%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ109^5 : 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 : n001.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 08:21:03 AM UTC 2026
% Result : Theorem 2.53s 0.60s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 4
% Syntax : Number of formulae : 87 ( 29 unt; 0 typ; 2 def)
% Number of atoms : 824 ( 185 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 1443 ( 75 ~; 134 |; 42 &;1112 @)
% ( 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 : 34 ( 30 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 > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > $i ).
thf(func_def_26,type,
sK9: ( $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > $i ).
thf(func_def_27,type,
sK10: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > $i ).
thf(func_def_28,type,
sK11: ( $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > $i ).
thf(func_def_29,type,
sK12: ( $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > $i ).
thf(func_def_30,type,
sK13: ( $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 @ X0 ) @ ( s @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_L9000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( cCKB6_BLACK @ ( s @ X0 ) @ ( 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 @ X0 ) @ ( s @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ X0 @ X1 )
= $true )
=> ( ( cCKB6_BLACK @ ( s @ X0 ) @ ( s @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ ( s @ X0 ) @ ( s @ X1 ) )
!= $true )
& ( ( cCKB6_BLACK @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( cCKB6_BLACK @ ( s @ sK0 ) @ ( 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 @ sK0 ) @ ( 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 @ sK0 )
@ ( 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 @ sK0 ) @ ( 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 @ sK0 ) @ ( 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 @ sK0 ) @ ( s @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
( $false
= ( sK4 @ ( s @ sK0 ) @ ( 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(f229,plain,
( ( $true = $false )
| ( $false
= ( sK4 @ sK0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f32,f41]) ).
thf(f238,plain,
( $false
= ( sK4 @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f229]) ).
thf(f670,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(f677,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,[],[f670]) ).
thf(f678,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,[],[f677]) ).
thf(f904,plain,
! [X0: $i > $i > $i,X1: $i] :
( ( $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
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $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,[],[f678]) ).
thf(f967,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 ) ) )
@ 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 )
| ( $false
= ( sK4
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
@ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ),
inference(constrained_superposition,[],[f904,f41]) ).
thf(f1035,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $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 )
| ( $false
= ( sK4
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( sK4 @ Y0
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
@ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ),
inference(trivial_inequality_removal,[],[f967]) ).
thf(f1036,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( $false
= ( sK4 @ c1 @ c1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ),
inference(beta-eta_normalization,[],[f1035]) ).
thf(f1043,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ),
inference(forward_demodulation,[],[f1036,f35]) ).
thf(f1044,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ),
inference(trivial_inequality_removal,[],[f1043]) ).
thf(f1047,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ),
inference(forward_demodulation,[],[f1044,f238]) ).
thf(f1048,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( ( sK2 @ sK4 )
!= X1 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ),
inference(trivial_inequality_removal,[],[f1047]) ).
thf(f1050,definition,
( spl5_19
<=> ! [X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( ( sK2 @ sK4 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition]) ).
thf(f1051,plain,
( ! [X1: $i] :
( ( ( sK2 @ sK4 )
!= X1 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) ) )
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f1050]) ).
thf(f1053,definition,
( spl5_20
<=> ! [X0: $i > $i > $o] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition]) ).
thf(f1054,plain,
( ! [X0: $i > $i > $o] :
( ( sK4 != X0 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) ) )
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f1053]) ).
thf(f1056,plain,
( spl5_20
| spl5_19 ),
inference(avatar_split_clause,[],[f1048,f1050,f1053]) ).
thf(f1143,plain,
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ sK4 ) ) )
| ~ spl5_19 ),
inference(equality_resolution,[],[f1051]) ).
thf(f1150,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_19 ),
inference(constrained_superposition,[],[f27,f1143]) ).
thf(f1166,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_19 ),
inference(trivial_inequality_removal,[],[f1150]) ).
thf(f1167,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_19 ),
inference(beta-eta_normalization,[],[f1166]) ).
thf(f1272,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_19 ),
inference(equality_resolution,[],[f1167]) ).
thf(f1275,plain,
( ( $false
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ c1
@ c1 )
@ c1 ) )
| ( $true
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ sK0
@ sK1 )
@ sK1 ) )
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f1272]) ).
thf(f1276,plain,
( ( $false
= ( sK4 @ c1 @ c1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_19 ),
inference(beta-eta_normalization,[],[f1275]) ).
thf(f1278,plain,
( ( $true = $false )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_19 ),
inference(forward_demodulation,[],[f1276,f35]) ).
thf(f1279,plain,
( ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f1278]) ).
thf(f1288,plain,
( ( $true = $false )
| ~ spl5_19 ),
inference(forward_demodulation,[],[f1279,f238]) ).
thf(f1289,plain,
( $false
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f1288]) ).
thf(f1290,plain,
~ spl5_19,
inference(avatar_contradiction_clause,[],[f1289]) ).
thf(f1293,plain,
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ sK4 ) ) )
| ~ spl5_20 ),
inference(equality_resolution,[],[f1054]) ).
thf(f1300,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_20 ),
inference(constrained_superposition,[],[f27,f1293]) ).
thf(f1316,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_20 ),
inference(trivial_inequality_removal,[],[f1300]) ).
thf(f1317,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_20 ),
inference(beta-eta_normalization,[],[f1316]) ).
thf(f2547,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_20 ),
inference(equality_resolution,[],[f1317]) ).
thf(f2550,plain,
( ( $false
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ c1
@ c1 )
@ c1 ) )
| ( $true
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ sK0
@ sK1 )
@ sK1 ) )
| ~ spl5_20 ),
inference(trivial_inequality_removal,[],[f2547]) ).
thf(f2551,plain,
( ( $false
= ( sK4 @ c1 @ c1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_20 ),
inference(beta-eta_normalization,[],[f2550]) ).
thf(f2553,plain,
( ( $true = $false )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_20 ),
inference(forward_demodulation,[],[f2551,f35]) ).
thf(f2554,plain,
( ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_20 ),
inference(trivial_inequality_removal,[],[f2553]) ).
thf(f2556,plain,
( ( $true = $false )
| ~ spl5_20 ),
inference(forward_demodulation,[],[f2554,f238]) ).
thf(f2557,plain,
( $false
| ~ spl5_20 ),
inference(trivial_inequality_removal,[],[f2556]) ).
thf(f2558,plain,
~ spl5_20,
inference(avatar_contradiction_clause,[],[f2557]) ).
cnf(s12,plain,
( spl5_19
| spl5_20 ),
inference(sat_conversion,[],[f1056]) ).
cnf(s14,plain,
~ spl5_19,
inference(sat_conversion,[],[f1290]) ).
cnf(s26,plain,
~ spl5_20,
inference(sat_conversion,[],[f2558]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s12,s26,s14]) ).
thf(f2559,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ109^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n001.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:30:20 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 Running first-order model finding
% 0.08/0.19 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
% 2.53/0.60 % (1230129)Will run a generic schedule for satisfiability detection.
% 2.53/0.60 % (1230138)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3647567148:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.53/0.60 % (1230138)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.53/0.60 % (1230135)% WARNING: option uhcvi not known.
% 2.53/0.60 % (1230139)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1888691942:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.53/0.60 % (1230137)dis+10_1_sil=32000:sp=arity:random_seed=3436073612:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.53/0.60 % (1230135)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2426874435:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.53/0.60 % (1230136)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1732152223:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.53/0.60 % (1230140)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1586097513:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.53/0.60 % (1230135)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.53/0.60 % (1230135)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.53/0.60 % (1230134)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4125912502_2999 on theBenchmark for (2999ds/0Mi)
% 2.53/0.60 % Exception at run slice level
% 2.53/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.53/0.60 % (1230138)Instruction limit reached!
% 2.53/0.60 % (1230138)------------------------------
% 2.53/0.60 % (1230138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.60 % (1230138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.60 % (1230138)CaDiCaL version: 2.1.3
% 2.53/0.60 % (1230138)Termination reason: Instruction limit
% 2.53/0.60 % (1230138)Termination phase: Saturation
% 2.53/0.60 % (1230138)Time elapsed: 0.030 s
% 2.53/0.60 % (1230138)Peak memory usage: 13 MB
% 2.53/0.60 % (1230138)Instructions burned: 117 (million)
% 2.53/0.60 % (1230149)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=868093842:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.53/0.60 % (1230148)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1765769763:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.53/0.60 % Exception at run slice level
% 2.53/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.53/0.60 % (1230137)Instruction limit reached!
% 2.53/0.60 % (1230137)------------------------------
% 2.53/0.60 % (1230137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.60 % (1230137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.60 % (1230137)CaDiCaL version: 2.1.3
% 2.53/0.60 % (1230137)Termination reason: Instruction limit
% 2.53/0.60 % (1230137)Termination phase: Saturation
% 2.53/0.60 % (1230137)Time elapsed: 0.050 s
% 2.53/0.60 % (1230137)Peak memory usage: 12 MB
% 2.53/0.60 % (1230137)Instructions burned: 104 (million)
% 2.53/0.60 % (1230152)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=1541567509:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.53/0.60 % (1230152)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.53/0.60 % (1230152)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.53/0.60 % (1230153)ott-21_1_sil=16000:fs=off:random_seed=929594362:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.53/0.60 % (1230149)Instruction limit reached!
% 2.53/0.60 % (1230149)------------------------------
% 2.53/0.60 % (1230149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.60 % (1230149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.60 % (1230149)CaDiCaL version: 2.1.3
% 2.53/0.60 % (1230149)Termination reason: Instruction limit
% 2.53/0.60 % (1230149)Termination phase: Saturation
% 2.53/0.60 % (1230149)Time elapsed: 0.035 s
% 2.53/0.60 % (1230149)Peak memory usage: 13 MB
% 2.53/0.60 % (1230149)Instructions burned: 135 (million)
% 2.53/0.60 % (1230140)Instruction limit reached!
% 2.53/0.60 % (1230140)------------------------------
% 2.53/0.60 % (1230140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.60 % (1230140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.60 % (1230140)CaDiCaL version: 2.1.3
% 2.53/0.60 % (1230140)Termination reason: Instruction limit
% 2.53/0.60 % (1230140)Termination phase: Saturation
% 2.53/0.60 % (1230140)Time elapsed: 0.077 s
% 2.53/0.60 % (1230140)Peak memory usage: 13 MB
% 2.53/0.60 % (1230140)Instructions burned: 160 (million)
% 2.53/0.60 % (1230139)Instruction limit reached!
% 2.53/0.60 % (1230139)------------------------------
% 2.53/0.60 % (1230139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.60 % (1230139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.60 % (1230139)CaDiCaL version: 2.1.3
% 2.53/0.60 % (1230139)Termination reason: Instruction limit
% 2.53/0.60 % (1230139)Termination phase: Saturation
% 2.53/0.60 % (1230139)Time elapsed: 0.080 s
% 2.53/0.60 % (1230139)Peak memory usage: 13 MB
% 2.53/0.60 % (1230139)Instructions burned: 133 (million)
% 2.53/0.60 % (1230156)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3650430203:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.53/0.60 % (1230157)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=99987188:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.53/0.60 % Exception at run slice level
% 2.53/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.53/0.60 % (1230158)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=260740094:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.53/0.60 % (1230161)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2310969186:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.53/0.60 % Exception at run slice level
% 2.53/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.53/0.60 % (1230164)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=2772341730: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)
% 2.53/0.60 % (1230164)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.53/0.60 % (1230153)Instruction limit reached!
% 2.53/0.60 % (1230153)------------------------------
% 2.53/0.60 % (1230153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.60 % (1230153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.60 % (1230153)CaDiCaL version: 2.1.3
% 2.53/0.60 % (1230153)Termination reason: Instruction limit
% 2.53/0.60 % (1230153)Termination phase: Saturation
% 2.53/0.60 % (1230153)Time elapsed: 0.082 s
% 2.53/0.60 % (1230153)Peak memory usage: 12 MB
% 2.53/0.60 % (1230153)Instructions burned: 181 (million)
% 2.53/0.60 % (1230166)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1792323168:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.53/0.60 % (1230166)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.53/0.60 % (1230156)Instruction limit reached!
% 2.53/0.60 % (1230156)------------------------------
% 2.53/0.60 % (1230156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.60 % (1230156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.60 % (1230156)CaDiCaL version: 2.1.3
% 2.53/0.60 % (1230156)Termination reason: Instruction limit
% 2.53/0.60 % (1230156)Termination phase: Saturation
% 2.53/0.60 % (1230156)Time elapsed: 0.125 s
% 2.53/0.60 % (1230156)Peak memory usage: 13 MB
% 2.53/0.60 % (1230156)Instructions burned: 494 (million)
% 2.53/0.60 % (1230168)fmb+10_1_sil=64000:random_seed=2310949602:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.53/0.60 % (1230168)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.53/0.60 % Exception at run slice level
% 2.53/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.53/0.60 % (1230170)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=148090812:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 2.53/0.60 % Exception at run slice level
% 2.53/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.53/0.60 % (1230172)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=154736788:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 2.53/0.60 % Exception at run slice level
% 2.53/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.53/0.60 % (1230174)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2309378328:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 2.53/0.60 % (1230174)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.53/0.60 % (1230135) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1230129-1230135"...
% 2.53/0.60 % (1230135)...printing done.
% 2.53/0.60 % (1230135)Refutation found. Thanks to Tanya!
% 2.53/0.60 % SZS status Theorem for theBenchmark
% 2.53/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/0.60 % (1230135)------------------------------
% 2.53/0.60 % (1230135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.60 % (1230135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.60 % (1230135)CaDiCaL version: 2.1.3
% 2.53/0.60 % (1230135)Termination reason: Refutation
% 2.53/0.60 % (1230135)Time elapsed: 0.358 s
% 2.53/0.60 % (1230135)Peak memory usage: 16 MB
% 2.53/0.60 % (1230135)Instructions burned: 798 (million)
% 2.53/0.60 % (1230129)Success in time 0.396 s
% 2.53/0.60 % Vampire exiting
%------------------------------------------------------------------------------