%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV252^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:38:08 AM UTC 2026
% Result : Theorem 0.39s 0.30s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 9
% Syntax : Number of formulae : 148 ( 21 unt; 0 typ; 8 def)
% Number of atoms : 1181 ( 156 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2389 ( 148 ~; 215 |; 112 &;1408 @)
% ( 11 <=>; 225 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 306 ( 306 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 32 usr; 16 con; 0-4 aty)
% ( 182 !!; 88 ??; 0 @@+; 0 @@-)
% Number of variables : 435 ( 0 sgn 73 !; 6 ?; 435 :)
% 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,
vAND: $o > $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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vIFF: $o > $o > $o ).
thf(func_def_11,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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_24,type,
sK8: $i > $o ).
thf(func_def_26,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_27,type,
sK11: ( $i > $o ) > $i ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i > $o] :
( ( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X0 @ X2 @ X3 ) ) )
& ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X0 @ X2 @ X3 ) ) ) )
=> ! [X1: $i] :
( ( X0
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X0 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X1 )
<=> ? [X4: $i > $o] :
( ( X4 @ X1 )
& ! [X3: $i] :
( ( X4 @ X3 )
=> ( X0 @ X4 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM2A_EXPANDED_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X0 @ X2 @ X3 ) ) )
& ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X0 @ X2 @ X3 ) ) ) )
=> ! [X1: $i] :
( ( X0
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X0 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X1 )
<=> ? [X4: $i > $o] :
( ( X4 @ X1 )
& ! [X3: $i] :
( ( X4 @ X3 )
=> ( X0 @ X4 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X4: $i] :
( ( X0 @ X1 @ X4 )
=> ( X0 @ X2 @ X4 ) ) )
& ! [X5: $i > $o,X6: $i > $o] :
( ! [X7: $i] :
( ( X5 @ X7 )
=> ( X6 @ X7 ) )
=> ! [X8: $i] :
( ( X0 @ X5 @ X8 )
=> ( X0 @ X6 @ X8 ) ) ) )
=> ! [X9: $i] :
( ( X0
@ ^ [X10: $i] :
? [X11: $i > $o] :
( ! [X12: $i] :
( ( X11 @ X12 )
=> ( X0 @ X11 @ X12 ) )
& ( X11 @ X10 ) )
@ X9 )
<=> ? [X13: $i > $o] :
( ( X13 @ X9 )
& ! [X14: $i] :
( ( X13 @ X14 )
=> ( X0 @ X13 @ X14 ) ) ) ) ),
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] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ) ) ),
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] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f5]) ).
thf(f9,plain,
( ( !! @ ( ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f8]) ).
thf(f10,plain,
( ( ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
@ Y1 )
= ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f9]) ).
thf(f12,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
= ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f14,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
= ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f12]) ).
thf(f15,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f12]) ).
thf(f16,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f15]) ).
thf(f17,plain,
! [X1: $i > $o] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ X1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ X1 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
= ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f14]) ).
thf(f22,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK1 )
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $false
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) )
| ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f23]) ).
thf(f27,definition,
( spl2_1
<=> ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f29,plain,
( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl2_2
<=> ( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f32,plain,
( ( $true
!= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f33,plain,
( ( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f24,f31,f27]) ).
thf(f36,definition,
( spl2_3
<=> ( $false
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f38,plain,
( ( $false
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl2_4
<=> ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f42,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) )
= $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f25,f40,f36]) ).
thf(f44,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) )
@ sK3 ) )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f33]) ).
thf(f45,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) ) )
& ( sK3 @ sK1 ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( ( $true
= ( sK3 @ sK1 ) )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) ) ) )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f50,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) )
@ X1 )
= $true )
| ~ spl2_2 ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f51,plain,
( ! [X1: $i] :
( $true
= ( ( sK3 @ X1 )
=> ( sK0 @ sK3 @ X1 ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ sK3 @ X1 ) )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl2_2 ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( ( $true
= ( $true
=> ( sK0 @ sK3 @ sK1 ) ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f51,f46]) ).
thf(f54,plain,
( ( $true
= ( sK0 @ sK3 @ sK1 ) )
| ~ spl2_2 ),
inference(boolean_simplification,[],[f53]) ).
thf(f61,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f62,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $true
= ( ( sK0 @ X2 @ X3 )
=> ( sK0 @ X1 @ X3 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f67,plain,
( ! [X0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( $true
= ( $true
=> ( sK0 @ X0 @ sK1 ) ) ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f62,f54]) ).
thf(f71,plain,
( ! [X0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK0 @ X0 @ sK1 ) ) )
| ~ spl2_2 ),
inference(boolean_simplification,[],[f67]) ).
thf(f78,plain,
( ! [X0: $i > $o] :
( ( $true
= ( sK0 @ X0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK4 @ X0 ) ) ) )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f71]) ).
thf(f79,plain,
( ! [X0: $i > $o] :
( ( ( ( sK3 @ ( sK4 @ X0 ) )
=> ( X0 @ ( sK4 @ X0 ) ) )
= $false )
| ( $true
= ( sK0 @ X0 @ sK1 ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
( ! [X0: $i > $o] :
( ( $true
= ( sK0 @ X0 @ sK1 ) )
| ( $false
= ( X0 @ ( sK4 @ X0 ) ) ) )
| ~ spl2_2 ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ! [X0: $i > $o] :
( ( $true
= ( sK0 @ X0 @ sK1 ) )
| ( $true
= ( sK3 @ ( sK4 @ X0 ) ) ) )
| ~ spl2_2 ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f94,plain,
( ( $true = $false )
| ( $false
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(constrained_superposition,[],[f38,f80]) ).
thf(f101,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f102,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0
@ ( sK4
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f108,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( Y0
@ ( sK4
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(pi_proxy_clausification,[],[f102]) ).
thf(f109,plain,
( ! [X1: $i > $o] :
( ( ( X1
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) ) ) )
= $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f111,plain,
( ( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) ) ) )
= $false )
| ( $false
= ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(constrained_superposition,[],[f109,f52]) ).
thf(f112,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) ) ) )
| ( $false
= ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(boolean_simplification,[],[f111]) ).
thf(f114,definition,
( spl2_5
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f116,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) ) ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f118,definition,
( spl2_6
<=> ( $false
= ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
thf(f120,plain,
( ( $false
= ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f121,plain,
( spl2_5
| spl2_6
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f112,f36,f31,f118,f114]) ).
thf(f168,plain,
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK0 @ ( sK0 @ sK3 ) @ Y0 ) )
@ sK5 )
= $false )
| ~ spl2_5 ),
inference(sigma_proxy_clausification,[],[f116]) ).
thf(f169,plain,
( ( ( ( sK0 @ sK3 @ sK5 )
=> ( sK0 @ ( sK0 @ sK3 ) @ sK5 ) )
= $false )
| ~ spl2_5 ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f172,plain,
( ( $true = $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) ) ) )
| ~ spl2_5 ),
inference(constrained_superposition,[],[f169,f62]) ).
thf(f174,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) ) ) )
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f192,plain,
( ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK0 @ sK3 @ Y0 ) )
@ ( sK4 @ ( sK0 @ sK3 ) ) )
= $false )
| ~ spl2_5 ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f193,plain,
( ( ( ( sK3 @ ( sK4 @ ( sK0 @ sK3 ) ) )
=> ( sK0 @ sK3 @ ( sK4 @ ( sK0 @ sK3 ) ) ) )
= $false )
| ~ spl2_5 ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_5 ),
inference(forward_demodulation,[],[f193,f51]) ).
thf(f195,plain,
( $false
| ~ spl2_2
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f196,plain,
( ~ spl2_2
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f195]) ).
thf(f211,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) )
@ X1 )
= $false )
| spl2_2 ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f212,plain,
( ! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) ) )
& ( X1 @ sK1 ) )
= $false )
| spl2_2 ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f217,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( sK0
@ ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) )
@ Y0 ) ) )
& $true ) )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f212,f29]) ).
thf(f222,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( sK0
@ ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) )
@ Y0 ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f217]) ).
thf(f226,plain,
( ( ( ^ [Y0: $i] :
( ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( sK0
@ ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) )
@ Y0 ) )
@ sK6 )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(sigma_proxy_clausification,[],[f222]) ).
thf(f227,plain,
( ( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK6 )
=> ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ sK6 ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f230,plain,
( ( $true = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f227,f62]) ).
thf(f232,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f233,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
=> ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) ) )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f252,plain,
( ( ( ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
=> ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) )
@ sK7 )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(sigma_proxy_clausification,[],[f233]) ).
thf(f253,plain,
( ( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK7 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
=> ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK7 ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK7 )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f255,plain,
( ( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK7 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl2_1
| spl2_2 ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f256,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK7 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK8 ) )
| ~ spl2_1
| spl2_2 ),
inference(sigma_proxy_clausification,[],[f255]) ).
thf(f257,plain,
( ( $true
= ( ( sK8 @ sK7 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( sK0 @ sK8 @ Y0 ) ) ) ) )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f258,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( sK0 @ sK8 @ Y0 ) ) ) )
| ~ spl2_1
| spl2_2 ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ( $true
= ( sK8 @ sK7 ) )
| ~ spl2_1
| spl2_2 ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f262,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( sK0 @ sK8 @ Y0 ) )
@ X1 ) )
| ~ spl2_1
| spl2_2 ),
inference(pi_proxy_clausification,[],[f258]) ).
thf(f263,plain,
( ! [X1: $i] :
( $true
= ( ( sK8 @ X1 )
=> ( sK0 @ sK8 @ X1 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f262]) ).
thf(f264,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ X1 ) )
| ( ( sK8 @ X1 )
= $false ) )
| ~ spl2_1
| spl2_2 ),
inference(imp_proxy_clausification,[],[f263]) ).
thf(f265,plain,
( ( $true
= ( $true
=> ( sK0 @ sK8 @ sK7 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f263,f259]) ).
thf(f266,plain,
( ( $true
= ( sK0 @ sK8 @ sK7 ) )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f265]) ).
thf(f268,plain,
( ! [X0: $i > $o] :
( ( $true
= ( $true
=> ( sK0 @ X0 @ sK7 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f62,f266]) ).
thf(f296,definition,
( spl2_8
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK8 @ Y0 )
=> ( sK0 @ ( sK0 @ sK8 ) @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
thf(f298,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK8 @ Y0 )
=> ( sK0 @ ( sK0 @ sK8 ) @ Y0 ) ) )
= $false )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f345,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[],[f33,f42]) ).
thf(f346,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f345]) ).
thf(f347,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f346]) ).
thf(f422,plain,
( ( $true
= ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( $true
!= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK1 ) ) ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f23,f81]) ).
thf(f438,plain,
( ( $true
= ( sK3
@ ( sK4
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f422,f33]) ).
thf(f442,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_6 ),
inference(forward_demodulation,[],[f438,f120]) ).
thf(f443,plain,
( $false
| ~ spl2_2
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f444,plain,
( ~ spl2_2
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f443]) ).
thf(f451,plain,
( ! [X0: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( $true
= ( sK0 @ X0 @ sK7 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f268]) ).
thf(f669,plain,
( ! [X0: $i > $o] :
( ( $true
= ( sK0 @ X0 @ sK7 ) )
| ( ( ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK11 @ X0 ) )
= $false ) )
| ~ spl2_1
| spl2_2 ),
inference(sigma_proxy_clausification,[],[f451]) ).
thf(f670,plain,
( ! [X0: $i > $o] :
( ( ( ( sK8 @ ( sK11 @ X0 ) )
=> ( X0 @ ( sK11 @ X0 ) ) )
= $false )
| ( $true
= ( sK0 @ X0 @ sK7 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f669]) ).
thf(f671,plain,
( ! [X0: $i > $o] :
( ( $true
= ( sK0 @ X0 @ sK7 ) )
| ( ( X0 @ ( sK11 @ X0 ) )
= $false ) )
| ~ spl2_1
| spl2_2 ),
inference(imp_proxy_clausification,[],[f670]) ).
thf(f703,plain,
( ( $true = $false )
| ( $false
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK11
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f254,f671]) ).
thf(f709,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK11
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f703]) ).
thf(f710,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0
@ ( sK11
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f709]) ).
thf(f733,plain,
( ! [X1: $i > $o] :
( $false
= ( ^ [Y0: $i > $o] :
( ( Y0
@ ( sK11
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl2_1
| spl2_2 ),
inference(pi_proxy_clausification,[],[f710]) ).
thf(f734,plain,
( ! [X1: $i > $o] :
( ( ( X1
@ ( sK11
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( sK0 @ X1 @ Y0 ) ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(beta-eta_normalization,[],[f733]) ).
thf(f736,plain,
( ( $false
= ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK8 @ Y0 )
=> ( sK0 @ ( sK0 @ sK8 ) @ Y0 ) ) ) ) )
| ( ( sK8
@ ( sK11
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(constrained_superposition,[],[f734,f264]) ).
thf(f738,plain,
( ( ( sK8
@ ( sK11
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK8 @ Y0 )
=> ( sK0 @ ( sK0 @ sK8 ) @ Y0 ) ) )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(boolean_simplification,[],[f736]) ).
thf(f741,definition,
( spl2_17
<=> ( ( sK8
@ ( sK11
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
thf(f743,plain,
( ( ( sK8
@ ( sK11
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f741]) ).
thf(f744,plain,
( spl2_8
| spl2_17
| ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f738,f31,f27,f741,f296]) ).
thf(f751,plain,
( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK7 ) )
| ( $false
= ( $false
=> ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK11
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl2_1
| spl2_2
| ~ spl2_17 ),
inference(constrained_superposition,[],[f670,f743]) ).
thf(f755,plain,
( ( $false
= ( $false
=> ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0
@ ( sK11
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK7 ) )
| ~ spl2_1
| spl2_2
| ~ spl2_17 ),
inference(beta-eta_normalization,[],[f751]) ).
thf(f756,plain,
( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK7 ) )
| ( $true = $false )
| ~ spl2_1
| spl2_2
| ~ spl2_17 ),
inference(boolean_simplification,[],[f755]) ).
thf(f757,plain,
( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK7 ) )
| ~ spl2_1
| spl2_2
| ~ spl2_17 ),
inference(trivial_inequality_removal,[],[f756]) ).
thf(f758,plain,
( ( $true = $false )
| ~ spl2_1
| spl2_2
| ~ spl2_17 ),
inference(forward_demodulation,[],[f757,f254]) ).
thf(f759,plain,
( $false
| ~ spl2_1
| spl2_2
| ~ spl2_17 ),
inference(trivial_inequality_removal,[],[f758]) ).
thf(f760,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_17 ),
inference(avatar_contradiction_clause,[],[f759]) ).
thf(f761,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK8 @ Y0 )
=> ( sK0 @ ( sK0 @ sK8 ) @ Y0 ) )
@ ( sK10 @ ( sK0 @ sK8 ) ) ) )
| ~ spl2_8 ),
inference(sigma_proxy_clausification,[],[f298]) ).
thf(f762,plain,
( ( ( ( sK0 @ sK8 @ ( sK10 @ ( sK0 @ sK8 ) ) )
=> ( sK0 @ ( sK0 @ sK8 ) @ ( sK10 @ ( sK0 @ sK8 ) ) ) )
= $false )
| ~ spl2_8 ),
inference(beta-eta_normalization,[],[f761]) ).
thf(f769,plain,
( ( $true = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( sK0 @ sK8 @ Y0 ) ) )
= $false )
| ~ spl2_8 ),
inference(constrained_superposition,[],[f62,f762]) ).
thf(f772,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( sK0 @ sK8 @ Y0 ) ) )
= $false )
| ~ spl2_8 ),
inference(trivial_inequality_removal,[],[f769]) ).
thf(f807,plain,
( ( ( ^ [Y0: $i] :
( ( sK8 @ Y0 )
=> ( sK0 @ sK8 @ Y0 ) )
@ ( sK10 @ sK8 ) )
= $false )
| ~ spl2_8 ),
inference(sigma_proxy_clausification,[],[f772]) ).
thf(f808,plain,
( ( ( ( sK8 @ ( sK10 @ sK8 ) )
=> ( sK0 @ sK8 @ ( sK10 @ sK8 ) ) )
= $false )
| ~ spl2_8 ),
inference(beta-eta_normalization,[],[f807]) ).
thf(f809,plain,
( ( $true = $false )
| ~ spl2_1
| spl2_2
| ~ spl2_8 ),
inference(forward_demodulation,[],[f808,f263]) ).
thf(f810,plain,
( $false
| ~ spl2_1
| spl2_2
| ~ spl2_8 ),
inference(trivial_inequality_removal,[],[f809]) ).
thf(f811,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f810]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( ~ spl2_2
| ~ spl2_3
| spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f121]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_5 ),
inference(sat_conversion,[],[f196]) ).
cnf(s14,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f347]) ).
cnf(s17,plain,
( ~ spl2_2
| ~ spl2_6 ),
inference(sat_conversion,[],[f444]) ).
cnf(s26,plain,
( ~ spl2_1
| spl2_2
| spl2_8
| spl2_17 ),
inference(sat_conversion,[],[f744]) ).
cnf(s28,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_17 ),
inference(sat_conversion,[],[f760]) ).
cnf(s31,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_8 ),
inference(sat_conversion,[],[f811]) ).
cnf(s32,plain,
~ spl2_2,
inference(rat,[],[s2,s3,s6,s14,s17]) ).
cnf(s33,plain,
spl2_1,
inference(rat,[],[s1,s32]) ).
cnf(s35,plain,
~ spl2_17,
inference(rat,[],[s28,s32,s33]) ).
cnf(s36,plain,
~ spl2_8,
inference(rat,[],[s31,s32,s33]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s26,s33,s32,s35,s36]) ).
thf(f812,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV252^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.14 % Computer : n012.cluster.edu
% 0.07/0.14 % Model : x86_64 x86_64
% 0.07/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.14 % Memory : 8046.5625MB
% 0.07/0.14 % OS : Linux 6.8.0-71-generic
% 0.07/0.14 % CPULimit : 300
% 0.07/0.14 % WCLimit : 300
% 0.07/0.14 % DateTime : Tue Sep 29 15:27:19 UTC 2026
% 0.07/0.14 % CPUTime :
% 0.07/0.15 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 Running higher-order theorem proving
% 0.07/0.18 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.29 % (245042)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.39/0.29 % (245053)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.39/0.29 % (245053)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
% 0.39/0.29 % (245053)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=3739515355:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.39/0.29 % (245049)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1934823924:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.39/0.29 % (245048)lrs+10_16_si=on:nwc=1.5:random_seed=1461651948:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.39/0.29 % (245051)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2758057771:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.39/0.29 % (245047)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2964186665:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.39/0.29 % (245050)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=3529516448: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_3000 on theBenchmark for (3000ds/634Mi)
% 0.39/0.29 % (245052)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1287995145:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.39/0.29 % (245049)Instruction limit reached!
% 0.39/0.29 % (245049)------------------------------
% 0.39/0.29 % (245049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.29 % (245049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.29 % (245049)CaDiCaL version: 2.1.3
% 0.39/0.29 % (245049)Termination reason: Instruction limit
% 0.39/0.29 % (245049)Termination phase: Saturation
% 0.39/0.29 % (245049)Time elapsed: 0.002 s
% 0.39/0.29 % (245049)Peak memory usage: 12 MB
% 0.39/0.29 % (245049)Instructions burned: 3 (million)
% 0.39/0.29 % (245048)Instruction limit reached!
% 0.39/0.29 % (245048)------------------------------
% 0.39/0.29 % (245048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.29 % (245048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.29 % (245048)CaDiCaL version: 2.1.3
% 0.39/0.29 % (245048)Termination reason: Instruction limit
% 0.39/0.29 % (245048)Termination phase: Saturation
% 0.39/0.29 % (245048)Time elapsed: 0.010 s
% 0.39/0.29 % (245048)Peak memory usage: 12 MB
% 0.39/0.29 % (245048)Instructions burned: 20 (million)
% 0.39/0.29 % (245051)Instruction limit reached!
% 0.39/0.29 % (245051)------------------------------
% 0.39/0.29 % (245051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.29 % (245051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.29 % (245051)CaDiCaL version: 2.1.3
% 0.39/0.29 % (245051)Termination reason: Instruction limit
% 0.39/0.29 % (245051)Termination phase: Saturation
% 0.39/0.29 % (245051)Time elapsed: 0.012 s
% 0.39/0.29 % (245051)Peak memory usage: 11 MB
% 0.39/0.29 % (245051)Instructions burned: 26 (million)
% 0.39/0.29 % (245061)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3400102973:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.39/0.29 % (245061)Instruction limit reached!
% 0.39/0.29 % (245061)------------------------------
% 0.39/0.29 % (245061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.29 % (245061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.29 % (245061)CaDiCaL version: 2.1.3
% 0.39/0.29 % (245061)Termination reason: Instruction limit
% 0.39/0.29 % (245061)Termination phase: Saturation
% 0.39/0.29 % (245061)Time elapsed: 0.001 s
% 0.39/0.29 % (245061)Peak memory usage: 12 MB
% 0.39/0.29 % (245061)Instructions burned: 2 (million)
% 0.39/0.29 % (245064)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.39/0.29 % (245063)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=862587304:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.39/0.30 % (245064)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2552264649:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.39/0.30 % (245066)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1517168106:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.39/0.30 % (245063)Instruction limit reached!
% 0.39/0.30 % (245063)------------------------------
% 0.39/0.30 % (245063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245063)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245063)Termination reason: Instruction limit
% 0.39/0.30 % (245063)Termination phase: Saturation
% 0.39/0.30 % (245063)Time elapsed: 0.003 s
% 0.39/0.30 % (245063)Peak memory usage: 12 MB
% 0.39/0.30 % (245063)Instructions burned: 5 (million)
% 0.39/0.30 % (245064)Instruction limit reached!
% 0.39/0.30 % (245064)------------------------------
% 0.39/0.30 % (245064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245064)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245064)Termination reason: Instruction limit
% 0.39/0.30 % (245064)Termination phase: Saturation
% 0.39/0.30 % (245064)Time elapsed: 0.004 s
% 0.39/0.30 % (245064)Peak memory usage: 12 MB
% 0.39/0.30 % (245064)Instructions burned: 7 (million)
% 0.39/0.30 % (245052)Instruction limit reached!
% 0.39/0.30 % (245052)------------------------------
% 0.39/0.30 % (245052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245052)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245052)Termination reason: Instruction limit
% 0.39/0.30 % (245052)Termination phase: Saturation
% 0.39/0.30 % (245052)Time elapsed: 0.037 s
% 0.39/0.30 % (245052)Peak memory usage: 12 MB
% 0.39/0.30 % (245052)Instructions burned: 76 (million)
% 0.39/0.30 % (245066)Instruction limit reached!
% 0.39/0.30 % (245066)------------------------------
% 0.39/0.30 % (245066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245066)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245066)Termination reason: Instruction limit
% 0.39/0.30 % (245066)Termination phase: Saturation
% 0.39/0.30 % (245066)Time elapsed: 0.007 s
% 0.39/0.30 % (245066)Peak memory usage: 12 MB
% 0.39/0.30 % (245066)Instructions burned: 13 (million)
% 0.39/0.30 % (245047)Instruction limit reached!
% 0.39/0.30 % (245047)------------------------------
% 0.39/0.30 % (245047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245047)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245047)Termination reason: Instruction limit
% 0.39/0.30 % (245047)Termination phase: Saturation
% 0.39/0.30 % (245047)Time elapsed: 0.041 s
% 0.39/0.30 % (245047)Peak memory usage: 12 MB
% 0.39/0.30 % (245047)Instructions burned: 87 (million)
% 0.39/0.30 % (245071)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
% 0.39/0.30 % (245071)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.39/0.30 % (245073)lrs+10_1_si=on:cs=on:random_seed=3202746970:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.39/0.30 % (245071)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=474742672:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.39/0.30 % (245072)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=1687660182:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.39/0.30 % (245073)Instruction limit reached!
% 0.39/0.30 % (245073)------------------------------
% 0.39/0.30 % (245073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245073)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245073)Termination reason: Instruction limit
% 0.39/0.30 % (245073)Termination phase: Saturation
% 0.39/0.30 % (245073)Time elapsed: 0.003 s
% 0.39/0.30 % (245073)Peak memory usage: 12 MB
% 0.39/0.30 % (245073)Instructions burned: 8 (million)
% 0.39/0.30 % (245074)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.39/0.30 % (245074)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=3016429117:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.39/0.30 % (245074)Instruction limit reached!
% 0.39/0.30 % (245074)------------------------------
% 0.39/0.30 % (245074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245074)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245074)Termination reason: Instruction limit
% 0.39/0.30 % (245074)Termination phase: Saturation
% 0.39/0.30 % (245074)Time elapsed: 0.001 s
% 0.39/0.30 % (245074)Peak memory usage: 11 MB
% 0.39/0.30 % (245074)Instructions burned: 3 (million)
% 0.39/0.30 % (245075)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3106662871:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.39/0.30 % (245053)Instruction limit reached!
% 0.39/0.30 % (245053)------------------------------
% 0.39/0.30 % (245053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245053)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245053)Termination reason: Instruction limit
% 0.39/0.30 % (245053)Termination phase: Saturation
% 0.39/0.30 % (245053)Time elapsed: 0.070 s
% 0.39/0.30 % (245053)Peak memory usage: 12 MB
% 0.39/0.30 % (245053)Instructions burned: 158 (million)
% 0.39/0.30 % (245083)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=765201607:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.39/0.30 % (245071)Instruction limit reached!
% 0.39/0.30 % (245071)------------------------------
% 0.39/0.30 % (245071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245071)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245071)Termination reason: Instruction limit
% 0.39/0.30 % (245071)Termination phase: Saturation
% 0.39/0.30 % (245071)Time elapsed: 0.024 s
% 0.39/0.30 % (245071)Peak memory usage: 12 MB
% 0.39/0.30 % (245071)Instructions burned: 29 (million)
% 0.39/0.30 % (245083)Instruction limit reached!
% 0.39/0.30 % (245083)------------------------------
% 0.39/0.30 % (245083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245083)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245083)Termination reason: Instruction limit
% 0.39/0.30 % (245083)Termination phase: Saturation
% 0.39/0.30 % (245083)Time elapsed: 0.008 s
% 0.39/0.30 % (245083)Peak memory usage: 12 MB
% 0.39/0.30 % (245083)Instructions burned: 27 (million)
% 0.39/0.30 % (245075)Instruction limit reached!
% 0.39/0.30 % (245075)------------------------------
% 0.39/0.30 % (245075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245075)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245075)Termination reason: Instruction limit
% 0.39/0.30 % (245075)Termination phase: Saturation
% 0.39/0.30 % (245075)Time elapsed: 0.020 s
% 0.39/0.30 % (245075)Peak memory usage: 12 MB
% 0.39/0.30 % (245075)Instructions burned: 39 (million)
% 0.39/0.30 % (245087)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2656700723:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.39/0.30 % (245080)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3765299276:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.39/0.30 % (245072) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-245042-245072"...
% 0.39/0.30 % (245089)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=777751990:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.39/0.30 % (245087)Instruction limit reached!
% 0.39/0.30 % (245087)------------------------------
% 0.39/0.30 % (245087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245087)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245087)Termination reason: Instruction limit
% 0.39/0.30 % (245087)Termination phase: Saturation
% 0.39/0.30 % (245087)Time elapsed: 0.008 s
% 0.39/0.30 % (245087)Peak memory usage: 12 MB
% 0.39/0.30 % (245087)Instructions burned: 15 (million)
% 0.39/0.30 % (245072)...printing done.
% 0.39/0.30 % (245072)Refutation found. Thanks to Tanya!
% 0.39/0.30 % SZS status Theorem for theBenchmark
% 0.39/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.39/0.30 % (245072)------------------------------
% 0.39/0.30 % (245072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.30 % (245072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.30 % (245072)CaDiCaL version: 2.1.3
% 0.39/0.30 % (245072)Termination reason: Refutation
% 0.39/0.30 % (245072)Time elapsed: 0.038 s
% 0.39/0.30 % (245072)Peak memory usage: 13 MB
% 0.39/0.30 % (245072)Instructions burned: 76 (million)
% 0.39/0.30 % (245042)Success in time 0.111 s
% 0.39/0.30 % Vampire exiting
%------------------------------------------------------------------------------