%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN015-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:49:00 PM UTC 2026
% Result : Unsatisfiable 0.81s 0.93s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 36
% Syntax : Number of formulae : 192 ( 10 unt; 20 def)
% Number of atoms : 629 ( 198 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 700 ( 263 ~; 417 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 21 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
m != n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_1) ).
fof(f2,negated_conjecture,
! [X0] :
( X0 = j
| X0 != k
| element(X0,j) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_2) ).
fof(f3,plain,
! [X0] :
( j = X0
| k != X0
| element(X0,j) ),
inference(reorient_equations,[],[f2]) ).
fof(f4,negated_conjecture,
! [X0] :
( X0 = j
| X0 = k
| ~ element(X0,j) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_3) ).
fof(f5,plain,
! [X0] :
( ~ element(X0,j)
| k = X0
| j = X0 ),
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
! [X0] :
( X0 = m
| ~ element(X0,m)
| f(X0) != m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_4) ).
fof(f7,plain,
! [X0] :
( m != f(X0)
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
! [X0] :
( X0 = m
| ~ element(X0,m)
| f(X0) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_5) ).
fof(f9,plain,
! [X0] :
( f(X0) != X0
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
! [X0] :
( X0 = m
| ~ element(X0,m)
| element(X0,f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_6) ).
fof(f11,plain,
! [X0] :
( element(X0,f(X0))
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
! [X0] :
( X0 = m
| ~ element(X0,m)
| element(f(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_7) ).
fof(f13,plain,
! [X0] :
( element(f(X0),X0)
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
! [X0,X1] :
( X0 = m
| element(X0,m)
| X1 = m
| X1 = X0
| ~ element(X0,X1)
| ~ element(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_8) ).
fof(f15,plain,
! [X0,X1] :
( element(X0,m)
| m = X0
| m = X1
| X0 = X1
| ~ element(X0,X1)
| ~ element(X1,X0) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
! [X0] :
( X0 = n
| element(X0,n)
| g(X0) != n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_9) ).
fof(f17,plain,
! [X0] :
( n != g(X0)
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
! [X0] :
( X0 = n
| element(X0,n)
| g(X0) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).
fof(f19,plain,
! [X0] :
( g(X0) != X0
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
! [X0] :
( X0 = n
| element(X0,n)
| element(X0,g(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
fof(f21,plain,
! [X0] :
( element(X0,g(X0))
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
! [X0] :
( X0 = n
| element(X0,n)
| element(g(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).
fof(f23,plain,
! [X0] :
( element(g(X0),X0)
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
! [X0,X1] :
( X0 = n
| ~ element(X0,n)
| X1 = n
| X1 = X0
| ~ element(X0,X1)
| ~ element(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).
fof(f25,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,n)
| n = X1
| X0 = X1
| ~ element(X0,X1)
| n = X0 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
! [X0] :
( X0 = k
| X0 != m
| element(X0,k) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).
fof(f27,plain,
! [X0] :
( k = X0
| m != X0
| element(X0,k) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
! [X0] :
( X0 = k
| X0 != n
| element(X0,k) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
fof(f29,plain,
! [X0] :
( k = X0
| n != X0
| element(X0,k) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
! [X0] :
( X0 = k
| X0 = m
| X0 = n
| ~ element(X0,k) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
fof(f31,plain,
! [X0] :
( ~ element(X0,k)
| m = X0
| n = X0
| k = X0 ),
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
( j = k
| element(k,j) ),
inference(equality_resolution,[],[f3]) ).
fof(f33,plain,
( m = k
| element(m,k) ),
inference(equality_resolution,[],[f27]) ).
fof(f34,plain,
( n = k
| element(n,k) ),
inference(equality_resolution,[],[f29]) ).
fof(f36,definition,
( spl0_1
<=> element(n,k) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f37,plain,
( element(n,k)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,definition,
( spl0_2
<=> n = k ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f40,plain,
( n = k
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f34,f39,f36]) ).
fof(f43,definition,
( spl0_3
<=> element(m,k) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f44,plain,
( element(m,k)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,definition,
( spl0_4
<=> m = k ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f47,plain,
( m = k
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f33,f46,f43]) ).
fof(f50,definition,
( spl0_5
<=> element(k,j) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f51,plain,
( element(k,j)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_6
<=> j = k ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f54,plain,
( j = k
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f32,f53,f50]) ).
fof(f56,plain,
( element(m,n)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f44,f40]) ).
fof(f60,plain,
( ~ element(j,m)
| m = j
| k = f(j)
| j = f(j) ),
inference(resolution,[],[f13,f5]) ).
fof(f61,plain,
( ~ element(j,m)
| m = j
| k = f(j) ),
inference(forward_subsumption_resolution,[],[f60,f9]) ).
fof(f63,definition,
( spl0_7
<=> k = f(j) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f64,plain,
( k = f(j)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,definition,
( spl0_8
<=> m = j ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f67,plain,
( m = j
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,definition,
( spl0_9
<=> element(j,m) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f70,plain,
( ~ element(j,m)
| spl0_9 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f71,plain,
( spl0_7
| spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f61,f69,f66,f63]) ).
fof(f72,plain,
( element(j,n)
| n = j
| k = g(j)
| j = g(j) ),
inference(resolution,[],[f23,f5]) ).
fof(f73,plain,
( element(j,n)
| n = j
| k = g(j) ),
inference(forward_subsumption_resolution,[],[f72,f19]) ).
fof(f75,definition,
( spl0_10
<=> k = g(j) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f76,plain,
( k = g(j)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,definition,
( spl0_11
<=> n = j ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f79,plain,
( n = j
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,definition,
( spl0_12
<=> element(j,n) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f82,plain,
( element(j,n)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( spl0_10
| spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f73,f81,f78,f75]) ).
fof(f87,plain,
( n != k
| element(j,n)
| n = j
| ~ spl0_10 ),
inference(superposition,[],[f17,f76]) ).
fof(f88,plain,
( element(j,n)
| n = j
| ~ spl0_2
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f87,f40]) ).
fof(f89,plain,
( j != k
| spl0_6 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f92,definition,
( spl0_13
<=> element(j,k) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f95,plain,
( spl0_11
| spl0_12
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f88,f75,f39,f81,f78]) ).
fof(f97,plain,
( m = f(k)
| n = f(k)
| k = f(k)
| ~ element(k,m)
| m = k ),
inference(resolution,[],[f31,f13]) ).
fof(f98,plain,
( m = g(k)
| n = g(k)
| k = g(k)
| element(k,n)
| n = k ),
inference(resolution,[],[f31,f23]) ).
fof(f101,plain,
( m = g(k)
| k = g(k)
| element(k,n)
| n = k ),
inference(forward_subsumption_resolution,[],[f98,f17]) ).
fof(f102,plain,
( n = f(k)
| k = f(k)
| ~ element(k,m)
| m = k ),
inference(forward_subsumption_resolution,[],[f97,f7]) ).
fof(f103,plain,
( n = f(k)
| ~ element(k,m)
| m = k ),
inference(forward_subsumption_resolution,[],[f102,f9]) ).
fof(f105,definition,
( spl0_14
<=> element(k,m) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f106,plain,
( ~ element(k,m)
| spl0_14 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,definition,
( spl0_15
<=> n = f(k) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f109,plain,
( n = f(k)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( spl0_4
| ~ spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f103,f108,f105,f46]) ).
fof(f114,plain,
( ! [X0] :
( ~ element(X0,n)
| k = X0
| n = X0 )
| ~ spl0_11 ),
inference(superposition,[],[f5,f79]) ).
fof(f118,definition,
( spl0_16
<=> ! [X0] :
( m = X0
| ~ element(X0,j)
| ~ element(j,X0)
| j = X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f119,plain,
( ! [X0] :
( ~ element(j,X0)
| ~ element(X0,j)
| m = X0
| j = X0 )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f124,definition,
( spl0_17
<=> ! [X0] :
( m = X0
| ~ element(X0,k)
| ~ element(k,X0)
| k = X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f125,plain,
( ! [X0] :
( ~ element(k,X0)
| ~ element(X0,k)
| m = X0
| k = X0 )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f130,plain,
( ~ element(k,n)
| m = n
| m = k
| ~ element(k,m)
| n = k
| ~ spl0_3 ),
inference(resolution,[],[f25,f44]) ).
fof(f183,plain,
( m = k
| m = n
| ~ spl0_2
| ~ spl0_3
| ~ spl0_11 ),
inference(resolution,[],[f114,f56]) ).
fof(f188,plain,
( m = k
| ~ spl0_2
| ~ spl0_3
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f183,f1]) ).
fof(f189,plain,
( spl0_4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f188,f78,f43,f39,f46]) ).
fof(f218,plain,
( ~ element(j,k)
| m = j
| j = k
| ~ spl0_5
| ~ spl0_17 ),
inference(resolution,[],[f125,f51]) ).
fof(f231,plain,
( ! [X0] :
( ~ element(X0,m)
| m = X0
| n = X0
| m = X0 )
| ~ spl0_4 ),
inference(superposition,[],[f31,f47]) ).
fof(f232,plain,
( element(n,m)
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f37,f47]) ).
fof(f237,plain,
( ! [X0] :
( ~ element(X0,m)
| m = X0
| n = X0 )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f259,plain,
( element(k,m)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f51,f67]) ).
fof(f261,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f259,f106]) ).
fof(f262,plain,
( ~ spl0_5
| ~ spl0_8
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f279,plain,
( element(j,k)
| ~ element(j,m)
| m = j
| ~ spl0_7 ),
inference(superposition,[],[f11,f64]) ).
fof(f284,plain,
( spl0_8
| ~ spl0_9
| spl0_13
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f279,f63,f92,f69,f66]) ).
fof(f290,plain,
( m = n
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f40,f47]) ).
fof(f294,plain,
( element(n,j)
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f51,f40]) ).
fof(f300,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f290,f1]) ).
fof(f301,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f300]) ).
fof(f304,definition,
( spl0_22
<=> element(k,n) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f307,plain,
( n != k
| spl0_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f318,plain,
( m = g(k)
| element(k,n)
| n = k ),
inference(forward_subsumption_resolution,[],[f101,f19]) ).
fof(f320,plain,
( element(k,n)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f322,definition,
( spl0_24
<=> m = g(k) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f323,plain,
( m = g(k)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f324,plain,
( spl0_2
| spl0_22
| spl0_24 ),
inference(avatar_split_clause,[],[f318,f322,f304,f39]) ).
fof(f331,plain,
( ! [X0] :
( ~ element(X0,k)
| k = X0
| k = X0 )
| ~ spl0_6 ),
inference(superposition,[],[f5,f54]) ).
fof(f332,plain,
( ! [X0] :
( ~ element(X0,k)
| k = X0 )
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f331]) ).
fof(f350,plain,
( m = k
| ~ spl0_3
| ~ spl0_6 ),
inference(resolution,[],[f332,f44]) ).
fof(f365,plain,
( ! [X0,X1] :
( m = X0
| n = X0
| m = X0
| m = X1
| X0 = X1
| ~ element(X0,X1)
| ~ element(X1,X0) )
| ~ spl0_4 ),
inference(resolution,[],[f237,f15]) ).
fof(f370,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| n = X0
| m = X1
| X0 = X1
| ~ element(X0,X1)
| m = X0 )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f365]) ).
fof(f415,definition,
( spl0_26
<=> element(n,j) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f416,plain,
( ~ element(n,j)
| spl0_26 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f421,plain,
( ! [X0] :
( n = f(X0)
| m = X0
| f(X0) = X0
| ~ element(f(X0),X0)
| m = f(X0)
| ~ element(X0,m)
| m = X0 )
| ~ spl0_4 ),
inference(resolution,[],[f370,f11]) ).
fof(f446,plain,
( ! [X0] :
( n = f(X0)
| m = X0
| f(X0) = X0
| ~ element(f(X0),X0)
| m = f(X0)
| ~ element(X0,m) )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f421]) ).
fof(f449,plain,
( ! [X0] :
( n = f(X0)
| m = X0
| f(X0) = X0
| m = f(X0)
| ~ element(X0,m) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f446,f13]) ).
fof(f452,plain,
( ! [X0] :
( n = f(X0)
| m = X0
| m = f(X0)
| ~ element(X0,m) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f449,f9]) ).
fof(f454,plain,
( ! [X0] :
( n = f(X0)
| m = X0
| ~ element(X0,m) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f452,f7]) ).
fof(f465,plain,
( ! [X0] :
( n != X0
| ~ element(X0,m)
| m = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_4 ),
inference(superposition,[],[f9,f454]) ).
fof(f471,plain,
( ! [X0] :
( n != X0
| ~ element(X0,m)
| m = X0 )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f465]) ).
fof(f473,plain,
( ! [X0] :
( ~ element(X0,m)
| m = X0 )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f471,f237]) ).
fof(f490,plain,
( m = n
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f473,f232]) ).
fof(f494,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f490,f1]) ).
fof(f495,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f494]) ).
fof(f498,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f294,f416]) ).
fof(f499,plain,
( ~ spl0_2
| ~ spl0_5
| spl0_26 ),
inference(avatar_contradiction_clause,[],[f498]) ).
fof(f504,plain,
( spl0_4
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f350,f53,f43,f46]) ).
fof(f519,plain,
( n != k
| ~ element(k,m)
| m = k
| ~ spl0_15 ),
inference(superposition,[],[f9,f109]) ).
fof(f520,plain,
( element(k,n)
| ~ element(k,m)
| m = k
| ~ spl0_15 ),
inference(superposition,[],[f11,f109]) ).
fof(f527,plain,
( ~ element(j,k)
| m = j
| ~ spl0_5
| spl0_6
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f218,f89]) ).
fof(f528,plain,
( ~ element(k,n)
| m = k
| ~ element(k,m)
| n = k
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f130,f1]) ).
fof(f529,plain,
( spl0_4
| ~ spl0_14
| spl0_22
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f520,f108,f304,f105,f46]) ).
fof(f531,plain,
( spl0_4
| ~ spl0_14
| ~ spl0_2
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f519,f108,f39,f105,f46]) ).
fof(f532,plain,
( spl0_8
| ~ spl0_13
| ~ spl0_5
| spl0_6
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f527,f124,f53,f50,f92,f66]) ).
fof(f533,plain,
( spl0_2
| ~ spl0_14
| spl0_4
| ~ spl0_22
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f528,f43,f304,f46,f105,f39]) ).
fof(f539,plain,
( ! [X0] :
( m = j
| m = X0
| j = X0
| ~ element(j,X0)
| ~ element(X0,j) )
| spl0_9 ),
inference(resolution,[],[f70,f15]) ).
fof(f540,plain,
( spl0_16
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f539,f69,f66,f118]) ).
fof(f541,plain,
( ! [X0] :
( m = k
| m = X0
| k = X0
| ~ element(k,X0)
| ~ element(X0,k) )
| spl0_14 ),
inference(resolution,[],[f106,f15]) ).
fof(f542,plain,
( spl0_17
| spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f541,f105,f46,f124]) ).
fof(f545,plain,
( element(k,m)
| element(k,n)
| n = k
| ~ spl0_24 ),
inference(superposition,[],[f21,f323]) ).
fof(f549,plain,
( element(k,n)
| n = k
| spl0_14
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f545,f106]) ).
fof(f551,plain,
( spl0_2
| spl0_22
| spl0_14
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f549,f322,f105,f304,f39]) ).
fof(f555,plain,
( ~ element(n,j)
| m = n
| n = j
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[],[f119,f82]) ).
fof(f562,plain,
( ~ element(n,j)
| n = j
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f555,f1]) ).
fof(f563,plain,
( spl0_11
| ~ spl0_26
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f562,f118,f81,f415,f78]) ).
fof(f565,plain,
( ~ element(n,k)
| m = n
| n = k
| ~ spl0_17
| ~ spl0_22 ),
inference(resolution,[],[f125,f320]) ).
fof(f572,plain,
( m = n
| n = k
| ~ spl0_1
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f565,f37]) ).
fof(f573,plain,
( n = k
| ~ spl0_1
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f572,f1]) ).
fof(f574,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f573,f307]) ).
fof(f575,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f574]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f55]) ).
cnf(s4,plain,
( spl0_7
| spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
( spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f83]) ).
cnf(s8,plain,
( ~ spl0_2
| ~ spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f95]) ).
cnf(s9,plain,
( spl0_4
| ~ spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f110]) ).
cnf(s12,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_11 ),
inference(sat_conversion,[],[f189]) ).
cnf(s20,plain,
( ~ spl0_5
| ~ spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f262]) ).
cnf(s24,plain,
( ~ spl0_7
| spl0_8
| ~ spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f284]) ).
cnf(s32,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f301]) ).
cnf(s41,plain,
( spl0_2
| spl0_22
| spl0_24 ),
inference(sat_conversion,[],[f324]) ).
cnf(s55,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f495]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_5
| spl0_26 ),
inference(sat_conversion,[],[f499]) ).
cnf(s60,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f504]) ).
cnf(s66,plain,
( spl0_4
| ~ spl0_14
| ~ spl0_15
| spl0_22 ),
inference(sat_conversion,[],[f529]) ).
cnf(s67,plain,
( ~ spl0_2
| spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f531]) ).
cnf(s68,plain,
( ~ spl0_5
| spl0_6
| spl0_8
| ~ spl0_13
| ~ spl0_17 ),
inference(sat_conversion,[],[f532]) ).
cnf(s69,plain,
( spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f533]) ).
cnf(s71,plain,
( spl0_8
| spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f540]) ).
cnf(s72,plain,
( spl0_4
| spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f542]) ).
cnf(s74,plain,
( spl0_2
| spl0_14
| spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f551]) ).
cnf(s76,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_26 ),
inference(sat_conversion,[],[f563]) ).
cnf(s77,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f575]) ).
cnf(s78,plain,
( spl0_12
| ~ spl0_2
| spl0_11 ),
inference(rat,[],[s5,s8]) ).
cnf(s79,plain,
( spl0_8
| spl0_7
| spl0_16 ),
inference(rat,[],[s71,s4]) ).
cnf(s80,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s67,s9,s32]) ).
cnf(s81,plain,
~ spl0_2,
inference(rat,[],[s24,s79,s71,s68,s20,s72,s80,s76,s78,s57,s3,s12,s60,s2,s32]) ).
cnf(s82,plain,
spl0_1,
inference(rat,[],[s1,s81]) ).
cnf(s83,plain,
~ spl0_4,
inference(rat,[],[s55,s82]) ).
cnf(s85,plain,
spl0_3,
inference(rat,[],[s2,s83]) ).
cnf(s87,plain,
spl0_14,
inference(rat,[],[s74,s41,s77,s72,s81,s82,s83]) ).
cnf(s88,plain,
spl0_15,
inference(rat,[],[s9,s83,s87]) ).
cnf(s89,plain,
~ spl0_22,
inference(rat,[],[s69,s85,s81,s83,s87]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s66,s87,s83,s89,s88]) ).
fof(f576,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:21:05 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 0.81/0.93 % (242861)Input is clausal, will run a generic CNF schedule.
% 0.81/0.93 % (242870)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2689627163:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.81/0.93 % (242870)First to succeed.
% 0.81/0.93 % (242870)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-242861"
% 0.81/0.93 % (242871)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3658849888:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.81/0.93 % (242872)dis-21_1_sil=8000:lcm=predicate:random_seed=3612892429:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.81/0.93 % (242868)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=917888717:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.81/0.93 % (242869)lrs+10_1_sil=8000:sp=occurrence:random_seed=1550949694:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.81/0.93 % (242867)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2842476590:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.81/0.93 % (242866)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=2470600835:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.81/0.93 % (242869)Also succeeded, but the first one will report.
% 0.81/0.93 % (242871)Also succeeded, but the first one will report.
% 0.81/0.93 % (242872)Instruction limit reached!
% 0.81/0.93 % (242872)------------------------------
% 0.81/0.93 % (242872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.81/0.93 % (242872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.93 % (242872)CaDiCaL version: 2.1.3
% 0.81/0.93 % (242872)Termination reason: Instruction limit
% 0.81/0.93 % (242872)Termination phase: Saturation
% 0.81/0.93 % (242872)Time elapsed: 0.052 s
% 0.81/0.93 % (242872)Peak memory usage: 88 MB
% 0.81/0.93 % (242872)Instructions burned: 118 (million)
% 0.81/0.93 % (242870)Refutation found. Thanks to Tanya!
% 0.81/0.93 % SZS status Unsatisfiable for theBenchmark
% 0.81/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.12 % (242870)------------------------------
% 2.54/1.12 % (242870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.12 % (242870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.12 % (242870)CaDiCaL version: 2.1.3
% 2.54/1.12 % (242870)Termination reason: Refutation
% 2.54/1.12 % (242870)Time elapsed: 0.009 s
% 2.54/1.12 % (242870)Peak memory usage: 89 MB
% 2.54/1.12 % (242870)Instructions burned: 20 (million)
% 2.54/1.12 % (242870)------------------------------
% 2.54/1.12 % (242870)------------------------------
% 2.54/1.12 % (242861)Success in time 0.275 s
% 2.54/1.12 % Vampire exiting
%------------------------------------------------------------------------------