%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN551+3 : 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 : 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 02:00:56 PM UTC 2026
% Result : Theorem 3.12s 1.09s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 125 ( 11 unt; 12 def)
% Number of atoms : 412 ( 170 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 536 ( 249 ~; 242 |; 23 &)
% ( 15 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 60 ( 0 sgn 44 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
( X0 = f(g(X0))
& ! [X1] :
( X1 = f(g(X1))
=> X1 = X0 ) )
<=> ? [X0] :
( X0 = g(f(X0))
& ! [X1] :
( X1 = g(f(X1))
=> X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_cute_thing) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( X0 = f(g(X0))
& ! [X1] :
( X1 = f(g(X1))
=> X1 = X0 ) )
<=> ? [X0] :
( X0 = g(f(X0))
& ! [X1] :
( X1 = g(f(X1))
=> X1 = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
( X0 = f(g(X0))
& ! [X1] :
( X1 = f(g(X1))
=> X1 = X0 ) )
<=> ? [X2] :
( g(f(X2)) = X2
& ! [X3] :
( g(f(X3)) = X3
=> X2 = X3 ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
( X0 = f(g(X0))
& ! [X1] :
( X1 = X0
| f(g(X1)) != X1 ) )
<~> ? [X2] :
( g(f(X2)) = X2
& ! [X3] :
( X2 = X3
| g(f(X3)) != X3 ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ! [X2] :
( g(f(X2)) != X2
| ? [X3] :
( X2 != X3
& g(f(X3)) = X3 ) )
| ! [X0] :
( f(g(X0)) != X0
| ? [X1] :
( X0 != X1
& f(g(X1)) = X1 ) ) )
& ( ? [X2] :
( g(f(X2)) = X2
& ! [X3] :
( X2 = X3
| g(f(X3)) != X3 ) )
| ? [X0] :
( X0 = f(g(X0))
& ! [X1] :
( X1 = X0
| f(g(X1)) != X1 ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ! [X0] :
( g(f(X0)) != X0
| ? [X1] :
( X0 != X1
& g(f(X1)) = X1 ) )
| ! [X2] :
( f(g(X2)) != X2
| ? [X3] :
( X2 != X3
& f(g(X3)) = X3 ) ) )
& ( ? [X4] :
( g(f(X4)) = X4
& ! [X5] :
( X4 = X5
| g(f(X5)) != X5 ) )
| ? [X6] :
( f(g(X6)) = X6
& ! [X7] :
( X6 = X7
| f(g(X7)) != X7 ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ! [X0] :
( g(f(X0)) != X0
| ( sK0(X0) != X0
& sK0(X0) = g(f(sK0(X0))) ) )
| ! [X2] :
( f(g(X2)) != X2
| ( sK1(X2) != X2
& sK1(X2) = f(g(sK1(X2))) ) ) )
& ( ( sK2 = g(f(sK2))
& ! [X5] :
( sK2 = X5
| g(f(X5)) != X5 ) )
| ( sK3 = f(g(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,
! [X5] :
( sK2 = X5
| g(f(X5)) != X5
| sK3 = f(g(sK3)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X7] :
( sK2 = g(f(sK2))
| sK3 = X7
| f(g(X7)) != X7 ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
( sK2 = g(f(sK2))
| sK3 = f(g(sK3)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X0] :
( g(f(X0)) != X0
| sK0(X0) = g(f(sK0(X0)))
| f(g(X2)) != X2
| sK1(X2) = f(g(sK1(X2))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2,X0] :
( g(f(X0)) != X0
| sK0(X0) = g(f(sK0(X0)))
| f(g(X2)) != X2
| sK1(X2) != X2 ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X2,X0] :
( g(f(X0)) != X0
| sK0(X0) != X0
| f(g(X2)) != X2
| sK1(X2) = f(g(sK1(X2))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X0] :
( g(f(X0)) != X0
| sK0(X0) != X0
| f(g(X2)) != X2
| sK1(X2) != X2 ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,definition,
( spl4_1
<=> ! [X7] :
( sK3 = X7
| f(g(X7)) != X7 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f18,plain,
( ! [X7] :
( f(g(X7)) != X7
| sK3 = X7 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f20,definition,
( spl4_2
<=> ! [X5] :
( sK2 = X5
| g(f(X5)) != X5 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f21,plain,
( ! [X5] :
( g(f(X5)) != X5
| sK2 = X5 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f22,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f8,f20,f17]) ).
fof(f24,definition,
( spl4_3
<=> sK3 = f(g(sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f26,plain,
( sK3 = f(g(sK3))
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f27,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f9,f20,f24]) ).
fof(f29,definition,
( spl4_4
<=> sK2 = g(f(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f30,plain,
( sK2 != g(f(sK2))
| spl4_4 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( sK2 = g(f(sK2))
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( spl4_1
| spl4_4 ),
inference(avatar_split_clause,[],[f10,f29,f17]) ).
fof(f33,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f11,f29,f24]) ).
fof(f35,definition,
( spl4_5
<=> ! [X2] :
( f(g(X2)) != X2
| sK1(X2) = f(g(sK1(X2))) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f36,plain,
( ! [X2] :
( f(g(X2)) != X2
| sK1(X2) = f(g(sK1(X2))) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,definition,
( spl4_6
<=> ! [X0] :
( g(f(X0)) != X0
| sK0(X0) = g(f(sK0(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f39,plain,
( ! [X0] :
( g(f(X0)) != X0
| sK0(X0) = g(f(sK0(X0))) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f12,f38,f35]) ).
fof(f42,definition,
( spl4_7
<=> ! [X2] :
( f(g(X2)) != X2
| sK1(X2) != X2 ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f43,plain,
( ! [X2] :
( sK1(X2) != X2
| f(g(X2)) != X2 )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( spl4_7
| spl4_6 ),
inference(avatar_split_clause,[],[f13,f38,f42]) ).
fof(f46,definition,
( spl4_8
<=> ! [X0] :
( g(f(X0)) != X0
| sK0(X0) != X0 ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f47,plain,
( ! [X0] :
( sK0(X0) != X0
| g(f(X0)) != X0 )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( spl4_5
| spl4_8 ),
inference(avatar_split_clause,[],[f14,f46,f35]) ).
fof(f49,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[],[f15,f46,f42]) ).
fof(f50,plain,
( f(sK2) != f(sK2)
| sK1(f(sK2)) = f(g(sK1(f(sK2))))
| ~ spl4_4
| ~ spl4_5 ),
inference(superposition,[],[f36,f31]) ).
fof(f51,plain,
( sK1(f(sK2)) = f(g(sK1(f(sK2))))
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f50]) ).
fof(f53,plain,
( g(sK1(f(sK2))) != g(sK1(f(sK2)))
| sK2 = g(sK1(f(sK2)))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5 ),
inference(superposition,[],[f21,f51]) ).
fof(f54,plain,
( sK2 = g(sK1(f(sK2)))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f53]) ).
fof(f56,plain,
( f(sK2) = sK1(f(sK2))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5 ),
inference(superposition,[],[f51,f54]) ).
fof(f63,definition,
( spl4_10
<=> f(sK2) = sK1(f(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f64,plain,
( f(sK2) = sK1(f(sK2))
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,plain,
( spl4_10
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f56,f35,f29,f20,f63]) ).
fof(f68,plain,
( sK2 != sK2
| sK0(sK2) = g(f(sK0(sK2)))
| ~ spl4_4
| ~ spl4_6 ),
inference(superposition,[],[f39,f31]) ).
fof(f69,plain,
( sK0(sK2) = g(f(sK0(sK2)))
| ~ spl4_4
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f68]) ).
fof(f71,plain,
( sK0(sK2) != sK0(sK2)
| sK2 = sK0(sK2)
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6 ),
inference(superposition,[],[f21,f69]) ).
fof(f72,plain,
( sK2 = sK0(sK2)
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f71]) ).
fof(f75,plain,
( sK2 != sK2
| sK2 != g(f(sK2))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f47,f72]) ).
fof(f76,plain,
( sK2 != g(f(sK2))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f75]) ).
fof(f77,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(forward_subsumption_resolution,[],[f76,f31]) ).
fof(f78,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f77]) ).
fof(f86,plain,
( f(sK2) != f(sK2)
| f(sK2) != f(g(f(sK2)))
| ~ spl4_7
| ~ spl4_10 ),
inference(superposition,[],[f43,f64]) ).
fof(f87,plain,
( f(sK2) != f(g(f(sK2)))
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f86]) ).
fof(f88,plain,
( f(sK2) != f(sK2)
| ~ spl4_4
| ~ spl4_7
| ~ spl4_10 ),
inference(forward_demodulation,[],[f87,f31]) ).
fof(f89,plain,
( $false
| ~ spl4_4
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f88]) ).
fof(f90,plain,
( ~ spl4_4
| ~ spl4_7
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[],[f89]) ).
fof(f91,plain,
( sK3 != sK3
| sK1(sK3) = f(g(sK1(sK3)))
| ~ spl4_3
| ~ spl4_5 ),
inference(superposition,[],[f36,f26]) ).
fof(f92,plain,
( g(sK3) != g(sK3)
| sK2 = g(sK3)
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[],[f21,f26]) ).
fof(f93,plain,
( sK2 = g(sK3)
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f92]) ).
fof(f94,plain,
( sK1(sK3) = f(g(sK1(sK3)))
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f91]) ).
fof(f95,plain,
( f(sK2) = sK3
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[],[f26,f93]) ).
fof(f98,definition,
( spl4_11
<=> sK1(sK3) = f(g(sK1(sK3))) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f100,plain,
( sK1(sK3) = f(g(sK1(sK3)))
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f102,definition,
( spl4_12
<=> f(sK2) = sK3 ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
fof(f103,plain,
( f(sK2) = sK3
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f106,plain,
( spl4_12
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f95,f24,f20,f102]) ).
fof(f107,plain,
( sK2 != g(sK3)
| spl4_4
| ~ spl4_12 ),
inference(superposition,[],[f30,f103]) ).
fof(f109,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| spl4_4
| ~ spl4_12 ),
inference(forward_subsumption_resolution,[],[f107,f93]) ).
fof(f110,plain,
( ~ spl4_2
| ~ spl4_3
| spl4_4
| ~ spl4_12 ),
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f111,plain,
( spl4_11
| ~ spl4_3
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f94,f35,f24,f98]) ).
fof(f112,plain,
( sK1(sK3) != sK1(sK3)
| sK3 = sK1(sK3)
| ~ spl4_1
| ~ spl4_11 ),
inference(superposition,[],[f18,f100]) ).
fof(f115,plain,
( sK3 = sK1(sK3)
| ~ spl4_1
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f112]) ).
fof(f117,plain,
( sK3 != sK3
| sK3 != f(g(sK3))
| ~ spl4_1
| ~ spl4_7
| ~ spl4_11 ),
inference(superposition,[],[f43,f115]) ).
fof(f118,plain,
( sK3 != f(g(sK3))
| ~ spl4_1
| ~ spl4_7
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f117]) ).
fof(f119,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_7
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f118,f26]) ).
fof(f120,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_7
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f119]) ).
fof(f121,plain,
( g(sK3) != g(sK3)
| sK0(g(sK3)) = g(f(sK0(g(sK3))))
| ~ spl4_3
| ~ spl4_6 ),
inference(superposition,[],[f39,f26]) ).
fof(f124,plain,
( sK0(g(sK3)) = g(f(sK0(g(sK3))))
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f121]) ).
fof(f127,plain,
( f(sK0(g(sK3))) != f(sK0(g(sK3)))
| sK3 = f(sK0(g(sK3)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(superposition,[],[f18,f124]) ).
fof(f130,plain,
( sK3 = f(sK0(g(sK3)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f127]) ).
fof(f132,plain,
( g(sK3) = sK0(g(sK3))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(superposition,[],[f124,f130]) ).
fof(f139,definition,
( spl4_14
<=> g(sK3) = sK0(g(sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
fof(f140,plain,
( g(sK3) = sK0(g(sK3))
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f143,plain,
( spl4_14
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f132,f38,f24,f17,f139]) ).
fof(f146,plain,
( g(sK3) != g(sK3)
| g(sK3) != g(f(g(sK3)))
| ~ spl4_8
| ~ spl4_14 ),
inference(superposition,[],[f47,f140]) ).
fof(f147,plain,
( g(sK3) != g(f(g(sK3)))
| ~ spl4_8
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f146]) ).
fof(f148,plain,
( g(sK3) != g(sK3)
| ~ spl4_3
| ~ spl4_8
| ~ spl4_14 ),
inference(forward_demodulation,[],[f147,f26]) ).
fof(f149,plain,
( $false
| ~ spl4_3
| ~ spl4_8
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f148]) ).
fof(f150,plain,
( ~ spl4_3
| ~ spl4_8
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f149]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f40]) ).
cnf(s6,plain,
( spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f44]) ).
cnf(s7,plain,
( spl4_5
| spl4_8 ),
inference(sat_conversion,[],[f48]) ).
cnf(s8,plain,
( spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f49]) ).
cnf(s10,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| spl4_10 ),
inference(sat_conversion,[],[f67]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8 ),
inference(sat_conversion,[],[f78]) ).
cnf(s16,plain,
( ~ spl4_4
| ~ spl4_7
| ~ spl4_10 ),
inference(sat_conversion,[],[f90]) ).
cnf(s18,plain,
( ~ spl4_2
| ~ spl4_3
| spl4_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s19,plain,
( ~ spl4_2
| ~ spl4_3
| spl4_4
| ~ spl4_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s20,plain,
( ~ spl4_3
| ~ spl4_5
| spl4_11 ),
inference(sat_conversion,[],[f111]) ).
cnf(s21,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_7
| ~ spl4_11 ),
inference(sat_conversion,[],[f120]) ).
cnf(s23,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| spl4_14 ),
inference(sat_conversion,[],[f143]) ).
cnf(s24,plain,
( ~ spl4_3
| ~ spl4_8
| ~ spl4_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s25,plain,
( spl4_5
| spl4_1 ),
inference(rat,[],[s11,s5,s7,s3,s1]) ).
cnf(s26,plain,
( ~ spl4_5
| ~ spl4_4
| ~ spl4_2 ),
inference(rat,[],[s11,s6,s8,s16,s10]) ).
cnf(s27,plain,
spl4_1,
inference(rat,[],[s26,s25,s1,s3]) ).
cnf(s28,plain,
( ~ spl4_4
| ~ spl4_2 ),
inference(rat,[],[s11,s5,s7,s26]) ).
cnf(s29,plain,
~ spl4_2,
inference(rat,[],[s19,s18,s4,s28]) ).
cnf(s30,plain,
spl4_3,
inference(rat,[],[s2,s29]) ).
cnf(s31,plain,
spl4_5,
inference(rat,[],[s23,s24,s5,s7,s27,s30]) ).
cnf(s32,plain,
spl4_11,
inference(rat,[],[s20,s30,s31]) ).
cnf(s33,plain,
~ spl4_7,
inference(rat,[],[s21,s30,s27,s32]) ).
cnf(s34,plain,
spl4_8,
inference(rat,[],[s8,s33]) ).
cnf(s35,plain,
spl4_6,
inference(rat,[],[s6,s33]) ).
cnf(s36,plain,
~ spl4_14,
inference(rat,[],[s24,s30,s34]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s23,s30,s27,s36,s35]) ).
fof(f151,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN551+3 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 16:28:14 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 3.12/1.09 % (4137752)Detected formulas, will run a generic FOF schedule.
% 3.12/1.09 % (4137763)dis-21_1_sil=8000:lcm=predicate:random_seed=1062646075: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)
% 3.12/1.09 % (4137763)Refutation not found, incomplete strategy
% 3.12/1.09 % (4137763)------------------------------
% 3.12/1.09 % (4137763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.09 % (4137763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.09 % (4137763)CaDiCaL version: 2.1.3
% 3.12/1.09 % (4137763)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.09 % (4137763)Time elapsed: 0.001 s
% 3.12/1.09 % (4137763)Peak memory usage: 88 MB
% 3.12/1.09 % (4137763)Instructions burned: 1 (million)
% 3.12/1.09 % (4137757)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=1516842232:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.12/1.09 % (4137760)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=382357759:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.12/1.09 % (4137759)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=2983847890:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.12/1.09 % (4137761)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2251565105:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.12/1.09 % (4137762)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2649534914:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.12/1.09 % (4137758)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=1151788561:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.12/1.09 % (4137762)First to succeed.
% 3.12/1.09 % (4137760)Also succeeded, but the first one will report.
% 3.12/1.09 % (4137762)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4137752"
% 3.12/1.09 % (4137761)Also succeeded, but the first one will report.
% 3.12/1.09 % (4137763)------------------------------
% 3.12/1.09 % (4137763)------------------------------
% 3.12/1.09 % (4137771)lrs+10_1_sil=8000:sp=occurrence:random_seed=4076866091:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.12/1.09 % (4137771)Also succeeded, but the first one will report.
% 3.12/1.09 % (4137762)Refutation found. Thanks to Tanya!
% 3.12/1.09 % SZS status Theorem for theBenchmark
% 3.12/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.29 % (4137762)------------------------------
% 3.69/1.29 % (4137762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (4137762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (4137762)CaDiCaL version: 2.1.3
% 3.69/1.29 % (4137762)Termination reason: Refutation
% 3.69/1.29 % (4137762)Time elapsed: 0.006 s
% 3.69/1.29 % (4137762)Peak memory usage: 89 MB
% 3.69/1.29 % (4137762)Instructions burned: 7 (million)
% 3.69/1.29 % (4137762)------------------------------
% 3.69/1.29 % (4137762)------------------------------
% 3.69/1.29 % (4137752)Success in time 0.442 s
% 3.69/1.29 % Vampire exiting
%------------------------------------------------------------------------------