%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO041_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 02:24:49 PM UTC 2026
% Result : Theorem 3.18s 1.08s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 27
% Syntax : Number of formulae : 230 ( 18 unt; 0 typ; 25 def)
% Number of atoms : 883 ( 82 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 649 ( 267 ~; 316 |; 33 &)
% ( 31 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 279 ( 271 fml; 8 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 32 ( 29 usr; 29 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 4 ( 0 sgn 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
bG0: $o ).
tff(func_def_3,type,
bG1: $o ).
tff(func_def_4,type,
bG2: $o ).
tff(func_def_5,type,
bG3: $o ).
tff(func_def_6,type,
bG4: $o ).
tff(func_def_7,type,
bG5: $o ).
tff(func_def_8,type,
bG6: $o ).
tff(pred_def_2,type,
f: $o > $o ).
tff(pred_def_3,type,
g: $o > $o ).
tff(f1,conjecture,
~ ( ( x != y )
& ( g(x) = y )
& ( g(y) = x )
& ( f(f(f(x))) = g(f(x)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',3) ).
tff(f2,negated_conjecture,
~ ~ ( ( x != y )
& ( g(x) = y )
& ( g(y) = x )
& ( f(f(f(x))) = g(f(x)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,definition,
( x
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f4,definition,
( f(bG0)
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f5,definition,
( f(bG1)
<=> ( $true = bG2 ) ),
introduced(definition,[new_symbols(definition,[bG2])],[fool_formula_definition]) ).
tff(f6,definition,
( x
<=> ( $true = bG3 ) ),
introduced(definition,[new_symbols(definition,[bG3])],[fool_formula_definition]) ).
tff(f7,definition,
( f(bG3)
<=> ( $true = bG4 ) ),
introduced(definition,[new_symbols(definition,[bG4])],[fool_formula_definition]) ).
tff(f8,definition,
( y
<=> ( $true = bG5 ) ),
introduced(definition,[new_symbols(definition,[bG5])],[fool_formula_definition]) ).
tff(f9,definition,
( x
<=> ( $true = bG6 ) ),
introduced(definition,[new_symbols(definition,[bG6])],[fool_formula_definition]) ).
tff(f10,plain,
~ ~ ( ( x
<~> y )
& ( g(bG6)
<=> y )
& ( g(bG5)
<=> x )
& ( f(bG2)
<=> g(bG4) ) ),
inference(fool_elimination,[],[f2,f9,f8,f7,f6,f5,f4,f3]) ).
tff(f11,plain,
( ( x
<~> y )
& ( g(bG6)
<=> y )
& ( g(bG5)
<=> x )
& ( f(bG2)
<=> g(bG4) ) ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
( ( x
| ( $true != bG6 ) )
& ( ( $true = bG6 )
| ~ x ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f13,plain,
( ( y
| ( $true != bG5 ) )
& ( ( $true = bG5 )
| ~ y ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f14,plain,
( ( f(bG3)
| ( $true != bG4 ) )
& ( ( $true = bG4 )
| ~ f(bG3) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f15,plain,
( ( x
| ( $true != bG3 ) )
& ( ( $true = bG3 )
| ~ x ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f16,plain,
( ( f(bG1)
| ( $true != bG2 ) )
& ( ( $true = bG2 )
| ~ f(bG1) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f17,plain,
( ( f(bG0)
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ f(bG0) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f18,plain,
( ( x
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ x ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f19,plain,
( ( ~ y
| ~ x )
& ( y
| x )
& ( g(bG6)
| ~ y )
& ( y
| ~ g(bG6) )
& ( g(bG5)
| ~ x )
& ( x
| ~ g(bG5) )
& ( f(bG2)
| ~ g(bG4) )
& ( g(bG4)
| ~ f(bG2) ) ),
inference(nnf_transformation,[],[f11]) ).
tff(f20,plain,
( ( ~ y
| ~ x )
& ( y
| x )
& ( g(bG6)
| ~ y )
& ( y
| ~ g(bG6) )
& ( g(bG5)
| ~ x )
& ( x
| ~ g(bG5) )
& ( f(bG2)
| ~ g(bG4) )
& ( g(bG4)
| ~ f(bG2) ) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
( ( $true = bG6 )
| ~ x ),
inference(cnf_transformation,[],[f12]) ).
tff(f22,plain,
( x
| ( $true != bG6 ) ),
inference(cnf_transformation,[],[f12]) ).
tff(f23,plain,
( ( $true = bG5 )
| ~ y ),
inference(cnf_transformation,[],[f13]) ).
tff(f24,plain,
( y
| ( $true != bG5 ) ),
inference(cnf_transformation,[],[f13]) ).
tff(f25,plain,
( ( $true = bG4 )
| ~ f(bG3) ),
inference(cnf_transformation,[],[f14]) ).
tff(f26,plain,
( f(bG3)
| ( $true != bG4 ) ),
inference(cnf_transformation,[],[f14]) ).
tff(f27,plain,
( ( $true = bG3 )
| ~ x ),
inference(cnf_transformation,[],[f15]) ).
tff(f28,plain,
( x
| ( $true != bG3 ) ),
inference(cnf_transformation,[],[f15]) ).
tff(f29,plain,
( ( $true = bG2 )
| ~ f(bG1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f30,plain,
( f(bG1)
| ( $true != bG2 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f31,plain,
( ( $true = bG1 )
| ~ f(bG0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f32,plain,
( f(bG0)
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f17]) ).
tff(f33,plain,
( ( bG0 = $true )
| ~ x ),
inference(cnf_transformation,[],[f18]) ).
tff(f34,plain,
( x
| ( bG0 != $true ) ),
inference(cnf_transformation,[],[f18]) ).
tff(f35,plain,
( g(bG4)
| ~ f(bG2) ),
inference(cnf_transformation,[],[f20]) ).
tff(f36,plain,
( f(bG2)
| ~ g(bG4) ),
inference(cnf_transformation,[],[f20]) ).
tff(f37,plain,
( x
| ~ g(bG5) ),
inference(cnf_transformation,[],[f20]) ).
tff(f38,plain,
( g(bG5)
| ~ x ),
inference(cnf_transformation,[],[f20]) ).
tff(f39,plain,
( y
| ~ g(bG6) ),
inference(cnf_transformation,[],[f20]) ).
tff(f40,plain,
( g(bG6)
| ~ y ),
inference(cnf_transformation,[],[f20]) ).
tff(f41,plain,
( y
| x ),
inference(cnf_transformation,[],[f20]) ).
tff(f42,plain,
( ~ y
| ~ x ),
inference(cnf_transformation,[],[f20]) ).
tff(f44,plain,
! [X0: $o] :
( ( $false = (X0) )
| ( $true = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f46,definition,
( spl7_1
<=> f(bG2) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f47,plain,
( f(bG2)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f48,plain,
( ~ f(bG2)
| spl7_1 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f50,definition,
( spl7_2
<=> g(bG4) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f51,plain,
( ~ g(bG4)
| spl7_2 ),
inference(avatar_component_clause,[],[f50]) ).
tff(f52,plain,
( g(bG4)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f50]) ).
tff(f53,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f35,f50,f46]) ).
tff(f54,plain,
( ~ spl7_2
| spl7_1 ),
inference(avatar_split_clause,[],[f36,f46,f50]) ).
tff(f56,definition,
( spl7_3
<=> g(bG5) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
tff(f57,plain,
( g(bG5)
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f58,plain,
( ~ g(bG5)
| spl7_3 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f60,definition,
( spl7_4
<=> x ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f63,plain,
( ~ spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f37,f60,f56]) ).
tff(f64,plain,
( ~ spl7_4
| spl7_3 ),
inference(avatar_split_clause,[],[f38,f56,f60]) ).
tff(f66,definition,
( spl7_5
<=> g(bG6) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
tff(f67,plain,
( g(bG6)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f66]) ).
tff(f68,plain,
( ~ g(bG6)
| spl7_5 ),
inference(avatar_component_clause,[],[f66]) ).
tff(f70,definition,
( spl7_6
<=> y ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
tff(f73,plain,
( ~ spl7_5
| spl7_6 ),
inference(avatar_split_clause,[],[f39,f70,f66]) ).
tff(f74,plain,
( ~ spl7_6
| spl7_5 ),
inference(avatar_split_clause,[],[f40,f66,f70]) ).
tff(f75,plain,
( spl7_4
| spl7_6 ),
inference(avatar_split_clause,[],[f41,f70,f60]) ).
tff(f76,plain,
( ~ spl7_4
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f42,f70,f60]) ).
tff(f78,definition,
( spl7_7
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
tff(f79,plain,
( ( bG0 != $true )
| spl7_7 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f80,plain,
( ( bG0 = $true )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f81,plain,
( ~ spl7_4
| spl7_7 ),
inference(avatar_split_clause,[],[f33,f78,f60]) ).
tff(f82,plain,
( ~ spl7_7
| spl7_4 ),
inference(avatar_split_clause,[],[f34,f60,f78]) ).
tff(f84,definition,
( spl7_8
<=> f(bG0) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
tff(f85,plain,
( f(bG0)
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f86,plain,
( ~ f(bG0)
| spl7_8 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f88,definition,
( spl7_9
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
tff(f89,plain,
( ( $true != bG1 )
| spl7_9 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f90,plain,
( ( $true = bG1 )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f91,plain,
( ~ spl7_8
| spl7_9 ),
inference(avatar_split_clause,[],[f31,f88,f84]) ).
tff(f92,plain,
( ~ spl7_9
| spl7_8 ),
inference(avatar_split_clause,[],[f32,f84,f88]) ).
tff(f94,definition,
( spl7_10
<=> f(bG1) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
tff(f95,plain,
( f(bG1)
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f94]) ).
tff(f96,plain,
( ~ f(bG1)
| spl7_10 ),
inference(avatar_component_clause,[],[f94]) ).
tff(f98,definition,
( spl7_11
<=> ( $true = bG2 ) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
tff(f99,plain,
( ( $true != bG2 )
| spl7_11 ),
inference(avatar_component_clause,[],[f98]) ).
tff(f100,plain,
( ( $true = bG2 )
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f98]) ).
tff(f101,plain,
( ~ spl7_10
| spl7_11 ),
inference(avatar_split_clause,[],[f29,f98,f94]) ).
tff(f102,plain,
( ~ spl7_11
| spl7_10 ),
inference(avatar_split_clause,[],[f30,f94,f98]) ).
tff(f104,definition,
( spl7_12
<=> ( $true = bG3 ) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
tff(f105,plain,
( ( $true != bG3 )
| spl7_12 ),
inference(avatar_component_clause,[],[f104]) ).
tff(f106,plain,
( ( $true = bG3 )
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f104]) ).
tff(f107,plain,
( ~ spl7_4
| spl7_12 ),
inference(avatar_split_clause,[],[f27,f104,f60]) ).
tff(f108,plain,
( ~ spl7_12
| spl7_4 ),
inference(avatar_split_clause,[],[f28,f60,f104]) ).
tff(f110,definition,
( spl7_13
<=> f(bG3) ),
introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition]) ).
tff(f111,plain,
( f(bG3)
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f110]) ).
tff(f112,plain,
( ~ f(bG3)
| spl7_13 ),
inference(avatar_component_clause,[],[f110]) ).
tff(f114,definition,
( spl7_14
<=> ( $true = bG4 ) ),
introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition]) ).
tff(f116,plain,
( ( $true = bG4 )
| ~ spl7_14 ),
inference(avatar_component_clause,[],[f114]) ).
tff(f117,plain,
( ~ spl7_13
| spl7_14 ),
inference(avatar_split_clause,[],[f25,f114,f110]) ).
tff(f118,plain,
( ~ spl7_14
| spl7_13 ),
inference(avatar_split_clause,[],[f26,f110,f114]) ).
tff(f120,definition,
( spl7_15
<=> ( $true = bG5 ) ),
introduced(definition,[new_symbols(definition,[spl7_15])],[avatar_definition]) ).
tff(f122,plain,
( ( $true = bG5 )
| ~ spl7_15 ),
inference(avatar_component_clause,[],[f120]) ).
tff(f123,plain,
( ~ spl7_6
| spl7_15 ),
inference(avatar_split_clause,[],[f23,f120,f70]) ).
tff(f124,plain,
( ~ spl7_15
| spl7_6 ),
inference(avatar_split_clause,[],[f24,f70,f120]) ).
tff(f126,definition,
( spl7_16
<=> ( $true = bG6 ) ),
introduced(definition,[new_symbols(definition,[spl7_16])],[avatar_definition]) ).
tff(f127,plain,
( ( $true != bG6 )
| spl7_16 ),
inference(avatar_component_clause,[],[f126]) ).
tff(f128,plain,
( ( $true = bG6 )
| ~ spl7_16 ),
inference(avatar_component_clause,[],[f126]) ).
tff(f129,plain,
( ~ spl7_4
| spl7_16 ),
inference(avatar_split_clause,[],[f21,f126,f60]) ).
tff(f130,plain,
( ~ spl7_16
| spl7_4 ),
inference(avatar_split_clause,[],[f22,f60,f126]) ).
tff(f131,plain,
( ~ g($true)
| spl7_3
| ~ spl7_15 ),
inference(superposition,[],[f58,f122]) ).
tff(f134,plain,
( ~ f($false)
| ( bG0 = $true )
| spl7_8 ),
inference(superposition,[],[f86,f44]) ).
tff(f136,plain,
( ~ f($false)
| ( $true = bG1 )
| spl7_10 ),
inference(superposition,[],[f96,f44]) ).
tff(f138,plain,
( ~ f($false)
| ( $true = bG2 )
| spl7_1 ),
inference(superposition,[],[f48,f44]) ).
tff(f140,plain,
( ~ f($false)
| ( $true = bG3 )
| spl7_13 ),
inference(superposition,[],[f112,f44]) ).
tff(f142,plain,
( ~ g($false)
| ( $true = bG4 )
| spl7_2 ),
inference(superposition,[],[f51,f44]) ).
tff(f146,plain,
( g($false)
| ( $true = bG6 )
| ~ spl7_5 ),
inference(superposition,[],[f67,f44]) ).
tff(f149,plain,
( g($false)
| ~ spl7_5
| spl7_16 ),
inference(forward_subsumption_resolution,[],[f146,f127]) ).
tff(f151,plain,
( ~ f($false)
| spl7_12
| spl7_13 ),
inference(forward_subsumption_resolution,[],[f140,f105]) ).
tff(f152,plain,
( ~ f($false)
| spl7_1
| spl7_11 ),
inference(forward_subsumption_resolution,[],[f138,f99]) ).
tff(f153,plain,
( ~ f($false)
| spl7_9
| spl7_10 ),
inference(forward_subsumption_resolution,[],[f136,f89]) ).
tff(f154,plain,
( ~ f($false)
| spl7_7
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f134,f79]) ).
tff(f158,plain,
( ( $true = bG4 )
| spl7_2
| ~ spl7_5
| spl7_16 ),
inference(forward_subsumption_resolution,[],[f142,f149]) ).
tff(f159,plain,
( spl7_14
| spl7_2
| ~ spl7_5
| spl7_16 ),
inference(avatar_split_clause,[],[f158,f126,f66,f50,f114]) ).
tff(f160,plain,
( f($false)
| ( $true = bG3 )
| ~ spl7_13 ),
inference(superposition,[],[f111,f44]) ).
tff(f162,plain,
( ! [X0: $o] :
( ~ f((X0))
| ( $true = (X0) ) )
| spl7_1
| spl7_11 ),
inference(superposition,[],[f152,f44]) ).
tff(f169,plain,
( ( $true = bG3 )
| spl7_1
| spl7_11
| ~ spl7_13 ),
inference(resolution,[],[f162,f111]) ).
tff(f173,plain,
( spl7_12
| spl7_1
| spl7_11
| ~ spl7_13 ),
inference(avatar_split_clause,[],[f169,f110,f98,f46,f104]) ).
tff(f174,plain,
( g($false)
| ( $true = bG5 )
| ~ spl7_3 ),
inference(superposition,[],[f57,f44]) ).
tff(f176,definition,
( spl7_17
<=> g($false) ),
introduced(definition,[new_symbols(definition,[spl7_17])],[avatar_definition]) ).
tff(f178,plain,
( g($false)
| ~ spl7_17 ),
inference(avatar_component_clause,[],[f176]) ).
tff(f179,plain,
( spl7_15
| spl7_17
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f174,f56,f176,f120]) ).
tff(f183,definition,
( spl7_18
<=> f($false) ),
introduced(definition,[new_symbols(definition,[spl7_18])],[avatar_definition]) ).
tff(f185,plain,
( ~ f($false)
| spl7_18 ),
inference(avatar_component_clause,[],[f183]) ).
tff(f187,plain,
( spl7_12
| spl7_18
| ~ spl7_13 ),
inference(avatar_split_clause,[],[f160,f110,f183,f104]) ).
tff(f197,plain,
( ! [X0: $o] :
( g((X0))
| ( $true = (X0) ) )
| ~ spl7_17 ),
inference(superposition,[],[f178,f44]) ).
tff(f201,plain,
( f($true)
| ~ spl7_9
| ~ spl7_10 ),
inference(superposition,[],[f95,f90]) ).
tff(f208,plain,
( ~ f($true)
| spl7_1
| ~ spl7_11 ),
inference(superposition,[],[f48,f100]) ).
tff(f216,plain,
( $false
| spl7_1
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(forward_subsumption_resolution,[],[f201,f208]) ).
tff(f217,plain,
( spl7_1
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(avatar_contradiction_clause,[],[f216]) ).
tff(f218,plain,
( f($true)
| ~ spl7_1
| ~ spl7_11 ),
inference(forward_demodulation,[],[f47,f100]) ).
tff(f219,plain,
( g($true)
| ~ spl7_2
| ~ spl7_14 ),
inference(forward_demodulation,[],[f52,f116]) ).
tff(f220,plain,
( $false
| ~ spl7_2
| spl7_3
| ~ spl7_14
| ~ spl7_15 ),
inference(forward_subsumption_resolution,[],[f219,f131]) ).
tff(f221,plain,
( ~ spl7_2
| spl7_3
| ~ spl7_14
| ~ spl7_15 ),
inference(avatar_contradiction_clause,[],[f220]) ).
tff(f224,plain,
( ~ spl7_18
| spl7_7
| spl7_8 ),
inference(avatar_split_clause,[],[f154,f84,f78,f183]) ).
tff(f225,plain,
( ~ spl7_18
| spl7_9
| spl7_10 ),
inference(avatar_split_clause,[],[f153,f94,f88,f183]) ).
tff(f226,plain,
( ~ spl7_18
| spl7_12
| spl7_13 ),
inference(avatar_split_clause,[],[f151,f110,f104,f183]) ).
tff(f235,plain,
( ! [X0: $o] :
( ~ f((X0))
| ( $true = (X0) ) )
| spl7_18 ),
inference(superposition,[],[f185,f44]) ).
tff(f236,plain,
( f($false)
| ( bG0 = $true )
| ~ spl7_8 ),
inference(superposition,[],[f85,f44]) ).
tff(f237,plain,
( ( bG0 = $true )
| ~ spl7_8
| spl7_18 ),
inference(forward_subsumption_resolution,[],[f236,f185]) ).
tff(f238,plain,
( spl7_7
| ~ spl7_8
| spl7_18 ),
inference(avatar_split_clause,[],[f237,f183,f84,f78]) ).
tff(f243,plain,
( ( $true = bG1 )
| ~ spl7_10
| spl7_18 ),
inference(resolution,[],[f95,f235]) ).
tff(f246,plain,
( spl7_9
| ~ spl7_10
| spl7_18 ),
inference(avatar_split_clause,[],[f243,f183,f94,f88]) ).
tff(f258,plain,
( ~ f($true)
| ~ spl7_12
| spl7_13 ),
inference(superposition,[],[f112,f106]) ).
tff(f260,plain,
( $false
| ~ spl7_1
| ~ spl7_11
| ~ spl7_12
| spl7_13 ),
inference(forward_subsumption_resolution,[],[f258,f218]) ).
tff(f261,plain,
( ~ spl7_1
| ~ spl7_11
| ~ spl7_12
| spl7_13 ),
inference(avatar_contradiction_clause,[],[f260]) ).
tff(f264,plain,
( ~ f($true)
| ~ spl7_9
| spl7_10 ),
inference(forward_demodulation,[],[f96,f90]) ).
tff(f265,plain,
( f($true)
| ~ spl7_12
| ~ spl7_13 ),
inference(forward_demodulation,[],[f111,f106]) ).
tff(f267,plain,
( ( $true = bG4 )
| spl7_2
| ~ spl7_17 ),
inference(resolution,[],[f51,f197]) ).
tff(f270,plain,
( spl7_14
| spl7_2
| ~ spl7_17 ),
inference(avatar_split_clause,[],[f267,f176,f50,f114]) ).
tff(f272,plain,
( $false
| ~ spl7_9
| spl7_10
| ~ spl7_12
| ~ spl7_13 ),
inference(forward_subsumption_resolution,[],[f265,f264]) ).
tff(f273,plain,
( ~ spl7_9
| spl7_10
| ~ spl7_12
| ~ spl7_13 ),
inference(avatar_contradiction_clause,[],[f272]) ).
tff(f274,plain,
( ~ f($true)
| ~ spl7_7
| spl7_8 ),
inference(forward_demodulation,[],[f86,f80]) ).
tff(f277,plain,
( $false
| ~ spl7_7
| spl7_8
| ~ spl7_12
| ~ spl7_13 ),
inference(forward_subsumption_resolution,[],[f274,f265]) ).
tff(f278,plain,
( ~ spl7_7
| spl7_8
| ~ spl7_12
| ~ spl7_13 ),
inference(avatar_contradiction_clause,[],[f277]) ).
tff(f279,plain,
( f($true)
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f85,f80]) ).
tff(f281,plain,
( f($false)
| ( $true = bG2 )
| ~ spl7_1 ),
inference(superposition,[],[f47,f44]) ).
tff(f298,plain,
( ~ g($true)
| spl7_5
| ~ spl7_16 ),
inference(superposition,[],[f68,f128]) ).
tff(f300,plain,
( $false
| ~ spl7_2
| spl7_5
| ~ spl7_14
| ~ spl7_16 ),
inference(forward_subsumption_resolution,[],[f298,f219]) ).
tff(f301,plain,
( ~ spl7_2
| spl7_5
| ~ spl7_14
| ~ spl7_16 ),
inference(avatar_contradiction_clause,[],[f300]) ).
tff(f304,plain,
( spl7_11
| spl7_18
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f281,f46,f183,f98]) ).
tff(f306,plain,
( $false
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| spl7_10 ),
inference(forward_subsumption_resolution,[],[f279,f264]) ).
tff(f307,plain,
( ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| spl7_10 ),
inference(avatar_contradiction_clause,[],[f306]) ).
cnf(s1,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s2,plain,
( spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f54]) ).
cnf(s3,plain,
( ~ spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s4,plain,
( spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
( ~ spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f74]) ).
cnf(s7,plain,
( spl7_4
| spl7_6 ),
inference(sat_conversion,[],[f75]) ).
cnf(s8,plain,
( ~ spl7_4
| ~ spl7_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s9,plain,
( ~ spl7_4
| spl7_7 ),
inference(sat_conversion,[],[f81]) ).
cnf(s10,plain,
( spl7_4
| ~ spl7_7 ),
inference(sat_conversion,[],[f82]) ).
cnf(s11,plain,
( ~ spl7_8
| spl7_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s12,plain,
( spl7_8
| ~ spl7_9 ),
inference(sat_conversion,[],[f92]) ).
cnf(s13,plain,
( ~ spl7_10
| spl7_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s14,plain,
( spl7_10
| ~ spl7_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s15,plain,
( ~ spl7_4
| spl7_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s16,plain,
( spl7_4
| ~ spl7_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s17,plain,
( ~ spl7_13
| spl7_14 ),
inference(sat_conversion,[],[f117]) ).
cnf(s18,plain,
( spl7_13
| ~ spl7_14 ),
inference(sat_conversion,[],[f118]) ).
cnf(s19,plain,
( ~ spl7_6
| spl7_15 ),
inference(sat_conversion,[],[f123]) ).
cnf(s20,plain,
( spl7_6
| ~ spl7_15 ),
inference(sat_conversion,[],[f124]) ).
cnf(s21,plain,
( ~ spl7_4
| spl7_16 ),
inference(sat_conversion,[],[f129]) ).
cnf(s22,plain,
( spl7_4
| ~ spl7_16 ),
inference(sat_conversion,[],[f130]) ).
cnf(s24,plain,
( spl7_2
| ~ spl7_5
| spl7_14
| spl7_16 ),
inference(sat_conversion,[],[f159]) ).
cnf(s26,plain,
( spl7_1
| spl7_11
| spl7_12
| ~ spl7_13 ),
inference(sat_conversion,[],[f173]) ).
cnf(s28,plain,
( ~ spl7_3
| spl7_15
| spl7_17 ),
inference(sat_conversion,[],[f179]) ).
cnf(s32,plain,
( spl7_12
| ~ spl7_13
| spl7_18 ),
inference(sat_conversion,[],[f187]) ).
cnf(s39,plain,
( spl7_1
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(sat_conversion,[],[f217]) ).
cnf(s40,plain,
( ~ spl7_2
| spl7_3
| ~ spl7_14
| ~ spl7_15 ),
inference(sat_conversion,[],[f221]) ).
cnf(s42,plain,
( spl7_7
| spl7_8
| ~ spl7_18 ),
inference(sat_conversion,[],[f224]) ).
cnf(s43,plain,
( spl7_9
| spl7_10
| ~ spl7_18 ),
inference(sat_conversion,[],[f225]) ).
cnf(s44,plain,
( spl7_12
| spl7_13
| ~ spl7_18 ),
inference(sat_conversion,[],[f226]) ).
cnf(s48,plain,
( spl7_7
| ~ spl7_8
| spl7_18 ),
inference(sat_conversion,[],[f238]) ).
cnf(s51,plain,
( spl7_9
| ~ spl7_10
| spl7_18 ),
inference(sat_conversion,[],[f246]) ).
cnf(s53,plain,
( ~ spl7_1
| ~ spl7_11
| ~ spl7_12
| spl7_13 ),
inference(sat_conversion,[],[f261]) ).
cnf(s55,plain,
( spl7_2
| spl7_14
| ~ spl7_17 ),
inference(sat_conversion,[],[f270]) ).
cnf(s57,plain,
( ~ spl7_9
| spl7_10
| ~ spl7_12
| ~ spl7_13 ),
inference(sat_conversion,[],[f273]) ).
cnf(s58,plain,
( ~ spl7_7
| spl7_8
| ~ spl7_12
| ~ spl7_13 ),
inference(sat_conversion,[],[f278]) ).
cnf(s63,plain,
( ~ spl7_2
| spl7_5
| ~ spl7_14
| ~ spl7_16 ),
inference(sat_conversion,[],[f301]) ).
cnf(s64,plain,
( ~ spl7_1
| spl7_11
| spl7_18 ),
inference(sat_conversion,[],[f304]) ).
cnf(s65,plain,
( ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| spl7_10 ),
inference(sat_conversion,[],[f307]) ).
cnf(s66,plain,
( spl7_4
| spl7_1 ),
inference(rat,[],[s39,s11,s14,s42,s26,s32,s18,s24,s6,s7,s10,s16,s22,s2]) ).
cnf(s67,plain,
spl7_1,
inference(rat,[],[s39,s13,s57,s11,s58,s18,s55,s28,s20,s4,s8,s9,s15,s66,s2]) ).
cnf(s68,plain,
spl7_2,
inference(rat,[],[s1,s67]) ).
cnf(s69,plain,
( spl7_18
| spl7_7 ),
inference(rat,[],[s51,s14,s12,s64,s48,s67]) ).
cnf(s70,plain,
spl7_3,
inference(rat,[],[s69,s44,s17,s40,s19,s7,s10,s16,s4,s68]) ).
cnf(s71,plain,
spl7_4,
inference(rat,[],[s3,s70]) ).
cnf(s72,plain,
spl7_16,
inference(rat,[],[s21,s71]) ).
cnf(s73,plain,
spl7_12,
inference(rat,[],[s15,s71]) ).
cnf(s74,plain,
spl7_7,
inference(rat,[],[s9,s71]) ).
cnf(s75,plain,
~ spl7_6,
inference(rat,[],[s8,s71]) ).
cnf(s77,plain,
~ spl7_5,
inference(rat,[],[s5,s75]) ).
cnf(s79,plain,
~ spl7_14,
inference(rat,[],[s63,s72,s68,s77]) ).
cnf(s80,plain,
~ spl7_13,
inference(rat,[],[s17,s79]) ).
cnf(s81,plain,
~ spl7_11,
inference(rat,[],[s53,s73,s67,s80]) ).
cnf(s82,plain,
spl7_18,
inference(rat,[],[s64,s67,s81]) ).
cnf(s83,plain,
~ spl7_10,
inference(rat,[],[s13,s81]) ).
cnf(s84,plain,
spl7_9,
inference(rat,[],[s43,s82,s83]) ).
cnf(s85,plain,
spl7_8,
inference(rat,[],[s12,s84]) ).
cnf(s86,plain,
$false,
inference(rat,[],[s65,s83,s74,s85,s84]) ).
tff(f308,plain,
$false,
inference(avatar_sat_refutation,[],[s86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO041_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n009.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 17:23:00 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 3.18/1.08 % (3229024)Detected formulas, will run a generic FOF schedule.
% 3.18/1.08 % (3229032)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2795801810:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.18/1.08 % (3229032)Refutation not found, incomplete strategy
% 3.18/1.08 % (3229032)------------------------------
% 3.18/1.08 % (3229032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.08 % (3229032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.08 % (3229032)CaDiCaL version: 2.1.3
% 3.18/1.08 % (3229032)Termination reason: Refutation not found, incomplete strategy
% 3.18/1.08 % (3229032)Time elapsed: 0.002 s
% 3.18/1.08 % (3229032)Peak memory usage: 88 MB
% 3.18/1.08 % (3229032)Instructions burned: 2 (million)
% 3.18/1.08 % (3229029)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=773175286:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.18/1.08 % (3229033)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2205345560:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.18/1.08 % (3229035)dis-21_1_sil=8000:lcm=predicate:random_seed=4005593476: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)
% 3.18/1.08 % (3229031)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=1285283530:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.18/1.08 % (3229030)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=1480642280:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.18/1.08 % (3229034)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4092187089:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.18/1.08 % (3229035)Refutation not found, incomplete strategy
% 3.18/1.08 % (3229035)------------------------------
% 3.18/1.08 % (3229035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.08 % (3229035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.08 % (3229035)CaDiCaL version: 2.1.3
% 3.18/1.08 % (3229035)Termination reason: Refutation not found, incomplete strategy
% 3.18/1.08 % (3229035)Time elapsed: 0.002 s
% 3.18/1.08 % (3229035)Peak memory usage: 88 MB
% 3.18/1.08 % (3229035)Instructions burned: 1 (million)
% 3.18/1.08 % (3229034)First to succeed.
% 3.18/1.08 % (3229034)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3229024"
% 3.18/1.08 % (3229033)Also succeeded, but the first one will report.
% 3.18/1.08 % (3229032)------------------------------
% 3.18/1.08 % (3229032)------------------------------
% 3.18/1.08 % (3229043)lrs+10_1_sil=8000:sp=occurrence:random_seed=1459002840:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.18/1.08 % (3229043)Also succeeded, but the first one will report.
% 3.18/1.08 % (3229035)------------------------------
% 3.18/1.08 % (3229035)------------------------------
% 3.18/1.08 % (3229034)Refutation found. Thanks to Tanya!
% 3.18/1.08 % SZS status Theorem for theBenchmark
% 3.18/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.27 % (3229034)------------------------------
% 3.65/1.27 % (3229034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.27 % (3229034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.27 % (3229034)CaDiCaL version: 2.1.3
% 3.65/1.27 % (3229034)Termination reason: Refutation
% 3.65/1.27 % (3229034)Time elapsed: 0.008 s
% 3.65/1.27 % (3229034)Peak memory usage: 90 MB
% 3.65/1.27 % (3229034)Instructions burned: 9 (million)
% 3.65/1.27 % (3229034)------------------------------
% 3.65/1.27 % (3229034)------------------------------
% 3.65/1.27 % (3229024)Success in time 0.431 s
% 3.65/1.27 % Vampire exiting
%------------------------------------------------------------------------------