%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO060^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:48:50 AM UTC 2026
% Result : Theorem 2.62s 0.64s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 13
% Syntax : Number of formulae : 139 ( 61 unt; 0 typ; 4 def)
% Number of atoms : 1054 ( 220 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1276 ( 101 ~; 169 |; 0 &; 836 @)
% ( 4 <=>; 92 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 42 usr; 10 con; 0-4 aty)
% ( 74 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 287 ( 0 sgn 98 !; 0 ?; 287 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
a: $i > $o ).
thf(func_def_22,type,
b: $i > $o ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_29,type,
vOR: $o > $o > $o ).
thf(func_def_30,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
sK3: $i > $i ).
thf(func_def_39,type,
sK4: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f9,axiom,
( inot
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',inot) ).
thf(f13,axiom,
( ior
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ior) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,conjecture,
ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f24,negated_conjecture,
~ ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f29,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f30,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f32,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f36,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f37,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f39,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f42,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f47,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f48,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f55,plain,
ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ),
inference(rectify,[],[f22]) ).
thf(f56,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ) )
= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
~ ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f58,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(flattening,[],[f58]) ).
thf(f64,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f65,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f68,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f69,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f70,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f74,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f79,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f83,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ) )
= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f84,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f88,plain,
( inot
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f70,f64,f68]) ).
thf(f91,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f74,f65,f68,f68]) ).
thf(f96,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) ) ) ),
inference(definition_unfolding,[],[f83,f79,f91,f88,f69,f88,f69]) ).
thf(f97,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) ) ) ) ),
inference(definition_unfolding,[],[f84,f79,f91,f88,f69,f88,f69]) ).
thf(f98,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f100]) ).
thf(f102,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f100]) ).
thf(f103,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f102]) ).
thf(f104,plain,
( $false
= ( ( irel @ sK0 @ sK1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( $true
= ( irel @ sK0 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f107,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f105]) ).
thf(f108,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK1 @ X1 )
=> ( b @ X1 ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK1 @ X1 ) )
| ( $true
= ( b @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f109]) ).
thf(f111,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f101]) ).
thf(f112,plain,
( $false
= ( ( irel @ sK0 @ sK2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f114,plain,
( $true
= ( irel @ sK0 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f115,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f113]) ).
thf(f116,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK2 @ X1 )
=> ( a @ X1 ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK2 @ X1 ) )
| ( $true
= ( a @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f119,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f120,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) )
@ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) )
@ ( sK3 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) )
@ ( sK3 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) )
@ ( sK4 @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( b @ ( sK3 @ X2 ) ) ) )
| ( $false
= ( ( irel @ X3 @ ( sK4 @ X3 ) )
=> ( a @ ( sK4 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( b @ ( sK3 @ X2 ) ) )
| ( $false
= ( ( irel @ X3 @ ( sK4 @ X3 ) )
=> ( a @ ( sK4 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( irel @ X2 @ ( sK3 @ X2 ) ) )
| ( $false
= ( ( irel @ X3 @ ( sK4 @ X3 ) )
=> ( a @ ( sK4 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X2 @ ( sK3 @ X2 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( a @ ( sK4 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( irel @ X2 @ ( sK3 @ X2 ) ) )
| ( $true
= ( irel @ X3 @ ( sK4 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f134]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( b @ ( sK3 @ X2 ) ) )
| ( $false
= ( a @ ( sK4 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X3 @ ( sK4 @ X3 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( b @ ( sK3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f243,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( b @ ( sK3 @ sK1 ) ) )
| ( $false
= ( a @ ( sK4 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f106,f137]) ).
thf(f250,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( b @ ( sK3 @ sK1 ) ) )
| ( $false
= ( a @ ( sK4 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f286,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( b @ ( sK3 @ sK1 ) ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ X0 @ sK1 ) )
| ( $false
= ( a @ ( sK4 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f110,f135]) ).
thf(f304,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( b @ ( sK3 @ sK1 ) ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ X0 @ sK1 ) )
| ( $false
= ( a @ ( sK4 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f286]) ).
thf(f361,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( a @ ( sK4 @ sK2 ) ) )
| ( $false
= ( irel @ X0 @ sK2 ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( b @ ( sK3 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f118,f138]) ).
thf(f381,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( a @ ( sK4 @ sK2 ) ) )
| ( $false
= ( irel @ X0 @ sK2 ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( b @ ( sK3 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f470,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( a @ ( sK4 @ sK2 ) ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ X0 @ sK2 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f118,f136]) ).
thf(f475,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( a @ ( sK4 @ sK2 ) ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ X0 @ sK2 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f470]) ).
thf(f854,definition,
( spl5_6
<=> ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( a @ ( sK4 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f855,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( a @ ( sK4 @ X0 ) ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f854]) ).
thf(f860,definition,
( spl5_7
<=> ( $false
= ( b @ ( sK3 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f861,plain,
( ( $false
!= ( b @ ( sK3 @ sK1 ) ) )
| spl5_7 ),
inference(avatar_component_clause,[],[f860]) ).
thf(f862,plain,
( ( $false
= ( b @ ( sK3 @ sK1 ) ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f860]) ).
thf(f863,plain,
( spl5_7
| spl5_6 ),
inference(avatar_split_clause,[],[f250,f854,f860]) ).
thf(f888,plain,
( ( $true = $false )
| ( $false
= ( a @ ( sK4 @ sK2 ) ) )
| ~ spl5_6 ),
inference(constrained_superposition,[],[f114,f855]) ).
thf(f889,plain,
( ( $false
= ( a @ ( sK4 @ sK2 ) ) )
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f888]) ).
thf(f911,definition,
( spl5_8
<=> ( $false
= ( a @ ( sK4 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f912,plain,
( ( $false
!= ( a @ ( sK4 @ sK2 ) ) )
| spl5_8 ),
inference(avatar_component_clause,[],[f911]) ).
thf(f913,plain,
( ( $false
= ( a @ ( sK4 @ sK2 ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f911]) ).
thf(f915,definition,
( spl5_9
<=> ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( b @ ( sK3 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f916,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( b @ ( sK3 @ X0 ) ) ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f915]) ).
thf(f948,plain,
( ( $true = $false )
| ( $false
= ( b @ ( sK3 @ sK1 ) ) )
| ~ spl5_9 ),
inference(constrained_superposition,[],[f106,f916]) ).
thf(f951,plain,
( ( $false
= ( b @ ( sK3 @ sK1 ) ) )
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f948]) ).
thf(f1062,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ X0 @ sK1 ) )
| ( $false
= ( a @ ( sK4 @ X1 ) ) ) )
| ~ spl5_7 ),
inference(forward_demodulation,[],[f304,f862]) ).
thf(f1063,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ X0 @ sK1 ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( a @ ( sK4 @ X1 ) ) ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1062]) ).
thf(f1087,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( a @ ( sK4 @ X0 ) ) ) )
| ~ spl5_7 ),
inference(constrained_superposition,[],[f106,f1063]) ).
thf(f1110,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( a @ ( sK4 @ X0 ) ) ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1087]) ).
thf(f1226,plain,
( spl5_6
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f1110,f860,f854]) ).
thf(f1317,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ X0 @ sK2 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) ) )
| ~ spl5_8 ),
inference(forward_demodulation,[],[f475,f913]) ).
thf(f1318,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ X0 @ sK2 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) ) )
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f1317]) ).
thf(f1365,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( b @ ( sK3 @ sK1 ) ) )
| ( $false
= ( irel @ X0 @ sK1 ) )
| ( $false
= ( irel @ X0 @ sK2 ) ) )
| ~ spl5_8 ),
inference(constrained_superposition,[],[f110,f1318]) ).
thf(f1376,plain,
( ! [X0: $i] :
( ( $true
= ( b @ ( sK3 @ sK1 ) ) )
| ( $false
= ( irel @ X0 @ sK1 ) )
| ( $false
= ( irel @ X0 @ sK2 ) ) )
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f1365]) ).
thf(f1422,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ X0 @ sK1 ) )
| ( $false
= ( irel @ X0 @ sK2 ) ) )
| ~ spl5_7
| ~ spl5_8 ),
inference(forward_demodulation,[],[f1376,f862]) ).
thf(f1423,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ X0 @ sK2 ) )
| ( $false
= ( irel @ X0 @ sK1 ) ) )
| ~ spl5_7
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f1422]) ).
thf(f1755,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK1 ) )
| ~ spl5_7
| ~ spl5_8 ),
inference(constrained_superposition,[],[f114,f1423]) ).
thf(f1756,plain,
( ( $false
= ( irel @ sK0 @ sK1 ) )
| ~ spl5_7
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f1755]) ).
thf(f1821,plain,
( ( $true = $false )
| ~ spl5_7
| ~ spl5_8 ),
inference(constrained_superposition,[],[f1756,f106]) ).
thf(f1833,plain,
( $false
| ~ spl5_7
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f1821]) ).
thf(f1834,plain,
( ~ spl5_7
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f1833]) ).
thf(f1838,plain,
( $false
| ~ spl5_6
| spl5_8 ),
inference(forward_subsumption_resolution,[],[f889,f912]) ).
thf(f1839,plain,
( ~ spl5_6
| spl5_8 ),
inference(avatar_contradiction_clause,[],[f1838]) ).
thf(f1919,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( irel @ X0 @ sK2 ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( b @ ( sK3 @ X1 ) ) ) )
| ~ spl5_8 ),
inference(forward_demodulation,[],[f381,f913]) ).
thf(f1920,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ X0 @ sK2 ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( b @ ( sK3 @ X1 ) ) ) )
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f1919]) ).
thf(f1940,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( b @ ( sK3 @ X0 ) ) ) )
| ~ spl5_8 ),
inference(constrained_superposition,[],[f114,f1920]) ).
thf(f1959,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( b @ ( sK3 @ X0 ) ) ) )
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f1940]) ).
thf(f1979,plain,
( $false
| spl5_7
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f951,f861]) ).
thf(f1980,plain,
( spl5_7
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f1979]) ).
thf(f3369,plain,
( spl5_9
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f1959,f911,f915]) ).
cnf(s4,plain,
( spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f863]) ).
cnf(s12,plain,
( spl5_6
| ~ spl5_7 ),
inference(sat_conversion,[],[f1226]) ).
cnf(s14,plain,
( ~ spl5_7
| ~ spl5_8 ),
inference(sat_conversion,[],[f1834]) ).
cnf(s15,plain,
( ~ spl5_6
| spl5_8 ),
inference(sat_conversion,[],[f1839]) ).
cnf(s17,plain,
( spl5_7
| ~ spl5_9 ),
inference(sat_conversion,[],[f1980]) ).
cnf(s19,plain,
( ~ spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f3369]) ).
cnf(s20,plain,
~ spl5_8,
inference(rat,[],[s17,s14,s19]) ).
cnf(s21,plain,
~ spl5_6,
inference(rat,[],[s15,s20]) ).
cnf(s23,plain,
~ spl5_7,
inference(rat,[],[s12,s21]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s4,s23,s21]) ).
thf(f3370,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO060^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.18 % Computer : n008.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 16:26:24 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.21 Running first-order model finding
% 0.12/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.62/0.64 % (3370979)Will run a generic schedule for satisfiability detection.
% 2.62/0.64 % (3370988)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1081132053:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.62/0.64 % (3370988)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.62/0.64 % (3370985)% WARNING: option uhcvi not known.
% 2.62/0.64 % (3370985)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2488236323:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.62/0.64 % (3370984)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1067714481_2999 on theBenchmark for (2999ds/0Mi)
% 2.62/0.64 % (3370986)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=286318674:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.62/0.64 % (3370987)dis+10_1_sil=32000:sp=arity:random_seed=2962154499:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.62/0.64 % (3370989)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2431417070:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.62/0.64 % (3370990)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4109598072:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.62/0.64 % (3370985)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3370985)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.62/0.64 % (3370988)Instruction limit reached!
% 2.62/0.64 % (3370988)------------------------------
% 2.62/0.64 % (3370988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3370988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3370988)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3370988)Termination reason: Instruction limit
% 2.62/0.64 % (3370988)Termination phase: Saturation
% 2.62/0.64 % (3370988)Time elapsed: 0.029 s
% 2.62/0.64 % (3370988)Peak memory usage: 12 MB
% 2.62/0.64 % (3370988)Instructions burned: 119 (million)
% 2.62/0.64 % (3370998)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=986992812:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3371000)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4209920927:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.62/0.64 % (3371001)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=3921217214:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.62/0.64 % (3371001)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.62/0.64 % (3371001)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.62/0.64 % (3370987)Instruction limit reached!
% 2.62/0.64 % (3370987)------------------------------
% 2.62/0.64 % (3370987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3370987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3370987)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3370987)Termination reason: Instruction limit
% 2.62/0.64 % (3370987)Termination phase: Saturation
% 2.62/0.64 % (3370987)Time elapsed: 0.052 s
% 2.62/0.64 % (3370987)Peak memory usage: 12 MB
% 2.62/0.64 % (3370987)Instructions burned: 104 (million)
% 2.62/0.64 % (3370989)Instruction limit reached!
% 2.62/0.64 % (3370989)------------------------------
% 2.62/0.64 % (3370989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3370989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3370989)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3370989)Termination reason: Instruction limit
% 2.62/0.64 % (3370989)Termination phase: Saturation
% 2.62/0.64 % (3370989)Time elapsed: 0.066 s
% 2.62/0.64 % (3370989)Peak memory usage: 12 MB
% 2.62/0.64 % (3370989)Instructions burned: 133 (million)
% 2.62/0.64 % (3371000)Instruction limit reached!
% 2.62/0.64 % (3371000)------------------------------
% 2.62/0.64 % (3371000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3371000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3371000)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3371000)Termination reason: Instruction limit
% 2.62/0.64 % (3371000)Termination phase: Saturation
% 2.62/0.64 % (3371000)Time elapsed: 0.035 s
% 2.62/0.64 % (3371000)Peak memory usage: 12 MB
% 2.62/0.64 % (3371000)Instructions burned: 133 (million)
% 2.62/0.64 % (3370990)Instruction limit reached!
% 2.62/0.64 % (3370990)------------------------------
% 2.62/0.64 % (3370990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3370990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3370990)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3370990)Termination reason: Instruction limit
% 2.62/0.64 % (3370990)Termination phase: Saturation
% 2.62/0.64 % (3370990)Time elapsed: 0.072 s
% 2.62/0.64 % (3370990)Peak memory usage: 12 MB
% 2.62/0.64 % (3370990)Instructions burned: 161 (million)
% 2.62/0.64 % (3371004)ott-21_1_sil=16000:fs=off:random_seed=3777707605:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/0.64 % (3371006)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2133849780:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3371005)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3436800383:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 2.62/0.64 % (3371008)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=439017453:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.62/0.64 % (3371010)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3370804148:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3371014)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=3814071897: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)
% 2.62/0.64 % (3371014)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.62/0.64 % (3371004)Instruction limit reached!
% 2.62/0.64 % (3371004)------------------------------
% 2.62/0.64 % (3371004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3371004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3371004)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3371004)Termination reason: Instruction limit
% 2.62/0.64 % (3371004)Termination phase: Saturation
% 2.62/0.64 % (3371004)Time elapsed: 0.081 s
% 2.62/0.64 % (3371004)Peak memory usage: 12 MB
% 2.62/0.64 % (3371004)Instructions burned: 181 (million)
% 2.62/0.64 % (3371016)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4052590576:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.62/0.64 % (3371016)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.62/0.64 % (3371014)Instruction limit reached!
% 2.62/0.64 % (3371014)------------------------------
% 2.62/0.64 % (3371014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3371014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3371014)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3371014)Termination reason: Instruction limit
% 2.62/0.64 % (3371014)Termination phase: Saturation
% 2.62/0.64 % (3371014)Time elapsed: 0.154 s
% 2.62/0.64 % (3371014)Peak memory usage: 13 MB
% 2.62/0.64 % (3371014)Instructions burned: 697 (million)
% 2.62/0.64 % (3371018)fmb+10_1_sil=64000:random_seed=625074447:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.62/0.64 % (3371018)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3371020)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3052094639:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3371022)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3347069885:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3371024)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1571363657:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 2.62/0.64 % (3371024)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.62/0.64 % (3371001)Instruction limit reached!
% 2.62/0.64 % (3371001)------------------------------
% 2.62/0.64 % (3371001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3371001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3371001)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3371001)Termination reason: Instruction limit
% 2.62/0.64 % (3371001)Termination phase: Saturation
% 2.62/0.64 % (3371001)Time elapsed: 0.275 s
% 2.62/0.64 % (3371001)Peak memory usage: 13 MB
% 2.62/0.64 % (3371001)Instructions burned: 686 (million)
% 2.62/0.64 % (3371005)Instruction limit reached!
% 2.62/0.64 % (3371005)------------------------------
% 2.62/0.64 % (3371005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3371005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3371005)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3371005)Termination reason: Instruction limit
% 2.62/0.64 % (3371005)Termination phase: Saturation
% 2.62/0.64 % (3371005)Time elapsed: 0.242 s
% 2.62/0.64 % (3371005)Peak memory usage: 12 MB
% 2.62/0.64 % (3371005)Instructions burned: 478 (million)
% 2.62/0.64 % (3371026)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=423051195:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 2.62/0.64 % (3371026)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.62/0.64 % (3371026)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.62/0.64 % (3371027)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=706719972:i=6324_2996 on theBenchmark for (2996ds/6324Mi)
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3371037)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3757123768:fmbsr=2.30978:i=2174_2996 on theBenchmark for (2996ds/2174Mi)
% 2.62/0.64 % Exception at run slice level
% 2.62/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.62/0.64 % (3371024) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3370979-3371024"...
% 2.62/0.64 % (3371024)...printing done.
% 2.62/0.64 % (3371024)Refutation found. Thanks to Tanya!
% 2.62/0.64 % SZS status Theorem for theBenchmark
% 2.62/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/0.64 % (3371024)------------------------------
% 2.62/0.64 % (3371024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.64 % (3371024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.64 % (3371024)CaDiCaL version: 2.1.3
% 2.62/0.64 % (3371024)Termination reason: Refutation
% 2.62/0.64 % (3371024)Time elapsed: 0.072 s
% 2.62/0.64 % (3371024)Peak memory usage: 13 MB
% 2.62/0.64 % (3371024)Instructions burned: 298 (million)
% 2.62/0.64 % (3370979)Success in time 0.418 s
% 2.62/0.64 % Vampire exiting
%------------------------------------------------------------------------------