%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV244^6 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 0.76s 0.38s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 7
% Syntax : Number of formulae : 132 ( 20 unt; 0 typ; 6 def)
% Number of atoms : 1017 ( 139 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2021 ( 133 ~; 185 |; 94 &;1188 @)
% ( 9 <=>; 186 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 257 ( 257 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 29 usr; 13 con; 0-4 aty)
% ( 151 !!; 75 ??; 0 @@+; 0 @@-)
% Number of variables : 369 ( 0 sgn 62 !; 6 ?; 369 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vNOT: $o > $o ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
db3:
!>[X0: $tType] : X0 ).
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_12,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
sK0: ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
sK3: $i > $o ).
thf(func_def_20,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_23,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_25,type,
sK9: $i > $o ).
thf(func_def_26,type,
sK10: ( $i > $o ) > $i ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X1: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X0 @ X2 @ X3 ) ) )
=> ! [X1: $i] :
( ( X0
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ( X4 @ X3 )
& ! [X5: $i] :
( ( X4 @ X5 )
=> ( X0 @ X4 @ X5 ) ) )
@ X1 )
<=> ? [X4: $i > $o] :
( ! [X3: $i] :
( ( X4 @ X3 )
=> ( X0 @ X4 @ X3 ) )
& ( X4 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM2A_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X1: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X0 @ X2 @ X3 ) ) )
=> ! [X1: $i] :
( ( X0
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ( X4 @ X3 )
& ! [X5: $i] :
( ( X4 @ X5 )
=> ( X0 @ X4 @ X5 ) ) )
@ X1 )
<=> ? [X4: $i > $o] :
( ! [X3: $i] :
( ( X4 @ X3 )
=> ( X0 @ X4 @ X3 ) )
& ( X4 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X4: $i] :
( ( X0 @ X2 @ X4 )
=> ( X0 @ X1 @ X4 ) ) )
=> ! [X5: $i] :
( ( X0
@ ^ [X6: $i] :
? [X7: $i > $o] :
( ( X7 @ X6 )
& ! [X8: $i] :
( ( X7 @ X8 )
=> ( X0 @ X7 @ X8 ) ) )
@ X5 )
<=> ? [X9: $i > $o] :
( ! [X10: $i] :
( ( X9 @ X10 )
=> ( X0 @ X9 @ X10 ) )
& ( X9 @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( ( !! @ ( ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f8]) ).
thf(f11,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
= ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f13,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
= ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f11]) ).
thf(f15,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X1: $i > $o] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ X1 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ X1 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ X2 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
= ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f13]) ).
thf(f21,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 )
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 ) )
| ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 )
= $false ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f26,definition,
( spl2_1
<=> ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f28,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 )
= $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f30,definition,
( spl2_2
<=> ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f31,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
!= $false )
| spl2_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f32,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f24,f30,f26]) ).
thf(f35,definition,
( spl2_3
<=> ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f37,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f39,definition,
( spl2_4
<=> ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK1 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f23,f39,f35]) ).
thf(f43,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f37,f32]) ).
thf(f44,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f45,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f44]) ).
thf(f46,plain,
( ( ( ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK3 )
= $true )
| spl2_2 ),
inference(sigma_proxy_clausification,[],[f31]) ).
thf(f47,plain,
( ( $true
= ( ( sK3 @ sK1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) ) ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) ) )
= $true )
| spl2_2 ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( ( sK3 @ sK1 )
= $true )
| spl2_2 ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f52,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) )
@ X1 )
= $true )
| spl2_2 ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f53,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
=> ( sK0 @ sK3 @ X1 ) )
= $true )
| spl2_2 ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK3 @ X1 )
= $false ) )
| spl2_2 ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
( ( $true
= ( $true
=> ( sK0 @ sK3 @ sK1 ) ) )
| spl2_2 ),
inference(constrained_superposition,[],[f53,f49]) ).
thf(f56,plain,
( ( $true
= ( sK0 @ sK3 @ sK1 ) )
| spl2_2 ),
inference(boolean_simplification,[],[f55]) ).
thf(f64,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ X2 @ Y0 ) )
@ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f65,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $true
= ( ( sK0 @ X1 @ X3 )
=> ( sK0 @ X2 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f70,plain,
( ! [X0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( $true
= ( $true
=> ( sK0 @ X0 @ sK1 ) ) ) )
| spl2_2 ),
inference(constrained_superposition,[],[f65,f56]) ).
thf(f75,plain,
( ! [X0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK0 @ X0 @ sK1 ) ) )
| spl2_2 ),
inference(boolean_simplification,[],[f70]) ).
thf(f81,plain,
( ! [X0: $i > $o] :
( ( $true
= ( sK0 @ X0 @ sK1 ) )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK4 @ X0 ) )
= $false ) )
| spl2_2 ),
inference(sigma_proxy_clausification,[],[f75]) ).
thf(f82,plain,
( ! [X0: $i > $o] :
( ( ( ( sK3 @ ( sK4 @ X0 ) )
=> ( X0 @ ( sK4 @ X0 ) ) )
= $false )
| ( $true
= ( sK0 @ X0 @ sK1 ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
( ! [X0: $i > $o] :
( ( $true
= ( sK0 @ X0 @ sK1 ) )
| ( ( X0 @ ( sK4 @ X0 ) )
= $false ) )
| spl2_2 ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ! [X0: $i > $o] :
( ( $true
= ( sK0 @ X0 @ sK1 ) )
| ( $true
= ( sK3 @ ( sK4 @ X0 ) ) ) )
| spl2_2 ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f106,plain,
( ( $true = $false )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f83,f28]) ).
thf(f112,plain,
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f113,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK4
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f120,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK4
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) )
@ X1 )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(pi_proxy_clausification,[],[f113]) ).
thf(f121,plain,
( ! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) ) )
& ( X1
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f123,plain,
( ( ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) ) )
& $true )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f121,f54]) ).
thf(f124,plain,
( ( ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f123]) ).
thf(f126,definition,
( spl2_7
<=> ( ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
thf(f128,plain,
( ( ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f130,definition,
( spl2_8
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
thf(f132,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) ) )
= $false )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f133,plain,
( spl2_7
| spl2_8
| ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f124,f30,f26,f130,f126]) ).
thf(f135,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $false )
| ~ spl2_2 ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f136,plain,
( ! [X1: $i > $o] :
( ( ( X1 @ sK1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) ) ) )
= $false )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f150,plain,
( ( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( sK0
@ ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f136,f41]) ).
thf(f155,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( sK0
@ ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(boolean_simplification,[],[f150]) ).
thf(f159,plain,
( ( ( ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( sK0
@ ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) )
@ sK6 )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f160,plain,
( ( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK6 )
=> ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK6 ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f164,plain,
( ( $true = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f65,f160]) ).
thf(f165,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f164]) ).
thf(f166,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f187,plain,
( ( ( ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) )
@ sK8 )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f188,plain,
( ( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK8 ) ) )
=> ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK8 ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK8 )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK8 ) ) )
= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK8 ) )
@ sK9 ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( sK0 @ sK9 @ Y0 ) ) )
& ( sK9 @ sK8 ) )
= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
( ( ( sK9 @ sK8 )
= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(and_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( sK0 @ sK9 @ Y0 ) ) )
= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(and_proxy_clausification,[],[f192]) ).
thf(f197,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( sK0 @ sK9 @ Y0 ) )
@ X1 )
= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f198,plain,
( ! [X1: $i] :
( ( ( sK9 @ X1 )
=> ( sK0 @ sK9 @ X1 ) )
= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f200,plain,
( ( $true
= ( $true
=> ( sK0 @ sK9 @ sK8 ) ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f198,f193]) ).
thf(f201,plain,
( ( ( sK0 @ sK9 @ sK8 )
= $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(boolean_simplification,[],[f200]) ).
thf(f203,plain,
( ! [X0: $i > $o] :
( ( $true
= ( $true
=> ( sK0 @ X0 @ sK8 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f65,f201]) ).
thf(f207,plain,
( ! [X0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( ( sK0 @ X0 @ sK8 )
= $true ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(boolean_simplification,[],[f203]) ).
thf(f352,plain,
( ! [X0: $i > $o] :
( ( ( sK0 @ X0 @ sK8 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK10 @ X0 ) )
= $false ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f353,plain,
( ! [X0: $i > $o] :
( ( ( ( sK9 @ ( sK10 @ X0 ) )
=> ( X0 @ ( sK10 @ X0 ) ) )
= $false )
| ( ( sK0 @ X0 @ sK8 )
= $true ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f352]) ).
thf(f354,plain,
( ! [X0: $i > $o] :
( ( ( sK0 @ X0 @ sK8 )
= $true )
| ( ( X0 @ ( sK10 @ X0 ) )
= $false ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(imp_proxy_clausification,[],[f353]) ).
thf(f355,plain,
( ! [X0: $i > $o] :
( ( ( sK0 @ X0 @ sK8 )
= $true )
| ( $true
= ( sK9 @ ( sK10 @ X0 ) ) ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(imp_proxy_clausification,[],[f353]) ).
thf(f378,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK10
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f189,f354]) ).
thf(f383,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( sK10
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f378]) ).
thf(f384,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK10
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f383]) ).
thf(f393,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0
@ ( sK10
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) )
@ X1 )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(pi_proxy_clausification,[],[f384]) ).
thf(f394,plain,
( ! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) ) )
& ( X1
@ ( sK10
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f393]) ).
thf(f408,plain,
( ( $true
= ( sK9
@ ( sK10
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f189,f355]) ).
thf(f414,plain,
( ( $true
= ( sK9
@ ( sK10
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f408]) ).
thf(f420,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( sK0 @ sK9 @ Y0 ) ) )
& $true )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f394,f414]) ).
thf(f426,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( sK0 @ sK9 @ Y0 ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(boolean_simplification,[],[f420]) ).
thf(f427,plain,
( ( ( ^ [Y0: $i] :
( ( sK9 @ Y0 )
=> ( sK0 @ sK9 @ Y0 ) )
@ ( sK7 @ sK9 ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(sigma_proxy_clausification,[],[f426]) ).
thf(f428,plain,
( ( ( ( sK9 @ ( sK7 @ sK9 ) )
=> ( sK0 @ sK9 @ ( sK7 @ sK9 ) ) )
= $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f427]) ).
thf(f429,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[],[f428,f198]) ).
thf(f430,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f431,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f430]) ).
thf(f438,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
=> ( sK0 @ sK3 @ X1 ) )
= $true )
| spl2_2 ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f480,plain,
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) )
@ ( sK7 @ ( sK0 @ sK3 ) ) )
= $false )
| ~ spl2_8 ),
inference(sigma_proxy_clausification,[],[f132]) ).
thf(f481,plain,
( ( $false
= ( ( sK0 @ sK3 @ ( sK7 @ ( sK0 @ sK3 ) ) )
=> ( sK0 @ ( sK0 @ sK3 ) @ ( sK7 @ ( sK0 @ sK3 ) ) ) ) )
| ~ spl2_8 ),
inference(beta-eta_normalization,[],[f480]) ).
thf(f485,plain,
( ( $true = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) ) )
= $false )
| ~ spl2_8 ),
inference(constrained_superposition,[],[f481,f65]) ).
thf(f487,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) ) )
= $false )
| ~ spl2_8 ),
inference(trivial_inequality_removal,[],[f485]) ).
thf(f516,plain,
( ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) )
@ ( sK4 @ ( sK0 @ sK3 ) ) )
= $false )
| ~ spl2_8 ),
inference(sigma_proxy_clausification,[],[f487]) ).
thf(f517,plain,
( ( ( ( sK3 @ ( sK4 @ ( sK0 @ sK3 ) ) )
=> ( sK0 @ sK3 @ ( sK4 @ ( sK0 @ sK3 ) ) ) )
= $false )
| ~ spl2_8 ),
inference(beta-eta_normalization,[],[f516]) ).
thf(f518,plain,
( ( $true = $false )
| spl2_2
| ~ spl2_8 ),
inference(forward_demodulation,[],[f517,f438]) ).
thf(f519,plain,
( $false
| spl2_2
| ~ spl2_8 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f520,plain,
( spl2_2
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f519]) ).
thf(f598,plain,
( ( ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $true )
| ( $true = $false )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f28,f84]) ).
thf(f610,plain,
( ( ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f598]) ).
thf(f616,plain,
( ( $true = $false )
| ~ spl2_1
| spl2_2
| ~ spl2_7 ),
inference(forward_demodulation,[],[f610,f128]) ).
thf(f617,plain,
( $false
| ~ spl2_1
| spl2_2
| ~ spl2_7 ),
inference(trivial_inequality_removal,[],[f616]) ).
thf(f618,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_7 ),
inference(avatar_contradiction_clause,[],[f617]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f45]) ).
cnf(s7,plain,
( ~ spl2_1
| spl2_2
| spl2_7
| spl2_8 ),
inference(sat_conversion,[],[f133]) ).
cnf(s17,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f431]) ).
cnf(s28,plain,
( spl2_2
| ~ spl2_8 ),
inference(sat_conversion,[],[f520]) ).
cnf(s33,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_7 ),
inference(sat_conversion,[],[f618]) ).
cnf(s35,plain,
~ spl2_2,
inference(rat,[],[s2,s3,s17]) ).
cnf(s36,plain,
~ spl2_8,
inference(rat,[],[s28,s35]) ).
cnf(s38,plain,
spl2_1,
inference(rat,[],[s1,s35]) ).
cnf(s40,plain,
spl2_7,
inference(rat,[],[s7,s36,s35,s38]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s33,s35,s38,s40]) ).
thf(f622,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV244^6 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:31:49 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.76/0.38 % (485709)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.76/0.38 % (485714)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4088183549:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.76/0.38 % (485715)lrs+10_16_si=on:nwc=1.5:random_seed=4126932596:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.76/0.38 % (485716)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=838418055:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.76/0.38 % (485716)Instruction limit reached!
% 0.76/0.38 % (485716)------------------------------
% 0.76/0.38 % (485716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485716)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485716)Termination reason: Instruction limit
% 0.76/0.38 % (485716)Termination phase: Saturation
% 0.76/0.38 % (485716)Time elapsed: 0.003 s
% 0.76/0.38 % (485716)Peak memory usage: 12 MB
% 0.76/0.38 % (485716)Instructions burned: 4 (million)
% 0.76/0.38 % (485720)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.76/0.38 % (485720)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
% 0.76/0.38 % (485718)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3488344268:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.76/0.38 % (485720)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=2871016429:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.76/0.38 % (485715)Instruction limit reached!
% 0.76/0.38 % (485715)------------------------------
% 0.76/0.38 % (485715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485715)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485715)Termination reason: Instruction limit
% 0.76/0.38 % (485715)Termination phase: Saturation
% 0.76/0.38 % (485715)Time elapsed: 0.012 s
% 0.76/0.38 % (485715)Peak memory usage: 12 MB
% 0.76/0.38 % (485715)Instructions burned: 19 (million)
% 0.76/0.38 % (485717)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=2582659889: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)
% 0.76/0.38 % (485714)Instruction limit reached!
% 0.76/0.38 % (485714)------------------------------
% 0.76/0.38 % (485714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485714)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485714)Termination reason: Instruction limit
% 0.76/0.38 % (485714)Termination phase: Saturation
% 0.76/0.38 % (485714)Time elapsed: 0.026 s
% 0.76/0.38 % (485714)Peak memory usage: 12 MB
% 0.76/0.38 % (485714)Instructions burned: 89 (million)
% 0.76/0.38 % (485719)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=681709300:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.76/0.38 % (485718)Instruction limit reached!
% 0.76/0.38 % (485718)------------------------------
% 0.76/0.38 % (485718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485718)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485718)Termination reason: Instruction limit
% 0.76/0.38 % (485718)Termination phase: Saturation
% 0.76/0.38 % (485718)Time elapsed: 0.014 s
% 0.76/0.38 % (485718)Peak memory usage: 12 MB
% 0.76/0.38 % (485718)Instructions burned: 26 (million)
% 0.76/0.38 % (485724)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1822351157:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.76/0.38 % (485724)Instruction limit reached!
% 0.76/0.38 % (485724)------------------------------
% 0.76/0.38 % (485724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485724)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485724)Termination reason: Instruction limit
% 0.76/0.38 % (485724)Termination phase: Saturation
% 0.76/0.38 % (485724)Time elapsed: 0.003 s
% 0.76/0.38 % (485724)Peak memory usage: 12 MB
% 0.76/0.38 % (485724)Instructions burned: 4 (million)
% 0.76/0.38 % (485730)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.76/0.38 % (485730)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=422077202:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.76/0.38 % (485728)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=385331752:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.76/0.38 % (485730)Instruction limit reached!
% 0.76/0.38 % (485730)------------------------------
% 0.76/0.38 % (485730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485730)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485730)Termination reason: Instruction limit
% 0.76/0.38 % (485730)Termination phase: Saturation
% 0.76/0.38 % (485730)Time elapsed: 0.003 s
% 0.76/0.38 % (485730)Peak memory usage: 12 MB
% 0.76/0.38 % (485730)Instructions burned: 9 (million)
% 0.76/0.38 % (485728)Instruction limit reached!
% 0.76/0.38 % (485728)------------------------------
% 0.76/0.38 % (485728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485728)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485728)Termination reason: Instruction limit
% 0.76/0.38 % (485728)Termination phase: Saturation
% 0.76/0.38 % (485728)Time elapsed: 0.004 s
% 0.76/0.38 % (485728)Peak memory usage: 12 MB
% 0.76/0.38 % (485728)Instructions burned: 6 (million)
% 0.76/0.38 % (485736)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=3032680838:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.76/0.38 % (485731)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=544104996:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.76/0.38 % (485737)lrs+10_1_si=on:cs=on:random_seed=1854068688:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.76/0.38 % (485733)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
% 0.76/0.38 % (485733)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.76/0.38 % (485737)Instruction limit reached!
% 0.76/0.38 % (485737)------------------------------
% 0.76/0.38 % (485737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485737)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485737)Termination reason: Instruction limit
% 0.76/0.38 % (485737)Termination phase: Saturation
% 0.76/0.38 % (485737)Time elapsed: 0.006 s
% 0.76/0.38 % (485737)Peak memory usage: 12 MB
% 0.76/0.38 % (485737)Instructions burned: 9 (million)
% 0.76/0.38 % (485733)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2408341258:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.76/0.38 % (485731)Instruction limit reached!
% 0.76/0.38 % (485731)------------------------------
% 0.76/0.38 % (485731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485731)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485731)Termination reason: Instruction limit
% 0.76/0.38 % (485731)Termination phase: Saturation
% 0.76/0.38 % (485731)Time elapsed: 0.017 s
% 0.76/0.38 % (485731)Peak memory usage: 12 MB
% 0.76/0.38 % (485731)Instructions burned: 13 (million)
% 0.76/0.38 % (485741)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.76/0.38 % (485741)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=2681266013:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.76/0.38 % (485736) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-485709-485736"...
% 0.76/0.38 % (485741)Instruction limit reached!
% 0.76/0.38 % (485741)------------------------------
% 0.76/0.38 % (485741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485743)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1002085328:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.76/0.38 % (485741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485741)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485741)Termination reason: Instruction limit
% 0.76/0.38 % (485741)Termination phase: Saturation
% 0.76/0.38 % (485741)Time elapsed: 0.002 s
% 0.76/0.38 % (485741)Peak memory usage: 12 MB
% 0.76/0.38 % (485741)Instructions burned: 3 (million)
% 0.76/0.38 % (485733)Instruction limit reached!
% 0.76/0.38 % (485733)------------------------------
% 0.76/0.38 % (485733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485733)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485733)Termination reason: Instruction limit
% 0.76/0.38 % (485733)Termination phase: Saturation
% 0.76/0.38 % (485733)Time elapsed: 0.021 s
% 0.76/0.38 % (485733)Peak memory usage: 12 MB
% 0.76/0.38 % (485733)Instructions burned: 29 (million)
% 0.76/0.38 % (485736)...printing done.
% 0.76/0.38 % (485719)Instruction limit reached!
% 0.76/0.38 % (485719)------------------------------
% 0.76/0.38 % (485719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485719)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485719)Termination reason: Instruction limit
% 0.76/0.38 % (485719)Termination phase: Saturation
% 0.76/0.38 % (485719)Time elapsed: 0.071 s
% 0.76/0.38 % (485719)Peak memory usage: 13 MB
% 0.76/0.38 % (485719)Instructions burned: 76 (million)
% 0.76/0.38 % (485736)Refutation found. Thanks to Tanya!
% 0.76/0.38 % SZS status Theorem for theBenchmark
% 0.76/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.76/0.38 % (485736)------------------------------
% 0.76/0.38 % (485736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.38 % (485736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.38 % (485736)CaDiCaL version: 2.1.3
% 0.76/0.38 % (485736)Termination reason: Refutation
% 0.76/0.38 % (485736)Time elapsed: 0.036 s
% 0.76/0.38 % (485736)Peak memory usage: 13 MB
% 0.76/0.38 % (485736)Instructions burned: 62 (million)
% 0.76/0.38 % (485709)Success in time 0.123 s
% 0.76/0.38 % Vampire exiting
%------------------------------------------------------------------------------