%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV243^5 : 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 : n019.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 08:38:06 AM UTC 2026
% Result : Theorem 0.75s 0.38s
% Output : Refutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 9
% Syntax : Number of formulae : 152 ( 19 unt; 0 typ; 8 def)
% Number of atoms : 1128 ( 152 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2190 ( 169 ~; 226 |; 101 &;1259 @)
% ( 11 <=>; 193 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 232 ( 232 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 29 usr; 15 con; 0-4 aty)
% ( 149 !!; 82 ??; 0 @@+; 0 @@-)
% Number of variables : 379 ( 0 sgn 59 !; 6 ?; 379 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cK: ( a > $o ) > a > $o ).
thf(func_def_2,type,
vNOT: $o > $o ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
vIFF: $o > $o > $o ).
thf(func_def_10,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
sK0: a ).
thf(func_def_17,type,
sK2: a > $o ).
thf(func_def_18,type,
sK3: a ).
thf(func_def_19,type,
sK4: ( a > $o ) > a ).
thf(func_def_20,type,
sK5: a ).
thf(func_def_21,type,
sK6: a > $o ).
thf(func_def_22,type,
sK7: ( a > $o ) > a ).
thf(func_def_23,type,
sK8: ( a > $o ) > a ).
thf(f1,conjecture,
( ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( cK @ X0 @ X2 ) ) )
=> ! [X2: a] :
( ( cK
@ ^ [X3: a] :
? [X4: a > $o] :
( ( X4 @ X3 )
& ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) ) )
@ X2 )
<=> ? [X4: a > $o] :
( ! [X3: a] :
( ( X4 @ X3 )
=> ( cK @ X4 @ X3 ) )
& ( X4 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM116_C_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( cK @ X0 @ X2 ) ) )
=> ! [X2: a] :
( ( cK
@ ^ [X3: a] :
? [X4: a > $o] :
( ( X4 @ X3 )
& ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) ) )
@ X2 )
<=> ? [X4: a > $o] :
( ! [X3: a] :
( ( X4 @ X3 )
=> ( cK @ X4 @ X3 ) )
& ( X4 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X3: a] :
( ( cK @ X0 @ X3 )
=> ( cK @ X1 @ X3 ) ) )
=> ! [X4: a] :
( ( cK
@ ^ [X5: a] :
? [X6: a > $o] :
( ( X6 @ X5 )
& ! [X7: a] :
( ( X6 @ X7 )
=> ( cK @ X6 @ X7 ) ) )
@ X4 )
<=> ? [X8: a > $o] :
( ! [X9: a] :
( ( X8 @ X9 )
=> ( cK @ X8 @ X9 ) )
& ( X8 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
= ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
= ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
= ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
= ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f8]) ).
thf(f10,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f8]) ).
thf(f13,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f10]) ).
thf(f14,plain,
! [X1: a > $o] :
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( cK @ X1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
! [X2: a > $o,X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( cK @ X1 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X2: a > $o,X1: a > $o] :
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
! [X2: a > $o,X1: a > $o] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( $false
= ( ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
= ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f9]) ).
thf(f19,plain,
( $false
= ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
!= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f20]) ).
thf(f24,definition,
( spl1_1
<=> ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f25,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
!= $false )
| spl1_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f26,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f28,definition,
( spl1_2
<=> ( $false
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f30,plain,
( ( $false
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f31,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f22,f28,f24]) ).
thf(f33,definition,
( spl1_3
<=> ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f34,plain,
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
!= $true )
| spl1_3 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f35,plain,
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f37,definition,
( spl1_4
<=> ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f39,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f21,f37,f33]) ).
thf(f43,plain,
( ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) )
@ sK2 ) )
| spl1_1 ),
inference(sigma_proxy_clausification,[],[f25]) ).
thf(f44,plain,
( ( ( ( sK2 @ sK0 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) ) ) )
= $true )
| spl1_1 ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) ) )
= $true )
| spl1_1 ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( $true
= ( sK2 @ sK0 ) )
| spl1_1 ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f49,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) )
@ X1 )
= $true )
| spl1_1 ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f50,plain,
( ! [X1: a] :
( ( ( sK2 @ X1 )
=> ( cK @ sK2 @ X1 ) )
= $true )
| spl1_1 ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
( ! [X1: a] :
( ( ( cK @ sK2 @ X1 )
= $true )
| ( $false
= ( sK2 @ X1 ) ) )
| spl1_1 ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( ( ( $true
=> ( cK @ sK2 @ sK0 ) )
= $true )
| spl1_1 ),
inference(constrained_superposition,[],[f50,f46]) ).
thf(f53,plain,
( ( $true
= ( cK @ sK2 @ sK0 ) )
| spl1_1 ),
inference(boolean_simplification,[],[f52]) ).
thf(f57,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(constrained_superposition,[],[f30,f35]) ).
thf(f61,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f62,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f61]) ).
thf(f66,plain,
( ! [X1: a > $o] :
( $false
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f67,plain,
( ! [X1: a > $o] :
( $false
= ( ( X1 @ sK0 )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f69,plain,
( ( $false
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK
@ ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f67,f35]) ).
thf(f70,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK
@ ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(boolean_simplification,[],[f69]) ).
thf(f71,plain,
( ( $false
= ( ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK
@ ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) )
@ sK3 ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(sigma_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( $false
= ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK3 )
=> ( cK
@ ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK3 ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f83,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X1 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f84,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $true
= ( ( cK @ X2 @ X3 )
=> ( cK @ X1 @ X3 ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f134,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) )
| ( $false = $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f84,f72]) ).
thf(f141,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f142,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f159,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) )
@ sK5 ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f160,plain,
( ( $false
= ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) ) )
=> ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) )
@ sK6 )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cK @ sK6 @ Y0 ) ) )
& ( sK6 @ sK5 ) )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( $true
= ( sK6 @ sK5 ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(and_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cK @ sK6 @ Y0 ) ) )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(and_proxy_clausification,[],[f164]) ).
thf(f171,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cK @ sK6 @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f172,plain,
( ! [X1: a] :
( ( ( sK6 @ X1 )
=> ( cK @ sK6 @ X1 ) )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ! [X1: a] :
( ( $true
= ( cK @ sK6 @ X1 ) )
| ( $false
= ( sK6 @ X1 ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f177,plain,
( ( ( $true
=> ( cK @ sK6 @ sK5 ) )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f172,f165]) ).
thf(f201,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_4 ),
inference(forward_demodulation,[],[f39,f26]) ).
thf(f202,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f203,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f202]) ).
thf(f204,plain,
( ( $true
= ( cK @ sK6 @ sK5 ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(boolean_simplification,[],[f177]) ).
thf(f207,plain,
( ! [X1: a] :
( ( ( sK6 @ X1 )
=> ( cK @ sK6 @ X1 ) )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f224,plain,
( ! [X0: a > $o] :
( ( ( $true
=> ( cK @ X0 @ sK5 ) )
= $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f84,f204]) ).
thf(f227,plain,
( ! [X0: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( ( cK @ X0 @ sK5 )
= $true ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(boolean_simplification,[],[f224]) ).
thf(f301,plain,
( ! [X0: a > $o] :
( ( ( cK @ X0 @ sK5 )
= $true )
| ( $false
= ( ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK7 @ X0 ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(sigma_proxy_clausification,[],[f227]) ).
thf(f302,plain,
( ! [X0: a > $o] :
( ( $false
= ( ( sK6 @ ( sK7 @ X0 ) )
=> ( X0 @ ( sK7 @ X0 ) ) ) )
| ( ( cK @ X0 @ sK5 )
= $true ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
( ! [X0: a > $o] :
( ( ( cK @ X0 @ sK5 )
= $true )
| ( $false
= ( X0 @ ( sK7 @ X0 ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(imp_proxy_clausification,[],[f302]) ).
thf(f304,plain,
( ! [X0: a > $o] :
( ( ( cK @ X0 @ sK5 )
= $true )
| ( ( sK6 @ ( sK7 @ X0 ) )
= $true ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(imp_proxy_clausification,[],[f302]) ).
thf(f317,plain,
( ( $false = $true )
| ( $false
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f161,f303]) ).
thf(f322,plain,
( ( $false
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f323,plain,
( ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK7
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f328,plain,
( ! [X1: a > $o] :
( $false
= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK7
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) )
@ X1 ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f323]) ).
thf(f329,plain,
( ! [X1: a > $o] :
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) )
& ( X1
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f328]) ).
thf(f331,plain,
( ( $false
= ( sK6
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( cK @ sK6 @ Y0 )
=> ( cK @ ( cK @ sK6 ) @ Y0 ) ) )
& $true ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f329,f173]) ).
thf(f332,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK @ sK6 @ Y0 )
=> ( cK @ ( cK @ sK6 ) @ Y0 ) ) ) )
| ( $false
= ( sK6
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(boolean_simplification,[],[f331]) ).
thf(f334,definition,
( spl1_8
<=> ( $false
= ( sK6
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
thf(f336,plain,
( ( $false
= ( sK6
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f334]) ).
thf(f338,definition,
( spl1_9
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK @ sK6 @ Y0 )
=> ( cK @ ( cK @ sK6 ) @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
thf(f340,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK @ sK6 @ Y0 )
=> ( cK @ ( cK @ sK6 ) @ Y0 ) ) ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f338]) ).
thf(f341,plain,
( spl1_8
| spl1_9
| ~ spl1_1
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f332,f33,f24,f338,f334]) ).
thf(f347,plain,
( ! [X0: a > $o] :
( ( ( $true
=> ( cK @ X0 @ sK0 ) )
= $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| spl1_1 ),
inference(constrained_superposition,[],[f84,f53]) ).
thf(f350,plain,
( ! [X0: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( ( cK @ X0 @ sK0 )
= $true ) )
| spl1_1 ),
inference(boolean_simplification,[],[f347]) ).
thf(f380,plain,
( ! [X0: a > $o] :
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK8 @ X0 ) ) )
| ( ( cK @ X0 @ sK0 )
= $true ) )
| spl1_1 ),
inference(sigma_proxy_clausification,[],[f350]) ).
thf(f381,plain,
( ! [X0: a > $o] :
( ( $false
= ( ( sK2 @ ( sK8 @ X0 ) )
=> ( X0 @ ( sK8 @ X0 ) ) ) )
| ( ( cK @ X0 @ sK0 )
= $true ) )
| spl1_1 ),
inference(beta-eta_normalization,[],[f380]) ).
thf(f382,plain,
( ! [X0: a > $o] :
( ( ( cK @ X0 @ sK0 )
= $true )
| ( $false
= ( X0 @ ( sK8 @ X0 ) ) ) )
| spl1_1 ),
inference(imp_proxy_clausification,[],[f381]) ).
thf(f397,plain,
( ( $false = $true )
| ( $false
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK8
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| spl1_1
| ~ spl1_2 ),
inference(constrained_superposition,[],[f30,f382]) ).
thf(f403,plain,
( ( $false
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK8
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| spl1_1
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f404,plain,
( ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK8
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ) )
| spl1_1
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f403]) ).
thf(f413,plain,
( ! [X1: a > $o] :
( $false
= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK8
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) )
@ X1 ) )
| spl1_1
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f404]) ).
thf(f414,plain,
( ! [X1: a > $o] :
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) )
& ( X1
@ ( sK8
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) )
| spl1_1
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f413]) ).
thf(f416,plain,
( ( ( sK2
@ ( sK8
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( cK @ sK2 @ Y0 )
=> ( cK @ ( cK @ sK2 ) @ Y0 ) ) )
& $true ) )
| spl1_1
| ~ spl1_2 ),
inference(constrained_superposition,[],[f414,f51]) ).
thf(f417,plain,
( ( ( sK2
@ ( sK8
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK @ sK2 @ Y0 )
=> ( cK @ ( cK @ sK2 ) @ Y0 ) ) ) )
| spl1_1
| ~ spl1_2 ),
inference(boolean_simplification,[],[f416]) ).
thf(f419,definition,
( spl1_10
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK @ sK2 @ Y0 )
=> ( cK @ ( cK @ sK2 ) @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
thf(f421,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK @ sK2 @ Y0 )
=> ( cK @ ( cK @ sK2 ) @ Y0 ) ) ) )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f419]) ).
thf(f423,definition,
( spl1_11
<=> ( ( sK2
@ ( sK8
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
thf(f425,plain,
( ( ( sK2
@ ( sK8
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f423]) ).
thf(f426,plain,
( spl1_10
| spl1_11
| spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f417,f28,f24,f423,f419]) ).
thf(f427,plain,
( ( $false
= ( ^ [Y0: a] :
( ( cK @ sK2 @ Y0 )
=> ( cK @ ( cK @ sK2 ) @ Y0 ) )
@ ( sK4 @ ( cK @ sK2 ) ) ) )
| ~ spl1_10 ),
inference(sigma_proxy_clausification,[],[f421]) ).
thf(f428,plain,
( ( $false
= ( ( cK @ sK2 @ ( sK4 @ ( cK @ sK2 ) ) )
=> ( cK @ ( cK @ sK2 ) @ ( sK4 @ ( cK @ sK2 ) ) ) ) )
| ~ spl1_10 ),
inference(beta-eta_normalization,[],[f427]) ).
thf(f433,plain,
( ( $false = $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) ) ) )
| ~ spl1_10 ),
inference(constrained_superposition,[],[f84,f428]) ).
thf(f435,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) ) ) )
| ~ spl1_10 ),
inference(trivial_inequality_removal,[],[f433]) ).
thf(f463,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) )
@ ( sK4 @ sK2 ) ) )
| ~ spl1_10 ),
inference(sigma_proxy_clausification,[],[f435]) ).
thf(f464,plain,
( ( $false
= ( ( sK2 @ ( sK4 @ sK2 ) )
=> ( cK @ sK2 @ ( sK4 @ sK2 ) ) ) )
| ~ spl1_10 ),
inference(beta-eta_normalization,[],[f463]) ).
thf(f465,plain,
( ( $false = $true )
| spl1_1
| ~ spl1_10 ),
inference(forward_demodulation,[],[f464,f50]) ).
thf(f466,plain,
( $false
| spl1_1
| ~ spl1_10 ),
inference(trivial_inequality_removal,[],[f465]) ).
thf(f467,plain,
( spl1_1
| ~ spl1_10 ),
inference(avatar_contradiction_clause,[],[f466]) ).
thf(f489,plain,
( ( $false
= ( $false
=> ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK8
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $true )
| spl1_1
| ~ spl1_11 ),
inference(constrained_superposition,[],[f381,f425]) ).
thf(f492,plain,
( ( $false
= ( $false
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK8
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $true )
| spl1_1
| ~ spl1_11 ),
inference(beta-eta_normalization,[],[f489]) ).
thf(f493,plain,
( ( $false = $true )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $true )
| spl1_1
| ~ spl1_11 ),
inference(boolean_simplification,[],[f492]) ).
thf(f494,plain,
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $true )
| spl1_1
| ~ spl1_11 ),
inference(trivial_inequality_removal,[],[f493]) ).
thf(f496,plain,
( $false
| spl1_1
| spl1_3
| ~ spl1_11 ),
inference(forward_subsumption_resolution,[],[f494,f34]) ).
thf(f497,plain,
( spl1_1
| spl1_3
| ~ spl1_11 ),
inference(avatar_contradiction_clause,[],[f496]) ).
thf(f768,plain,
( ( $false = $true )
| ( ( sK6
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f304,f161]) ).
thf(f779,plain,
( ( ( sK6
@ ( sK7
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f768]) ).
thf(f790,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_3
| ~ spl1_8 ),
inference(forward_demodulation,[],[f779,f336]) ).
thf(f791,plain,
( $false
| ~ spl1_1
| ~ spl1_3
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f790]) ).
thf(f792,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_8 ),
inference(avatar_contradiction_clause,[],[f791]) ).
thf(f804,plain,
( ( $false
= ( ^ [Y0: a] :
( ( cK @ sK6 @ Y0 )
=> ( cK @ ( cK @ sK6 ) @ Y0 ) )
@ ( sK4 @ ( cK @ sK6 ) ) ) )
| ~ spl1_9 ),
inference(sigma_proxy_clausification,[],[f340]) ).
thf(f805,plain,
( ( $false
= ( ( cK @ sK6 @ ( sK4 @ ( cK @ sK6 ) ) )
=> ( cK @ ( cK @ sK6 ) @ ( sK4 @ ( cK @ sK6 ) ) ) ) )
| ~ spl1_9 ),
inference(beta-eta_normalization,[],[f804]) ).
thf(f812,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cK @ sK6 @ Y0 ) ) ) )
| ( $false = $true )
| ~ spl1_9 ),
inference(constrained_superposition,[],[f84,f805]) ).
thf(f814,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cK @ sK6 @ Y0 ) ) ) )
| ~ spl1_9 ),
inference(trivial_inequality_removal,[],[f812]) ).
thf(f846,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cK @ sK6 @ Y0 ) )
@ ( sK4 @ sK6 ) ) )
| ~ spl1_9 ),
inference(sigma_proxy_clausification,[],[f814]) ).
thf(f847,plain,
( ( $false
= ( ( sK6 @ ( sK4 @ sK6 ) )
=> ( cK @ sK6 @ ( sK4 @ sK6 ) ) ) )
| ~ spl1_9 ),
inference(beta-eta_normalization,[],[f846]) ).
thf(f848,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_3
| ~ spl1_9 ),
inference(forward_demodulation,[],[f847,f207]) ).
thf(f849,plain,
( $false
| ~ spl1_1
| ~ spl1_3
| ~ spl1_9 ),
inference(trivial_inequality_removal,[],[f848]) ).
thf(f850,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[],[f849]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s5,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f62]) ).
cnf(s11,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f203]) ).
cnf(s15,plain,
( ~ spl1_1
| ~ spl1_3
| spl1_8
| spl1_9 ),
inference(sat_conversion,[],[f341]) ).
cnf(s16,plain,
( spl1_1
| ~ spl1_2
| spl1_10
| spl1_11 ),
inference(sat_conversion,[],[f426]) ).
cnf(s19,plain,
( spl1_1
| ~ spl1_10 ),
inference(sat_conversion,[],[f467]) ).
cnf(s21,plain,
( spl1_1
| spl1_3
| ~ spl1_11 ),
inference(sat_conversion,[],[f497]) ).
cnf(s26,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_8 ),
inference(sat_conversion,[],[f792]) ).
cnf(s29,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_9 ),
inference(sat_conversion,[],[f850]) ).
cnf(s30,plain,
( ~ spl1_2
| spl1_1
| spl1_10 ),
inference(rat,[],[s21,s5,s16]) ).
cnf(s31,plain,
spl1_1,
inference(rat,[],[s30,s1,s19]) ).
cnf(s32,plain,
~ spl1_4,
inference(rat,[],[s11,s31]) ).
cnf(s34,plain,
spl1_3,
inference(rat,[],[s2,s32]) ).
cnf(s35,plain,
~ spl1_9,
inference(rat,[],[s29,s31,s34]) ).
cnf(s36,plain,
~ spl1_8,
inference(rat,[],[s26,s31,s34]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s15,s35,s31,s36,s34]) ).
thf(f851,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV243^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.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 15:27:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.75/0.38 % (917393)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.75/0.38 % (917402)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2555195792:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.75/0.38 % (917402)Instruction limit reached!
% 0.75/0.38 % (917402)------------------------------
% 0.75/0.38 % (917402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917402)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917402)Termination reason: Instruction limit
% 0.75/0.38 % (917402)Termination phase: Saturation
% 0.75/0.38 % (917402)Time elapsed: 0.002 s
% 0.75/0.38 % (917402)Peak memory usage: 12 MB
% 0.75/0.38 % (917402)Instructions burned: 5 (million)
% 0.75/0.38 % (917401)lrs+10_16_si=on:nwc=1.5:random_seed=966490555:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.75/0.38 % (917400)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1102868823:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.75/0.38 % (917403)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=2656947333: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)
% 0.75/0.38 % (917417)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3178351909:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.75/0.38 % (917417)Instruction limit reached!
% 0.75/0.38 % (917417)------------------------------
% 0.75/0.38 % (917417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917417)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917417)Termination reason: Instruction limit
% 0.75/0.38 % (917417)Termination phase: Saturation
% 0.75/0.38 % (917417)Time elapsed: 0.001 s
% 0.75/0.38 % (917417)Peak memory usage: 12 MB
% 0.75/0.38 % (917417)Instructions burned: 2 (million)
% 0.75/0.38 % (917408)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.75/0.38 % (917408)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
% 0.75/0.38 % (917401)Instruction limit reached!
% 0.75/0.38 % (917401)------------------------------
% 0.75/0.38 % (917401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917401)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917401)Termination reason: Instruction limit
% 0.75/0.38 % (917401)Termination phase: Saturation
% 0.75/0.38 % (917401)Time elapsed: 0.012 s
% 0.75/0.38 % (917401)Peak memory usage: 12 MB
% 0.75/0.38 % (917401)Instructions burned: 19 (million)
% 0.75/0.38 % (917405)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1730191961:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.75/0.38 % (917422)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3024235715:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.75/0.38 % (917422)Instruction limit reached!
% 0.75/0.38 % (917422)------------------------------
% 0.75/0.38 % (917422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917408)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=1701366555:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.75/0.38 % (917422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917422)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917422)Termination reason: Instruction limit
% 0.75/0.38 % (917422)Termination phase: Saturation
% 0.75/0.38 % (917422)Time elapsed: 0.002 s
% 0.75/0.38 % (917422)Peak memory usage: 12 MB
% 0.75/0.38 % (917422)Instructions burned: 6 (million)
% 0.75/0.38 % (917406)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=394014538:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.75/0.38 % (917424)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.75/0.38 % (917427)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2346988115:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.75/0.38 % (917424)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=850403752:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.75/0.38 % (917427)Instruction limit reached!
% 0.75/0.38 % (917427)------------------------------
% 0.75/0.38 % (917427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917427)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917427)Termination reason: Instruction limit
% 0.75/0.38 % (917427)Termination phase: Saturation
% 0.75/0.38 % (917427)Time elapsed: 0.004 s
% 0.75/0.38 % (917427)Peak memory usage: 12 MB
% 0.75/0.38 % (917427)Instructions burned: 12 (million)
% 0.75/0.38 % (917424)Instruction limit reached!
% 0.75/0.38 % (917424)------------------------------
% 0.75/0.38 % (917424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917424)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917424)Termination reason: Instruction limit
% 0.75/0.38 % (917424)Termination phase: Saturation
% 0.75/0.38 % (917424)Time elapsed: 0.004 s
% 0.75/0.38 % (917424)Peak memory usage: 12 MB
% 0.75/0.38 % (917405)Instruction limit reached!
% 0.75/0.38 % (917405)------------------------------
% 0.75/0.38 % (917405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917424)Instructions burned: 7 (million)
% 0.75/0.38 % (917405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917405)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917405)Termination reason: Instruction limit
% 0.75/0.38 % (917405)Termination phase: Saturation
% 0.75/0.38 % (917405)Time elapsed: 0.022 s
% 0.75/0.38 % (917405)Peak memory usage: 12 MB
% 0.75/0.38 % (917405)Instructions burned: 25 (million)
% 0.75/0.38 % (917400)Instruction limit reached!
% 0.75/0.38 % (917400)------------------------------
% 0.75/0.38 % (917400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917431)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
% 0.75/0.38 % (917400)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917400)Termination reason: Instruction limit
% 0.75/0.38 % (917400)Termination phase: Saturation
% 0.75/0.38 % (917400)Time elapsed: 0.050 s
% 0.75/0.38 % (917431)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.75/0.38 % (917400)Peak memory usage: 12 MB
% 0.75/0.38 % (917400)Instructions burned: 88 (million)
% 0.75/0.38 % (917431)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1212502645:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.75/0.38 % (917433)lrs+10_1_si=on:cs=on:random_seed=1880353110:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.75/0.38 % (917432)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1751002451:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.75/0.38 % (917433)Instruction limit reached!
% 0.75/0.38 % (917433)------------------------------
% 0.75/0.38 % (917433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917433)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917433)Termination reason: Instruction limit
% 0.75/0.38 % (917433)Termination phase: Saturation
% 0.75/0.38 % (917433)Time elapsed: 0.006 s
% 0.75/0.38 % (917433)Peak memory usage: 12 MB
% 0.75/0.38 % (917433)Instructions burned: 8 (million)
% 0.75/0.38 % (917435)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.75/0.38 % (917439)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4293533716:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.75/0.38 % (917431)Instruction limit reached!
% 0.75/0.38 % (917431)------------------------------
% 0.75/0.38 % (917431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917431)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917431)Termination reason: Instruction limit
% 0.75/0.38 % (917431)Termination phase: Saturation
% 0.75/0.38 % (917431)Time elapsed: 0.025 s
% 0.75/0.38 % (917431)Peak memory usage: 12 MB
% 0.75/0.38 % (917431)Instructions burned: 28 (million)
% 0.75/0.38 % (917435)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1200875064:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.75/0.38 % (917439)Refutation not found, incomplete strategy
% 0.75/0.38 % (917439)------------------------------
% 0.75/0.38 % (917439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917439)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917439)Termination reason: Refutation not found, incomplete strategy
% 0.75/0.38 % (917439)Time elapsed: 0.008 s
% 0.75/0.38 % (917439)Peak memory usage: 12 MB
% 0.75/0.38 % (917439)Instructions burned: 24 (million)
% 0.75/0.38 % (917439)------------------------------
% 0.75/0.38 % (917439)------------------------------
% 0.75/0.38 % (917435)Instruction limit reached!
% 0.75/0.38 % (917435)------------------------------
% 0.75/0.38 % (917435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917435)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917435)Termination reason: Instruction limit
% 0.75/0.38 % (917435)Termination phase: Saturation
% 0.75/0.38 % (917435)Time elapsed: 0.002 s
% 0.75/0.38 % (917435)Peak memory usage: 12 MB
% 0.75/0.38 % (917435)Instructions burned: 4 (million)
% 0.75/0.38 % (917443)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2289111054:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.75/0.38 % (917441)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2143372023:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.75/0.38 % (917406)Instruction limit reached!
% 0.75/0.38 % (917406)------------------------------
% 0.75/0.38 % (917406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917406)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917406)Termination reason: Instruction limit
% 0.75/0.38 % (917406)Termination phase: Saturation
% 0.75/0.38 % (917406)Time elapsed: 0.075 s
% 0.75/0.38 % (917406)Peak memory usage: 12 MB
% 0.75/0.38 % (917406)Instructions burned: 76 (million)
% 0.75/0.38 % (917432) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-917393-917432"...
% 0.75/0.38 % (917443)Instruction limit reached!
% 0.75/0.38 % (917443)------------------------------
% 0.75/0.38 % (917443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917443)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917443)Termination reason: Instruction limit
% 0.75/0.38 % (917443)Termination phase: Saturation
% 0.75/0.38 % (917443)Time elapsed: 0.008 s
% 0.75/0.38 % (917443)Peak memory usage: 12 MB
% 0.75/0.38 % (917443)Instructions burned: 29 (million)
% 0.75/0.38 % (917444)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2343379123:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.75/0.38 % (917432)...printing done.
% 0.75/0.38 % (917432)Refutation found. Thanks to Tanya!
% 0.75/0.38 % SZS status Theorem for theBenchmark
% 0.75/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.75/0.38 % (917432)------------------------------
% 0.75/0.38 % (917432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.38 % (917432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.38 % (917432)CaDiCaL version: 2.1.3
% 0.75/0.38 % (917432)Termination reason: Refutation
% 0.75/0.38 % (917432)Time elapsed: 0.043 s
% 0.75/0.38 % (917432)Peak memory usage: 13 MB
% 0.75/0.38 % (917432)Instructions burned: 75 (million)
% 0.75/0.38 % (917393)Success in time 0.139 s
% 0.75/0.38 % Vampire exiting
%------------------------------------------------------------------------------