%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ103^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Wed Sep 30 08:20:54 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 100 ( 27 unt; 0 typ; 11 def)
% Number of atoms : 593 ( 130 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 623 ( 90 ~; 142 |; 21 &; 286 @)
% ( 8 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 26 usr; 16 con; 0-4 aty)
% ( 30 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 71 ( 0 sgn 25 !; 1 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_NUM: $i > $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
vAND: $o > $o > $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sF2: $o ).
thf(func_def_15,type,
sF3: $o ).
thf(func_def_16,type,
sK4: $i > $o ).
thf(func_def_17,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_18,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_19,type,
sK7: $i > $o ).
thf(f1,axiom,
( cCKB6_NUM
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_NUM_def) ).
thf(f2,conjecture,
! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_L3000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i] :
( ( ( cCKB6_NUM @ X0 )
= $true )
=> ( ( cCKB6_NUM @ ( s @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( cCKB6_NUM
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i] :
( ( ( cCKB6_NUM @ ( s @ X0 ) )
!= $true )
& ( ( cCKB6_NUM @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
( ( ( cCKB6_NUM @ ( s @ sK0 ) )
!= $true )
& ( $true
= ( cCKB6_NUM @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( $true
= ( cCKB6_NUM @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( cCKB6_NUM @ ( s @ sK0 ) )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( s @ sK0 ) ) ),
inference(definition_unfolding,[],[f12,f10]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f11,f10]) ).
thf(f17,definition,
( sF1
= ( s @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f18,plain,
( ( s @ sK0 )
= sF1 ),
inference(reorient_equations,[],[f17]) ).
thf(f19,definition,
( sF2
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sF1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f20,plain,
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sF1 )
= sF2 ),
inference(reorient_equations,[],[f19]) ).
thf(f21,plain,
$true != sF2,
inference(definition_folding,[],[f15,f20,f18]) ).
thf(f22,definition,
( sF3
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f23,plain,
sF3 = $true,
inference(definition_folding,[],[f16,f22]) ).
thf(f25,plain,
( ( $true = sF2 )
| ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sF1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f20]) ).
thf(f26,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sF1 ) ) )
= $false )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
( ( $true = sF2 )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sF1 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( ( ( ( sK4 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) )
=> ( sK4 @ sF1 ) )
= $false )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
( ( ( sK4 @ sF1 )
= $false )
| ( $true = sF2 ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( ( ( sK4 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) )
= $true )
| ( $true = sF2 ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
= $true )
| ( $true = sF2 ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( $true = sF2 )
| ( $true
= ( sK4 @ c1 ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f33,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 )
= $true )
| ( $true = sF2 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f34,plain,
! [X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ X1 ) ) ) )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ ( s @ X1 ) ) )
| ( ( sK4 @ X1 )
= $false )
| ( $true = sF2 ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f46,plain,
( ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) )
| ( sF3 = $false ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f47,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) ) )
= $true )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X1: $i > $o] :
( ( ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ X1 )
= $true )
| ( sF3 = $false ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X1: $i > $o] :
( ( sF3 = $false )
| ( $true
= ( ( ( X1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) ) )
=> ( X1 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X1: $i > $o] :
( ( sF3 = $false )
| ( ( X1 @ sK0 )
= $true )
| ( ( ( X1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK0 )
= $true )
| ( sF3 = $false )
| ( ( X1 @ c1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X1: $i > $o] :
( ( ( X1 @ c1 )
= $false )
| ( sF3 = $false )
| ( ( X1 @ sK0 )
= $true )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) )
@ ( sK6 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK0 )
= $true )
| ( ( ( X1 @ ( sK6 @ X1 ) )
=> ( X1 @ ( s @ ( sK6 @ X1 ) ) ) )
= $false )
| ( ( X1 @ c1 )
= $false )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( s @ ( sK6 @ X1 ) ) )
= $false )
| ( ( X1 @ sK0 )
= $true )
| ( ( X1 @ c1 )
= $false )
| ( sF3 = $false ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: $i > $o] :
( ( ( X1 @ c1 )
= $false )
| ( $true
= ( X1 @ ( sK6 @ X1 ) ) )
| ( ( X1 @ sK0 )
= $true )
| ( sF3 = $false ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f67,definition,
( spl8_1
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f71,definition,
( spl8_2
<=> ( $true
= ( sK4 @ c1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f73,plain,
( ( $true
= ( sK4 @ c1 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f74,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f32,f71,f67]) ).
thf(f76,definition,
( spl8_3
<=> ! [X1: $i] :
( ( $true
= ( sK4 @ ( s @ X1 ) ) )
| ( ( sK4 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f77,plain,
( ! [X1: $i] :
( ( $true
= ( sK4 @ ( s @ X1 ) ) )
| ( ( sK4 @ X1 )
= $false ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f78,plain,
( spl8_1
| spl8_3 ),
inference(avatar_split_clause,[],[f35,f76,f67]) ).
thf(f80,definition,
( spl8_4
<=> ( ( sK4 @ sF1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f82,plain,
( ( ( sK4 @ sF1 )
= $false )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f83,plain,
( spl8_4
| spl8_1 ),
inference(avatar_split_clause,[],[f29,f67,f80]) ).
thf(f96,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f21,f67]) ).
thf(f98,definition,
( spl8_8
<=> ( sF3 = $false ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f100,plain,
( ( sF3 = $false )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f98]) ).
thf(f102,definition,
( spl8_9
<=> ! [X1: $i > $o] :
( ( ( X1 @ c1 )
= $false )
| ( ( X1 @ sK0 )
= $true )
| ( $true
= ( X1 @ ( sK6 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f103,plain,
( ! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK6 @ X1 ) ) )
| ( ( X1 @ sK0 )
= $true )
| ( ( X1 @ c1 )
= $false ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f104,plain,
( spl8_8
| spl8_9 ),
inference(avatar_split_clause,[],[f55,f102,f98]) ).
thf(f106,definition,
( spl8_10
<=> ! [X1: $i > $o] :
( ( ( X1 @ ( s @ ( sK6 @ X1 ) ) )
= $false )
| ( ( X1 @ c1 )
= $false )
| ( ( X1 @ sK0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f107,plain,
( ! [X1: $i > $o] :
( ( ( X1 @ ( s @ ( sK6 @ X1 ) ) )
= $false )
| ( ( X1 @ sK0 )
= $true )
| ( ( X1 @ c1 )
= $false ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f108,plain,
( spl8_8
| spl8_10 ),
inference(avatar_split_clause,[],[f54,f106,f98]) ).
thf(f114,definition,
( spl8_12
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition]) ).
thf(f116,plain,
( ( sF3 = $true )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f127,plain,
spl8_12,
inference(avatar_split_clause,[],[f23,f114]) ).
thf(f140,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_12 ),
inference(forward_demodulation,[],[f116,f100]) ).
thf(f141,plain,
( $false
| ~ spl8_8
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f142,plain,
( ~ spl8_8
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[],[f141]) ).
thf(f147,plain,
( ( ( sK4 @ sF1 )
= $true )
| ( ( sK4 @ sK0 )
= $false )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f77,f18]) ).
thf(f148,plain,
( ( ( sK4 @ sK0 )
= $false )
| ( $true = $false )
| ~ spl8_3
| ~ spl8_4 ),
inference(forward_demodulation,[],[f147,f82]) ).
thf(f149,plain,
( ( ( sK4 @ sK0 )
= $false )
| ~ spl8_3
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f152,plain,
( ( ( sK4 @ sK0 )
= $true )
| ( ( sK4 @ ( sK6 @ sK4 ) )
= $false )
| ( $true = $false )
| ( ( sK4 @ c1 )
= $false )
| ~ spl8_3
| ~ spl8_10 ),
inference(constrained_superposition,[],[f107,f77]) ).
thf(f155,plain,
( ( ( sK4 @ sK0 )
= $true )
| ( ( sK4 @ ( sK6 @ sK4 ) )
= $false )
| ( ( sK4 @ c1 )
= $false )
| ~ spl8_3
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f158,plain,
( ( ( sK4 @ c1 )
= $false )
| ( $true = $false )
| ( ( sK4 @ ( sK6 @ sK4 ) )
= $false )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_10 ),
inference(forward_demodulation,[],[f155,f149]) ).
thf(f159,plain,
( ( ( sK4 @ c1 )
= $false )
| ( ( sK4 @ ( sK6 @ sK4 ) )
= $false )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f158]) ).
thf(f162,plain,
( ( ( sK4 @ ( sK6 @ sK4 ) )
= $false )
| ( $true = $false )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_10 ),
inference(forward_demodulation,[],[f159,f73]) ).
thf(f163,plain,
( ( ( sK4 @ ( sK6 @ sK4 ) )
= $false )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f162]) ).
thf(f168,plain,
( ( $true = $false )
| ( ( sK4 @ c1 )
= $false )
| ( ( sK4 @ sK0 )
= $true )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_9
| ~ spl8_10 ),
inference(constrained_superposition,[],[f103,f163]) ).
thf(f171,plain,
( ( ( sK4 @ sK0 )
= $true )
| ( ( sK4 @ c1 )
= $false )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_9
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f174,plain,
( ( $true = $false )
| ( ( sK4 @ c1 )
= $false )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_9
| ~ spl8_10 ),
inference(forward_demodulation,[],[f171,f149]) ).
thf(f175,plain,
( ( ( sK4 @ c1 )
= $false )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_9
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f179,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_9
| ~ spl8_10 ),
inference(forward_demodulation,[],[f175,f73]) ).
thf(f180,plain,
( $false
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_9
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f181,plain,
( ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_9
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f180]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f74]) ).
cnf(s2,plain,
( spl8_1
| spl8_3 ),
inference(sat_conversion,[],[f78]) ).
cnf(s3,plain,
( spl8_1
| spl8_4 ),
inference(sat_conversion,[],[f83]) ).
cnf(s6,plain,
~ spl8_1,
inference(sat_conversion,[],[f96]) ).
cnf(s7,plain,
( spl8_8
| spl8_9 ),
inference(sat_conversion,[],[f104]) ).
cnf(s8,plain,
( spl8_8
| spl8_10 ),
inference(sat_conversion,[],[f108]) ).
cnf(s12,plain,
spl8_12,
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( ~ spl8_8
| ~ spl8_12 ),
inference(sat_conversion,[],[f142]) ).
cnf(s15,plain,
( ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_9
| ~ spl8_10 ),
inference(sat_conversion,[],[f181]) ).
cnf(s16,plain,
~ spl8_8,
inference(rat,[],[s13,s12]) ).
cnf(s17,plain,
spl8_10,
inference(rat,[],[s8,s16]) ).
cnf(s18,plain,
spl8_9,
inference(rat,[],[s7,s16]) ).
cnf(s19,plain,
spl8_4,
inference(rat,[],[s3,s6]) ).
cnf(s20,plain,
spl8_3,
inference(rat,[],[s2,s6]) ).
cnf(s21,plain,
~ spl8_2,
inference(rat,[],[s15,s17,s18,s19,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s21,s6]) ).
thf(f182,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ103^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:24:33 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.29 % (2839291)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (2839302)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (2839302)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.29 % (2839302)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2230790073:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (2839298)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=151941264:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (2839297)lrs+10_16_si=on:nwc=1.5:random_seed=2590240554:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (2839296)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1201704089:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (2839302) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2839291-2839302"...
% 0.22/0.29 % (2839300)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2710369026:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (2839301)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1835825601:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (2839299)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1581290958:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.29 % (2839298)Refutation not found, incomplete strategy
% 0.22/0.29 % (2839298)------------------------------
% 0.22/0.29 % (2839298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2839298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2839298)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2839298)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.29 % (2839298)Time elapsed: 0.001 s
% 0.22/0.29 % (2839298)Peak memory usage: 12 MB
% 0.22/0.29 % (2839298)Instructions burned: 1 (million)
% 0.22/0.29 % (2839302)...printing done.
% 0.22/0.29 % (2839298)------------------------------
% 0.22/0.29 % (2839298)------------------------------
% 0.22/0.29 % (2839302)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (2839302)------------------------------
% 0.22/0.29 % (2839302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2839302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2839302)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2839302)Termination reason: Refutation
% 0.22/0.29 % (2839302)Time elapsed: 0.003 s
% 0.22/0.29 % (2839302)Peak memory usage: 13 MB
% 0.22/0.29 % (2839302)Instructions burned: 8 (million)
% 0.22/0.29 % (2839291)Success in time 0.035 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------