%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ114^5 : 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 : n026.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 2.75s 0.66s
% Output : Refutation 2.75s
% 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 : 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 > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > $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 > $o ) > $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 @ ( s @ ( s @ X0 ) ) ) @ ( s @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_L10000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( cCKB6_BLACK @ ( s @ ( s @ ( 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 @ ( s @ ( s @ X0 ) ) ) @ ( s @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ X0 @ X1 )
= $true )
=> ( ( cCKB6_BLACK @ ( s @ ( s @ ( s @ X0 ) ) ) @ ( s @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ ( s @ ( s @ ( s @ X0 ) ) ) @ ( s @ X1 ) )
!= $true )
& ( ( cCKB6_BLACK @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( cCKB6_BLACK @ ( s @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( s @ sK0 ) ) ) @ ( s @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
( $false
= ( sK4 @ ( s @ ( s @ ( 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(f494,plain,
( ( $true = $false )
| ( $false
= ( sK4 @ ( s @ ( s @ sK0 ) ) @ sK1 ) ) ),
inference(constrained_superposition,[],[f32,f41]) ).
thf(f512,plain,
( $false
= ( sK4 @ ( s @ ( s @ sK0 ) ) @ sK1 ) ),
inference(trivial_inequality_removal,[],[f494]) ).
thf(f656,plain,
( ( $true = $false )
| ( $false
= ( sK4 @ sK0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f512,f42]) ).
thf(f660,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(f667,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,[],[f660]) ).
thf(f668,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,[],[f667]) ).
thf(f674,plain,
( $false
= ( sK4 @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f656]) ).
thf(f946,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,[],[f668]) ).
thf(f1038,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,[],[f946,f41]) ).
thf(f1106,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,[],[f1038]) ).
thf(f1107,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,[],[f1106]) ).
thf(f1114,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,[],[f1107,f35]) ).
thf(f1115,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,[],[f1114]) ).
thf(f1118,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,[],[f1115,f674]) ).
thf(f1119,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,[],[f1118]) ).
thf(f1121,definition,
( spl5_22
<=> ! [X1: $i] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) )
| ( ( sK2 @ sK4 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_22])],[avatar_definition]) ).
thf(f1122,plain,
( ! [X1: $i] :
( ( ( sK2 @ sK4 )
!= X1 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ X1 ) ) )
| ~ spl5_22 ),
inference(avatar_component_clause,[],[f1121]) ).
thf(f1124,definition,
( spl5_23
<=> ! [X0: $i > $i > $o] :
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) )
| ( sK4 != X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_23])],[avatar_definition]) ).
thf(f1125,plain,
( ! [X0: $i > $i > $o] :
( ( sK4 != X0 )
| ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ X0 ) ) ) )
| ~ spl5_23 ),
inference(avatar_component_clause,[],[f1124]) ).
thf(f1127,plain,
( spl5_23
| spl5_22 ),
inference(avatar_split_clause,[],[f1119,f1121,f1124]) ).
thf(f1214,plain,
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ sK4 ) ) )
| ~ spl5_22 ),
inference(equality_resolution,[],[f1122]) ).
thf(f1312,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_22 ),
inference(constrained_superposition,[],[f27,f1214]) ).
thf(f1328,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_22 ),
inference(trivial_inequality_removal,[],[f1312]) ).
thf(f1329,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_22 ),
inference(beta-eta_normalization,[],[f1328]) ).
thf(f1345,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_22 ),
inference(equality_resolution,[],[f1329]) ).
thf(f1348,plain,
( ( $false
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ c1
@ c1 )
@ c1 ) )
| ( $true
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ sK0
@ sK1 )
@ sK1 ) )
| ~ spl5_22 ),
inference(trivial_inequality_removal,[],[f1345]) ).
thf(f1349,plain,
( ( $false
= ( sK4 @ c1 @ c1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_22 ),
inference(beta-eta_normalization,[],[f1348]) ).
thf(f1351,plain,
( ( $true = $false )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_22 ),
inference(forward_demodulation,[],[f1349,f35]) ).
thf(f1352,plain,
( ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_22 ),
inference(trivial_inequality_removal,[],[f1351]) ).
thf(f1361,plain,
( ( $true = $false )
| ~ spl5_22 ),
inference(forward_demodulation,[],[f1352,f674]) ).
thf(f1362,plain,
( $false
| ~ spl5_22 ),
inference(trivial_inequality_removal,[],[f1361]) ).
thf(f1363,plain,
~ spl5_22,
inference(avatar_contradiction_clause,[],[f1362]) ).
thf(f1365,plain,
( ( $false
= ( sK4 @ ( sK3 @ sK4 ) @ ( sK2 @ sK4 ) ) )
| ~ spl5_23 ),
inference(equality_resolution,[],[f1125]) ).
thf(f1584,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_23 ),
inference(constrained_superposition,[],[f27,f1365]) ).
thf(f1600,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_23 ),
inference(trivial_inequality_removal,[],[f1584]) ).
thf(f1601,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_23 ),
inference(beta-eta_normalization,[],[f1600]) ).
thf(f2673,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_23 ),
inference(equality_resolution,[],[f1601]) ).
thf(f2676,plain,
( ( $false
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ c1
@ c1 )
@ c1 ) )
| ( $true
= ( sK4
@ ( ^ [Y0: $i,Y1: $i] : Y0
@ sK0
@ sK1 )
@ sK1 ) )
| ~ spl5_23 ),
inference(trivial_inequality_removal,[],[f2673]) ).
thf(f2677,plain,
( ( $false
= ( sK4 @ c1 @ c1 ) )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_23 ),
inference(beta-eta_normalization,[],[f2676]) ).
thf(f2679,plain,
( ( $true = $false )
| ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_23 ),
inference(forward_demodulation,[],[f2677,f35]) ).
thf(f2680,plain,
( ( $true
= ( sK4 @ sK0 @ sK1 ) )
| ~ spl5_23 ),
inference(trivial_inequality_removal,[],[f2679]) ).
thf(f2682,plain,
( ( $true = $false )
| ~ spl5_23 ),
inference(forward_demodulation,[],[f2680,f674]) ).
thf(f2683,plain,
( $false
| ~ spl5_23 ),
inference(trivial_inequality_removal,[],[f2682]) ).
thf(f2684,plain,
~ spl5_23,
inference(avatar_contradiction_clause,[],[f2683]) ).
cnf(s22,plain,
( spl5_22
| spl5_23 ),
inference(sat_conversion,[],[f1127]) ).
cnf(s24,plain,
~ spl5_22,
inference(sat_conversion,[],[f1363]) ).
cnf(s36,plain,
~ spl5_23,
inference(sat_conversion,[],[f2684]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s22,s36,s24]) ).
thf(f2685,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ114^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:27:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 2.75/0.66 % (578718)Will run a generic schedule for satisfiability detection.
% 2.75/0.66 % (578723)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2427057556_2999 on theBenchmark for (2999ds/0Mi)
% 2.75/0.66 % Exception at run slice level
% 2.75/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.75/0.66 % (578724)% WARNING: option uhcvi not known.
% 2.75/0.66 % (578724)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=547814717:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.75/0.66 % (578728)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=29396560:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.75/0.66 % (578727)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1291838370:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.75/0.66 % (578724)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.75/0.66 % (578724)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.75/0.66 % (578727)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.75/0.66 % (578731)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=688278593:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.75/0.66 % Exception at run slice level
% 2.75/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.75/0.66 % (578729)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=685910030:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.75/0.66 % (578737)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2538088960:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.75/0.66 % (578726)dis+10_1_sil=32000:sp=arity:random_seed=3699395563:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.75/0.66 % (578725)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4075953302:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.75/0.66 % (578737)Instruction limit reached!
% 2.75/0.66 % (578737)------------------------------
% 2.75/0.66 % (578737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578737)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578737)Termination reason: Instruction limit
% 2.75/0.66 % (578737)Termination phase: Saturation
% 2.75/0.66 % (578737)Time elapsed: 0.035 s
% 2.75/0.66 % (578737)Peak memory usage: 13 MB
% 2.75/0.66 % (578737)Instructions burned: 133 (million)
% 2.75/0.66 % (578727)Instruction limit reached!
% 2.75/0.66 % (578727)------------------------------
% 2.75/0.66 % (578727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578727)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578727)Termination reason: Instruction limit
% 2.75/0.66 % (578727)Termination phase: Saturation
% 2.75/0.66 % (578727)Time elapsed: 0.055 s
% 2.75/0.66 % (578727)Peak memory usage: 13 MB
% 2.75/0.66 % (578727)Instructions burned: 117 (million)
% 2.75/0.66 % (578741)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=3710533721:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.75/0.66 % (578741)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.75/0.66 % (578741)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.75/0.66 % (578728)Instruction limit reached!
% 2.75/0.66 % (578728)------------------------------
% 2.75/0.66 % (578728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578728)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578728)Termination reason: Instruction limit
% 2.75/0.66 % (578728)Termination phase: Saturation
% 2.75/0.66 % (578728)Time elapsed: 0.068 s
% 2.75/0.66 % (578728)Peak memory usage: 12 MB
% 2.75/0.66 % (578728)Instructions burned: 133 (million)
% 2.75/0.66 % (578726)Instruction limit reached!
% 2.75/0.66 % (578726)------------------------------
% 2.75/0.66 % (578726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578726)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578726)Termination reason: Instruction limit
% 2.75/0.66 % (578726)Termination phase: Saturation
% 2.75/0.66 % (578726)Time elapsed: 0.051 s
% 2.75/0.66 % (578726)Peak memory usage: 12 MB
% 2.75/0.66 % (578726)Instructions burned: 103 (million)
% 2.75/0.66 % (578742)ott-21_1_sil=16000:fs=off:random_seed=1265020703:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.75/0.66 % (578744)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4023206786:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.75/0.66 % (578729)Instruction limit reached!
% 2.75/0.66 % (578729)------------------------------
% 2.75/0.66 % (578729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578729)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578729)Termination reason: Instruction limit
% 2.75/0.66 % (578729)Termination phase: Saturation
% 2.75/0.66 % (578729)Time elapsed: 0.085 s
% 2.75/0.66 % (578729)Peak memory usage: 13 MB
% 2.75/0.66 % (578729)Instructions burned: 161 (million)
% 2.75/0.66 % (578745)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2396443895:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.75/0.66 % Exception at run slice level
% 2.75/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.75/0.66 % (578748)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2509741489:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.75/0.66 % (578750)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3467682061:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.75/0.66 % Exception at run slice level
% 2.75/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.75/0.66 % (578753)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=851895674: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)
% 2.75/0.66 % (578753)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.75/0.66 % (578742)Instruction limit reached!
% 2.75/0.66 % (578742)------------------------------
% 2.75/0.66 % (578742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578742)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578742)Termination reason: Instruction limit
% 2.75/0.66 % (578742)Termination phase: Saturation
% 2.75/0.66 % (578742)Time elapsed: 0.083 s
% 2.75/0.66 % (578742)Peak memory usage: 12 MB
% 2.75/0.66 % (578742)Instructions burned: 182 (million)
% 2.75/0.66 % (578755)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2958569169:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.75/0.66 % (578755)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.75/0.66 % (578744)Instruction limit reached!
% 2.75/0.66 % (578744)------------------------------
% 2.75/0.66 % (578744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578744)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578744)Termination reason: Instruction limit
% 2.75/0.66 % (578744)Termination phase: Saturation
% 2.75/0.66 % (578744)Time elapsed: 0.227 s
% 2.75/0.66 % (578744)Peak memory usage: 13 MB
% 2.75/0.66 % (578744)Instructions burned: 479 (million)
% 2.75/0.66 % (578753)Instruction limit reached!
% 2.75/0.66 % (578753)------------------------------
% 2.75/0.66 % (578753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578753)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578753)Termination reason: Instruction limit
% 2.75/0.66 % (578753)Termination phase: Saturation
% 2.75/0.66 % (578753)Time elapsed: 0.187 s
% 2.75/0.66 % (578753)Peak memory usage: 18 MB
% 2.75/0.66 % (578753)Instructions burned: 694 (million)
% 2.75/0.66 % (578758)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1870960910:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 2.75/0.66 % Exception at run slice level
% 2.75/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.75/0.66 % (578757)fmb+10_1_sil=64000:random_seed=968436547:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.75/0.66 % (578757)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.75/0.66 % Exception at run slice level
% 2.75/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.75/0.66 % (578760)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3352359603:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 2.75/0.66 % Exception at run slice level
% 2.75/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.75/0.66 % (578762)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1307085504:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 2.75/0.66 % (578762)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.75/0.66 % (578764)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2609724633:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 2.75/0.66 % (578764)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.75/0.66 % (578764)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.75/0.66 % (578724) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-578718-578724"...
% 2.75/0.66 % (578724)...printing done.
% 2.75/0.66 % (578724)Refutation found. Thanks to Tanya!
% 2.75/0.66 % SZS status Theorem for theBenchmark
% 2.75/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/0.66 % (578724)------------------------------
% 2.75/0.66 % (578724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.66 % (578724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.66 % (578724)CaDiCaL version: 2.1.3
% 2.75/0.66 % (578724)Termination reason: Refutation
% 2.75/0.66 % (578724)Time elapsed: 0.387 s
% 2.75/0.66 % (578724)Peak memory usage: 16 MB
% 2.75/0.66 % (578724)Instructions burned: 854 (million)
% 2.75/0.66 % (578718)Success in time 0.431 s
% 2.75/0.66 % Vampire exiting
%------------------------------------------------------------------------------