%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO040_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:24:48 PM UTC 2026
% Result : Theorem 2.79s 1.05s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 20
% Syntax : Number of formulae : 167 ( 19 unt; 0 typ; 18 def)
% Number of atoms : 619 ( 72 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 425 ( 182 ~; 219 |; 6 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 214 ( 212 fml; 2 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 23 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 1 ( 0 sgn 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
h: $o > $i ).
tff(func_def_1,type,
bG0: $o ).
tff(func_def_4,type,
bG1: $o ).
tff(func_def_5,type,
bG2: $o ).
tff(func_def_6,type,
bG3: $o ).
tff(func_def_7,type,
bG4: $o ).
tff(func_def_8,type,
bG5: $o ).
tff(pred_def_1,type,
f: $o > $o ).
tff(f1,conjecture,
h(f(f(f(x)))) = h(f(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',2) ).
tff(f2,negated_conjecture,
( ( ~ h(f(f(f(x)))) ) = h(f(x)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
( ( ~ h(f(f(f(x)))) ) = h(f(x)) ),
inference(rectify,[],[f2]) ).
tff(f4,definition,
( x
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f5,definition,
( f(bG0)
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f6,definition,
( f(bG1)
<=> ( $true = bG2 ) ),
introduced(definition,[new_symbols(definition,[bG2])],[fool_formula_definition]) ).
tff(f7,definition,
( f(bG2)
<=> ( $true = bG3 ) ),
introduced(definition,[new_symbols(definition,[bG3])],[fool_formula_definition]) ).
tff(f8,definition,
( x
<=> ( $true = bG4 ) ),
introduced(definition,[new_symbols(definition,[bG4])],[fool_formula_definition]) ).
tff(f9,definition,
( f(bG4)
<=> ( $true = bG5 ) ),
introduced(definition,[new_symbols(definition,[bG5])],[fool_formula_definition]) ).
tff(f10,plain,
( ( ~ h(bG3) ) = h(bG5) ),
inference(fool_elimination,[],[f3,f9,f8,f7,f6,f5,f4]) ).
tff(f11,plain,
h(bG3) != h(bG5),
inference(flattening,[],[f10]) ).
tff(f12,plain,
( ( f(bG4)
| ( $true != bG5 ) )
& ( ( $true = bG5 )
| ~ f(bG4) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f13,plain,
( ( x
| ( $true != bG4 ) )
& ( ( $true = bG4 )
| ~ x ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f14,plain,
( ( f(bG2)
| ( $true != bG3 ) )
& ( ( $true = bG3 )
| ~ f(bG2) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f15,plain,
( ( f(bG1)
| ( $true != bG2 ) )
& ( ( $true = bG2 )
| ~ f(bG1) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f16,plain,
( ( f(bG0)
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ f(bG0) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f17,plain,
( ( x
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ x ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f18,plain,
( ( $true = bG5 )
| ~ f(bG4) ),
inference(cnf_transformation,[],[f12]) ).
tff(f19,plain,
( f(bG4)
| ( $true != bG5 ) ),
inference(cnf_transformation,[],[f12]) ).
tff(f20,plain,
( ( $true = bG4 )
| ~ x ),
inference(cnf_transformation,[],[f13]) ).
tff(f21,plain,
( x
| ( $true != bG4 ) ),
inference(cnf_transformation,[],[f13]) ).
tff(f22,plain,
( ( $true = bG3 )
| ~ f(bG2) ),
inference(cnf_transformation,[],[f14]) ).
tff(f23,plain,
( f(bG2)
| ( $true != bG3 ) ),
inference(cnf_transformation,[],[f14]) ).
tff(f24,plain,
( ( $true = bG2 )
| ~ f(bG1) ),
inference(cnf_transformation,[],[f15]) ).
tff(f25,plain,
( f(bG1)
| ( $true != bG2 ) ),
inference(cnf_transformation,[],[f15]) ).
tff(f26,plain,
( ( $true = bG1 )
| ~ f(bG0) ),
inference(cnf_transformation,[],[f16]) ).
tff(f27,plain,
( f(bG0)
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f28,plain,
( ( bG0 = $true )
| ~ x ),
inference(cnf_transformation,[],[f17]) ).
tff(f29,plain,
( x
| ( bG0 != $true ) ),
inference(cnf_transformation,[],[f17]) ).
tff(f30,plain,
h(bG3) != h(bG5),
inference(cnf_transformation,[],[f11]) ).
tff(f32,plain,
! [X0: $o] :
( ( $false = (X0) )
| ( $true = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f34,definition,
( spl6_1
<=> x ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f38,definition,
( spl6_2
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f39,plain,
( ( bG0 != $true )
| spl6_2 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f40,plain,
( ( bG0 = $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f41,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f28,f38,f34]) ).
tff(f42,plain,
( ~ spl6_2
| spl6_1 ),
inference(avatar_split_clause,[],[f29,f34,f38]) ).
tff(f44,definition,
( spl6_3
<=> f(bG0) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f45,plain,
( f(bG0)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f46,plain,
( ~ f(bG0)
| spl6_3 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f48,definition,
( spl6_4
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
tff(f49,plain,
( ( $true != bG1 )
| spl6_4 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f50,plain,
( ( $true = bG1 )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f51,plain,
( ~ spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f26,f48,f44]) ).
tff(f52,plain,
( ~ spl6_4
| spl6_3 ),
inference(avatar_split_clause,[],[f27,f44,f48]) ).
tff(f54,definition,
( spl6_5
<=> f(bG1) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
tff(f55,plain,
( f(bG1)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f54]) ).
tff(f56,plain,
( ~ f(bG1)
| spl6_5 ),
inference(avatar_component_clause,[],[f54]) ).
tff(f58,definition,
( spl6_6
<=> ( $true = bG2 ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
tff(f59,plain,
( ( $true != bG2 )
| spl6_6 ),
inference(avatar_component_clause,[],[f58]) ).
tff(f60,plain,
( ( $true = bG2 )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f58]) ).
tff(f61,plain,
( ~ spl6_5
| spl6_6 ),
inference(avatar_split_clause,[],[f24,f58,f54]) ).
tff(f62,plain,
( ~ spl6_6
| spl6_5 ),
inference(avatar_split_clause,[],[f25,f54,f58]) ).
tff(f64,definition,
( spl6_7
<=> f(bG2) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
tff(f65,plain,
( f(bG2)
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f66,plain,
( ~ f(bG2)
| spl6_7 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f68,definition,
( spl6_8
<=> ( $true = bG3 ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
tff(f70,plain,
( ( $true = bG3 )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f68]) ).
tff(f71,plain,
( ~ spl6_7
| spl6_8 ),
inference(avatar_split_clause,[],[f22,f68,f64]) ).
tff(f72,plain,
( ~ spl6_8
| spl6_7 ),
inference(avatar_split_clause,[],[f23,f64,f68]) ).
tff(f74,definition,
( spl6_9
<=> ( $true = bG4 ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
tff(f75,plain,
( ( $true != bG4 )
| spl6_9 ),
inference(avatar_component_clause,[],[f74]) ).
tff(f76,plain,
( ( $true = bG4 )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f74]) ).
tff(f77,plain,
( ~ spl6_1
| spl6_9 ),
inference(avatar_split_clause,[],[f20,f74,f34]) ).
tff(f78,plain,
( ~ spl6_9
| spl6_1 ),
inference(avatar_split_clause,[],[f21,f34,f74]) ).
tff(f80,definition,
( spl6_10
<=> f(bG4) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
tff(f81,plain,
( f(bG4)
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f80]) ).
tff(f82,plain,
( ~ f(bG4)
| spl6_10 ),
inference(avatar_component_clause,[],[f80]) ).
tff(f84,definition,
( spl6_11
<=> ( $true = bG5 ) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
tff(f85,plain,
( ( $true != bG5 )
| spl6_11 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f86,plain,
( ( $true = bG5 )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f87,plain,
( ~ spl6_10
| spl6_11 ),
inference(avatar_split_clause,[],[f18,f84,f80]) ).
tff(f88,plain,
( ~ spl6_11
| spl6_10 ),
inference(avatar_split_clause,[],[f19,f80,f84]) ).
tff(f91,plain,
( ~ f($false)
| ( bG0 = $true )
| spl6_3 ),
inference(superposition,[],[f46,f32]) ).
tff(f93,plain,
( ~ f($false)
| ( $true = bG1 )
| spl6_5 ),
inference(superposition,[],[f56,f32]) ).
tff(f98,plain,
( ~ f($false)
| ( $true = bG4 )
| spl6_10 ),
inference(superposition,[],[f82,f32]) ).
tff(f100,plain,
( ( h(bG3) != h($false) )
| ( $true = bG5 ) ),
inference(superposition,[],[f30,f32]) ).
tff(f102,plain,
( ( h(bG3) != h($false) )
| spl6_11 ),
inference(forward_subsumption_resolution,[],[f100,f85]) ).
tff(f103,plain,
( ~ f($false)
| spl6_9
| spl6_10 ),
inference(forward_subsumption_resolution,[],[f98,f75]) ).
tff(f105,plain,
( ~ f($false)
| spl6_4
| spl6_5 ),
inference(forward_subsumption_resolution,[],[f93,f49]) ).
tff(f106,plain,
( ~ f($false)
| spl6_2
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f91,f39]) ).
tff(f107,plain,
( ( h($false) != h($false) )
| ( $true = bG3 )
| spl6_11 ),
inference(superposition,[],[f102,f32]) ).
tff(f108,plain,
( ( $true = bG3 )
| spl6_11 ),
inference(trivial_inequality_removal,[],[f107]) ).
tff(f111,plain,
( spl6_8
| spl6_11 ),
inference(avatar_split_clause,[],[f108,f84,f68]) ).
tff(f112,plain,
( f($false)
| ( $true = bG2 )
| ~ spl6_7 ),
inference(superposition,[],[f65,f32]) ).
tff(f113,plain,
( f($false)
| spl6_6
| ~ spl6_7 ),
inference(forward_subsumption_resolution,[],[f112,f59]) ).
tff(f118,plain,
( $false
| spl6_6
| ~ spl6_7
| spl6_9
| spl6_10 ),
inference(forward_subsumption_resolution,[],[f113,f103]) ).
tff(f119,plain,
( spl6_6
| ~ spl6_7
| spl6_9
| spl6_10 ),
inference(avatar_contradiction_clause,[],[f118]) ).
tff(f129,plain,
( ( h(bG3) != h($true) )
| ~ spl6_11 ),
inference(superposition,[],[f30,f86]) ).
tff(f131,plain,
( ( h($true) != h($true) )
| ~ spl6_8
| ~ spl6_11 ),
inference(forward_demodulation,[],[f129,f70]) ).
tff(f132,plain,
( $false
| ~ spl6_8
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f131]) ).
tff(f133,plain,
( ~ spl6_8
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[],[f132]) ).
tff(f136,plain,
( ~ f($false)
| ( $true = bG2 )
| spl6_7 ),
inference(superposition,[],[f66,f32]) ).
tff(f145,plain,
( ~ f($true)
| ~ spl6_2
| spl6_3 ),
inference(superposition,[],[f46,f40]) ).
tff(f148,plain,
( f($true)
| ~ spl6_9
| ~ spl6_10 ),
inference(superposition,[],[f81,f76]) ).
tff(f150,plain,
( $false
| ~ spl6_2
| spl6_3
| ~ spl6_9
| ~ spl6_10 ),
inference(forward_subsumption_resolution,[],[f148,f145]) ).
tff(f151,plain,
( ~ spl6_2
| spl6_3
| ~ spl6_9
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f150]) ).
tff(f152,plain,
( f($true)
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f45,f40]) ).
tff(f154,plain,
( ~ f($true)
| ~ spl6_4
| spl6_5 ),
inference(superposition,[],[f56,f50]) ).
tff(f156,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| spl6_5 ),
inference(forward_subsumption_resolution,[],[f154,f152]) ).
tff(f157,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| spl6_5 ),
inference(avatar_contradiction_clause,[],[f156]) ).
tff(f158,plain,
( f($true)
| ~ spl6_4
| ~ spl6_5 ),
inference(forward_demodulation,[],[f55,f50]) ).
tff(f160,definition,
( spl6_13
<=> f($false) ),
introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition]) ).
tff(f163,plain,
( spl6_6
| ~ spl6_13
| spl6_7 ),
inference(avatar_split_clause,[],[f136,f64,f160,f58]) ).
tff(f169,plain,
( ~ f($true)
| ~ spl6_2
| spl6_3 ),
inference(forward_demodulation,[],[f46,f40]) ).
tff(f170,plain,
( ~ spl6_13
| spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f105,f54,f48,f160]) ).
tff(f172,plain,
( ~ f($true)
| ~ spl6_9
| spl6_10 ),
inference(forward_demodulation,[],[f82,f76]) ).
tff(f181,plain,
( f($false)
| ( $true = bG1 )
| ~ spl6_5 ),
inference(superposition,[],[f55,f32]) ).
tff(f182,plain,
( spl6_4
| spl6_13
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f181,f54,f160,f48]) ).
tff(f183,plain,
( f($false)
| ( $true = bG2 )
| ~ spl6_7 ),
inference(superposition,[],[f65,f32]) ).
tff(f184,plain,
( spl6_6
| spl6_13
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f183,f64,f160,f58]) ).
tff(f187,plain,
( f($true)
| ~ spl6_6
| ~ spl6_7 ),
inference(superposition,[],[f65,f60]) ).
tff(f189,plain,
( $false
| ~ spl6_2
| spl6_3
| ~ spl6_6
| ~ spl6_7 ),
inference(forward_subsumption_resolution,[],[f187,f169]) ).
tff(f190,plain,
( ~ spl6_2
| spl6_3
| ~ spl6_6
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f189]) ).
tff(f192,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_9
| spl6_10 ),
inference(forward_subsumption_resolution,[],[f172,f152]) ).
tff(f193,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_9
| spl6_10 ),
inference(avatar_contradiction_clause,[],[f192]) ).
tff(f194,plain,
( ~ spl6_13
| spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f106,f44,f38,f160]) ).
tff(f195,plain,
( ~ spl6_13
| spl6_9
| spl6_10 ),
inference(avatar_split_clause,[],[f103,f80,f74,f160]) ).
tff(f196,plain,
( f($false)
| ( bG0 = $true )
| ~ spl6_3 ),
inference(superposition,[],[f45,f32]) ).
tff(f197,plain,
( spl6_2
| spl6_13
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f196,f44,f160,f38]) ).
tff(f198,plain,
( ~ f($true)
| ~ spl6_6
| spl6_7 ),
inference(forward_demodulation,[],[f66,f60]) ).
tff(f200,plain,
( f($false)
| ( $true = bG4 )
| ~ spl6_10 ),
inference(superposition,[],[f81,f32]) ).
tff(f201,plain,
( spl6_9
| spl6_13
| ~ spl6_10 ),
inference(avatar_split_clause,[],[f200,f80,f160,f74]) ).
tff(f202,plain,
( $false
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(forward_subsumption_resolution,[],[f198,f158]) ).
tff(f203,plain,
( ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(avatar_contradiction_clause,[],[f202]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
( ~ spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s4,plain,
( spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f52]) ).
cnf(s5,plain,
( ~ spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f61]) ).
cnf(s6,plain,
( spl6_5
| ~ spl6_6 ),
inference(sat_conversion,[],[f62]) ).
cnf(s7,plain,
( ~ spl6_7
| spl6_8 ),
inference(sat_conversion,[],[f71]) ).
cnf(s8,plain,
( spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f72]) ).
cnf(s9,plain,
( ~ spl6_1
| spl6_9 ),
inference(sat_conversion,[],[f77]) ).
cnf(s10,plain,
( spl6_1
| ~ spl6_9 ),
inference(sat_conversion,[],[f78]) ).
cnf(s11,plain,
( ~ spl6_10
| spl6_11 ),
inference(sat_conversion,[],[f87]) ).
cnf(s12,plain,
( spl6_10
| ~ spl6_11 ),
inference(sat_conversion,[],[f88]) ).
cnf(s14,plain,
( spl6_8
| spl6_11 ),
inference(sat_conversion,[],[f111]) ).
cnf(s15,plain,
( spl6_6
| ~ spl6_7
| spl6_9
| spl6_10 ),
inference(sat_conversion,[],[f119]) ).
cnf(s17,plain,
( ~ spl6_8
| ~ spl6_11 ),
inference(sat_conversion,[],[f133]) ).
cnf(s21,plain,
( ~ spl6_2
| spl6_3
| ~ spl6_9
| ~ spl6_10 ),
inference(sat_conversion,[],[f151]) ).
cnf(s22,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f157]) ).
cnf(s23,plain,
( spl6_6
| spl6_7
| ~ spl6_13 ),
inference(sat_conversion,[],[f163]) ).
cnf(s25,plain,
( spl6_4
| spl6_5
| ~ spl6_13 ),
inference(sat_conversion,[],[f170]) ).
cnf(s30,plain,
( spl6_4
| ~ spl6_5
| spl6_13 ),
inference(sat_conversion,[],[f182]) ).
cnf(s31,plain,
( spl6_6
| ~ spl6_7
| spl6_13 ),
inference(sat_conversion,[],[f184]) ).
cnf(s32,plain,
( ~ spl6_2
| spl6_3
| ~ spl6_6
| ~ spl6_7 ),
inference(sat_conversion,[],[f190]) ).
cnf(s33,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_9
| spl6_10 ),
inference(sat_conversion,[],[f193]) ).
cnf(s34,plain,
( spl6_2
| spl6_3
| ~ spl6_13 ),
inference(sat_conversion,[],[f194]) ).
cnf(s35,plain,
( spl6_9
| spl6_10
| ~ spl6_13 ),
inference(sat_conversion,[],[f195]) ).
cnf(s36,plain,
( spl6_2
| ~ spl6_3
| spl6_13 ),
inference(sat_conversion,[],[f197]) ).
cnf(s38,plain,
( spl6_9
| ~ spl6_10
| spl6_13 ),
inference(sat_conversion,[],[f201]) ).
cnf(s39,plain,
( ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f203]) ).
cnf(s40,plain,
( spl6_3
| spl6_1 ),
inference(rat,[],[s8,s15,s14,s6,s12,s30,s38,s4,s34,s10,s2]) ).
cnf(s41,plain,
spl6_1,
inference(rat,[],[s39,s6,s23,s7,s17,s11,s35,s3,s36,s40,s2,s10]) ).
cnf(s42,plain,
spl6_9,
inference(rat,[],[s9,s41]) ).
cnf(s43,plain,
spl6_2,
inference(rat,[],[s1,s41]) ).
cnf(s44,plain,
spl6_3,
inference(rat,[],[s25,s31,s5,s32,s8,s14,s12,s21,s4,s43,s42]) ).
cnf(s45,plain,
spl6_4,
inference(rat,[],[s3,s44]) ).
cnf(s46,plain,
spl6_10,
inference(rat,[],[s33,s43,s42,s44]) ).
cnf(s47,plain,
spl6_5,
inference(rat,[],[s22,s44,s43,s45]) ).
cnf(s48,plain,
spl6_11,
inference(rat,[],[s11,s46]) ).
cnf(s49,plain,
spl6_6,
inference(rat,[],[s5,s47]) ).
cnf(s50,plain,
~ spl6_8,
inference(rat,[],[s17,s48]) ).
cnf(s51,plain,
spl6_7,
inference(rat,[],[s39,s47,s45,s49]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s7,s50,s51]) ).
tff(f204,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO040_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n004.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 17:22:52 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.79/1.05 % (534332)Detected formulas, will run a generic FOF schedule.
% 2.79/1.05 % (534340)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3796472590:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.79/1.05 % (534340)Refutation not found, incomplete strategy
% 2.79/1.05 % (534340)------------------------------
% 2.79/1.05 % (534340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.05 % (534340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.05 % (534340)CaDiCaL version: 2.1.3
% 2.79/1.05 % (534340)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.05 % (534340)Time elapsed: 0.001 s
% 2.79/1.05 % (534340)Peak memory usage: 88 MB
% 2.79/1.05 % (534340)Instructions burned: 1 (million)
% 2.79/1.05 % (534342)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=318830608:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.79/1.05 % (534343)dis-21_1_sil=8000:lcm=predicate:random_seed=198228859: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)
% 2.79/1.05 % (534341)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1384806014:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.79/1.05 % (534337)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=162062456:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.79/1.05 % (534338)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=2155461356:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.79/1.05 % (534339)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=3007582879:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.79/1.05 % (534342)First to succeed.
% 2.79/1.05 % (534343)Refutation not found, incomplete strategy
% 2.79/1.05 % (534343)------------------------------
% 2.79/1.05 % (534343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.05 % (534343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.05 % (534343)CaDiCaL version: 2.1.3
% 2.79/1.05 % (534343)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.05 % (534343)Time elapsed: 0.002 s
% 2.79/1.05 % (534343)Peak memory usage: 88 MB
% 2.79/1.05 % (534343)Instructions burned: 1 (million)
% 2.79/1.05 % (534342)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-534332"
% 2.79/1.05 % (534341)Also succeeded, but the first one will report.
% 2.79/1.05 % (534340)------------------------------
% 2.79/1.05 % (534340)------------------------------
% 2.79/1.05 % (534351)lrs+10_1_sil=8000:sp=occurrence:random_seed=3178996196:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.79/1.05 % (534351)Also succeeded, but the first one will report.
% 2.79/1.05 % (534343)------------------------------
% 2.79/1.05 % (534343)------------------------------
% 2.79/1.05 % (534342)Refutation found. Thanks to Tanya!
% 2.79/1.05 % SZS status Theorem for theBenchmark
% 2.79/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.24 % (534342)------------------------------
% 3.47/1.24 % (534342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.24 % (534342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.24 % (534342)CaDiCaL version: 2.1.3
% 3.47/1.24 % (534342)Termination reason: Refutation
% 3.47/1.24 % (534342)Time elapsed: 0.006 s
% 3.47/1.24 % (534342)Peak memory usage: 90 MB
% 3.47/1.24 % (534342)Instructions burned: 6 (million)
% 3.47/1.24 % (534342)------------------------------
% 3.47/1.24 % (534342)------------------------------
% 3.47/1.24 % (534332)Success in time 0.402 s
% 3.47/1.24 % Vampire exiting
%------------------------------------------------------------------------------