82/3.99 % (1604319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.82/3.99 % (1604319)CaDiCaL version: 2.1.3
% 20.82/3.99 % (1604319)Termination reason: Refutation not found, incomplete strategy
% 20.82/3.99 % (1604319)Time elapsed: 0.002 s
% 20.82/3.99 % (1604319)Peak memory usage: 87 MB
% 20.82/3.99 % (1604320)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=423661662:st=3:i=13193:sd=3:ss=axioms_2975 on theBenchmark for (2975ds/13193Mi)
% 20.82/3.99 % (1604245)Refutation found. Thanks to Tanya!
% 20.82/3.99 % SZS status Theorem for theBenchmark
% 20.82/3.99 % SZS output start Proof for theBenchmark
% See solution above
% 22.80/4.29 % (1604245)------------------------------
% 22.80/4.29 % (1604245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 22.80/4.29 % (1604245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.80/4.29 % (1604245)CaDiCaL version: 2.1.3
% 22.80/4.29 % (1604245)Termination reason: Refutation
% 22.80/4.29 % (1604245)Time elapsed: 2.458 s
% 22.80/4.29 % (1604245)Peak memory usage: 141 MB
% 22.80/4.29 % (1604245)Instructions burned: 2446 (million)
% 22.80/4.29 % (1604245)------------------------------
% 22.80/4.29 % (1604245)------------------------------
% 22.80/4.29 % (1604168)Success in time 3.142 s
% 22.80/4.29 % Vampire exiting
%------------------------------------------------------------------------------