%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL403+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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:18 AM UTC 2026
% Result : Theorem 12.45s 2.73s
% Output : Refutation 13.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 6
% Syntax : Number of formulae : 93 ( 16 unt; 3 def)
% Number of atoms : 244 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 303 ( 152 ~; 146 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 283 ( 0 sgn 283 !; 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(x,implies(n(y),n(implies(x,y))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f3) ).
fof(f4,negated_conjecture,
~ is_a_theorem(implies(x,implies(n(y),n(implies(x,y))))),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ is_a_theorem(implies(x,implies(n(y),n(implies(x,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(x,implies(n(y),n(implies(x,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(f14,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,[],[f14,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,[],[f14,f8]) ).
fof(f18,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,[],[f18,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,f14]) ).
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(f89,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(n(X0),X0),X0))
| ~ is_a_theorem(X1) )
| ~ spl0_2 ),
inference(resolution,[],[f83,f8]) ).
fof(f92,definition,
( spl0_4
<=> ! [X0] : is_a_theorem(implies(implies(n(X0),X0),X0)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f93,plain,
( ! [X0] : is_a_theorem(implies(implies(n(X0),X0),X0))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( spl0_1
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f89,f24,f92,f21]) ).
fof(f97,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(f103,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) )
| ~ spl0_2 ),
inference(resolution,[],[f97,f8]) ).
fof(f107,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,[],[f103,f8]) ).
fof(f113,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(n(X1),X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f107,f93]) ).
fof(f114,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,[],[f107,f97]) ).
fof(f116,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f107,f12]) ).
fof(f128,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(n(X1),X0)) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f113,f103]) ).
fof(f147,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2))
| is_a_theorem(X2) )
| ~ spl0_2 ),
inference(resolution,[],[f116,f16]) ).
fof(f168,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,[],[f147,f114]) ).
fof(f203,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,[],[f168,f31]) ).
fof(f216,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(n(X0),X1),X2),implies(X0,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f168,f32]) ).
fof(f218,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(n(X0),X0),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f168,f83]) ).
fof(f235,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,[],[f203,f8]) ).
fof(f241,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,[],[f216,f107]) ).
fof(f274,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,[],[f235,f103]) ).
fof(f275,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(n(implies(X0,X2)),implies(X1,X2)))
| is_a_theorem(implies(implies(X0,X1),implies(X0,X2))) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f235,f128]) ).
fof(f302,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X0,X1)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f275,f83]) ).
fof(f309,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X1),implies(implies(X1,X0),X0)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f302,f235]) ).
fof(f319,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),n(X1)),implies(X1,X0)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f309,f241]) ).
fof(f381,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(n(X2),n(X1))))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f319,f107]) ).
fof(f396,plain,
( ! [X0,X1] : is_a_theorem(implies(n(X0),implies(X0,X1)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f381,f12]) ).
fof(f400,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f396,f275]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,implies(X1,X2))))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f400,f107]) ).
fof(f492,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f471,f274]) ).
fof(f519,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,implies(X0,X1)))
| is_a_theorem(implies(X3,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f492,f107]) ).
fof(f567,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f519,f12]) ).
fof(f591,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f567,f97]) ).
fof(f592,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X0),implies(implies(X0,X1),X1)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f567,f218]) ).
fof(f639,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X1,X2)) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f591,f8]) ).
fof(f684,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X0),implies(X1,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f639,f471]) ).
fof(f695,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
| ~ spl0_4 ),
inference(resolution,[],[f684,f235]) ).
fof(f993,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
| ~ spl0_4 ),
inference(resolution,[],[f592,f107]) ).
fof(f1005,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
| ~ spl0_4 ),
inference(resolution,[],[f993,f103]) ).
fof(f1161,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),implies(implies(X0,X2),X2)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1005,f396]) ).
fof(f1189,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X0),X1)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1161,f567]) ).
fof(f1198,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),implies(X2,X0)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1189,f147]) ).
fof(f1253,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X0),X0)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1198,f695]) ).
fof(f1277,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
| ~ spl0_4 ),
inference(resolution,[],[f1198,f107]) ).
fof(f1324,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,n(X0)),implies(X1,n(X0))))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1277,f218]) ).
fof(f1350,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,n(X0)),n(X0))))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1324,f695]) ).
fof(f1541,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X1),X1)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1253,f235]) ).
fof(f1550,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X1,X2),X0),X1)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1253,f567]) ).
fof(f1569,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X0,X2),X2)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1541,f567]) ).
fof(f1599,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),X2),X1),implies(X0,X1)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f1550,f147]) ).
fof(f1634,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
| ~ spl0_4 ),
inference(resolution,[],[f1599,f107]) ).
fof(f2666,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
| ~ spl0_4 ),
inference(resolution,[],[f1634,f103]) ).
fof(f2706,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f2666,f1569]) ).
fof(f2707,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(n(X0),X2)))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f2666,f216]) ).
fof(f2940,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
| ~ spl0_4 ),
inference(resolution,[],[f2707,f107]) ).
fof(f3331,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(n(X1),n(X0))))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f2940,f1350]) ).
fof(f3381,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(unit_resulting_resolution,[],[f8,f10,f2706,f3331]) ).
fof(f3402,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f3381]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s9,plain,
~ spl0_1,
inference(sat_conversion,[],[f67]) ).
cnf(s22,plain,
( spl0_1
| ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f94]) ).
cnf(s28,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f3402]) ).
cnf(s30,plain,
spl0_2,
inference(rat,[],[s1,s9]) ).
cnf(s31,plain,
~ spl0_4,
inference(rat,[],[s28,s30]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s22,s9,s31,s30]) ).
fof(f3403,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL403+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:39:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 12.45/2.73 % (3687294)Detected formulas, will run a generic FOF schedule.
% 12.45/2.73 % (3687326)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1514524412:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.45/2.73 % (3687326)Refutation not found, incomplete strategy
% 12.45/2.73 % (3687326)------------------------------
% 12.45/2.73 % (3687326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687326)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687326)Termination reason: Refutation not found, incomplete strategy
% 12.45/2.73 % (3687326)Time elapsed: 0.001 s
% 12.45/2.73 % (3687326)Peak memory usage: 87 MB
% 12.45/2.73 % (3687323)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=1278934889:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.45/2.73 % (3687325)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=648571165:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.45/2.73 % (3687324)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=397343438:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.45/2.73 % (3687329)dis-21_1_sil=8000:lcm=predicate:random_seed=1657823173: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)
% 12.45/2.73 % (3687327)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=187217329:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.45/2.73 % (3687328)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3839871669:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.45/2.73 % (3687327)Instruction limit reached!
% 12.45/2.73 % (3687327)------------------------------
% 12.45/2.73 % (3687327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687327)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687327)Termination reason: Instruction limit
% 12.45/2.73 % (3687327)Termination phase: Saturation
% 12.45/2.73 % (3687327)Time elapsed: 0.076 s
% 12.45/2.73 % (3687327)Peak memory usage: 87 MB
% 12.45/2.73 % (3687327)Instructions burned: 120 (million)
% 12.45/2.73 % (3687326)------------------------------
% 12.45/2.73 % (3687326)------------------------------
% 12.45/2.73 % (3687329)Instruction limit reached!
% 12.45/2.73 % (3687329)------------------------------
% 12.45/2.73 % (3687329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687329)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687329)Termination reason: Instruction limit
% 12.45/2.73 % (3687329)Termination phase: Saturation
% 12.45/2.73 % (3687329)Time elapsed: 0.083 s
% 12.45/2.73 % (3687329)Peak memory usage: 89 MB
% 12.45/2.73 % (3687329)Instructions burned: 129 (million)
% 12.45/2.73 % (3687328)Instruction limit reached!
% 12.45/2.73 % (3687328)------------------------------
% 12.45/2.73 % (3687328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687328)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687328)Termination reason: Instruction limit
% 12.45/2.73 % (3687328)Termination phase: Saturation
% 12.45/2.73 % (3687328)Time elapsed: 0.143 s
% 12.45/2.73 % (3687328)Peak memory usage: 89 MB
% 12.45/2.73 % (3687328)Instructions burned: 148 (million)
% 12.45/2.73 % (3687338)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1157387608:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.45/2.73 % (3687339)lrs+1011_1_sil=32000:sp=occurrence:random_seed=459388342:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.45/2.73 % (3687337)lrs+10_1_sil=8000:sp=occurrence:random_seed=3882517267:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.45/2.73 % (3687338)Instruction limit reached!
% 12.45/2.73 % (3687338)------------------------------
% 12.45/2.73 % (3687338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687338)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687338)Termination reason: Instruction limit
% 12.45/2.73 % (3687338)Termination phase: Saturation
% 12.45/2.73 % (3687338)Time elapsed: 0.050 s
% 12.45/2.73 % (3687338)Peak memory usage: 88 MB
% 12.45/2.73 % (3687338)Instructions burned: 157 (million)
% 12.45/2.73 % (3687340)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=656888824:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 12.45/2.73 % (3687352)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=751843048:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 12.45/2.73 % (3687352)Refutation not found, incomplete strategy
% 12.45/2.73 % (3687352)------------------------------
% 12.45/2.73 % (3687352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687352)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687352)Termination reason: Refutation not found, incomplete strategy
% 12.45/2.73 % (3687352)Time elapsed: 0.001 s
% 12.45/2.73 % (3687352)Peak memory usage: 87 MB
% 12.45/2.73 % (3687337)Instruction limit reached!
% 12.45/2.73 % (3687337)------------------------------
% 12.45/2.73 % (3687337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687337)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687337)Termination reason: Instruction limit
% 12.45/2.73 % (3687337)Termination phase: Saturation
% 12.45/2.73 % (3687337)Time elapsed: 0.265 s
% 12.45/2.73 % (3687337)Peak memory usage: 90 MB
% 12.45/2.73 % (3687337)Instructions burned: 285 (million)
% 12.45/2.73 % (3687339)Instruction limit reached!
% 12.45/2.73 % (3687339)------------------------------
% 12.45/2.73 % (3687339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687339)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687339)Termination reason: Instruction limit
% 12.45/2.73 % (3687339)Termination phase: Saturation
% 12.45/2.73 % (3687339)Time elapsed: 0.292 s
% 12.45/2.73 % (3687339)Peak memory usage: 89 MB
% 12.45/2.73 % (3687339)Instructions burned: 326 (million)
% 12.45/2.73 % (3687340)Instruction limit reached!
% 12.45/2.73 % (3687340)------------------------------
% 12.45/2.73 % (3687340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687340)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687340)Termination reason: Instruction limit
% 12.45/2.73 % (3687340)Termination phase: Saturation
% 12.45/2.73 % (3687340)Time elapsed: 0.208 s
% 12.45/2.73 % (3687340)Peak memory usage: 88 MB
% 12.45/2.73 % (3687340)Instructions burned: 249 (million)
% 12.45/2.73 % (3687362)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1111981811:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 12.45/2.73 % (3687363)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4250446167:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 12.45/2.73 % (3687352)------------------------------
% 12.45/2.73 % (3687352)------------------------------
% 12.45/2.73 % (3687366)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1782274765:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 12.45/2.73 % (3687363)Instruction limit reached!
% 12.45/2.73 % (3687363)------------------------------
% 12.45/2.73 % (3687363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687363)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687363)Termination reason: Instruction limit
% 12.45/2.73 % (3687363)Termination phase: Saturation
% 12.45/2.73 % (3687363)Time elapsed: 0.063 s
% 12.45/2.73 % (3687363)Peak memory usage: 88 MB
% 12.45/2.73 % (3687363)Instructions burned: 115 (million)
% 12.45/2.73 % (3687366)Instruction limit reached!
% 12.45/2.73 % (3687366)------------------------------
% 12.45/2.73 % (3687366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687366)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687366)Termination reason: Instruction limit
% 12.45/2.73 % (3687366)Termination phase: Saturation
% 12.45/2.73 % (3687366)Time elapsed: 0.071 s
% 12.45/2.73 % (3687366)Peak memory usage: 87 MB
% 12.45/2.73 % (3687366)Instructions burned: 128 (million)
% 12.45/2.73 % (3687369)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2152781368:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 12.45/2.73 % (3687371)lrs+10_1_sil=8000:sp=occurrence:random_seed=47257497:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 12.45/2.73 % (3687369)Instruction limit reached!
% 12.45/2.73 % (3687369)------------------------------
% 12.45/2.73 % (3687369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687369)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687369)Termination reason: Instruction limit
% 12.45/2.73 % (3687369)Termination phase: Saturation
% 12.45/2.73 % (3687369)Time elapsed: 0.062 s
% 12.45/2.73 % (3687369)Peak memory usage: 88 MB
% 12.45/2.73 % (3687369)Instructions burned: 116 (million)
% 12.45/2.73 % (3687372)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=242477327:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 12.45/2.73 % (3687372)Refutation not found, incomplete strategy
% 12.45/2.73 % (3687372)------------------------------
% 12.45/2.73 % (3687372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687372)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687372)Termination reason: Refutation not found, incomplete strategy
% 12.45/2.73 % (3687372)Time elapsed: 0.001 s
% 12.45/2.73 % (3687372)Peak memory usage: 87 MB
% 12.45/2.73 % (3687377)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4027483455:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 12.45/2.73 % (3687372)------------------------------
% 12.45/2.73 % (3687372)------------------------------
% 12.45/2.73 % (3687324)First to succeed.
% 12.45/2.73 % (3687484)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3509070708:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2985 on theBenchmark for (2985ds/134Mi)
% 12.45/2.73 % (3687324)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3687294"
% 12.45/2.73 % (3687371)Instruction limit reached!
% 12.45/2.73 % (3687371)------------------------------
% 12.45/2.73 % (3687371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687371)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687371)Termination reason: Instruction limit
% 12.45/2.73 % (3687371)Termination phase: Saturation
% 12.45/2.73 % (3687371)Time elapsed: 0.555 s
% 12.45/2.73 % (3687371)Peak memory usage: 96 MB
% 12.45/2.73 % (3687371)Instructions burned: 908 (million)
% 12.45/2.73 % (3687484)Instruction limit reached!
% 12.45/2.73 % (3687484)------------------------------
% 12.45/2.73 % (3687484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687484)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687484)Termination reason: Instruction limit
% 12.45/2.73 % (3687484)Termination phase: Saturation
% 12.45/2.73 % (3687484)Time elapsed: 0.077 s
% 12.45/2.73 % (3687484)Peak memory usage: 88 MB
% 12.45/2.73 % (3687484)Instructions burned: 135 (million)
% 12.45/2.73 % (3687531)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3283946171:st=8:i=592:sd=3:ep=RST:ss=axioms_2983 on theBenchmark for (2983ds/592Mi)
% 12.45/2.73 % (3687531)Refutation not found, incomplete strategy
% 12.45/2.73 % (3687531)------------------------------
% 12.45/2.73 % (3687531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.45/2.73 % (3687531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.45/2.73 % (3687531)CaDiCaL version: 2.1.3
% 12.45/2.73 % (3687531)Termination reason: Refutation not found, incomplete strategy
% 12.45/2.73 % (3687531)Time elapsed: 0.001 s
% 12.45/2.73 % (3687531)Peak memory usage: 88 MB
% 12.45/2.73 % (3687534)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2348592648:st=3:i=13193:sd=3:ss=axioms_2982 on theBenchmark for (2982ds/13193Mi)
% 12.45/2.73 % (3687324)Refutation found. Thanks to Tanya!
% 12.45/2.73 % SZS status Theorem for theBenchmark
% 12.45/2.73 % SZS output start Proof for theBenchmark
% See solution above
% 13.85/2.92 % (3687324)------------------------------
% 13.85/2.92 % (3687324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.85/2.92 % (3687324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.92 % (3687324)CaDiCaL version: 2.1.3
% 13.85/2.92 % (3687324)Termination reason: Refutation
% 13.85/2.92 % (3687324)Time elapsed: 1.457 s
% 13.85/2.92 % (3687324)Peak memory usage: 138 MB
% 13.85/2.92 % (3687324)Instructions burned: 2053 (million)
% 13.85/2.92 % (3687324)------------------------------
% 13.85/2.92 % (3687324)------------------------------
% 13.85/2.92 % (3687294)Success in time 1.882 s
% 13.85/2.92 % Vampire exiting
%------------------------------------------------------------------------------