%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV223^5 : 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 : n008.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 08:38:03 AM UTC 2026
% Result : Theorem 0.14s 0.29s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 144 ( 12 unt; 0 typ; 11 def)
% Number of atoms : 1065 ( 338 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1383 ( 143 ~; 295 |; 170 &; 649 @)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 168 ( 168 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 16 con; 0-4 aty)
% ( 0 !!; 115 ??; 0 @@+; 0 @@-)
% Number of variables : 295 ( 0 sgn 72 !; 15 ?; 295 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: b > a ).
thf(func_def_1,type,
w: ( b > $o ) > $o ).
thf(func_def_3,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK1: a ).
thf(func_def_15,type,
sK2: a > $o ).
thf(func_def_16,type,
sK3: b ).
thf(func_def_17,type,
sK4: b > $o ).
thf(func_def_18,type,
sK5: b > $o ).
thf(func_def_19,type,
sK6: b > $o ).
thf(func_def_20,type,
sK7: a > b ).
thf(func_def_21,type,
sK8: ( a > $o ) > ( b > $o ) > a ).
thf(func_def_22,type,
sK9: ( a > $o ) > ( b > $o ) > b ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ? [X2: b > $o] :
( ( w @ X2 )
& ( X2 @ X1 ) ) ) )
= ( ^ [X3: a] :
? [X2: a > $o] :
( ? [X1: b > $o] :
( ( X2
= ( ^ [X0: a] :
? [X4: b] :
( ( X0
= ( f @ X4 ) )
& ( X1 @ X4 ) ) ) )
& ( w @ X1 ) )
& ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5204_pme) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ? [X2: b > $o] :
( ( w @ X2 )
& ( X2 @ X1 ) ) ) )
!= ( ^ [X3: a] :
? [X2: a > $o] :
( ? [X1: b > $o] :
( ( X2
= ( ^ [X0: a] :
? [X4: b] :
( ( X0
= ( f @ X4 ) )
& ( X1 @ X4 ) ) ) )
& ( w @ X1 ) )
& ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a] :
? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ? [X2: b > $o] :
( ( w @ X2 )
& ( X2 @ X1 ) ) ) )
!= ( ^ [X3: a] :
? [X4: a > $o] :
( ? [X5: b > $o] :
( ( X4
= ( ^ [X6: a] :
? [X7: b] :
( ( ( f @ X7 )
= X6 )
& ( X5 @ X7 ) ) ) )
& ( w @ X5 ) )
& ( X4 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,definition,
( spl0_1
<=> ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) ) ) )
| spl0_1 ),
inference(avatar_component_clause,[],[f9]) ).
thf(f12,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f6,f9]) ).
thf(f13,plain,
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK1 )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) )
@ sK1 ) )
| spl0_1 ),
inference(negative_extensionality,[],[f11]) ).
thf(f14,plain,
( ( $true
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK1 ) )
| spl0_1 ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK1 )
= $false )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) )
@ sK1 )
= $false )
| spl0_1 ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f16,plain,
( ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) ) ) )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) )
& ( ( f @ Y0 )
= sK1 ) ) )
= $false )
| spl0_1 ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ! [X1: a > $o] :
( ( $false
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) )
@ X1 ) )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) )
& ( ( f @ Y0 )
= sK1 ) ) )
= $false ) )
| spl0_1 ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ! [X2: b,X1: a > $o] :
( ( ( ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) )
& ( ( f @ Y0 )
= sK1 ) )
@ X2 )
= $false )
| ( $false
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) )
@ X1 ) ) )
| spl0_1 ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ! [X2: b,X1: a > $o] :
( ( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) ) )
& ( ( f @ X2 )
= sK1 ) )
= $false )
| ( ( ( X1 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
= $false ) )
| spl0_1 ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ! [X2: b,X1: a > $o] :
( ( ( ( X1 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
= $false )
| ( ( ( f @ X2 )
= sK1 )
= $false )
| ( $false
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) ) ) ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ! [X2: b,X1: a > $o] :
( ( ( X1 @ sK1 )
= $false )
| ( $false
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) ) ) )
| ( ( ( f @ X2 )
= sK1 )
= $false )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) )
= $false ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ! [X2: b,X3: b > $o,X1: a > $o] :
( ( ( X1 @ sK1 )
= $false )
| ( $false
= ( ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) )
@ X3 ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) )
= $false )
| ( ( ( f @ X2 )
= sK1 )
= $false ) )
| spl0_1 ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( ( X1 @ sK1 )
= $false )
| ( ( ( f @ X2 )
= sK1 )
= $false )
| ( $false
= ( ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ X4 )
= $false ) )
| spl0_1 ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( $false
= ( ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) )
@ X3 ) )
| ( ( X1 @ sK1 )
= $false )
| ( sK1
!= ( f @ X2 ) )
| ( ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ X4 )
= $false ) )
| spl0_1 ),
inference(equality_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( ( ( w @ X4 )
& ( X1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) )
= $false )
| ( $false
= ( ( X3 @ X2 )
& ( w @ X3 ) ) )
| ( sK1
!= ( f @ X2 ) )
| ( ( X1 @ sK1 )
= $false ) )
| spl0_1 ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
( ! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( ( X1 @ sK1 )
= $false )
| ( ( X1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $false )
| ( ( w @ X4 )
= $false )
| ( sK1
!= ( f @ X2 ) )
| ( $false
= ( ( X3 @ X2 )
& ( w @ X3 ) ) ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X1 )
| ( $false
= ( ( X3 @ X2 )
& ( w @ X3 ) ) )
| ( ( X1 @ sK1 )
= $false )
| ( ( w @ X4 )
= $false )
| ( sK1
!= ( f @ X2 ) ) )
| spl0_1 ),
inference(equality_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( ( X3 @ X2 )
= $false )
| ( ( w @ X3 )
= $false )
| ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X1 )
| ( ( w @ X4 )
= $false )
| ( ( X1 @ sK1 )
= $false )
| ( sK1
!= ( f @ X2 ) ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) )
& ( ( f @ Y0 )
= sK1 ) ) ) )
| spl0_1 ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f30,plain,
( ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) )
@ sK2 ) )
| ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) )
& ( ( f @ Y0 )
= sK1 ) ) ) )
| spl0_1 ),
inference(sigma_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $true
= ( ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) )
& ( ( f @ Y0 )
= sK1 ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) )
@ sK2 ) )
| spl0_1 ),
inference(sigma_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( ( ( sK2 @ sK1 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK3 )
& ( w @ Y0 ) ) )
& ( ( f @ sK3 )
= sK1 ) ) )
| spl0_1 ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
( ( $true
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK3 )
& ( w @ Y0 ) ) )
& ( ( f @ sK3 )
= sK1 ) ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( $true
= ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK3 )
& ( w @ Y0 ) ) )
& ( ( f @ sK3 )
= sK1 ) ) )
| ( $true
= ( sK2 @ sK1 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ( $true
= ( ( f @ sK3 )
= sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( ( $true
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK3 )
& ( w @ Y0 ) ) ) )
| ( $true
= ( sK2 @ sK1 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f37,plain,
( ( $true
= ( ^ [Y0: b > $o] :
( ( Y0 @ sK3 )
& ( w @ Y0 ) )
@ sK4 ) )
| ( $true
= ( sK2 @ sK1 ) )
| spl0_1 ),
inference(sigma_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( ( $true
= ( ( sK4 @ sK3 )
& ( w @ sK4 ) ) )
| ( $true
= ( sK2 @ sK1 ) )
| spl0_1 ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ( $true
= ( w @ sK4 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ( ( sK4 @ sK3 )
= $true )
| spl0_1 ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f41,plain,
( ( sK1
= ( f @ sK3 ) )
| ( $true
= ( sK2 @ sK1 ) )
| spl0_1 ),
inference(equality_proxy_clausification,[],[f35]) ).
thf(f42,plain,
( ( $true
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ sK5 ) )
| ( $true
= ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK3 )
& ( w @ Y0 ) ) )
& ( ( f @ sK3 )
= sK1 ) ) )
| spl0_1 ),
inference(sigma_proxy_clausification,[],[f33]) ).
thf(f43,plain,
( ( $true
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ sK5 ) )
| ( $true
= ( ( f @ sK3 )
= sK1 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK3 )
& ( w @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ sK5 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f45,plain,
( ( $true
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: b > $o] :
( ( Y0 @ sK3 )
& ( w @ Y0 ) )
@ sK6 ) )
| spl0_1 ),
inference(sigma_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( $true
= ( ( sK6 @ sK3 )
& ( w @ sK6 ) ) )
| ( $true
= ( ( w @ sK5 )
& ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) )
| spl0_1 ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
( ( $true
= ( ( w @ sK5 )
& ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) )
| ( $true
= ( w @ sK6 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( $true
= ( ( w @ sK5 )
& ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) )
| ( $true
= ( sK6 @ sK3 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f46]) ).
thf(f49,plain,
( ( $true
= ( sK6 @ sK3 ) )
| ( ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $true )
| spl0_1 ),
inference(and_proxy_clausification,[],[f48]) ).
thf(f50,plain,
( ( $true
= ( w @ sK5 ) )
| ( $true
= ( sK6 @ sK3 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f48]) ).
thf(f51,plain,
( ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( sK6 @ sK3 ) )
| spl0_1 ),
inference(equality_proxy_clausification,[],[f49]) ).
thf(f52,plain,
( ( $true
= ( w @ sK6 ) )
| ( ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $true )
| spl0_1 ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f53,plain,
( ( $true
= ( w @ sK5 ) )
| ( $true
= ( w @ sK6 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f54,plain,
( ( $true
= ( w @ sK6 ) )
| ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| spl0_1 ),
inference(equality_proxy_clausification,[],[f52]) ).
thf(f55,plain,
( ( sK1
= ( f @ sK3 ) )
| ( $true
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ sK5 ) )
| spl0_1 ),
inference(equality_proxy_clausification,[],[f43]) ).
thf(f56,plain,
( ( sK1
= ( f @ sK3 ) )
| ( $true
= ( ( w @ sK5 )
& ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) )
| spl0_1 ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
( ( ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ( sK1
= ( f @ sK3 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( ( sK1
= ( f @ sK3 ) )
| ( $true
= ( w @ sK5 ) )
| spl0_1 ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f59,plain,
( ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( sK1
= ( f @ sK3 ) )
| spl0_1 ),
inference(equality_proxy_clausification,[],[f57]) ).
thf(f61,definition,
( spl0_2
<=> ! [X4: b > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X1 )
| ( ( X1 @ sK1 )
= $false )
| ( ( w @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f62,plain,
( ! [X1: a > $o,X4: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X1 )
| ( ( X1 @ sK1 )
= $false )
| ( ( w @ X4 )
= $false ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f64,definition,
( spl0_3
<=> ! [X2: b,X3: b > $o] :
( ( ( X3 @ X2 )
= $false )
| ( sK1
!= ( f @ X2 ) )
| ( ( w @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f65,plain,
( ! [X2: b,X3: b > $o] :
( ( ( w @ X3 )
= $false )
| ( ( X3 @ X2 )
= $false )
| ( sK1
!= ( f @ X2 ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f66,plain,
( spl0_2
| spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f28,f9,f64,f61]) ).
thf(f68,definition,
( spl0_4
<=> ( $true
= ( sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f70,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f72,definition,
( spl0_5
<=> ( ( sK4 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f74,plain,
( ( ( sK4 @ sK3 )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f75,plain,
( spl0_4
| spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f40,f9,f72,f68]) ).
thf(f77,definition,
( spl0_6
<=> ( $true
= ( w @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f79,plain,
( ( $true
= ( w @ sK4 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f80,plain,
( spl0_4
| spl0_6
| spl0_1 ),
inference(avatar_split_clause,[],[f39,f9,f77,f68]) ).
thf(f82,definition,
( spl0_7
<=> ( sK1
= ( f @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f84,plain,
( ( sK1
= ( f @ sK3 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f85,plain,
( spl0_7
| spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f41,f9,f68,f82]) ).
thf(f87,definition,
( spl0_8
<=> ( $true
= ( sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
thf(f89,plain,
( ( $true
= ( sK6 @ sK3 ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f91,definition,
( spl0_9
<=> ( $true
= ( w @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
thf(f93,plain,
( ( $true
= ( w @ sK5 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f94,plain,
( spl0_8
| spl0_9
| spl0_1 ),
inference(avatar_split_clause,[],[f50,f9,f91,f87]) ).
thf(f96,definition,
( spl0_10
<=> ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
thf(f98,plain,
( ( sK2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f96]) ).
thf(f99,plain,
( spl0_10
| spl0_8
| spl0_1 ),
inference(avatar_split_clause,[],[f51,f9,f87,f96]) ).
thf(f101,definition,
( spl0_11
<=> ( $true
= ( w @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
thf(f103,plain,
( ( $true
= ( w @ sK6 ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f104,plain,
( spl0_9
| spl0_11
| spl0_1 ),
inference(avatar_split_clause,[],[f53,f9,f101,f91]) ).
thf(f105,plain,
( spl0_10
| spl0_11
| spl0_1 ),
inference(avatar_split_clause,[],[f54,f9,f101,f96]) ).
thf(f106,plain,
( spl0_9
| spl0_7
| spl0_1 ),
inference(avatar_split_clause,[],[f58,f9,f82,f91]) ).
thf(f107,plain,
( spl0_7
| spl0_10
| spl0_1 ),
inference(avatar_split_clause,[],[f59,f9,f96,f82]) ).
thf(f108,plain,
( ! [X0: b] :
( ( $true = $false )
| ( ( sK5 @ X0 )
= $false )
| ( ( f @ X0 )
!= sK1 ) )
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f65,f93]) ).
thf(f110,plain,
( ! [X0: b] :
( ( ( sK5 @ X0 )
= $false )
| ( ( f @ X0 )
!= sK1 ) )
| ~ spl0_3
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f112,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ X1 )
= ( sK2 @ X1 ) )
| ~ spl0_10 ),
inference(argument_congruence,[],[f98]) ).
thf(f113,plain,
( ! [X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ X1 ) )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl0_10 ),
inference(iff_proxy_clausification,[],[f112]) ).
thf(f120,plain,
( ! [X1: a] :
( ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( sK5 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) ) )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl0_10 ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f121,plain,
( ! [X1: a] :
( ( $true
= ( ^ [Y0: b] :
( ( sK5 @ Y0 )
& ( ( f @ Y0 )
= X1 ) )
@ ( sK7 @ X1 ) ) )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl0_10 ),
inference(sigma_proxy_clausification,[],[f120]) ).
thf(f122,plain,
( ! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ( sK5 @ ( sK7 @ X1 ) )
& ( ( f @ ( sK7 @ X1 ) )
= X1 ) ) ) )
| ~ spl0_10 ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f123,plain,
( ! [X1: a] :
( ( $true
= ( ( f @ ( sK7 @ X1 ) )
= X1 ) )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl0_10 ),
inference(and_proxy_clausification,[],[f122]) ).
thf(f124,plain,
( ! [X1: a] :
( ( $true
= ( sK5 @ ( sK7 @ X1 ) ) )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl0_10 ),
inference(and_proxy_clausification,[],[f122]) ).
thf(f125,plain,
( ! [X1: a] :
( ( ( f @ ( sK7 @ X1 ) )
= X1 )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl0_10 ),
inference(equality_proxy_clausification,[],[f123]) ).
thf(f127,plain,
( ! [X0: a] :
( ( $true = $false )
| ( ( sK2 @ X0 )
= $false )
| ( ( f @ ( sK7 @ X0 ) )
!= sK1 ) )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f110,f124]) ).
thf(f128,plain,
( ! [X0: a] :
( ( ( f @ ( sK7 @ X0 ) )
!= sK1 )
| ( ( sK2 @ X0 )
= $false ) )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f130,plain,
( ! [X0: a] :
( ( sK1 != X0 )
| ( ( sK2 @ X0 )
= $false )
| ( ( sK2 @ X0 )
= $false ) )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f128,f125]) ).
thf(f131,plain,
( ! [X0: a] :
( ( ( sK2 @ X0 )
= $false )
| ( sK1 != X0 ) )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(duplicate_literal_removal,[],[f130]) ).
thf(f134,plain,
( ( $true = $false )
| ( sK1 != sK1 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f70,f131]) ).
thf(f139,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f140,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f139]) ).
thf(f143,plain,
( ! [X0: b] :
( ( ( f @ X0 )
!= sK1 )
| ( $true = $false )
| ( ( sK6 @ X0 )
= $false ) )
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f103,f65]) ).
thf(f145,plain,
( ! [X0: b] :
( ( ( sK6 @ X0 )
= $false )
| ( ( f @ X0 )
!= sK1 ) )
| ~ spl0_3
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f148,plain,
( ( $true = $false )
| ( sK1
!= ( f @ sK3 ) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f89,f145]) ).
thf(f150,plain,
( ( sK1
!= ( f @ sK3 ) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f153,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f150,f84]) ).
thf(f154,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f153]) ).
thf(f157,plain,
( ! [X0: b > $o] :
( ( ( w @ X0 )
= $false )
| ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X0 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK1 )
= $false ) )
| ~ spl0_2 ),
inference(equality_resolution,[],[f62]) ).
thf(f171,plain,
( ! [X0: b > $o] :
( ( ( w @ X0 )
= $false )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( X0 @ Y0 )
& ( ( f @ Y0 )
= sK1 ) ) )
= $false ) )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f172,plain,
( ! [X0: b > $o,X1: b] :
( ( ( ^ [Y0: b] :
( ( X0 @ Y0 )
& ( ( f @ Y0 )
= sK1 ) )
@ X1 )
= $false )
| ( ( w @ X0 )
= $false ) )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ! [X0: b > $o,X1: b] :
( ( ( w @ X0 )
= $false )
| ( ( ( X0 @ X1 )
& ( ( f @ X1 )
= sK1 ) )
= $false ) )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
( ! [X0: b > $o,X1: b] :
( ( ( X0 @ X1 )
= $false )
| ( ( w @ X0 )
= $false )
| ( ( ( f @ X1 )
= sK1 )
= $false ) )
| ~ spl0_2 ),
inference(and_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ! [X0: b > $o,X1: b] :
( ( ( w @ X0 )
= $false )
| ( ( f @ X1 )
!= sK1 )
| ( ( X0 @ X1 )
= $false ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[],[f174]) ).
thf(f178,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f175,f61,f64]) ).
thf(f183,plain,
( ! [X0: b] :
( ( ( sK4 @ X0 )
= $false )
| ( $true = $false )
| ( ( f @ X0 )
!= sK1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f79,f65]) ).
thf(f185,plain,
( ! [X0: b] :
( ( ( sK4 @ X0 )
= $false )
| ( ( f @ X0 )
!= sK1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f194,plain,
( ( $true = $false )
| ( sK1
!= ( f @ sK3 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f74,f185]) ).
thf(f196,plain,
( ( sK1
!= ( f @ sK3 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f199,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f196,f84]) ).
thf(f200,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f199]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f12]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s3,plain,
( spl0_1
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f75]) ).
cnf(s4,plain,
( spl0_1
| spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f80]) ).
cnf(s5,plain,
( spl0_1
| spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f85]) ).
cnf(s6,plain,
( spl0_1
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f94]) ).
cnf(s7,plain,
( spl0_1
| spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f99]) ).
cnf(s8,plain,
( spl0_1
| spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s9,plain,
( spl0_1
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f105]) ).
cnf(s10,plain,
( spl0_1
| spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f106]) ).
cnf(s11,plain,
( spl0_1
| spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s13,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f140]) ).
cnf(s15,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(sat_conversion,[],[f154]) ).
cnf(s16,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f178]) ).
cnf(s18,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f200]) ).
cnf(s19,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s18,s3,s4,s5,s1]) ).
cnf(s20,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s13,s10,s11,s19,s1]) ).
cnf(s21,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s15,s7,s9,s20,s1]) ).
cnf(s22,plain,
~ spl0_3,
inference(rat,[],[s15,s6,s8,s13,s21,s20,s19,s1]) ).
cnf(s23,plain,
~ spl0_2,
inference(rat,[],[s16,s22]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s2,s1,s22,s23]) ).
thf(f201,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV223^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.19 % Computer : n008.cluster.edu
% 0.14/0.19 % Model : x86_64 x86_64
% 0.14/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.19 % Memory : 8046.5625MB
% 0.14/0.19 % OS : Linux 6.8.0-71-generic
% 0.14/0.19 % CPULimit : 300
% 0.14/0.19 % WCLimit : 300
% 0.14/0.19 % DateTime : Tue Sep 29 15:24:09 UTC 2026
% 0.14/0.19 % CPUTime :
% 0.14/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.22 Running higher-order theorem proving
% 0.14/0.23 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
% 0.14/0.29 % (3296272)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.14/0.29 % (3296278)lrs+10_16_si=on:nwc=1.5:random_seed=4189122659:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.14/0.29 % (3296277)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=205479095:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.14/0.29 % (3296278)Instruction limit reached!
% 0.14/0.29 % (3296278)------------------------------
% 0.14/0.29 % (3296278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.29 % (3296278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.29 % (3296278)CaDiCaL version: 2.1.3
% 0.14/0.29 % (3296278)Termination reason: Instruction limit
% 0.14/0.29 % (3296278)Termination phase: Saturation
% 0.14/0.29 % (3296278)Time elapsed: 0.007 s
% 0.14/0.29 % (3296278)Peak memory usage: 12 MB
% 0.14/0.29 % (3296278)Instructions burned: 23 (million)
% 0.14/0.29 % (3296280)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=2306282498: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)
% 0.14/0.29 % (3296279)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=380883744:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.14/0.29 % (3296279)Refutation not found, incomplete strategy
% 0.14/0.29 % (3296279)------------------------------
% 0.14/0.29 % (3296279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.29 % (3296279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.29 % (3296279)CaDiCaL version: 2.1.3
% 0.14/0.29 % (3296279)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.29 % (3296279)Time elapsed: 0.001 s
% 0.14/0.29 % (3296279)Peak memory usage: 12 MB
% 0.14/0.29 % (3296279)Instructions burned: 1 (million)
% 0.14/0.29 % (3296282)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1377520557:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.14/0.29 % (3296279)------------------------------
% 0.14/0.29 % (3296279)------------------------------
% 0.14/0.29 % (3296280) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3296272-3296280"...
% 0.14/0.29 % (3296287)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1250981592:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.14/0.29 % (3296280)...printing done.
% 0.14/0.29 % (3296287)Instruction limit reached!
% 0.14/0.29 % (3296287)------------------------------
% 0.14/0.29 % (3296287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.29 % (3296287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.29 % (3296287)CaDiCaL version: 2.1.3
% 0.14/0.29 % (3296287)Termination reason: Instruction limit
% 0.14/0.29 % (3296287)Termination phase: Saturation
% 0.14/0.29 % (3296287)Time elapsed: 0.001 s
% 0.14/0.29 % (3296287)Peak memory usage: 12 MB
% 0.14/0.29 % (3296287)Instructions burned: 2 (million)
% 0.14/0.29 % (3296283)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.14/0.29 % (3296283)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
% 0.14/0.29 % (3296280)Refutation found. Thanks to Tanya!
% 0.14/0.29 % SZS status Theorem for theBenchmark
% 0.14/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.30 % (3296280)------------------------------
% 0.14/0.30 % (3296280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.30 % (3296280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.30 % (3296280)CaDiCaL version: 2.1.3
% 0.14/0.30 % (3296280)Termination reason: Refutation
% 0.14/0.30 % (3296280)Time elapsed: 0.012 s
% 0.14/0.30 % (3296280)Peak memory usage: 13 MB
% 0.14/0.30 % (3296280)Instructions burned: 17 (million)
% 0.14/0.30 % (3296272)Success in time 0.053 s
% 0.14/0.30 % Vampire exiting
%------------------------------------------------------------------------------