%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN551+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 02:00:56 PM UTC 2026
% Result : Theorem 3.05s 1.09s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 112 ( 6 unt; 10 def)
% Number of atoms : 438 ( 190 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 604 ( 278 ~; 289 |; 15 &)
% ( 21 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 73 ( 0 sgn 57 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
! [X1] :
( X1 = f(g(X1))
<=> X0 = X1 )
<=> ? [X0] :
! [X1] :
( X1 = g(f(X1))
<=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_cute_thing) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( X1 = f(g(X1))
<=> X0 = X1 )
<=> ? [X0] :
! [X1] :
( X1 = g(f(X1))
<=> X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
! [X1] :
( X1 = f(g(X1))
<=> X0 = X1 )
<=> ? [X2] :
! [X3] :
( g(f(X3)) = X3
<=> X2 = X3 ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
! [X1] :
( X1 = f(g(X1))
<=> X0 = X1 )
<~> ? [X2] :
! [X3] :
( g(f(X3)) = X3
<=> X2 = X3 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ! [X2] :
? [X3] :
( ( X2 != X3
| g(f(X3)) != X3 )
& ( X2 = X3
| g(f(X3)) = X3 ) )
| ! [X0] :
? [X1] :
( ( X0 != X1
| f(g(X1)) != X1 )
& ( X0 = X1
| X1 = f(g(X1)) ) ) )
& ( ? [X2] :
! [X3] :
( ( g(f(X3)) = X3
| X2 != X3 )
& ( X2 = X3
| g(f(X3)) != X3 ) )
| ? [X0] :
! [X1] :
( ( X1 = f(g(X1))
| X0 != X1 )
& ( X0 = X1
| f(g(X1)) != X1 ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ! [X0] :
? [X1] :
( ( X0 != X1
| g(f(X1)) != X1 )
& ( X0 = X1
| g(f(X1)) = X1 ) )
| ! [X2] :
? [X3] :
( ( X2 != X3
| f(g(X3)) != X3 )
& ( X2 = X3
| f(g(X3)) = X3 ) ) )
& ( ? [X4] :
! [X5] :
( ( g(f(X5)) = X5
| X4 != X5 )
& ( X4 = X5
| g(f(X5)) != X5 ) )
| ? [X6] :
! [X7] :
( ( f(g(X7)) = X7
| X6 != X7 )
& ( X6 = X7
| f(g(X7)) != X7 ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ! [X0] :
( ( sK0(X0) != X0
| sK0(X0) != g(f(sK0(X0))) )
& ( sK0(X0) = X0
| sK0(X0) = g(f(sK0(X0))) ) )
| ! [X2] :
( ( sK1(X2) != X2
| sK1(X2) != f(g(sK1(X2))) )
& ( sK1(X2) = X2
| sK1(X2) = f(g(sK1(X2))) ) ) )
& ( ! [X5] :
( ( g(f(X5)) = X5
| sK2 != X5 )
& ( sK2 = X5
| g(f(X5)) != X5 ) )
| ! [X7] :
( ( f(g(X7)) = X7
| sK3 != X7 )
& ( sK3 = X7
| f(g(X7)) != X7 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X1,sK0(X0)),skolemize(X3,sK1(X2)),skolemize(X4,sK2),skolemize(X6,sK3)],[f6]) ).
fof(f8,plain,
! [X7,X5] :
( sK2 = X5
| g(f(X5)) != X5
| sK3 = X7
| f(g(X7)) != X7 ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X7,X5] :
( sK2 = X5
| g(f(X5)) != X5
| f(g(X7)) = X7
| sK3 != X7 ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X7,X5] :
( g(f(X5)) = X5
| sK2 != X5
| sK3 = X7
| f(g(X7)) != X7 ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X7,X5] :
( g(f(X5)) = X5
| sK2 != X5
| f(g(X7)) = X7
| sK3 != X7 ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X0] :
( sK0(X0) = X0
| sK0(X0) = g(f(sK0(X0)))
| sK1(X2) = X2
| sK1(X2) = f(g(sK1(X2))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2,X0] :
( sK0(X0) = X0
| sK0(X0) = g(f(sK0(X0)))
| sK1(X2) != X2
| sK1(X2) != f(g(sK1(X2))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X2,X0] :
( sK0(X0) != X0
| sK0(X0) != g(f(sK0(X0)))
| sK1(X2) = X2
| sK1(X2) = f(g(sK1(X2))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X0] :
( sK0(X0) != X0
| sK0(X0) != g(f(sK0(X0)))
| sK1(X2) != X2
| sK1(X2) != f(g(sK1(X2))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X7] :
( sK2 = g(f(sK2))
| f(g(X7)) = X7
| sK3 != X7 ),
inference(equality_resolution,[],[f11]) ).
fof(f17,plain,
( sK2 = g(f(sK2))
| sK3 = f(g(sK3)) ),
inference(equality_resolution,[],[f16]) ).
fof(f18,plain,
! [X7] :
( sK2 = g(f(sK2))
| sK3 = X7
| f(g(X7)) != X7 ),
inference(equality_resolution,[],[f10]) ).
fof(f19,plain,
! [X5] :
( sK2 = X5
| g(f(X5)) != X5
| sK3 = f(g(sK3)) ),
inference(equality_resolution,[],[f9]) ).
fof(f21,definition,
( spl4_1
<=> ! [X7] :
( sK3 = X7
| f(g(X7)) != X7 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f22,plain,
( ! [X7] :
( f(g(X7)) != X7
| sK3 = X7 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,definition,
( spl4_2
<=> ! [X5] :
( sK2 = X5
| g(f(X5)) != X5 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f25,plain,
( ! [X5] :
( g(f(X5)) != X5
| sK2 = X5 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f8,f24,f21]) ).
fof(f28,definition,
( spl4_3
<=> sK3 = f(g(sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f30,plain,
( sK3 = f(g(sK3))
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f19,f24,f28]) ).
fof(f33,definition,
( spl4_4
<=> sK2 = g(f(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f35,plain,
( sK2 = g(f(sK2))
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
( spl4_1
| spl4_4 ),
inference(avatar_split_clause,[],[f18,f33,f21]) ).
fof(f37,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f17,f33,f28]) ).
fof(f39,definition,
( spl4_5
<=> ! [X2] :
( sK1(X2) = X2
| sK1(X2) = f(g(sK1(X2))) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f40,plain,
( ! [X2] :
( sK1(X2) = X2
| sK1(X2) = f(g(sK1(X2))) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,definition,
( spl4_6
<=> ! [X0] :
( sK0(X0) = X0
| sK0(X0) = g(f(sK0(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f43,plain,
( ! [X0] :
( sK0(X0) = X0
| sK0(X0) = g(f(sK0(X0))) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f12,f42,f39]) ).
fof(f46,definition,
( spl4_7
<=> ! [X2] :
( sK1(X2) != X2
| sK1(X2) != f(g(sK1(X2))) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f47,plain,
( ! [X2] :
( sK1(X2) != f(g(sK1(X2)))
| sK1(X2) != X2 )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( spl4_7
| spl4_6 ),
inference(avatar_split_clause,[],[f13,f42,f46]) ).
fof(f50,definition,
( spl4_8
<=> ! [X0] :
( sK0(X0) != X0
| sK0(X0) != g(f(sK0(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f51,plain,
( ! [X0] :
( sK0(X0) != g(f(sK0(X0)))
| sK0(X0) != X0 )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f52,plain,
( spl4_5
| spl4_8 ),
inference(avatar_split_clause,[],[f14,f50,f39]) ).
fof(f53,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[],[f15,f50,f46]) ).
fof(f54,plain,
( ! [X0] :
( f(g(X0)) != X0
| X0 != X0
| sK1(X0) = f(g(sK1(X0))) )
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f47,f40]) ).
fof(f55,plain,
( ! [X0] :
( f(g(X0)) != X0
| sK1(X0) = f(g(sK1(X0))) )
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f54]) ).
fof(f56,plain,
( f(sK2) != f(sK2)
| sK1(f(sK2)) = f(g(sK1(f(sK2))))
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f55,f35]) ).
fof(f57,plain,
( sK1(f(sK2)) = f(g(sK1(f(sK2))))
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f56]) ).
fof(f61,plain,
( g(sK1(f(sK2))) != g(sK1(f(sK2)))
| sK2 = g(sK1(f(sK2)))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f25,f57]) ).
fof(f62,plain,
( sK2 = g(sK1(f(sK2)))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f61]) ).
fof(f67,plain,
( f(sK2) = sK1(f(sK2))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f57,f62]) ).
fof(f68,plain,
( f(sK2) != sK1(f(sK2))
| f(sK2) != sK1(f(sK2))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f47,f62]) ).
fof(f70,plain,
( f(sK2) != sK1(f(sK2))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f76,definition,
( spl4_10
<=> f(sK2) = sK1(f(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f80,plain,
( ~ spl4_10
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f70,f46,f39,f33,f24,f76]) ).
fof(f81,plain,
( spl4_10
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f67,f46,f39,f33,f24,f76]) ).
fof(f82,plain,
( ! [X0] :
( g(f(X0)) != X0
| X0 != X0
| sK0(X0) = g(f(sK0(X0))) )
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f51,f43]) ).
fof(f83,plain,
( ! [X0] :
( g(f(X0)) != X0
| sK0(X0) = g(f(sK0(X0))) )
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f82]) ).
fof(f84,plain,
( sK2 != sK2
| sK0(sK2) = g(f(sK0(sK2)))
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f83,f35]) ).
fof(f85,plain,
( sK0(sK2) = g(f(sK0(sK2)))
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f84]) ).
fof(f89,plain,
( sK0(sK2) != sK0(sK2)
| sK2 = sK0(sK2)
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f25,f85]) ).
fof(f90,plain,
( sK2 = sK0(sK2)
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f89]) ).
fof(f94,plain,
( sK2 != g(f(sK2))
| sK2 != sK2
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f51,f90]) ).
fof(f95,plain,
( sK2 != g(f(sK2))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f94]) ).
fof(f96,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(forward_subsumption_resolution,[],[f95,f35]) ).
fof(f97,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f100,plain,
( g(sK3) != g(sK3)
| sK0(g(sK3)) = g(f(sK0(g(sK3))))
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f83,f30]) ).
fof(f101,plain,
( sK0(g(sK3)) = g(f(sK0(g(sK3))))
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f100]) ).
fof(f121,plain,
( f(sK0(g(sK3))) != f(sK0(g(sK3)))
| sK3 = f(sK0(g(sK3)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f22,f101]) ).
fof(f122,plain,
( sK3 = f(sK0(g(sK3)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f121]) ).
fof(f127,plain,
( g(sK3) = sK0(g(sK3))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f101,f122]) ).
fof(f128,plain,
( g(sK3) != sK0(g(sK3))
| g(sK3) != sK0(g(sK3))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f51,f122]) ).
fof(f130,plain,
( g(sK3) != sK0(g(sK3))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(duplicate_literal_removal,[],[f128]) ).
fof(f136,definition,
( spl4_12
<=> g(sK3) = sK0(g(sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
fof(f140,plain,
( ~ spl4_12
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f130,f50,f42,f28,f21,f136]) ).
fof(f141,plain,
( spl4_12
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f127,f50,f42,f28,f21,f136]) ).
fof(f142,plain,
( ! [X0] :
( f(g(X0)) != X0
| X0 != X0
| sK1(X0) = f(g(sK1(X0))) )
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f47,f40]) ).
fof(f143,plain,
( ! [X0] :
( f(g(X0)) != X0
| sK1(X0) = f(g(sK1(X0))) )
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f142]) ).
fof(f144,plain,
( sK3 != sK3
| sK1(sK3) = f(g(sK1(sK3)))
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f143,f30]) ).
fof(f145,plain,
( sK1(sK3) = f(g(sK1(sK3)))
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f144]) ).
fof(f149,plain,
( sK1(sK3) != sK1(sK3)
| sK3 = sK1(sK3)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f22,f145]) ).
fof(f150,plain,
( sK3 = sK1(sK3)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f149]) ).
fof(f154,plain,
( sK3 != f(g(sK3))
| sK3 != sK3
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f47,f150]) ).
fof(f155,plain,
( sK3 != f(g(sK3))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f154]) ).
fof(f156,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f155,f30]) ).
fof(f157,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f156]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f31]) ).
cnf(s3,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s5,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f44]) ).
cnf(s6,plain,
( spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f48]) ).
cnf(s7,plain,
( spl4_5
| spl4_8 ),
inference(sat_conversion,[],[f52]) ).
cnf(s8,plain,
( spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f53]) ).
cnf(s10,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7
| ~ spl4_10 ),
inference(sat_conversion,[],[f80]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7
| spl4_10 ),
inference(sat_conversion,[],[f81]) ).
cnf(s12,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s15,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_12 ),
inference(sat_conversion,[],[f140]) ).
cnf(s16,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| spl4_12 ),
inference(sat_conversion,[],[f141]) ).
cnf(s17,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7 ),
inference(sat_conversion,[],[f157]) ).
cnf(s18,plain,
( spl4_5
| spl4_1 ),
inference(rat,[],[s12,s5,s7,s3,s1]) ).
cnf(s19,plain,
( ~ spl4_7
| ~ spl4_5
| ~ spl4_4
| ~ spl4_2 ),
inference(rat,[],[s11,s10]) ).
cnf(s20,plain,
( ~ spl4_5
| ~ spl4_2
| ~ spl4_4 ),
inference(rat,[],[s12,s6,s8,s19]) ).
cnf(s21,plain,
spl4_1,
inference(rat,[],[s20,s18,s1,s3]) ).
cnf(s22,plain,
( ~ spl4_4
| ~ spl4_2 ),
inference(rat,[],[s12,s5,s7,s20]) ).
cnf(s23,plain,
( ~ spl4_8
| ~ spl4_6
| ~ spl4_3 ),
inference(rat,[],[s15,s16,s21]) ).
cnf(s24,plain,
( spl4_7
| ~ spl4_3 ),
inference(rat,[],[s23,s6,s8]) ).
cnf(s25,plain,
( ~ spl4_7
| ~ spl4_3 ),
inference(rat,[],[s23,s5,s7,s17,s21]) ).
cnf(s26,plain,
~ spl4_3,
inference(rat,[],[s25,s24]) ).
cnf(s27,plain,
spl4_4,
inference(rat,[],[s4,s26]) ).
cnf(s28,plain,
spl4_2,
inference(rat,[],[s2,s26]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s22,s28,s27]) ).
fof(f158,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN551+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n007.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 16:26:10 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.05/1.09 % (2535905)Detected formulas, will run a generic FOF schedule.
% 3.05/1.09 % (2535911)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=1944050308:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.05/1.09 % (2535910)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=1954898422:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.05/1.09 % (2535912)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=2056154024:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.05/1.09 % (2535915)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=803776796:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.05/1.09 % (2535914)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3716784273:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.05/1.09 % (2535916)dis-21_1_sil=8000:lcm=predicate:random_seed=2779726877:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.05/1.09 % (2535913)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4189085144:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.05/1.09 % (2535916)Refutation not found, incomplete strategy
% 3.05/1.09 % (2535916)------------------------------
% 3.05/1.09 % (2535916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.09 % (2535916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.09 % (2535916)CaDiCaL version: 2.1.3
% 3.05/1.09 % (2535916)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.09 % (2535916)Time elapsed: 0.002 s
% 3.05/1.09 % (2535916)Peak memory usage: 88 MB
% 3.05/1.09 % (2535916)Instructions burned: 1 (million)
% 3.05/1.09 % (2535915)First to succeed.
% 3.05/1.09 % (2535915)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2535905"
% 3.05/1.09 % (2535913)Also succeeded, but the first one will report.
% 3.05/1.09 % (2535914)Instruction limit reached!
% 3.05/1.09 % (2535914)------------------------------
% 3.05/1.09 % (2535914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.09 % (2535914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.09 % (2535914)CaDiCaL version: 2.1.3
% 3.05/1.09 % (2535914)Termination reason: Instruction limit
% 3.05/1.09 % (2535914)Termination phase: Saturation
% 3.05/1.09 % (2535914)Time elapsed: 0.054 s
% 3.05/1.09 % (2535914)Peak memory usage: 87 MB
% 3.05/1.09 % (2535914)Instructions burned: 120 (million)
% 3.05/1.09 % (2535924)lrs+10_1_sil=8000:sp=occurrence:random_seed=626400083:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.05/1.09 % (2535924)Also succeeded, but the first one will report.
% 3.05/1.09 % (2535916)------------------------------
% 3.05/1.09 % (2535916)------------------------------
% 3.05/1.09 % (2535915)Refutation found. Thanks to Tanya!
% 3.05/1.09 % SZS status Theorem for theBenchmark
% 3.05/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.18 % (2535915)------------------------------
% 3.58/1.18 % (2535915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.18 % (2535915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.18 % (2535915)CaDiCaL version: 2.1.3
% 3.58/1.18 % (2535915)Termination reason: Refutation
% 3.58/1.18 % (2535915)Time elapsed: 0.006 s
% 3.58/1.18 % (2535915)Peak memory usage: 90 MB
% 3.58/1.18 % (2535915)Instructions burned: 7 (million)
% 3.58/1.18 % (2535915)------------------------------
% 3.58/1.18 % (2535915)------------------------------
% 3.58/1.18 % (2535905)Success in time 0.435 s
% 3.58/1.18 % Vampire exiting
%------------------------------------------------------------------------------