%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU969^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:34:29 AM UTC 2026
% Result : Theorem 0.68s 0.36s
% Output : Refutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 18
% Syntax : Number of formulae : 175 ( 27 unt; 0 typ; 15 def)
% Number of atoms : 1125 ( 222 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 1453 ( 122 ~; 215 |; 53 &; 906 @)
% ( 15 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 21 con; 0-4 aty)
% ( 54 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 327 ( 57 sgn 62 !; 2 ?; 327 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_BLACK: $i > $i > $o ).
thf(func_def_3,type,
cCKB6_NUM: $i > $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
sK2: ( $i > $i > $o ) > $i ).
thf(func_def_18,type,
sK3: ( $i > $i > $o ) > $i ).
thf(func_def_19,type,
sK4: $i > $o ).
thf(func_def_20,type,
sK5: $i > $o ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( cCKB6_BLACK
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ( ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( ( X2 @ ( s @ X3 ) @ ( s @ X4 ) )
& ( X2 @ ( s @ ( s @ X3 ) ) @ X4 ) ) )
& ( X2 @ c1 @ c1 ) )
=> ( X2 @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_BLACK_def) ).
thf(f2,axiom,
( cCKB6_NUM
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_NUM_def) ).
thf(f3,conjecture,
! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( ( cCKB6_NUM @ X1 )
& ( cCKB6_NUM @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_L6000_pme) ).
thf(f4,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( ( cCKB6_NUM @ X1 )
& ( cCKB6_NUM @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( cCKB6_BLACK
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ( ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( ( X2 @ ( s @ X3 ) @ ( s @ X4 ) )
& ( X2 @ ( s @ ( s @ X3 ) ) @ X4 ) ) )
& ( X2 @ c1 @ c1 ) )
=> ( X2 @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( cCKB6_BLACK
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 )
& ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( cCKB6_NUM
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( ( cCKB6_NUM @ X1 )
& ( cCKB6_NUM @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ X0 @ X1 )
= $true )
=> ( ( ( cCKB6_NUM @ X1 )
= $true )
& ( ( cCKB6_NUM @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
? [X0: $i,X1: $i] :
( ( ( ( cCKB6_NUM @ X1 )
!= $true )
| ( ( cCKB6_NUM @ X0 )
!= $true ) )
& ( ( cCKB6_BLACK @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ( ( $true
!= ( cCKB6_NUM @ sK1 ) )
| ( $true
!= ( cCKB6_NUM @ sK0 ) ) )
& ( $true
= ( cCKB6_BLACK @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
thf(f13,plain,
( cCKB6_BLACK
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 )
& ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( $true
= ( cCKB6_BLACK @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( ( $true
!= ( cCKB6_NUM @ sK1 ) )
| ( $true
!= ( cCKB6_NUM @ sK0 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,plain,
( ( $true
!= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) )
| ( $true
!= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f16,f14,f14]) ).
thf(f20,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 )
& ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f15,f13]) ).
thf(f21,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 )
& ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) ) ) ) ) ) )
=> ( Y0 @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 )
& ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) ) ) ) ) ) )
=> ( Y0 @ sK0 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X1: $i > $i > $o] :
( $true
= ( ( ( X1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) )
=> ( X1 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( X1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(sigma_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 @ ( sK2 @ X1 ) )
=> ( ( X1 @ ( s @ ( s @ Y0 ) ) @ ( sK2 @ X1 ) )
& ( X1 @ ( s @ Y0 ) @ ( s @ ( sK2 @ X1 ) ) ) ) ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 @ ( sK2 @ X1 ) )
=> ( ( X1 @ ( s @ ( s @ Y0 ) ) @ ( sK2 @ X1 ) )
& ( X1 @ ( s @ Y0 ) @ ( s @ ( sK2 @ X1 ) ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(sigma_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( X1 @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) )
=> ( ( X1 @ ( s @ ( s @ ( sK3 @ X1 ) ) ) @ ( sK2 @ X1 ) )
& ( X1 @ ( s @ ( sK3 @ X1 ) ) @ ( s @ ( sK2 @ X1 ) ) ) ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( X1 @ ( s @ ( s @ ( sK3 @ X1 ) ) ) @ ( sK2 @ X1 ) )
& ( X1 @ ( s @ ( sK3 @ X1 ) ) @ ( s @ ( sK2 @ X1 ) ) ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f32,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( s @ ( s @ ( sK3 @ X1 ) ) ) @ ( sK2 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) )
| ( $false
= ( X1 @ ( s @ ( sK3 @ X1 ) ) @ ( s @ ( sK2 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f33,plain,
( ( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK1 ) ) ) )
| ( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f34,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK1 ) )
@ sK4 ) )
| ( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f33]) ).
thf(f35,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK1 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( ( $false
= ( ( ( sK4 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) )
=> ( sK4 @ sK1 ) ) )
| ( $false
= ( ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) )
=> ( sK5 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
( ( $false
= ( sK4 @ sK1 ) )
| ( $false
= ( ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) )
=> ( sK5 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( ( $true
= ( ( sK4 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) ) )
| ( $false
= ( ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) )
=> ( sK5 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f39,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) )
| ( $false
= ( ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) )
=> ( sK5 @ sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $true
= ( sK4 @ c1 ) )
| ( $false
= ( ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) )
=> ( sK5 @ sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f41,plain,
( ( $true
= ( sK4 @ c1 ) )
| ( $false
= ( sK5 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( $true
= ( sK4 @ c1 ) )
| ( $true
= ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f43,plain,
( ( $true
= ( sK4 @ c1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( sK4 @ c1 ) )
| ( $true
= ( sK5 @ c1 ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f45,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ c1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f46,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ c1 ) )
| ( $true
= ( ( sK5 @ X1 )
=> ( sK5 @ ( s @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ c1 ) )
| ( $false
= ( sK5 @ X1 ) )
| ( $true
= ( sK5 @ ( s @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) )
=> ( sK5 @ sK0 ) ) ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f49,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( sK5 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f51,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( sK5 @ c1 ) ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f53,plain,
! [X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ X1 ) ) ) )
| ( $true
= ( sK5 @ c1 ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ X1 ) )
| ( $true
= ( sK5 @ c1 ) )
| ( $true
= ( sK4 @ ( s @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ X1 ) ) ) )
| ( $true
= ( ( sK5 @ X2 )
=> ( sK5 @ ( s @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK4 @ X1 ) )
| ( $true
= ( ( sK5 @ X2 )
=> ( sK5 @ ( s @ X2 ) ) ) )
| ( $true
= ( sK4 @ ( s @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK4 @ X1 ) )
| ( $false
= ( sK5 @ X2 ) )
| ( $true
= ( sK4 @ ( s @ X1 ) ) )
| ( $true
= ( sK5 @ ( s @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ X1 ) ) ) )
| ( $false
= ( sK5 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f60,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ X1 ) )
| ( $false
= ( sK5 @ sK0 ) )
| ( $true
= ( sK4 @ ( s @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f61,plain,
( ( $false
= ( sK4 @ sK1 ) )
| ( $false
= ( sK5 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f62,plain,
( ( $false
= ( sK4 @ sK1 ) )
| ( $true
= ( ( sK5 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f63,plain,
( ( $false
= ( sK4 @ sK1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( ( $false
= ( sK4 @ sK1 ) )
| ( $true
= ( sK5 @ c1 ) ) ),
inference(and_proxy_clausification,[],[f62]) ).
thf(f65,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( s @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f66,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK1 ) )
| ( $true
= ( ( sK5 @ X1 )
=> ( sK5 @ ( s @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK1 ) )
| ( $false
= ( sK5 @ X1 ) )
| ( $true
= ( sK5 @ ( s @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f66]) ).
thf(f69,definition,
( spl6_1
<=> ( $true
= ( sK5 @ c1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f71,plain,
( ( $true
= ( sK5 @ c1 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f73,definition,
( spl6_2
<=> ( $true
= ( sK4 @ c1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f75,plain,
( ( $true
= ( sK4 @ c1 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f76,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f44,f73,f69]) ).
thf(f78,definition,
( spl6_3
<=> ! [X1: $i] :
( ( $false
= ( sK5 @ X1 ) )
| ( $true
= ( sK5 @ ( s @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f79,plain,
( ! [X1: $i] :
( ( $true
= ( sK5 @ ( s @ X1 ) ) )
| ( $false
= ( sK5 @ X1 ) ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f80,plain,
( spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f47,f73,f78]) ).
thf(f82,definition,
( spl6_4
<=> ( $false
= ( sK5 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f84,plain,
( ( $false
= ( sK5 @ sK0 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f85,plain,
( spl6_4
| spl6_2 ),
inference(avatar_split_clause,[],[f41,f73,f82]) ).
thf(f87,definition,
( spl6_5
<=> ! [X1: $i] :
( ( $false
= ( sK4 @ X1 ) )
| ( $true
= ( sK4 @ ( s @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f88,plain,
( ! [X1: $i] :
( ( $true
= ( sK4 @ ( s @ X1 ) ) )
| ( $false
= ( sK4 @ X1 ) ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f89,plain,
( spl6_1
| spl6_5 ),
inference(avatar_split_clause,[],[f54,f87,f69]) ).
thf(f90,plain,
( spl6_3
| spl6_5 ),
inference(avatar_split_clause,[],[f58,f87,f78]) ).
thf(f91,plain,
( spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f60,f87,f82]) ).
thf(f93,definition,
( spl6_6
<=> ( $false
= ( sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f95,plain,
( ( $false
= ( sK4 @ sK1 ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f96,plain,
( spl6_1
| spl6_6 ),
inference(avatar_split_clause,[],[f64,f93,f69]) ).
thf(f97,plain,
( spl6_3
| spl6_6 ),
inference(avatar_split_clause,[],[f67,f93,f78]) ).
thf(f98,plain,
( spl6_4
| spl6_6 ),
inference(avatar_split_clause,[],[f61,f93,f82]) ).
thf(f110,plain,
! [X0: $i > $i > $o] :
( ( $true
!= ( X0 @ c1 @ c1 ) )
| ( $true
= ( X0 @ sK0 @ sK1 ) )
| ( $false
= ( X0 @ c1 @ c1 ) )
| ( $false
!= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) ),
inference(equality_factoring,[],[f31]) ).
thf(f195,plain,
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $true = $false )
| ( $false
!= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f110,f75]) ).
thf(f212,plain,
( ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
!= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f213,plain,
( ( $true
= ( sK4 @ sK1 ) )
| ( $false
!= ( sK4
@ ( sK2
@ ^ [Y0: $i] : sK4 ) ) )
| ~ spl6_2 ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f250,definition,
( spl6_11
<=> ( $false
= ( sK4
@ ( sK2
@ ^ [Y0: $i] : sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
thf(f252,plain,
( ( $false
!= ( sK4
@ ( sK2
@ ^ [Y0: $i] : sK4 ) ) )
| spl6_11 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f254,definition,
( spl6_12
<=> ( $true
= ( sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition]) ).
thf(f256,plain,
( ( $true
= ( sK4 @ sK1 ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f254]) ).
thf(f257,plain,
( ~ spl6_11
| spl6_12
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f213,f73,f254,f250]) ).
thf(f350,plain,
( ( $false != $false )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) )
@ ( s
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) ) )
| spl6_11 ),
inference(constrained_superposition,[],[f252,f32]) ).
thf(f400,plain,
( ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) )
@ ( s
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) ) )
| spl6_11 ),
inference(trivial_inequality_removal,[],[f350]) ).
thf(f401,plain,
( ( $true
= ( sK4 @ sK1 ) )
| ( $false
= ( sK4 @ c1 ) )
| ( $false
= ( sK4
@ ( s
@ ( sK2
@ ^ [Y0: $i] : sK4 ) ) ) )
| spl6_11 ),
inference(beta-eta_normalization,[],[f400]) ).
thf(f454,definition,
( spl6_15
<=> ( $false
= ( sK4
@ ( s
@ ( sK2
@ ^ [Y0: $i] : sK4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_15])],[avatar_definition]) ).
thf(f456,plain,
( ( $false
= ( sK4
@ ( s
@ ( sK2
@ ^ [Y0: $i] : sK4 ) ) ) )
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f454]) ).
thf(f458,definition,
( spl6_16
<=> ( $false
= ( sK4 @ c1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_16])],[avatar_definition]) ).
thf(f460,plain,
( ( $false
= ( sK4 @ c1 ) )
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f458]) ).
thf(f461,plain,
( spl6_15
| spl6_16
| spl6_12
| spl6_11 ),
inference(avatar_split_clause,[],[f401,f250,f254,f458,f454]) ).
thf(f472,plain,
( ( $true = $false )
| ~ spl6_6
| ~ spl6_12 ),
inference(constrained_superposition,[],[f256,f95]) ).
thf(f489,plain,
( $false
| ~ spl6_6
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f472]) ).
thf(f490,plain,
( ~ spl6_6
| ~ spl6_12 ),
inference(avatar_contradiction_clause,[],[f489]) ).
thf(f514,plain,
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $true = $false )
| ( $false
!= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f110,f71]) ).
thf(f521,plain,
( ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
!= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f522,plain,
( ( $true
= ( sK5 @ sK0 ) )
| ( $false
!= ( sK5
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) ) )
| ~ spl6_1 ),
inference(beta-eta_normalization,[],[f521]) ).
thf(f540,definition,
( spl6_21
<=> ( $false
= ( sK5
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_21])],[avatar_definition]) ).
thf(f544,definition,
( spl6_22
<=> ( $true
= ( sK5 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_22])],[avatar_definition]) ).
thf(f546,plain,
( ( $true
= ( sK5 @ sK0 ) )
| ~ spl6_22 ),
inference(avatar_component_clause,[],[f544]) ).
thf(f547,plain,
( ~ spl6_21
| spl6_22
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f522,f69,f544,f540]) ).
thf(f608,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK5 @ X0 ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) )
@ ( s
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) ) ) )
| ( ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) )
!= X0 ) )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f79,f32]) ).
thf(f623,plain,
( ! [X0: $i] :
( ( $false
= ( sK5 @ X0 ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) )
@ ( s
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK5
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) ) ) )
| ( ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) )
!= X0 ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f608]) ).
thf(f624,plain,
( ! [X0: $i] :
( ( $false
= ( sK5 @ X0 ) )
| ( $true
= ( sK5 @ sK0 ) )
| ( $false
= ( sK5 @ c1 ) )
| ( $false
= ( sK5
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) ) ) )
| ( ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) )
!= X0 ) )
| ~ spl6_3 ),
inference(beta-eta_normalization,[],[f623]) ).
thf(f626,definition,
( spl6_23
<=> ! [X0: $i] :
( ( $false
= ( sK5 @ X0 ) )
| ( ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) )
!= X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_23])],[avatar_definition]) ).
thf(f627,plain,
( ! [X0: $i] :
( ( ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) )
!= X0 )
| ( $false
= ( sK5 @ X0 ) ) )
| ~ spl6_23 ),
inference(avatar_component_clause,[],[f626]) ).
thf(f629,definition,
( spl6_24
<=> ( $false
= ( sK5
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_24])],[avatar_definition]) ).
thf(f631,plain,
( ( $false
= ( sK5
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) ) ) )
| ~ spl6_24 ),
inference(avatar_component_clause,[],[f629]) ).
thf(f633,definition,
( spl6_25
<=> ( $false
= ( sK5 @ c1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_25])],[avatar_definition]) ).
thf(f635,plain,
( ( $false
= ( sK5 @ c1 ) )
| ~ spl6_25 ),
inference(avatar_component_clause,[],[f633]) ).
thf(f637,plain,
( spl6_24
| spl6_25
| spl6_22
| spl6_23
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f624,f78,f626,f544,f633,f629]) ).
thf(f687,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_25 ),
inference(constrained_superposition,[],[f635,f71]) ).
thf(f697,plain,
( $false
| ~ spl6_1
| ~ spl6_25 ),
inference(trivial_inequality_removal,[],[f687]) ).
thf(f698,plain,
( ~ spl6_1
| ~ spl6_25 ),
inference(avatar_contradiction_clause,[],[f697]) ).
thf(f1174,plain,
( ( $false
= ( sK5
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) ) ) )
| ~ spl6_23 ),
inference(equality_resolution,[],[f627]) ).
thf(f1175,plain,
( spl6_24
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f1174,f626,f629]) ).
thf(f1178,plain,
( ( $true = $false )
| ~ spl6_4
| ~ spl6_22 ),
inference(constrained_superposition,[],[f546,f84]) ).
thf(f1198,plain,
( $false
| ~ spl6_4
| ~ spl6_22 ),
inference(trivial_inequality_removal,[],[f1178]) ).
thf(f1199,plain,
( ~ spl6_4
| ~ spl6_22 ),
inference(avatar_contradiction_clause,[],[f1198]) ).
thf(f1222,plain,
( ( $true = $false )
| ( $false
= ( sK5
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) ) )
| ~ spl6_3
| ~ spl6_24 ),
inference(constrained_superposition,[],[f79,f631]) ).
thf(f1223,plain,
( ( $false
= ( sK5
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK5 @ Y0 ) ) ) )
| ~ spl6_3
| ~ spl6_24 ),
inference(trivial_inequality_removal,[],[f1222]) ).
thf(f1233,plain,
( spl6_21
| ~ spl6_3
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f1223,f629,f78,f540]) ).
thf(f1330,plain,
( ( $true = $false )
| ( $false
= ( sK4
@ ( sK2
@ ^ [Y0: $i] : sK4 ) ) )
| ~ spl6_5
| ~ spl6_15 ),
inference(constrained_superposition,[],[f88,f456]) ).
thf(f1331,plain,
( ( $false
= ( sK4
@ ( sK2
@ ^ [Y0: $i] : sK4 ) ) )
| ~ spl6_5
| ~ spl6_15 ),
inference(trivial_inequality_removal,[],[f1330]) ).
thf(f1341,plain,
( spl6_11
| ~ spl6_5
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f1331,f454,f87,f250]) ).
thf(f1343,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_16 ),
inference(constrained_superposition,[],[f460,f75]) ).
thf(f1359,plain,
( $false
| ~ spl6_2
| ~ spl6_16 ),
inference(trivial_inequality_removal,[],[f1343]) ).
thf(f1360,plain,
( ~ spl6_2
| ~ spl6_16 ),
inference(avatar_contradiction_clause,[],[f1359]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f76]) ).
cnf(s2,plain,
( spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f80]) ).
cnf(s3,plain,
( spl6_2
| spl6_4 ),
inference(sat_conversion,[],[f85]) ).
cnf(s4,plain,
( spl6_1
| spl6_5 ),
inference(sat_conversion,[],[f89]) ).
cnf(s5,plain,
( spl6_3
| spl6_5 ),
inference(sat_conversion,[],[f90]) ).
cnf(s6,plain,
( spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f91]) ).
cnf(s7,plain,
( spl6_1
| spl6_6 ),
inference(sat_conversion,[],[f96]) ).
cnf(s8,plain,
( spl6_3
| spl6_6 ),
inference(sat_conversion,[],[f97]) ).
cnf(s9,plain,
( spl6_4
| spl6_6 ),
inference(sat_conversion,[],[f98]) ).
cnf(s12,plain,
( ~ spl6_2
| ~ spl6_11
| spl6_12 ),
inference(sat_conversion,[],[f257]) ).
cnf(s15,plain,
( spl6_11
| spl6_12
| spl6_15
| spl6_16 ),
inference(sat_conversion,[],[f461]) ).
cnf(s19,plain,
( ~ spl6_6
| ~ spl6_12 ),
inference(sat_conversion,[],[f490]) ).
cnf(s21,plain,
( ~ spl6_1
| ~ spl6_21
| spl6_22 ),
inference(sat_conversion,[],[f547]) ).
cnf(s23,plain,
( ~ spl6_3
| spl6_22
| spl6_23
| spl6_24
| spl6_25 ),
inference(sat_conversion,[],[f637]) ).
cnf(s28,plain,
( ~ spl6_1
| ~ spl6_25 ),
inference(sat_conversion,[],[f698]) ).
cnf(s35,plain,
( ~ spl6_23
| spl6_24 ),
inference(sat_conversion,[],[f1175]) ).
cnf(s37,plain,
( ~ spl6_4
| ~ spl6_22 ),
inference(sat_conversion,[],[f1199]) ).
cnf(s38,plain,
( ~ spl6_3
| spl6_21
| ~ spl6_24 ),
inference(sat_conversion,[],[f1233]) ).
cnf(s41,plain,
( ~ spl6_5
| spl6_11
| ~ spl6_15 ),
inference(sat_conversion,[],[f1341]) ).
cnf(s44,plain,
( ~ spl6_2
| ~ spl6_16 ),
inference(sat_conversion,[],[f1360]) ).
cnf(s45,plain,
spl6_1,
inference(rat,[],[s15,s41,s12,s44,s19,s1,s4,s7]) ).
cnf(s46,plain,
~ spl6_25,
inference(rat,[],[s28,s45]) ).
cnf(s47,plain,
spl6_2,
inference(rat,[],[s23,s35,s38,s21,s37,s2,s3,s46,s45]) ).
cnf(s48,plain,
~ spl6_16,
inference(rat,[],[s44,s47]) ).
cnf(s49,plain,
( spl6_22
| ~ spl6_3 ),
inference(rat,[],[s23,s35,s38,s21,s46,s45]) ).
cnf(s50,plain,
spl6_4,
inference(rat,[],[s15,s41,s12,s19,s6,s9,s48,s47]) ).
cnf(s51,plain,
~ spl6_22,
inference(rat,[],[s37,s50]) ).
cnf(s53,plain,
~ spl6_3,
inference(rat,[],[s49,s51]) ).
cnf(s54,plain,
spl6_6,
inference(rat,[],[s8,s53]) ).
cnf(s55,plain,
spl6_5,
inference(rat,[],[s5,s53]) ).
cnf(s56,plain,
~ spl6_12,
inference(rat,[],[s19,s54]) ).
cnf(s57,plain,
~ spl6_11,
inference(rat,[],[s12,s47,s56]) ).
cnf(s58,plain,
~ spl6_15,
inference(rat,[],[s41,s55,s57]) ).
cnf(s59,plain,
$false,
inference(rat,[],[s15,s48,s56,s58,s57]) ).
thf(f1362,plain,
$false,
inference(avatar_sat_refutation,[],[s59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU969^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n011.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 14:53:41 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.68/0.36 % (186278)Will run a generic schedule for satisfiability detection.
% 0.68/0.36 % (186286)dis+10_1_sil=32000:sp=arity:random_seed=1423078273:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.68/0.36 % (186284)% WARNING: option uhcvi not known.
% 0.68/0.36 % (186283)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1231423408_2999 on theBenchmark for (2999ds/0Mi)
% 0.68/0.36 % (186284)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2904539349:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.68/0.36 % (186285)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=929275478:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.68/0.36 % (186287)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3906431244:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.68/0.36 % (186288)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=243439117:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.68/0.36 % (186289)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1289435707:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.68/0.36 % (186284)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.68/0.36 % (186287)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.68/0.36 % Exception at run slice level
% 0.68/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.68/0.36 % (186284)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.68/0.36 % (186286)Instruction limit reached!
% 0.68/0.36 % (186286)------------------------------
% 0.68/0.36 % (186286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.36 % (186286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.36 % (186286)CaDiCaL version: 2.1.3
% 0.68/0.36 % (186286)Termination reason: Instruction limit
% 0.68/0.36 % (186286)Termination phase: Saturation
% 0.68/0.36 % (186286)Time elapsed: 0.027 s
% 0.68/0.36 % (186286)Peak memory usage: 12 MB
% 0.68/0.36 % (186286)Instructions burned: 103 (million)
% 0.68/0.36 % (186297)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3602974362:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.68/0.36 % Exception at run slice level
% 0.68/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.68/0.36 % (186298)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4140353964:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.68/0.36 % (186300)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3015658575:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.68/0.36 % (186300)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.68/0.36 % (186300)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.68/0.36 % (186287)Instruction limit reached!
% 0.68/0.36 % (186287)------------------------------
% 0.68/0.36 % (186287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.36 % (186287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.36 % (186287)CaDiCaL version: 2.1.3
% 0.68/0.36 % (186287)Termination reason: Instruction limit
% 0.68/0.36 % (186287)Termination phase: Saturation
% 0.68/0.36 % (186287)Time elapsed: 0.056 s
% 0.68/0.36 % (186287)Peak memory usage: 12 MB
% 0.68/0.36 % (186287)Instructions burned: 116 (million)
% 0.68/0.36 % (186289) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-186278-186289"...
% 0.68/0.36 % (186288)Instruction limit reached!
% 0.68/0.36 % (186288)------------------------------
% 0.68/0.36 % (186288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.36 % (186288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.36 % (186288)CaDiCaL version: 2.1.3
% 0.68/0.36 % (186288)Termination reason: Instruction limit
% 0.68/0.36 % (186288)Termination phase: Saturation
% 0.68/0.36 % (186288)Time elapsed: 0.063 s
% 0.68/0.36 % (186288)Peak memory usage: 12 MB
% 0.68/0.36 % (186288)Instructions burned: 133 (million)
% 0.68/0.36 % (186298)Instruction limit reached!
% 0.68/0.36 % (186298)------------------------------
% 0.68/0.36 % (186298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.36 % (186298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.36 % (186298)CaDiCaL version: 2.1.3
% 0.68/0.36 % (186298)Termination reason: Instruction limit
% 0.68/0.36 % (186298)Termination phase: Saturation
% 0.68/0.36 % (186298)Time elapsed: 0.035 s
% 0.68/0.36 % (186298)Peak memory usage: 12 MB
% 0.68/0.36 % (186298)Instructions burned: 134 (million)
% 0.68/0.36 % (186289)...printing done.
% 0.68/0.36 % (186289)Refutation found. Thanks to Tanya!
% 0.68/0.36 % SZS status Theorem for theBenchmark
% 0.68/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.68/0.37 % (186289)------------------------------
% 0.68/0.37 % (186289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.37 % (186289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.37 % (186289)CaDiCaL version: 2.1.3
% 0.68/0.37 % (186289)Termination reason: Refutation
% 0.68/0.37 % (186289)Time elapsed: 0.066 s
% 0.68/0.37 % (186289)Peak memory usage: 13 MB
% 0.68/0.37 % (186289)Instructions burned: 126 (million)
% 0.68/0.37 % (186278)Success in time 0.104 s
% 0.68/0.37 % Vampire exiting
%------------------------------------------------------------------------------