%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO543^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:50:23 AM UTC 2026
% Result : Theorem 2.82s 0.66s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 7
% Syntax : Number of formulae : 87 ( 24 unt; 0 typ; 4 def)
% Number of atoms : 439 ( 237 equ; 3 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 600 ( 174 ~; 156 |; 42 &; 221 @)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 9 con; 0-4 aty)
% Number of variables : 162 ( 6 sgn 96 !; 5 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_2,type,
if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_5,type,
vOR: $o > $o > $o ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sK0: $o ).
thf(func_def_15,type,
sK1: $i > $i ).
thf(func_def_17,type,
sK3: ( $i > $i ) > $i > $i ).
thf(func_def_18,type,
sK4: ( $i > $i ) > $i > $i ).
thf(func_def_19,type,
sK5: $i > ( $i > ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_21,type,
sK7: $i > ( $i > ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_22,type,
sK8: ( $i > $i ) > $i ).
thf(func_def_23,type,
sK9: ( $i > $i ) > $i > $i ).
thf(f1,axiom,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] : ( X0 @ X1 )
=> ( X0 @ ( epsii @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceaxii) ).
thf(f2,axiom,
( if
= ( ^ [X0: $o,X1: $i > $i,X2: $i > $i] :
( epsii
@ ^ [X3: $i > $i] :
( ( ( X3 = X2 )
& ~ X0 )
| ( ( X3 = X1 )
& X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifd) ).
thf(f3,conjecture,
! [X0: $o,X1: $i > $i] :
( ( if @ X0 @ X1 @ X1 )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f4,negated_conjecture,
~ ! [X0: $o,X1: $i > $i] :
( ( if @ X0 @ X1 @ X1 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] : ( X0 @ X1 )
=> ( X0 @ ( epsii @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( epsii @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( if
= ( ^ [X0: $o,X1: $i > $i,X2: $i > $i] :
( epsii
@ ^ [X3: $i > $i] :
( ( ( X3 = X2 )
& ~ X0 )
| ( ( X3 = X1 )
& X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: ( $i > $i ) > $o] :
( ( ( X0 @ ( epsii @ X0 ) )
= $true )
| ! [X1: $i > $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f10,plain,
? [X0: $o,X1: $i > $i] :
( ( if @ X0 @ X1 @ X1 )
!= X1 ),
inference(ennf_transformation,[],[f4]) ).
thf(f11,plain,
( sK1
!= ( if @ sK0 @ sK1 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
thf(f12,plain,
! [X0: ( $i > $i ) > $o,X1: $i > $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epsii @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( sK1
!= ( if @ sK0 @ sK1 @ sK1 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
( sK1
!= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) )
@ sK0
@ sK1
@ sK1 ) ),
inference(definition_unfolding,[],[f14,f13]) ).
thf(f18,plain,
( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f26,plain,
( ( sK1 @ sK2 )
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f18]) ).
thf(f27,plain,
! [X0: $i > $i] :
( ( epsii @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[],[f12]) ).
thf(f30,plain,
! [X2: ( $i > $i ) > $o,X1: $i > $i] :
( ( $true
!= ( ^ [Y0: $i > $i] :
~ ( X2 @ Y0 )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i > $i] :
~ ( X2 @ Y0 )
@ ( epsii
@ ^ [Y0: $i > $i] :
~ ( X2 @ Y0 ) ) ) ) ),
inference(primitive_instantiation,[],[f12]) ).
thf(f37,plain,
! [X2: ( $i > $i ) > $o,X1: $i > $i] :
( ( $true
!= ( ~ ( X2 @ X1 ) ) )
| ( $true
= ( ~ ( X2
@ ( epsii
@ ^ [Y0: $i > $i] :
~ ( X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f38,plain,
! [X2: ( $i > $i ) > $o,X1: $i > $i] :
( ( $true
= ( X2 @ X1 ) )
| ( $true
= ( ~ ( X2
@ ( epsii
@ ^ [Y0: $i > $i] :
~ ( X2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: ( $i > $i ) > $o,X1: $i > $i] :
( ( $true
= ( X2 @ X1 ) )
| ( $false
= ( X2
@ ( epsii
@ ^ [Y0: $i > $i] :
~ ( X2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f38]) ).
thf(f42,plain,
! [X0: $i > $i,X1: $i] :
( ( epsii @ ( (=) @ X0 ) @ X1 )
= ( X0 @ X1 ) ),
inference(argument_congruence,[],[f27]) ).
thf(f106,plain,
! [X0: $i > $i] :
( ( epsii
@ ^ [Y0: $i > $i] :
~ ( ^ [Y1: $i > $i] : ( Y1 != X0 )
@ Y0 ) )
= X0 ),
inference(leibniz_equality_elimination,[],[f39]) ).
thf(f189,plain,
! [X0: $i > $i] :
( ( epsii
@ ^ [Y0: $i > $i] :
~ ( ( Y0 != X0 ) ) )
= X0 ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f190,plain,
! [X0: $i > $i] :
( ( epsii
@ ^ [Y0: $i > $i] : ( Y0 = X0 ) )
= X0 ),
inference(boolean_simplification,[],[f189]) ).
thf(f230,plain,
! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ( ( ^ [Y0: $i > $i] : X0 )
!= ( ^ [Y0: $i > $i] : X1 ) ) ),
inference(constrained_superposition,[],[f190,f190]) ).
thf(f239,plain,
! [X2: $i,X0: $i > $i,X1: $i > $i] :
( ( ( X0 @ X2 )
= ( X1 @ X2 ) )
| ( ( ^ [Y0: $i > $i] : X0 )
!= ( ^ [Y0: $i > $i] : X1 ) ) ),
inference(argument_congruence,[],[f230]) ).
thf(f248,plain,
! [X2: $i,X0: $i > $i,X1: ( $i > $i ) > $o] :
( ( ( ^ [Y0: $i > $i] : X0 )
!= ( ^ [Y0: $i > $i,Y1: $i] : Y1 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ ( epsii @ X1 @ X2 ) ) )
| ( ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) ) )
!= X1 )
| ( sK2 != X2 ) ),
inference(constrained_superposition,[],[f26,f239]) ).
thf(f303,plain,
! [X0: ( $i > $i ) > $o,X1: $i] :
( ( ( sK1 @ sK2 )
!= ( ^ [Y0: $i] : Y0
@ ( epsii @ X0 @ X1 ) ) )
| ( ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) ) )
!= X0 )
| ( sK2 != X1 ) ),
inference(equality_resolution,[],[f248]) ).
thf(f304,plain,
! [X0: ( $i > $i ) > $o,X1: $i] :
( ( ( sK1 @ sK2 )
!= ( epsii @ X0 @ X1 ) )
| ( ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) ) )
!= X0 )
| ( sK2 != X1 ) ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f341,plain,
! [X0: $i > $i,X1: $i] :
( ( ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) ) )
!= ( (=) @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 ) ),
inference(constrained_superposition,[],[f304,f42]) ).
thf(f360,plain,
! [X0: $i > $i,X1: $i] :
( ( ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) )
@ ( sK4 @ X0 ) )
!= ( X0
= ( sK4 @ X0 ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 ) ),
inference(negative_extensionality,[],[f341]) ).
thf(f361,plain,
! [X0: $i > $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) )
@ ( sK4 @ X0 ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( $true
= ( X0
= ( sK4 @ X0 ) ) ) ),
inference(xor_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X0: $i > $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) )
@ ( sK4 @ X0 ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( $false
= ( X0
= ( sK4 @ X0 ) ) ) ),
inference(xor_proxy_clausification,[],[f360]) ).
thf(f363,plain,
! [X0: $i > $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) )
@ ( sK4 @ X0 ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 ) ),
inference(equality_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X0: $i > $i,X1: $i] :
( ( $false
= ( ( sK0
& ( sK1
= ( sK4 @ X0 ) ) )
| ( ~ sK0
& ( sK1
= ( sK4 @ X0 ) ) ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 ) ),
inference(beta-eta_normalization,[],[f363]) ).
thf(f365,plain,
! [X0: $i > $i,X1: $i] :
( ( $false
= ( ~ sK0
& ( sK1
= ( sK4 @ X0 ) ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 ) ),
inference(or_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X0: $i > $i,X1: $i] :
( ( $false
= ( sK0
& ( sK1
= ( sK4 @ X0 ) ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 ) ),
inference(or_proxy_clausification,[],[f364]) ).
thf(f367,plain,
! [X0: $i > $i,X1: $i] :
( ( $false
= ( sK1
= ( sK4 @ X0 ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 )
| ( sK0 = $false ) ),
inference(and_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X0: $i > $i,X1: $i] :
( ( sK1
!= ( sK4 @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 )
| ( sK0 = $false ) ),
inference(equality_proxy_clausification,[],[f367]) ).
thf(f369,plain,
! [X0: $i > $i,X1: $i] :
( ( $false
= ( sK1
= ( sK4 @ X0 ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 )
| ( $false = ( ~ sK0 ) ) ),
inference(and_proxy_clausification,[],[f365]) ).
thf(f370,plain,
! [X0: $i > $i,X1: $i] :
( ( sK1
!= ( sK4 @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 )
| ( $false = ( ~ sK0 ) ) ),
inference(equality_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X0: $i > $i,X1: $i] :
( ( sK1
!= ( sK4 @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 )
| ( $true = sK0 ) ),
inference(not_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X0: $i > $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i > $i] :
( ( sK0
& ( sK1 = Y0 ) )
| ( ~ sK0
& ( sK1 = Y0 ) ) )
@ ( sK4 @ X0 ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
= X0 ) ),
inference(equality_proxy_clausification,[],[f361]) ).
thf(f373,plain,
! [X0: $i > $i,X1: $i] :
( ( $true
= ( ( sK0
& ( sK1
= ( sK4 @ X0 ) ) )
| ( ~ sK0
& ( sK1
= ( sK4 @ X0 ) ) ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
= X0 ) ),
inference(beta-eta_normalization,[],[f372]) ).
thf(f374,plain,
! [X0: $i > $i,X1: $i] :
( ( $true
= ( ~ sK0
& ( sK1
= ( sK4 @ X0 ) ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
= X0 )
| ( $true
= ( sK0
& ( sK1
= ( sK4 @ X0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X0: $i > $i,X1: $i] :
( ( $true
= ( sK1
= ( sK4 @ X0 ) ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
= X0 )
| ( $true
= ( sK0
& ( sK1
= ( sK4 @ X0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f374]) ).
thf(f381,plain,
! [X0: $i > $i,X1: $i] :
( ( sK1
= ( sK4 @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
= X0 )
| ( $true
= ( sK0
& ( sK1
= ( sK4 @ X0 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f375]) ).
thf(f382,plain,
! [X0: $i > $i,X1: $i] :
( ( sK1
= ( sK4 @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
= X0 )
| ( $true
= ( sK1
= ( sK4 @ X0 ) ) ) ),
inference(and_proxy_clausification,[],[f381]) ).
thf(f384,plain,
! [X0: $i > $i,X1: $i] :
( ( sK1
= ( sK4 @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
= X0 )
| ( sK1
= ( sK4 @ X0 ) ) ),
inference(equality_proxy_clausification,[],[f382]) ).
thf(f385,plain,
! [X0: $i > $i,X1: $i] :
( ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK1
= ( sK4 @ X0 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
= X0 ) ),
inference(duplicate_literal_removal,[],[f384]) ).
thf(f397,plain,
! [X1: $i] :
( ( sK1
= ( sK4
@ ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
| ( sK2 != X1 )
| ( ( ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
= ( sK4
@ ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
| ( sK2 != X1 ) ),
inference(equality_resolution,[],[f385]) ).
thf(f400,plain,
! [X1: $i] :
( ( sK1
= ( sK4
@ ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
| ( sK2 != X1 )
| ( ( ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
= ( sK4
@ ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) ),
inference(duplicate_literal_removal,[],[f397]) ).
thf(f401,plain,
! [X1: $i] :
( ( sK1
= ( sK4 @ sK1 ) )
| ( sK2 != X1 )
| ( sK1
= ( sK4 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f400]) ).
thf(f402,plain,
! [X1: $i] :
( ( sK1
= ( sK4 @ sK1 ) )
| ( sK2 != X1 ) ),
inference(duplicate_literal_removal,[],[f401]) ).
thf(f436,definition,
( spl6_1
<=> ! [X1: $i] : ( sK2 != X1 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f437,plain,
( ! [X1: $i] : ( sK2 != X1 )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f436]) ).
thf(f439,definition,
( spl6_2
<=> ( sK1
= ( sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f441,plain,
( ( sK1
= ( sK4 @ sK1 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f439]) ).
thf(f442,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f402,f439,f436]) ).
thf(f496,definition,
( spl6_3
<=> ( sK0 = $false ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f498,plain,
( ( sK0 = $false )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f496]) ).
thf(f500,definition,
( spl6_4
<=> ! [X0: $i > $i,X1: $i] :
( ( sK1
!= ( sK4 @ X0 ) )
| ( ( sK4 @ X0 )
!= X0 )
| ( sK2 != X1 )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f501,plain,
( ! [X0: $i > $i,X1: $i] :
( ( sK1
!= ( sK4 @ X0 ) )
| ( ( sK4 @ X0 )
!= X0 )
| ( sK2 != X1 )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f500]) ).
thf(f502,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f368,f500,f496]) ).
thf(f609,plain,
( ! [X0: $i > $i,X1: $i] :
( ( $true = $false )
| ( sK1
!= ( sK4 @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 ) )
| ~ spl6_3 ),
inference(forward_demodulation,[],[f371,f498]) ).
thf(f610,plain,
( ! [X0: $i > $i,X1: $i] :
( ( sK1
!= ( sK4 @ X0 ) )
| ( ( sK1 @ sK2 )
!= ( X0 @ X1 ) )
| ( sK2 != X1 )
| ( ( sK4 @ X0 )
!= X0 ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f609]) ).
thf(f611,plain,
( spl6_4
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f610,f496,f500]) ).
thf(f613,plain,
( ! [X0: $i] :
( ( sK1 != sK1 )
| ( sK1 != sK1 )
| ( sK2 != X0 )
| ( ( sK1 @ sK2 )
!= ( sK1 @ X0 ) ) )
| ~ spl6_2
| ~ spl6_4 ),
inference(constrained_superposition,[],[f501,f441]) ).
thf(f614,plain,
( ! [X0: $i] :
( ( sK1 != sK1 )
| ( sK2 != X0 )
| ( ( sK1 @ sK2 )
!= ( sK1 @ X0 ) ) )
| ~ spl6_2
| ~ spl6_4 ),
inference(duplicate_literal_removal,[],[f613]) ).
thf(f615,plain,
( ! [X0: $i] :
( ( ( sK1 @ sK2 )
!= ( sK1 @ X0 ) )
| ( sK2 != X0 ) )
| ~ spl6_2
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f614]) ).
thf(f638,plain,
( ( sK2 != sK2 )
| ~ spl6_2
| ~ spl6_4 ),
inference(equality_resolution,[],[f615]) ).
thf(f639,plain,
( $false
| ~ spl6_2
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f638]) ).
thf(f640,plain,
( ~ spl6_2
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f639]) ).
thf(f649,plain,
( $false
| ~ spl6_1 ),
inference(equality_resolution,[],[f437]) ).
thf(f650,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f649]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f442]) ).
cnf(s2,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f502]) ).
cnf(s3,plain,
( ~ spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f611]) ).
cnf(s4,plain,
( ~ spl6_2
| ~ spl6_4 ),
inference(sat_conversion,[],[f640]) ).
cnf(s5,plain,
~ spl6_1,
inference(sat_conversion,[],[f650]) ).
cnf(s6,plain,
spl6_2,
inference(rat,[],[s1,s5]) ).
cnf(s7,plain,
~ spl6_4,
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
~ spl6_3,
inference(rat,[],[s3,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s7,s8]) ).
thf(f651,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO543^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:12:11 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 2.82/0.66 % (3667725)Will run a generic schedule for satisfiability detection.
% 2.82/0.66 % (3667732)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3772207537:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.82/0.66 % (3667731)% WARNING: option uhcvi not known.
% 2.82/0.66 % (3667730)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3905717552_2999 on theBenchmark for (2999ds/0Mi)
% 2.82/0.66 % (3667731)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=486622431:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.82/0.66 % (3667733)dis+10_1_sil=32000:sp=arity:random_seed=520118200:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.82/0.66 % (3667734)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2798302544:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.82/0.66 % (3667731)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.82/0.66 % Exception at run slice level
% 2.82/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.82/0.66 % (3667731)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.82/0.66 % (3667734)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.82/0.66 % (3667735)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3560892624:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.82/0.66 % (3667736)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2216025181:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.82/0.66 % (3667742)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2607739504:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.82/0.66 % Exception at run slice level
% 2.82/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.82/0.66 % (3667746)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4112726388:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.82/0.66 % (3667733)Instruction limit reached!
% 2.82/0.66 % (3667733)------------------------------
% 2.82/0.66 % (3667733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667733)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667733)Termination reason: Instruction limit
% 2.82/0.66 % (3667733)Termination phase: Saturation
% 2.82/0.66 % (3667733)Time elapsed: 0.050 s
% 2.82/0.66 % (3667733)Peak memory usage: 12 MB
% 2.82/0.66 % (3667733)Instructions burned: 103 (million)
% 2.82/0.66 % (3667734)Instruction limit reached!
% 2.82/0.66 % (3667734)------------------------------
% 2.82/0.66 % (3667734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667734)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667734)Termination reason: Instruction limit
% 2.82/0.66 % (3667734)Termination phase: Saturation
% 2.82/0.66 % (3667734)Time elapsed: 0.057 s
% 2.82/0.66 % (3667734)Peak memory usage: 12 MB
% 2.82/0.66 % (3667734)Instructions burned: 117 (million)
% 2.82/0.66 % (3667748)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=947261768:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.82/0.66 % (3667748)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.82/0.66 % (3667748)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.82/0.66 % (3667749)ott-21_1_sil=16000:fs=off:random_seed=1474461520:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.82/0.66 % (3667735)Instruction limit reached!
% 2.82/0.66 % (3667735)------------------------------
% 2.82/0.66 % (3667735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667735)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667735)Termination reason: Instruction limit
% 2.82/0.66 % (3667735)Termination phase: Saturation
% 2.82/0.66 % (3667735)Time elapsed: 0.076 s
% 2.82/0.66 % (3667735)Peak memory usage: 13 MB
% 2.82/0.66 % (3667735)Instructions burned: 131 (million)
% 2.82/0.66 % (3667746)Instruction limit reached!
% 2.82/0.66 % (3667746)------------------------------
% 2.82/0.66 % (3667746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667746)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667746)Termination reason: Instruction limit
% 2.82/0.66 % (3667746)Termination phase: Saturation
% 2.82/0.66 % (3667746)Time elapsed: 0.068 s
% 2.82/0.66 % (3667746)Peak memory usage: 12 MB
% 2.82/0.66 % (3667746)Instructions burned: 132 (million)
% 2.82/0.66 % (3667752)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=238757660:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.82/0.66 % (3667736)Instruction limit reached!
% 2.82/0.66 % (3667736)------------------------------
% 2.82/0.66 % (3667736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667736)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667736)Termination reason: Instruction limit
% 2.82/0.66 % (3667736)Termination phase: Saturation
% 2.82/0.66 % (3667736)Time elapsed: 0.094 s
% 2.82/0.66 % (3667736)Peak memory usage: 13 MB
% 2.82/0.66 % (3667736)Instructions burned: 160 (million)
% 2.82/0.66 % (3667753)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=974134842:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.82/0.66 % Exception at run slice level
% 2.82/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.82/0.66 % (3667755)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2774305783:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.82/0.66 % (3667757)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1962866024:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.82/0.66 % Exception at run slice level
% 2.82/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.82/0.66 % (3667749)Instruction limit reached!
% 2.82/0.66 % (3667749)------------------------------
% 2.82/0.66 % (3667749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667749)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667749)Termination reason: Instruction limit
% 2.82/0.66 % (3667749)Termination phase: Saturation
% 2.82/0.66 % (3667749)Time elapsed: 0.083 s
% 2.82/0.66 % (3667749)Peak memory usage: 12 MB
% 2.82/0.66 % (3667749)Instructions burned: 182 (million)
% 2.82/0.66 % (3667760)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2480966444:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 2.82/0.66 % (3667760)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.82/0.66 % (3667761)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1439374922:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.82/0.66 % (3667761)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.82/0.66 % (3667748)Instruction limit reached!
% 2.82/0.66 % (3667748)------------------------------
% 2.82/0.66 % (3667748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667748)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667748)Termination reason: Instruction limit
% 2.82/0.66 % (3667748)Termination phase: Saturation
% 2.82/0.66 % (3667748)Time elapsed: 0.247 s
% 2.82/0.66 % (3667748)Peak memory usage: 13 MB
% 2.82/0.66 % (3667748)Instructions burned: 684 (million)
% 2.82/0.66 % (3667752)Instruction limit reached!
% 2.82/0.66 % (3667752)------------------------------
% 2.82/0.66 % (3667752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667752)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667752)Termination reason: Instruction limit
% 2.82/0.66 % (3667752)Termination phase: Saturation
% 2.82/0.66 % (3667752)Time elapsed: 0.218 s
% 2.82/0.66 % (3667752)Peak memory usage: 13 MB
% 2.82/0.66 % (3667752)Instructions burned: 478 (million)
% 2.82/0.66 % (3667764)fmb+10_1_sil=64000:random_seed=1637679057:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.82/0.66 % (3667764)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.82/0.66 % Exception at run slice level
% 2.82/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.82/0.66 % (3667765)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=979081672:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 2.82/0.66 % Exception at run slice level
% 2.82/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.82/0.66 % (3667767)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2401073944:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 2.82/0.66 % Exception at run slice level
% 2.82/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.82/0.66 % (3667769)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=780471562:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 2.82/0.66 % (3667769)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.82/0.66 % (3667771)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1630691638:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 2.82/0.66 % (3667771)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.82/0.66 % (3667771)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.82/0.66 % (3667769) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3667725-3667769"...
% 2.82/0.66 % (3667769)...printing done.
% 2.82/0.66 % (3667769)Refutation found. Thanks to Tanya!
% 2.82/0.66 % SZS status Theorem for theBenchmark
% 2.82/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/0.66 % (3667769)------------------------------
% 2.82/0.66 % (3667769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.66 % (3667769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.66 % (3667769)CaDiCaL version: 2.1.3
% 2.82/0.66 % (3667769)Termination reason: Refutation
% 2.82/0.66 % (3667769)Time elapsed: 0.033 s
% 2.82/0.66 % (3667769)Peak memory usage: 13 MB
% 2.82/0.66 % (3667769)Instructions burned: 64 (million)
% 2.82/0.66 % (3667725)Success in time 0.434 s
% 2.82/0.66 % Vampire exiting
%------------------------------------------------------------------------------