%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ113^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:21:04 AM UTC 2026
% Result : Theorem 5.48s 1.08s
% Output : Refutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 4
% Syntax : Number of formulae : 89 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 837 ( 188 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 1476 ( 75 ~; 135 |; 42 &;1144 @)
% ( 2 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 8 con; 0-4 aty)
% ( 38 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 342 ( 50 sgn 72 !; 2 ?; 342 :)
% 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_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK2: ( $i > $i > $o ) > $i ).
thf(func_def_17,type,
sK3: ( $i > $i > $o ) > $i ).
thf(func_def_18,type,
sK4: $i > $i > $o ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK6: ( $i > $i > $o ) > $i ).
thf(func_def_24,type,
sK7: ( $i > $i > $o ) > $i ).
thf(func_def_25,type,
sK8: ( $i > $i > $i ) > $i ).
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/sandbox2/benchmark/theBenchmark.p',cCKB6_BLACK_def) ).
thf(f2,conjecture,
! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_L11000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,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(f5,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,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ X0 @ X1 )
= $true )
=> ( ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) )
!= $true )
& ( ( cCKB6_BLACK @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( cCKB6_BLACK @ ( s @ ( s @ sK0 ) ) @ ( s @ ( s @ sK1 ) ) ) )
& ( $true
= ( cCKB6_BLACK @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,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,[],[f5]) ).
thf(f11,plain,
( $true
= ( cCKB6_BLACK @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
!= ( cCKB6_BLACK @ ( s @ ( s @ sK0 ) ) @ ( s @ ( s @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,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 ) ) )
@ ( s @ ( s @ sK0 ) )
@ ( s @ ( s @ sK1 ) ) ) ),
inference(definition_unfolding,[],[f12,f10]) ).
thf(f16,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,[],[f11,f10]) ).
thf(f17,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,[],[f16]) ).
thf(f18,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,[],[f17]) ).
thf(f19,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,[],[f18]) ).
thf(f20,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,[],[f19]) ).
thf(f21,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,[],[f20]) ).
thf(f22,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,[],[f21]) ).
thf(f23,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,[],[f22]) ).
thf(f24,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,[],[f23]) ).
thf(f25,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,[],[f24]) ).
thf(f26,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,[],[f25]) ).
thf(f27,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 @ sK1 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f28,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,[],[f26]) ).
thf(f29,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 @ ( s @ ( s @ sK0 ) ) @ ( s @ ( s @ sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f30,plain,
( $false
= ( ^ [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 @ ( s @ ( s @ sK0 ) ) @ ( s @ ( s @ sK1 ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( $false
= ( ( ( sK4 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( sK4 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( sK4 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) )
=> ( sK4 @ ( s @ ( s @ sK0 ) ) @ ( s @ ( s @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
( $false
= ( sK4 @ ( s @ ( s @ sK0 ) ) @ ( s @ ( s @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( $true
= ( ( sK4 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( sK4 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( sK4 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( sK4 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( sK4 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f35,plain,
( $true
= ( sK4 @ c1 @ c1 ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( sK4 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( sK4 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 @ X1 )
=> ( ( sK4 @ ( s @ ( s @ Y0 ) ) @ X1 )
& ( sK4 @ ( s @ Y0 ) @ ( s @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 @ X1 )
=> ( ( sK4 @ ( s @ ( s @ Y0 ) ) @ X1 )
& ( sK4 @ ( s @ Y0 ) @ ( s @ X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK4 @ X2 @ X1 )
=> ( ( sK4 @ ( s @ ( s @ X2 ) ) @ X1 )
& ( sK4 @ ( s @ X2 ) @ ( s @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK4 @ X2 @ X1 ) )
| ( $true
= ( ( sK4 @ ( s @ ( s @ X2 ) ) @ X1 )
& ( sK4 @ ( s @ X2 ) @ ( s @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ ( s @ X2 ) @ ( s @ X1 ) ) )
| ( $false
= ( sK4 @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ ( s @ ( s @ X2 ) ) @ X1 ) )
| ( $false
= ( sK4 @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f53,plain,
( ( $true = $false )
| ( $false
= ( sK4 @ ( s @ sK0 ) @ ( s @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f32,f41]) ).
thf(f54,plain,
( $false
= ( sK4 @ ( s @ sK0 ) @ ( s @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f105,plain,
( ( $true = $false )
| ( $false
= ( sK4 @ sK0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f41,f54]) ).
thf(f109,plain,
( $false
= ( sK4 @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f298,plain,
! [X2: $i,X0: $i > $i > $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ c1
@ c1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( s
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( sK4 @ X1 @ X2 ) )
| ( ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) )
!= X1 )
| ( ( X0
@ ( s
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X2 ) ),
inference(constrained_superposition,[],[f28,f42]) ).
thf(f302,plain,
! [X2: $i,X0: $i > $i > $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ c1
@ c1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( s
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( sK4 @ X1 @ X2 ) )
| ( ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) )
!= X1 )
| ( ( X0
@ ( s
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X2 ) ),
inference(trivial_inequality_removal,[],[f298]) ).
thf(f303,plain,
! [X2: $i,X0: $i > $i > $i,X1: $i] :
( ( ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) )
!= X1 )
| ( $false
= ( sK4 @ c1 @ ( X0 @ c1 @ c1 ) ) )
| ( $false
= ( sK4
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( X0
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( s
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( sK4 @ X1 @ X2 ) )
| ( $true
= ( sK4 @ sK0 @ ( X0 @ sK0 @ sK1 ) ) )
| ( ( X0
@ ( s
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X2 ) ),
inference(beta-eta_normalization,[],[f302]) ).
thf(f827,plain,
! [X0: $i > $i > $i,X1: $i] :
( ( $false
= ( sK4
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $false
= ( sK4
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( X0
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( s
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( sK4 @ c1 @ ( X0 @ c1 @ c1 ) ) )
| ( $true
= ( sK4 @ sK0 @ ( X0 @ sK0 @ sK1 ) ) )
| ( ( X0
@ ( s
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 ) ),
inference(equality_resolution,[],[f303]) ).
thf(f848,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK4
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
@ ( sK2 @ X0 ) ) )
| ( $false
= ( sK4
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
@ X1 ) )
| ( $false
= ( sK4 @ c1
@ ( ^ [Y0: $i,Y1: $i] : Y1
@ c1
@ c1 ) ) )
| ( $true
= ( sK4 @ sK0
@ ( ^ [Y0: $i,Y1: $i] : Y1
@ sK0
@ sK1 ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y1
@ ( s
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) )
!= X1 )
| ( sK4 != X0 ) ),
inference(constrained_superposition,[],[f41,f827]) ).
thf(f868,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( sK4
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
@ ( sK2 @ X0 ) ) )
| ( $false
= ( sK4
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
@ X1 ) )
| ( $false
= ( sK4 @ c1
@ ( ^ [Y0: $i,Y1: $i] : Y1
@ c1
@ c1 ) ) )
| ( $true
= ( sK4 @ sK0
@ ( ^ [Y0: $i,Y1: $i] : Y1
@ sK0
@ sK1 ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y1
@ ( s
@ ( s
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) )
!= X1 )
| ( sK4 != X0 ) ),
inference(trivial_inequality_removal,[],[f848]) ).
thf(f869,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( $false
= ( sK4 @ c1 @ c1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( sK4 != X0 ) ),
inference(beta-eta_normalization,[],[f868]) ).
thf(f905,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( sK4 != X0 ) ),
inference(forward_demodulation,[],[f869,f35]) ).
thf(f906,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( sK4 != X0 ) ),
inference(trivial_inequality_removal,[],[f905]) ).
thf(f913,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( sK4 != X0 ) ),
inference(forward_demodulation,[],[f906,f109]) ).
thf(f914,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( sK4 != X0 ) ),
inference(trivial_inequality_removal,[],[f913]) ).
thf(f926,definition,
( spl5_6
<=> ! [X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( ( sK2 @ sK4 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f927,plain,
( ! [X1: $i] :
( ( ( sK2 @ sK4 )
!= X1 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f926]) ).
thf(f929,definition,
( spl5_7
<=> ! [X0: $i > $i > $o] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f930,plain,
( ! [X0: $i > $i > $o] :
( ( sK4 != X0 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f929]) ).
thf(f931,plain,
( spl5_6
| spl5_7 ),
inference(avatar_split_clause,[],[f914,f929,f926]) ).
thf(f932,plain,
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ sK4 ) ) )
| ~ spl5_6 ),
inference(equality_resolution,[],[f927]) ).
thf(f939,plain,
( ! [X0: $i > $i > $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y0 )
!= X0 )
| ( ( sK3 @ sK4 )
!= ( X0
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
| ~ spl5_6 ),
inference(constrained_superposition,[],[f27,f932]) ).
thf(f955,plain,
( ! [X0: $i > $i > $i] :
( ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y0 )
!= X0 )
| ( ( sK3 @ sK4 )
!= ( X0
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f939]) ).
thf(f956,plain,
( ! [X0: $i > $i > $i] :
( ( ( sK3 @ sK4 )
!= ( X0
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) ) ) )
| ( $false
= ( sK4 @ ( X0 @ c1 @ c1 ) @ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y0 )
!= X0 )
| ( $true
= ( sK4 @ ( X0 @ sK0 @ sK1 ) @ sK1 ) ) )
| ~ spl5_6 ),
inference(beta-eta_normalization,[],[f955]) ).
thf(f975,plain,
( ( $false
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ c1
@ c1 )
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y0 )
!= ( ^ [Y0: $i,Y1: $i] : Y0 ) )
| ( $true
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ sK0
@ sK1 )
@ sK1 ) )
| ~ spl5_6 ),
inference(equality_resolution,[],[f956]) ).
thf(f978,plain,
( ( $false
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ c1
@ c1 )
@ c1 ) )
| ( $true
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ sK0
@ sK1 )
@ sK1 ) )
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f975]) ).
thf(f979,plain,
( ( $false
= ( sK4 @ c1 @ c1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_6 ),
inference(beta-eta_normalization,[],[f978]) ).
thf(f981,plain,
( ( $true = $false )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_6 ),
inference(forward_demodulation,[],[f979,f35]) ).
thf(f982,plain,
( ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f981]) ).
thf(f983,plain,
( ( $true = $false )
| ~ spl5_6 ),
inference(forward_demodulation,[],[f982,f109]) ).
thf(f984,plain,
( $false
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f983]) ).
thf(f985,plain,
~ spl5_6,
inference(avatar_contradiction_clause,[],[f984]) ).
thf(f993,plain,
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ sK4 ) ) )
| ~ spl5_7 ),
inference(equality_resolution,[],[f930]) ).
thf(f1000,plain,
( ! [X0: $i > $i > $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y0 )
!= X0 )
| ( ( sK3 @ sK4 )
!= ( X0
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
| ~ spl5_7 ),
inference(constrained_superposition,[],[f27,f993]) ).
thf(f1016,plain,
( ! [X0: $i > $i > $i] :
( ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK4 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y0 )
!= X0 )
| ( ( sK3 @ sK4 )
!= ( X0
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1000]) ).
thf(f1017,plain,
( ! [X0: $i > $i > $i] :
( ( ( sK3 @ sK4 )
!= ( X0
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ ( X0 @ Y0 @ Y1 ) @ Y1 ) ) ) )
| ( $false
= ( sK4 @ ( X0 @ c1 @ c1 ) @ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y0 )
!= X0 )
| ( $true
= ( sK4 @ ( X0 @ sK0 @ sK1 ) @ sK1 ) ) )
| ~ spl5_7 ),
inference(beta-eta_normalization,[],[f1016]) ).
thf(f1903,plain,
( ( $false
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ c1
@ c1 )
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y0 )
!= ( ^ [Y0: $i,Y1: $i] : Y0 ) )
| ( $true
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ sK0
@ sK1 )
@ sK1 ) )
| ~ spl5_7 ),
inference(equality_resolution,[],[f1017]) ).
thf(f1906,plain,
( ( $false
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ c1
@ c1 )
@ c1 ) )
| ( $true
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ sK0
@ sK1 )
@ sK1 ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1903]) ).
thf(f1907,plain,
( ( $false
= ( sK4 @ c1 @ c1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_7 ),
inference(beta-eta_normalization,[],[f1906]) ).
thf(f1909,plain,
( ( $true = $false )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_7 ),
inference(forward_demodulation,[],[f1907,f35]) ).
thf(f1910,plain,
( ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1909]) ).
thf(f1911,plain,
( ( $true = $false )
| ~ spl5_7 ),
inference(forward_demodulation,[],[f1910,f109]) ).
thf(f1912,plain,
( $false
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1911]) ).
thf(f1913,plain,
~ spl5_7,
inference(avatar_contradiction_clause,[],[f1912]) ).
cnf(s4,plain,
( spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f931]) ).
cnf(s5,plain,
~ spl5_6,
inference(sat_conversion,[],[f985]) ).
cnf(s13,plain,
~ spl5_7,
inference(sat_conversion,[],[f1913]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s4,s13,s5]) ).
thf(f1914,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ113^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:26:41 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.48/1.08 % (59161)Will run a generic schedule for satisfiability detection.
% 5.48/1.08 % (59166)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=906296664_2999 on theBenchmark for (2999ds/0Mi)
% 5.48/1.08 % (59169)dis+10_1_sil=32000:sp=arity:random_seed=2616207453:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59172)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=345611769:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.48/1.08 % (59167)% WARNING: option uhcvi not known.
% 5.48/1.08 % (59167)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1803693148:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.48/1.08 % (59167)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.48/1.08 % (59168)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=712998789:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.48/1.08 % (59167)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.48/1.08 % (59170)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4099606764:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.48/1.08 % (59170)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.48/1.08 % (59171)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1289555609:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.48/1.08 % (59175)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2403780085:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59182)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1731905193:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.48/1.08 % (59169)Instruction limit reached!
% 5.48/1.08 % (59169)------------------------------
% 5.48/1.08 % (59169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59169)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59169)Termination reason: Instruction limit
% 5.48/1.08 % (59169)Termination phase: Saturation
% 5.48/1.08 % (59169)Time elapsed: 0.046 s
% 5.48/1.08 % (59169)Peak memory usage: 12 MB
% 5.48/1.08 % (59169)Instructions burned: 105 (million)
% 5.48/1.08 % (59184)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=1362112802:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.48/1.08 % (59184)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.48/1.08 % (59184)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.48/1.08 % (59172)Instruction limit reached!
% 5.48/1.08 % (59172)------------------------------
% 5.48/1.08 % (59172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59172)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59172)Termination reason: Instruction limit
% 5.48/1.08 % (59172)Termination phase: Saturation
% 5.48/1.08 % (59172)Time elapsed: 0.080 s
% 5.48/1.08 % (59172)Peak memory usage: 13 MB
% 5.48/1.08 % (59172)Instructions burned: 161 (million)
% 5.48/1.08 % (59186)ott-21_1_sil=16000:fs=off:random_seed=1965492378:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.48/1.08 % (59170)Instruction limit reached!
% 5.48/1.08 % (59170)------------------------------
% 5.48/1.08 % (59170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59170)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59170)Termination reason: Instruction limit
% 5.48/1.08 % (59170)Termination phase: Saturation
% 5.48/1.08 % (59170)Time elapsed: 0.096 s
% 5.48/1.08 % (59170)Peak memory usage: 12 MB
% 5.48/1.08 % (59170)Instructions burned: 116 (million)
% 5.48/1.08 % (59182)Instruction limit reached!
% 5.48/1.08 % (59182)------------------------------
% 5.48/1.08 % (59182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59182)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59182)Termination reason: Instruction limit
% 5.48/1.08 % (59182)Termination phase: Saturation
% 5.48/1.08 % (59182)Time elapsed: 0.076 s
% 5.48/1.08 % (59182)Peak memory usage: 13 MB
% 5.48/1.08 % (59182)Instructions burned: 132 (million)
% 5.48/1.08 % (59171)Instruction limit reached!
% 5.48/1.08 % (59171)------------------------------
% 5.48/1.08 % (59171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59171)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59171)Termination reason: Instruction limit
% 5.48/1.08 % (59171)Termination phase: Saturation
% 5.48/1.08 % (59171)Time elapsed: 0.111 s
% 5.48/1.08 % (59171)Peak memory usage: 13 MB
% 5.48/1.08 % (59171)Instructions burned: 132 (million)
% 5.48/1.08 % (59188)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4175543808:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.48/1.08 % (59189)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1815252803:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59190)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4236014899:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.48/1.08 % (59193)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4114927006:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59196)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2126231290:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 5.48/1.08 % (59196)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.48/1.08 % (59186)Instruction limit reached!
% 5.48/1.08 % (59186)------------------------------
% 5.48/1.08 % (59186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59186)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59186)Termination reason: Instruction limit
% 5.48/1.08 % (59186)Termination phase: Saturation
% 5.48/1.08 % (59186)Time elapsed: 0.079 s
% 5.48/1.08 % (59186)Peak memory usage: 12 MB
% 5.48/1.08 % (59186)Instructions burned: 180 (million)
% 5.48/1.08 % (59198)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3338413106:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 5.48/1.08 % (59198)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.48/1.08 % (59196)Instruction limit reached!
% 5.48/1.08 % (59196)------------------------------
% 5.48/1.08 % (59196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59196)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59196)Termination reason: Instruction limit
% 5.48/1.08 % (59196)Termination phase: Saturation
% 5.48/1.08 % (59196)Time elapsed: 0.313 s
% 5.48/1.08 % (59196)Peak memory usage: 18 MB
% 5.48/1.08 % (59196)Instructions burned: 692 (million)
% 5.48/1.08 % (59201)fmb+10_1_sil=64000:random_seed=1737503645:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 5.48/1.08 % (59201)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59188)Instruction limit reached!
% 5.48/1.08 % (59188)------------------------------
% 5.48/1.08 % (59188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59188)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59188)Termination reason: Instruction limit
% 5.48/1.08 % (59188)Termination phase: Saturation
% 5.48/1.08 % (59188)Time elapsed: 0.397 s
% 5.48/1.08 % (59188)Peak memory usage: 13 MB
% 5.48/1.08 % (59188)Instructions burned: 478 (million)
% 5.48/1.08 % (59205)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=263805414:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59184)Instruction limit reached!
% 5.48/1.08 % (59184)------------------------------
% 5.48/1.08 % (59184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59184)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59184)Termination reason: Instruction limit
% 5.48/1.08 % (59184)Termination phase: Saturation
% 5.48/1.08 % (59184)Time elapsed: 0.473 s
% 5.48/1.08 % (59184)Peak memory usage: 14 MB
% 5.48/1.08 % (59184)Instructions burned: 685 (million)
% 5.48/1.08 % (59208)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=119829389:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 5.48/1.08 % (59208)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.48/1.08 % (59206)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3295881609:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59209)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4137920854:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 5.48/1.08 % (59209)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.48/1.08 % (59209)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.48/1.08 % (59198)Instruction limit reached!
% 5.48/1.08 % (59198)------------------------------
% 5.48/1.08 % (59198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59198)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59198)Termination reason: Instruction limit
% 5.48/1.08 % (59198)Termination phase: Saturation
% 5.48/1.08 % (59198)Time elapsed: 0.380 s
% 5.48/1.08 % (59198)Peak memory usage: 14 MB
% 5.48/1.08 % (59198)Instructions burned: 880 (million)
% 5.48/1.08 % (59212)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2487612720:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59214)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3903698368:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 5.48/1.08 % Exception at run slice level
% 5.48/1.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.48/1.08 % (59216)ott-2_1_sil=16000:newcnf=on:random_seed=2015445051:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 5.48/1.08 % (59216)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.48/1.08 % (59218)ott+10_1_sil=32000:tgt=ground:random_seed=1844760853:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 5.48/1.08 % (59208) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-59161-59208"...
% 5.48/1.08 % (59208)...printing done.
% 5.48/1.08 % (59208)Refutation found. Thanks to Tanya!
% 5.48/1.08 % SZS status Theorem for theBenchmark
% 5.48/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 5.48/1.08 % (59208)------------------------------
% 5.48/1.08 % (59208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.48/1.08 % (59208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.08 % (59208)CaDiCaL version: 2.1.3
% 5.48/1.08 % (59208)Termination reason: Refutation
% 5.48/1.08 % (59208)Time elapsed: 0.235 s
% 5.48/1.08 % (59208)Peak memory usage: 15 MB
% 5.48/1.08 % (59208)Instructions burned: 509 (million)
% 5.48/1.08 % (59161)Success in time 0.835 s
% 5.48/1.08 % Vampire exiting
%------------------------------------------------------------------------------