%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU854^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:31:48 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 90 ( 8 unt; 0 typ; 8 def)
% Number of atoms : 568 ( 162 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 651 ( 138 ~; 180 |; 57 &; 241 @)
% ( 13 <=>; 20 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 12 con; 0-4 aty)
% Number of variables : 103 ( 0 sgn 59 !; 18 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,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_10,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(func_def_13,type,
sK5: a ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ( X2
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) )
| ( X1 @ X4 ) ) ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM34_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ( X2
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) )
| ( X1 @ X4 ) ) ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) ) )
=> ( ( X1
= ( ^ [X5: a] :
( ( ( X1 @ X5 )
& ~ ( X2 @ X5 ) )
| ( X0 @ X5 ) ) ) )
<=> ! [X6: a] :
( ( X2 @ X6 )
=> ( X0 @ X6 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X1 @ X4 )
= $true ) ) )
=> ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X1 )
<=> ! [X6: a] :
( ( $true
= ( X2 @ X6 ) )
=> ( ( X0 @ X6 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X1 @ X4 )
= $true ) ) )
=> ( ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
=> ( $true
= ( X0 @ X5 ) ) )
<=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X2 @ X5 ) ) )
<~> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X1 ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X2 @ X5 ) ) )
<~> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X1 ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= X1 )
| ? [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
& ( $true
= ( X2 @ X5 ) ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X1 )
| ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X2 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f9,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= X1 )
| ? [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
& ( $true
= ( X2 @ X5 ) ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X1 )
| ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X2 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= X0 )
| ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X0 )
| ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X1 @ X4 )
!= $true ) ) )
& ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( ( X1 @ X5 )
!= $true ) )
& ! [X6: a] :
( ( $true
!= ( X2 @ X6 ) )
| ( ( X0 @ X6 )
= $true ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ( sK0
!= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
| ( ( $true
!= ( sK2 @ sK3 ) )
& ( $true
= ( sK1 @ sK3 ) ) ) )
& ( ( sK0
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
| ! [X4: a] :
( ( ( sK2 @ X4 )
= $true )
| ( ( sK1 @ X4 )
!= $true ) ) )
& ! [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
| ( ( sK1 @ X5 )
!= $true ) )
& ! [X6: a] :
( ( $true
!= ( sK2 @ X6 ) )
| ( $true
= ( sK0 @ X6 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f10]) ).
thf(f12,plain,
! [X6: a] :
( ( $true
!= ( sK2 @ X6 ) )
| ( $true
= ( sK0 @ X6 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f13,plain,
! [X5: a] :
( ( ( sK1 @ X5 )
!= $true )
| ( $true
= ( sK0 @ X5 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
! [X4: a] :
( ( ( sK1 @ X4 )
!= $true )
| ( sK0
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
| ( ( sK2 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
| ( $true
!= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,definition,
( spl4_1
<=> ( sK0
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f21,plain,
( ( sK0
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) )
| spl4_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f24,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f15,f24,f20]) ).
thf(f29,definition,
( spl4_3
<=> ! [X4: a] :
( ( ( sK1 @ X4 )
!= $true )
| ( ( sK2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f30,plain,
( ! [X4: a] :
( ( ( sK1 @ X4 )
!= $true )
| ( ( sK2 @ X4 )
= $true ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f31,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f14,f29,f20]) ).
thf(f33,definition,
( spl4_4
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f35,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| spl4_4 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f36,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f16,f33,f20]) ).
thf(f37,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK5 )
!= ( sK0 @ sK5 ) )
| spl4_1 ),
inference(negative_extensionality,[],[f22]) ).
thf(f38,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK5 )
= $true )
| spl4_1 ),
inference(xor_proxy_clausification,[],[f37]) ).
thf(f39,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK5 )
= $false )
| spl4_1 ),
inference(xor_proxy_clausification,[],[f37]) ).
thf(f40,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( ( sK2 @ sK5 )
| ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
= $false )
| spl4_1 ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| spl4_1 ),
inference(or_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| spl4_1 ),
inference(or_proxy_clausification,[],[f40]) ).
thf(f43,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) )
| spl4_1 ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f44,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK5 ) )
| spl4_1 ),
inference(not_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK5 ) )
| spl4_1 ),
inference(duplicate_literal_removal,[],[f44]) ).
thf(f46,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( ( ( sK2 @ sK5 )
| ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
= $true )
| spl4_1 ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f47,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| spl4_1 ),
inference(or_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| spl4_1 ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f51,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| spl4_1 ),
inference(duplicate_literal_removal,[],[f48]) ).
thf(f53,definition,
( spl4_5
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f55,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f57,definition,
( spl4_6
<=> ( ( sK2 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f59,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f60,plain,
( spl4_5
| spl4_6
| spl4_1 ),
inference(avatar_split_clause,[],[f42,f20,f57,f53]) ).
thf(f62,definition,
( spl4_7
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f64,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,plain,
( spl4_7
| spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f45,f20,f53,f62]) ).
thf(f67,plain,
( ( $true
= ( sK0 @ sK5 ) )
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f51,f12]) ).
thf(f69,definition,
( spl4_8
<=> ( $true
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f71,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f77,plain,
( spl4_8
| spl4_1 ),
inference(avatar_split_clause,[],[f67,f20,f69]) ).
thf(f78,plain,
( ( $true = $false )
| ~ spl4_5
| ~ spl4_8 ),
inference(forward_demodulation,[],[f55,f71]) ).
thf(f79,plain,
( $false
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
( ~ spl4_5
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f79]) ).
thf(f83,plain,
( ( $true != $true )
| ( $true
= ( sK2 @ sK5 ) )
| ~ spl4_3
| ~ spl4_7 ),
inference(constrained_superposition,[],[f30,f64]) ).
thf(f85,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl4_3
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f87,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_demodulation,[],[f85,f59]) ).
thf(f88,plain,
( $false
| ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f89,plain,
( ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f88]) ).
thf(f90,plain,
( ( $true != $true )
| ( ( sK0 @ sK3 )
= $true )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f13,f26]) ).
thf(f91,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f92,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ X1 ) )
| ~ spl4_1 ),
inference(argument_congruence,[],[f21]) ).
thf(f94,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ X1 )
= $true ) )
| ~ spl4_1 ),
inference(iff_proxy_clausification,[],[f92]) ).
thf(f95,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 )
= $false )
| ( $true
= ( ( sK2 @ X1 )
| ( ~ ( sK1 @ X1 )
& ( sK0 @ X1 ) ) ) ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 )
= $false )
| ( ( sK2 @ X1 )
= $true )
| ( $true
= ( ~ ( sK1 @ X1 )
& ( sK0 @ X1 ) ) ) )
| ~ spl4_1 ),
inference(or_proxy_clausification,[],[f95]) ).
thf(f98,plain,
( ! [X1: a] :
( ( ( ~ ( sK1 @ X1 ) )
= $true )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK2 @ X1 )
= $true ) )
| ~ spl4_1 ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( ! [X1: a] :
( ( ( sK2 @ X1 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl4_1 ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f113,plain,
( ( $true != $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ~ spl4_1
| spl4_4 ),
inference(constrained_superposition,[],[f35,f99]) ).
thf(f115,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ~ spl4_1
| spl4_4 ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f119,plain,
( ( $true = $false )
| ( ( sK0 @ sK3 )
= $false )
| ~ spl4_1
| ~ spl4_2
| spl4_4 ),
inference(forward_demodulation,[],[f115,f26]) ).
thf(f120,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_1
| ~ spl4_2
| spl4_4 ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f126,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_2
| spl4_4 ),
inference(forward_demodulation,[],[f120,f91]) ).
thf(f127,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| spl4_4 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f128,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_4 ),
inference(avatar_contradiction_clause,[],[f127]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s2,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f31]) ).
cnf(s3,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
( spl4_1
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f60]) ).
cnf(s5,plain,
( spl4_1
| spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f65]) ).
cnf(s7,plain,
( spl4_1
| spl4_8 ),
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
( ~ spl4_5
| ~ spl4_8 ),
inference(sat_conversion,[],[f80]) ).
cnf(s9,plain,
( ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(sat_conversion,[],[f89]) ).
cnf(s11,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f128]) ).
cnf(s13,plain,
spl4_1,
inference(rat,[],[s9,s5,s4,s8,s2,s7]) ).
cnf(s14,plain,
~ spl4_4,
inference(rat,[],[s3,s13]) ).
cnf(s15,plain,
spl4_2,
inference(rat,[],[s1,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s11,s13,s14,s15]) ).
thf(f132,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU854^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n010.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 14:40:33 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.26 % (2948825)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (2948839)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2774564209:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.26 % (2948839) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2948825-2948839"...
% 0.19/0.26 % (2948839)...printing done.
% 0.19/0.26 % (2948839)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (2948839)------------------------------
% 0.19/0.27 % (2948839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2948839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2948839)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2948839)Termination reason: Refutation
% 0.19/0.27 % (2948839)Time elapsed: 0.003 s
% 0.19/0.27 % (2948839)Peak memory usage: 13 MB
% 0.19/0.27 % (2948839)Instructions burned: 7 (million)
% 0.19/0.27 % (2948825)Success in time 0.038 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------