%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU856^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:34:18 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 120 ( 7 unt; 0 typ; 10 def)
% Number of atoms : 604 ( 130 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 603 ( 171 ~; 202 |; 49 &; 166 @)
% ( 14 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 16 con; 0-4 aty)
% Number of variables : 62 ( 18 sgn 22 !; 4 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vNOT: $o > $o ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(func_def_12,type,
sK4: a ).
thf(func_def_13,type,
sK5: a ).
thf(func_def_14,type,
sK6: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
<=> ( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
= ( ^ [X3: a] : $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM46_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
<=> ( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
= ( ^ [X3: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
<=> ( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
= ( ^ [X3: a] : $false ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
<=> ( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
<~> ( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] : $false ) )
| ( X0 != X1 ) )
& ( ( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) )
| ( X0 = X1 ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
| ( sK0 != sK1 ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
| ( sK0 = sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
| ( sK0 = sK1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
| ( sK0 != sK1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
( spl2_1
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f14,plain,
( ( sK0 != sK1 )
| spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f15,plain,
( ( sK0 = sK1 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f17,definition,
( spl2_2
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f18,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f20,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f8,f17,f13]) ).
thf(f21,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f9,f17,f13]) ).
thf(f22,plain,
( ( ( sK0 @ sK3 )
!= ( sK1 @ sK3 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f14]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f26,definition,
( spl2_3
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f27,plain,
( ( $false
!= ( sK1 @ sK3 ) )
| spl2_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f30,definition,
( spl2_4
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f32,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( spl2_3
| spl2_4
| spl2_1 ),
inference(avatar_split_clause,[],[f24,f13,f30,f26]) ).
thf(f35,definition,
( spl2_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f39,definition,
( spl2_6
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl2_5
| spl2_6
| spl2_1 ),
inference(avatar_split_clause,[],[f23,f13,f39,f35]) ).
thf(f43,plain,
( ( $false = $true )
| ~ spl2_3
| ~ spl2_5 ),
inference(forward_demodulation,[],[f37,f28]) ).
thf(f44,plain,
( $false
| ~ spl2_3
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f45,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f44]) ).
thf(f56,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[],[f19]) ).
thf(f57,plain,
( ! [X1: a] :
( ( $true
= ( ^ [Y0: a] : $false
@ X1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ X1 ) ) )
| ~ spl2_2 ),
inference(iff_proxy_clausification,[],[f56]) ).
thf(f70,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( ( ( sK1 @ X1 )
& ~ ( sK0 @ X1 ) )
| ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) ) ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f71,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) ) ) )
| ~ spl2_2 ),
inference(or_proxy_clausification,[],[f70]) ).
thf(f76,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( ~ ( sK1 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f77,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f83,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(constrained_superposition,[],[f28,f78]) ).
thf(f86,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f89,plain,
( spl2_4
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f86,f26,f17,f30]) ).
thf(f93,plain,
( ( ( ^ [Y0: a] : $false
@ sK4 )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK4 ) )
| spl2_2 ),
inference(negative_extensionality,[],[f18]) ).
thf(f94,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK4 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK4 ) )
| spl2_2 ),
inference(xor_proxy_clausification,[],[f93]) ).
thf(f103,plain,
( ( $false = $true )
| ( $true
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f104,plain,
( ( $false = $true )
| ( $true
= ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| spl2_2 ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( ( $false = $true )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| spl2_2 ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| spl2_2 ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f108,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) )
| spl2_2 ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f109,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) )
| spl2_2 ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f112,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK4 ) )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| spl2_2 ),
inference(not_proxy_clausification,[],[f105]) ).
thf(f119,definition,
( spl2_7
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
thf(f120,plain,
( ( $true
!= ( sK1 @ sK4 ) )
| spl2_7 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f121,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f123,definition,
( spl2_8
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
thf(f125,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f128,definition,
( spl2_9
<=> ( $false
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
thf(f129,plain,
( ( $false
!= ( sK0 @ sK4 ) )
| spl2_9 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f130,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f132,definition,
( spl2_10
<=> ( $false
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
thf(f134,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f169,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( ( sK1 @ X1 )
& ~ ( sK0 @ X1 ) ) ) )
| ~ spl2_2 ),
inference(or_proxy_clausification,[],[f70]) ).
thf(f170,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( ~ ( sK0 @ X1 ) ) )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $true
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f171]) ).
thf(f237,plain,
( ( $false = $true )
| ~ spl2_4
| ~ spl2_6 ),
inference(constrained_superposition,[],[f32,f41]) ).
thf(f243,plain,
( $false
| ~ spl2_4
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f244,plain,
( ~ spl2_4
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f243]) ).
thf(f255,plain,
( ( $false != $false )
| ( $true
= ( sK0 @ sK3 ) )
| ~ spl2_2
| spl2_3 ),
inference(constrained_superposition,[],[f27,f172]) ).
thf(f256,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl2_2
| spl2_3 ),
inference(trivial_inequality_removal,[],[f255]) ).
thf(f260,plain,
( ( $false = $true )
| ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(forward_demodulation,[],[f256,f32]) ).
thf(f261,plain,
( $false
| ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f260]) ).
thf(f262,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f261]) ).
thf(f327,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK4 ) )
| ( $true
= ( ~ ( sK0 @ sK4 ) ) )
| spl2_2 ),
inference(and_proxy_clausification,[],[f112]) ).
thf(f330,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| spl2_2 ),
inference(not_proxy_clausification,[],[f327]) ).
thf(f331,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| spl2_2 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f341,plain,
( spl2_7
| spl2_8
| spl2_2 ),
inference(avatar_split_clause,[],[f109,f17,f123,f119]) ).
thf(f343,plain,
( spl2_9
| spl2_10
| spl2_2 ),
inference(avatar_split_clause,[],[f331,f17,f132,f128]) ).
thf(f344,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( sK0 @ X1 ) )
| ~ spl2_1 ),
inference(argument_congruence,[],[f15]) ).
thf(f345,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl2_1 ),
inference(iff_proxy_clausification,[],[f344]) ).
thf(f346,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl2_1 ),
inference(iff_proxy_clausification,[],[f344]) ).
thf(f421,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK4 ) )
| ~ spl2_1
| ~ spl2_7 ),
inference(constrained_superposition,[],[f121,f346]) ).
thf(f424,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl2_1
| ~ spl2_7 ),
inference(trivial_inequality_removal,[],[f421]) ).
thf(f428,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_7
| ~ spl2_9 ),
inference(forward_demodulation,[],[f424,f130]) ).
thf(f429,plain,
( $false
| ~ spl2_1
| ~ spl2_7
| ~ spl2_9 ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f430,plain,
( ~ spl2_1
| ~ spl2_7
| ~ spl2_9 ),
inference(avatar_contradiction_clause,[],[f429]) ).
thf(f431,plain,
( ( $false = $true )
| ~ spl2_8
| ~ spl2_9 ),
inference(forward_demodulation,[],[f125,f130]) ).
thf(f432,plain,
( $false
| ~ spl2_8
| ~ spl2_9 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f433,plain,
( ~ spl2_8
| ~ spl2_9 ),
inference(avatar_contradiction_clause,[],[f432]) ).
thf(f435,plain,
( ( $true != $true )
| ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_1
| spl2_7 ),
inference(constrained_superposition,[],[f120,f345]) ).
thf(f438,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_1
| spl2_7 ),
inference(trivial_inequality_removal,[],[f435]) ).
thf(f439,plain,
( $false
| ~ spl2_1
| spl2_7
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f438,f129]) ).
thf(f440,plain,
( ~ spl2_1
| spl2_7
| spl2_9 ),
inference(avatar_contradiction_clause,[],[f439]) ).
thf(f441,plain,
( ( $false = $true )
| ~ spl2_7
| ~ spl2_10 ),
inference(forward_demodulation,[],[f121,f134]) ).
thf(f442,plain,
( $false
| ~ spl2_7
| ~ spl2_10 ),
inference(trivial_inequality_removal,[],[f441]) ).
thf(f443,plain,
( ~ spl2_7
| ~ spl2_10 ),
inference(avatar_contradiction_clause,[],[f442]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s3,plain,
( spl2_1
| spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s4,plain,
( spl2_1
| spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f42]) ).
cnf(s5,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f45]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f89]) ).
cnf(s14,plain,
( ~ spl2_4
| ~ spl2_6 ),
inference(sat_conversion,[],[f244]) ).
cnf(s15,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f262]) ).
cnf(s27,plain,
( spl2_2
| spl2_7
| spl2_8 ),
inference(sat_conversion,[],[f341]) ).
cnf(s29,plain,
( spl2_2
| spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f343]) ).
cnf(s36,plain,
( ~ spl2_1
| ~ spl2_7
| ~ spl2_9 ),
inference(sat_conversion,[],[f430]) ).
cnf(s37,plain,
( ~ spl2_8
| ~ spl2_9 ),
inference(sat_conversion,[],[f433]) ).
cnf(s38,plain,
( ~ spl2_1
| spl2_7
| spl2_9 ),
inference(sat_conversion,[],[f440]) ).
cnf(s39,plain,
( ~ spl2_7
| ~ spl2_10 ),
inference(sat_conversion,[],[f443]) ).
cnf(s40,plain,
( spl2_3
| spl2_1 ),
inference(rat,[],[s3,s15,s1]) ).
cnf(s41,plain,
spl2_1,
inference(rat,[],[s4,s14,s5,s6,s40,s1]) ).
cnf(s42,plain,
~ spl2_2,
inference(rat,[],[s2,s41]) ).
cnf(s43,plain,
spl2_7,
inference(rat,[],[s37,s27,s38,s42,s41]) ).
cnf(s44,plain,
~ spl2_10,
inference(rat,[],[s39,s43]) ).
cnf(s45,plain,
~ spl2_9,
inference(rat,[],[s36,s41,s43]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s29,s42,s44,s45]) ).
thf(f444,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU856^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:46:06 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.27 % (1340868)Will run a generic schedule for satisfiability detection.
% 0.21/0.27 % (1340877)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=630702949:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.27 % (1340877)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.27 % (1340874)% WARNING: option uhcvi not known.
% 0.21/0.27 % (1340877) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1340868-1340877"...
% 0.21/0.27 % (1340877)...printing done.
% 0.21/0.27 % (1340877)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (1340877)------------------------------
% 0.21/0.27 % (1340877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1340877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1340877)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1340877)Termination reason: Refutation
% 0.21/0.27 % (1340877)Time elapsed: 0.005 s
% 0.21/0.27 % (1340877)Peak memory usage: 12 MB
% 0.21/0.27 % (1340877)Instructions burned: 12 (million)
% 0.21/0.27 % (1340868)Success in time 0.035 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------