%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL376+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 : n019.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 11:52:10 AM UTC 2026
% Result : Theorem 10.36s 3.81s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 6
% Syntax : Number of formulae : 102 ( 17 unt; 3 def)
% Number of atoms : 237 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 272 ( 137 ~; 130 |; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 324 ( 0 sgn 324 !; 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(y,implies(z,implies(x,u))),implies(z,implies(x,u))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f3) ).
fof(f4,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(y,implies(z,implies(x,u))),implies(z,implies(x,u))))),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ is_a_theorem(implies(implies(x,y),implies(implies(y,implies(z,implies(x,u))),implies(z,implies(x,u))))),
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(y,implies(z,implies(x,u))),implies(z,implies(x,u))))),
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,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f12,f8]) ).
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(f16,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[],[f13,f12]) ).
fof(f18,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(f28,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,[],[f16,f11]) ).
fof(f31,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,[],[f28,f8]) ).
fof(f32,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(n(X1),X2)))),
inference(resolution,[],[f28,f18]) ).
fof(f35,definition,
( spl0_1
<=> ! [X8] : ~ is_a_theorem(X8) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f36,plain,
( ! [X8] : ~ is_a_theorem(X8)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,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(f39,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,[],[f38]) ).
fof(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f31,f38,f35]) ).
fof(f43,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,[],[f39,f8]) ).
fof(f45,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(n(X0),X1)))
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f32,f8]) ).
fof(f50,definition,
( spl0_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(n(X0),X1))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f51,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(n(X0),X1)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f52,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f45,f50,f35]) ).
fof(f64,plain,
( $false
| ~ spl0_1 ),
inference(unit_resulting_resolution,[],[f13,f9,f36]) ).
fof(f92,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f97,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,[],[f43,f12]) ).
fof(f102,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),implies(X3,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f97,f18]) ).
fof(f106,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f102,f43]) ).
fof(f113,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) )
| ~ spl0_2 ),
inference(resolution,[],[f106,f8]) ).
fof(f118,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,[],[f113,f8]) ).
fof(f125,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,[],[f118,f106]) ).
fof(f127,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f118,f12]) ).
fof(f144,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2))
| is_a_theorem(X2) )
| ~ spl0_2 ),
inference(resolution,[],[f127,f18]) ).
fof(f152,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f144,f106]) ).
fof(f160,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,[],[f144,f125]) ).
fof(f167,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X2,X0),X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f152,f8]) ).
fof(f169,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(implies(implies(n(X0),X0),X0),X1),X1))
| ~ spl0_2 ),
inference(resolution,[],[f167,f97]) ).
fof(f242,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,[],[f160,f97]) ).
fof(f271,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,[],[f242,f8]) ).
fof(f277,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X0,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f271,f169]) ).
fof(f282,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,[],[f271,f113]) ).
fof(f285,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(implies(X1,X4),implies(X0,X4)),X3))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X3))) )
| ~ spl0_2 ),
inference(resolution,[],[f271,f127]) ).
fof(f302,plain,
( ! [X2,X3,X0,X1,X4] :
( is_a_theorem(implies(implies(X1,X4),implies(X0,implies(implies(X4,X2),X3))))
| ~ is_a_theorem(implies(X0,implies(implies(X1,X2),X3))) )
| ~ spl0_2 ),
inference(resolution,[],[f282,f271]) ).
fof(f312,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X1),implies(implies(X1,X0),X0)))
| ~ spl0_2 ),
inference(resolution,[],[f277,f271]) ).
fof(f314,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,[],[f277,f118]) ).
fof(f315,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(n(X1),X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f277,f8]) ).
fof(f320,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f312,f167]) ).
fof(f323,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(n(X1),X0)) )
| ~ spl0_2 ),
inference(resolution,[],[f312,f8]) ).
fof(f327,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f320,f8]) ).
fof(f340,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X2,implies(X0,X1))))
| ~ spl0_2 ),
inference(resolution,[],[f285,f169]) ).
fof(f368,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(n(implies(X0,X1)),implies(X2,X1)))
| is_a_theorem(implies(implies(X0,X2),implies(X0,X1))) )
| ~ spl0_2 ),
inference(resolution,[],[f323,f271]) ).
fof(f438,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1)))
| ~ spl0_2 ),
inference(resolution,[],[f340,f160]) ).
fof(f603,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1))
| ~ spl0_2 ),
inference(resolution,[],[f438,f315]) ).
fof(f605,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X3,X3),X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f438,f118]) ).
fof(f648,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X2,X2),X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f603,f118]) ).
fof(f748,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl0_2 ),
inference(resolution,[],[f327,f271]) ).
fof(f771,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(implies(implies(X0,X3),implies(implies(X3,X1),X2)))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f748,f271]) ).
fof(f778,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(n(X1),X1)))
| is_a_theorem(implies(implies(X2,X0),implies(X2,X1))) )
| ~ spl0_2 ),
inference(resolution,[],[f748,f314]) ).
fof(f782,plain,
( ~ is_a_theorem(implies(implies(x,implies(z,implies(x,u))),implies(z,implies(x,u))))
| ~ spl0_2 ),
inference(resolution,[],[f771,f10]) ).
fof(f868,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(implies(X1,X1),X2)),implies(X0,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f778,f438]) ).
fof(f904,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(implies(X1,X2),X2)))
| ~ spl0_2 ),
inference(resolution,[],[f868,f271]) ).
fof(f913,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,implies(implies(X3,X3),X2))))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f868,f118]) ).
fof(f929,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,[],[f904,f118]) ).
fof(f947,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(implies(X0,X1),X3)))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X3))) )
| ~ spl0_2 ),
inference(resolution,[],[f913,f302]) ).
fof(f1040,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(n(X0),X0),implies(implies(X0,X1),X1)))
| ~ spl0_2 ),
inference(resolution,[],[f929,f312]) ).
fof(f1142,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))
| ~ spl0_2 ),
inference(resolution,[],[f947,f106]) ).
fof(f1188,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X1,X3))))
| ~ is_a_theorem(implies(X0,implies(X2,X3))) )
| ~ spl0_2 ),
inference(resolution,[],[f1142,f118]) ).
fof(f1227,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),implies(X2,X3)))
| is_a_theorem(implies(implies(X4,X2),implies(X4,X3))) )
| ~ spl0_2 ),
inference(resolution,[],[f1188,f144]) ).
fof(f1294,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,[],[f1040,f118]) ).
fof(f1308,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,[],[f1294,f113]) ).
fof(f1650,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(implies(X0,implies(implies(X1,X2),X3)),implies(X0,implies(X2,X3))))
| ~ spl0_2 ),
inference(resolution,[],[f1227,f106]) ).
fof(f1724,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ spl0_2 ),
inference(resolution,[],[f1650,f271]) ).
fof(f1766,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(X0,implies(implies(X4,X3),X1)))
| is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X3,X2)))) )
| ~ spl0_2 ),
inference(resolution,[],[f1724,f118]) ).
fof(f1792,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X4,X3),X0))
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X3,X2)))) )
| ~ spl0_2 ),
inference(resolution,[],[f1766,f113]) ).
fof(f2290,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(implies(X2,X3),implies(X0,X3))))
| ~ spl0_2 ),
inference(resolution,[],[f1792,f1040]) ).
fof(f2331,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)))
| ~ spl0_2 ),
inference(resolution,[],[f2290,f648]) ).
fof(f2354,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))))
| ~ spl0_2 ),
inference(resolution,[],[f2331,f271]) ).
fof(f2413,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2 ),
inference(resolution,[],[f2354,f8]) ).
fof(f2515,plain,
( ! [X0,X1] : is_a_theorem(implies(n(X0),implies(X0,X1)))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f2413,f51]) ).
fof(f2517,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),implies(implies(X0,X2),X2)))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f2515,f1308]) ).
fof(f2519,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f2515,f368]) ).
fof(f2574,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_3 ),
inference(resolution,[],[f2519,f118]) ).
fof(f2644,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X1,implies(X0,X2))) )
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f2574,f748]) ).
fof(f2705,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,implies(X1,X0)))
| is_a_theorem(implies(X3,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f2644,f118]) ).
fof(f2791,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(implies(implies(X0,X1),X2),X2)))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f2517,f271]) ).
fof(f2963,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X2,implies(X0,X1))))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f2791,f605]) ).
fof(f2973,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(unit_resulting_resolution,[],[f2705,f782,f2354,f2963]) ).
fof(f3013,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f2973]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s22,plain,
~ spl0_1,
inference(sat_conversion,[],[f92]) ).
cnf(s23,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f3013]) ).
cnf(s24,plain,
spl0_3,
inference(rat,[],[s2,s22]) ).
cnf(s25,plain,
~ spl0_2,
inference(rat,[],[s23,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s1,s25,s22]) ).
fof(f3014,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL376+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.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 15:37:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 10.36/3.81 % (3221287)Detected formulas, will run a generic FOF schedule.
% 10.36/3.81 % (3221292)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=2991141754:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.36/3.81 % (3221297)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3723792341:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.36/3.81 % (3221296)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2989424825:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.36/3.81 % (3221293)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=3387709278:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.36/3.81 % (3221298)dis-21_1_sil=8000:lcm=predicate:random_seed=1829762700:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.36/3.81 % (3221295)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3692772197:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.36/3.81 % (3221294)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=120421417:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.36/3.81 % (3221295)Refutation not found, incomplete strategy
% 10.36/3.81 % (3221295)------------------------------
% 10.36/3.81 % (3221295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221296)Refutation not found, incomplete strategy
% 10.36/3.81 % (3221296)------------------------------
% 10.36/3.81 % (3221296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221296)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221295)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221296)Termination reason: Refutation not found, incomplete strategy
% 10.36/3.81 % (3221296)Time elapsed: 0.001 s
% 10.36/3.81 % (3221295)Termination reason: Refutation not found, incomplete strategy
% 10.36/3.81 % (3221295)Time elapsed: 0.001 s
% 10.36/3.81 % (3221296)Peak memory usage: 87 MB
% 10.36/3.81 % (3221295)Peak memory usage: 87 MB
% 10.36/3.81 % (3221298)Instruction limit reached!
% 10.36/3.81 % (3221298)------------------------------
% 10.36/3.81 % (3221298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221298)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221298)Termination reason: Instruction limit
% 10.36/3.81 % (3221298)Termination phase: Saturation
% 10.36/3.81 % (3221298)Time elapsed: 0.130 s
% 10.36/3.81 % (3221298)Peak memory usage: 89 MB
% 10.36/3.81 % (3221298)Instructions burned: 130 (million)
% 10.36/3.81 % (3221297)Instruction limit reached!
% 10.36/3.81 % (3221297)------------------------------
% 10.36/3.81 % (3221297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221297)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221297)Termination reason: Instruction limit
% 10.36/3.81 % (3221297)Termination phase: Saturation
% 10.36/3.81 % (3221297)Time elapsed: 0.132 s
% 10.36/3.81 % (3221297)Peak memory usage: 88 MB
% 10.36/3.81 % (3221297)Instructions burned: 139 (million)
% 10.36/3.81 % (3221296)------------------------------
% 10.36/3.81 % (3221296)------------------------------
% 10.36/3.81 % (3221295)------------------------------
% 10.36/3.81 % (3221295)------------------------------
% 10.36/3.81 % (3221306)lrs+10_1_sil=8000:sp=occurrence:random_seed=995925155:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 10.36/3.81 % (3221307)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1853880183:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 10.36/3.81 % (3221307)Instruction limit reached!
% 10.36/3.81 % (3221307)------------------------------
% 10.36/3.81 % (3221307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221307)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221307)Termination reason: Instruction limit
% 10.36/3.81 % (3221307)Termination phase: Saturation
% 10.36/3.81 % (3221307)Time elapsed: 0.139 s
% 10.36/3.81 % (3221307)Peak memory usage: 89 MB
% 10.36/3.81 % (3221307)Instructions burned: 158 (million)
% 10.36/3.81 % (3221308)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4043071600:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 10.36/3.81 % (3221309)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=2445185547:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 10.36/3.81 % (3221306)Instruction limit reached!
% 10.36/3.81 % (3221306)------------------------------
% 10.36/3.81 % (3221306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221306)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221306)Termination reason: Instruction limit
% 10.36/3.81 % (3221306)Termination phase: Saturation
% 10.36/3.81 % (3221306)Time elapsed: 0.279 s
% 10.36/3.81 % (3221306)Peak memory usage: 90 MB
% 10.36/3.81 % (3221306)Instructions burned: 285 (million)
% 10.36/3.81 % (3221313)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3775790798:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 10.36/3.81 % (3221313)Refutation not found, incomplete strategy
% 10.36/3.81 % (3221313)------------------------------
% 10.36/3.81 % (3221313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221313)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221313)Termination reason: Refutation not found, incomplete strategy
% 10.36/3.81 % (3221313)Time elapsed: 0.002 s
% 10.36/3.81 % (3221313)Peak memory usage: 87 MB
% 10.36/3.81 % (3221309)Instruction limit reached!
% 10.36/3.81 % (3221309)------------------------------
% 10.36/3.81 % (3221309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221309)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221309)Termination reason: Instruction limit
% 10.36/3.81 % (3221309)Termination phase: Saturation
% 10.36/3.81 % (3221309)Time elapsed: 0.210 s
% 10.36/3.81 % (3221309)Peak memory usage: 88 MB
% 10.36/3.81 % (3221309)Instructions burned: 248 (million)
% 10.36/3.81 % (3221308)Instruction limit reached!
% 10.36/3.81 % (3221308)------------------------------
% 10.36/3.81 % (3221308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221308)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221308)Termination reason: Instruction limit
% 10.36/3.81 % (3221308)Termination phase: Saturation
% 10.36/3.81 % (3221308)Time elapsed: 0.301 s
% 10.36/3.81 % (3221308)Peak memory usage: 90 MB
% 10.36/3.81 % (3221308)Instructions burned: 325 (million)
% 10.36/3.81 % (3221316)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1313369065:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 10.36/3.81 % (3221318)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3124781666:cts=off:i=113:fsr=off:ss=included:sgt=4_2988 on theBenchmark for (2988ds/113Mi)
% 10.36/3.81 % (3221313)------------------------------
% 10.36/3.81 % (3221313)------------------------------
% 10.36/3.81 % (3221319)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1035552827:i=127:av=off:fsr=off:sup=off_2987 on theBenchmark for (2987ds/127Mi)
% 10.36/3.81 % (3221318)Instruction limit reached!
% 10.36/3.81 % (3221318)------------------------------
% 10.36/3.81 % (3221318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221318)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221318)Termination reason: Instruction limit
% 10.36/3.81 % (3221318)Termination phase: Saturation
% 10.36/3.81 % (3221318)Time elapsed: 0.103 s
% 10.36/3.81 % (3221318)Peak memory usage: 89 MB
% 10.36/3.81 % (3221318)Instructions burned: 114 (million)
% 10.36/3.81 % (3221319)Instruction limit reached!
% 10.36/3.81 % (3221319)------------------------------
% 10.36/3.81 % (3221319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221319)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221319)Termination reason: Instruction limit
% 10.36/3.81 % (3221319)Termination phase: Saturation
% 10.36/3.81 % (3221319)Time elapsed: 0.105 s
% 10.36/3.81 % (3221319)Peak memory usage: 87 MB
% 10.36/3.81 % (3221319)Instructions burned: 127 (million)
% 10.36/3.81 % (3221322)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1662630917:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2984 on theBenchmark for (2984ds/114Mi)
% 10.36/3.81 % (3221324)lrs+10_1_sil=8000:sp=occurrence:random_seed=206918458:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2984 on theBenchmark for (2984ds/907Mi)
% 10.36/3.81 % (3221325)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4028245930:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 10.36/3.81 % (3221325)Refutation not found, incomplete strategy
% 10.36/3.81 % (3221325)------------------------------
% 10.36/3.81 % (3221325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221325)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221325)Termination reason: Refutation not found, incomplete strategy
% 10.36/3.81 % (3221325)Time elapsed: 0.002 s
% 10.36/3.81 % (3221325)Peak memory usage: 88 MB
% 10.36/3.81 % (3221322)Instruction limit reached!
% 10.36/3.81 % (3221322)------------------------------
% 10.36/3.81 % (3221322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.36/3.81 % (3221322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.36/3.81 % (3221322)CaDiCaL version: 2.1.3
% 10.36/3.81 % (3221322)Termination reason: Instruction limit
% 10.36/3.81 % (3221322)Termination phase: Saturation
% 10.36/3.81 % (3221322)Time elapsed: 0.108 s
% 10.36/3.81 % (3221322)Peak memory usage: 88 MB
% 10.36/3.81 % (3221322)Instructions burned: 114 (million)
% 10.36/3.81 % (3221329)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=28814159:i=5202:ss=axioms:sgt=16_2980 on theBenchmark for (2980ds/5202Mi)
% 10.36/3.81 % (3221293)First to succeed.
% 10.36/3.81 % (3221293)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3221287"
% 10.36/3.81 % (3221325)------------------------------
% 10.36/3.81 % (3221325)------------------------------
% 10.36/3.81 % (3221331)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=905655532:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2976 on theBenchmark for (2976ds/134Mi)
% 10.36/3.81 % (3221293)Refutation found. Thanks to Tanya!
% 10.36/3.81 % SZS status Theorem for theBenchmark
% 10.36/3.81 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/4.15 % (3221293)------------------------------
% 0.21/4.15 % (3221293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/4.15 % (3221293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/4.15 % (3221293)CaDiCaL version: 2.1.3
% 0.21/4.15 % (3221293)Termination reason: Refutation
% 0.21/4.15 % (3221293)Time elapsed: 2.004 s
% 0.21/4.15 % (3221293)Peak memory usage: 137 MB
% 0.21/4.15 % (3221293)Instructions burned: 1915 (million)
% 0.21/4.15 % (3221293)------------------------------
% 0.21/4.15 % (3221293)------------------------------
% 0.21/4.15 % (3221287)Success in time 2.732 s
% 0.21/4.15 % Vampire exiting
%------------------------------------------------------------------------------