%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO462^4 : 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 : n006.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 08:50:09 AM UTC 2026
% Result : Theorem 0.25s 0.32s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 173 ( 47 unt; 0 typ; 8 def)
% Number of atoms : 1336 ( 234 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1655 ( 329 ~; 356 |; 0 &; 897 @)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 15 con; 0-4 aty)
% ( 65 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 304 ( 0 sgn 56 !; 0 ?; 304 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_b: $i > $i > $o ).
thf(func_def_33,type,
mbox_b: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_b: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_b @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',mbox_b) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_b @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_b @ p ) @ ( mbox_b @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_b @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_b @ p ) @ ( mbox_b @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f45,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f81,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f82,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f89,plain,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_b @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f90,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f96,plain,
~ ( mvalid @ ( mimplies @ ( mbox_b @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_b @ p ) @ ( mbox_b @ q ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
( ( mvalid @ ( mimplies @ ( mbox_b @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_b @ p ) @ ( mbox_b @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_b @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_b @ p ) @ ( mbox_b @ q ) ) ) )
!= $true ),
inference(flattening,[],[f97]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f103,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f104,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f106,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f126,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f130,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f134,plain,
( ( mvalid @ ( mimplies @ ( mbox_b @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_b @ p ) @ ( mbox_b @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f137,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f103,f101,f102,f101,f101]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f104,f102,f101]) ).
thf(f140,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f106,f137,f138,f138]) ).
thf(f149,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] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f134,f126,f138,f130,f140,f140,f130,f130]) ).
thf(f150,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f171,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK1 )
| ( q @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK1 )
| ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f192,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK1 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f195,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f196,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f199,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_b @ sK0 @ sK2 )
| ( p @ sK2 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_b @ sK0 @ sK2 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f204,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f208,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f210,plain,
( ( $false
= ( ~ ( rel_b @ sK0 @ sK2 )
| ( p @ sK2 ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( ~ ( rel_b @ sK0 @ sK2 ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f213,plain,
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( q @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f216,plain,
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( rel_b @ sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( q @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f218,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f219,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( rel_b @ sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f230,definition,
( spl4_1
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f231,plain,
( ! [X2: $i] :
( ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f230]) ).
thf(f233,definition,
( spl4_2
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f234,plain,
( ! [X1: $i] :
( ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f235,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f186,f233,f230]) ).
thf(f237,definition,
( spl4_3
<=> ( $true
= ( rel_b @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f239,plain,
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f240,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f193,f233,f237]) ).
thf(f242,definition,
( spl4_4
<=> ( $false
= ( q @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f244,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f245,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f194,f233,f242]) ).
thf(f247,definition,
( spl4_5
<=> ( $true
= ( rel_b @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f249,plain,
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f247]) ).
thf(f250,plain,
( spl4_1
| spl4_5 ),
inference(avatar_split_clause,[],[f206,f247,f230]) ).
thf(f252,definition,
( spl4_6
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f254,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f252]) ).
thf(f255,plain,
( spl4_1
| spl4_6 ),
inference(avatar_split_clause,[],[f208,f252,f230]) ).
thf(f257,definition,
( spl4_7
<=> ( $true
= ( rel_b @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f259,plain,
( ( $true
= ( rel_b @ sK0 @ sK3 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f260,plain,
( spl4_7
| spl4_5 ),
inference(avatar_split_clause,[],[f216,f247,f257]) ).
thf(f262,definition,
( spl4_8
<=> ( $false
= ( q @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f264,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f265,plain,
( spl4_8
| spl4_5 ),
inference(avatar_split_clause,[],[f214,f247,f262]) ).
thf(f266,plain,
( spl4_7
| spl4_6 ),
inference(avatar_split_clause,[],[f219,f252,f257]) ).
thf(f267,plain,
( spl4_8
| spl4_6 ),
inference(avatar_split_clause,[],[f217,f252,f262]) ).
thf(f279,plain,
( ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(constrained_superposition,[],[f249,f234]) ).
thf(f280,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f328,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ( $false
= ( q @ sK2 ) )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f249,f169]) ).
thf(f329,plain,
( ( $true
= ( p @ sK2 ) )
| ( $false
= ( q @ sK2 ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f328]) ).
thf(f336,plain,
( ( $true = $false )
| ( $false
= ( q @ sK2 ) )
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f329,f254]) ).
thf(f337,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f354,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(constrained_superposition,[],[f337,f280]) ).
thf(f360,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f354]) ).
thf(f361,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f360]) ).
thf(f383,plain,
( ( $true = $false )
| ( $true
= ( q @ sK3 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(constrained_superposition,[],[f259,f234]) ).
thf(f392,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f383]) ).
thf(f401,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(forward_demodulation,[],[f392,f264]) ).
thf(f402,plain,
( $false
| ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f403,plain,
( ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f402]) ).
thf(f444,plain,
( ( $true = $false )
| ( $true
= ( p @ sK1 ) )
| ~ spl4_1
| ~ spl4_3 ),
inference(constrained_superposition,[],[f231,f239]) ).
thf(f446,plain,
( ( $true = $false )
| ( $true
= ( q @ sK1 ) )
| ( $false
= ( p @ sK1 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f165,f239]) ).
thf(f447,plain,
( ( $true
= ( q @ sK1 ) )
| ( $false
= ( p @ sK1 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f449,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl4_1
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f444]) ).
thf(f453,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 ) )
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[],[f447,f244]) ).
thf(f454,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f467,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4 ),
inference(constrained_superposition,[],[f454,f449]) ).
thf(f473,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f467]) ).
thf(f474,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f473]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f235]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f240]) ).
cnf(s3,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f245]) ).
cnf(s4,plain,
( spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f250]) ).
cnf(s5,plain,
( spl4_1
| spl4_6 ),
inference(sat_conversion,[],[f255]) ).
cnf(s6,plain,
( spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f260]) ).
cnf(s7,plain,
( spl4_5
| spl4_8 ),
inference(sat_conversion,[],[f265]) ).
cnf(s8,plain,
( spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f266]) ).
cnf(s9,plain,
( spl4_6
| spl4_8 ),
inference(sat_conversion,[],[f267]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f361]) ).
cnf(s13,plain,
( ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f403]) ).
cnf(s23,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f474]) ).
cnf(s24,plain,
spl4_1,
inference(rat,[],[s11,s1,s4,s5]) ).
cnf(s26,plain,
( spl4_6
| ~ spl4_2 ),
inference(rat,[],[s13,s8,s9]) ).
cnf(s27,plain,
( ~ spl4_6
| ~ spl4_2 ),
inference(rat,[],[s13,s6,s7,s11]) ).
cnf(s28,plain,
~ spl4_2,
inference(rat,[],[s27,s26]) ).
cnf(s29,plain,
spl4_4,
inference(rat,[],[s3,s28]) ).
cnf(s30,plain,
spl4_3,
inference(rat,[],[s2,s28]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s23,s24,s29,s30]) ).
thf(f475,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO462^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 % Computer : n006.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 16:58:24 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.27 Running first-order model finding
% 0.09/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.32 % (1020879)Will run a generic schedule for satisfiability detection.
% 0.25/0.32 % (1020889)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4175381753:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.32 % (1020889)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.32 % (1020884)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1228837836_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.32 % (1020885)% WARNING: option uhcvi not known.
% 0.25/0.32 % (1020889) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1020879-1020889"...
% 0.25/0.32 % Exception at run slice level
% 0.25/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.32 % (1020885)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1353543389:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.32 % (1020886)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3518193131:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.32 % (1020888)dis+10_1_sil=32000:sp=arity:random_seed=1427088905:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.32 % (1020891)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2390878809:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.32 % (1020890)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1065833689:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.32 % (1020889)...printing done.
% 0.25/0.32 % (1020885)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.32 % (1020889)Refutation found. Thanks to Tanya!
% 0.25/0.32 % SZS status Theorem for theBenchmark
% 0.25/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.33 % (1020889)------------------------------
% 0.25/0.33 % (1020889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.33 % (1020889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.33 % (1020889)CaDiCaL version: 2.1.3
% 0.25/0.33 % (1020889)Termination reason: Refutation
% 0.25/0.33 % (1020889)Time elapsed: 0.016 s
% 0.25/0.33 % (1020889)Peak memory usage: 13 MB
% 0.25/0.33 % (1020889)Instructions burned: 32 (million)
% 0.25/0.33 % (1020879)Success in time 0.042 s
% 0.25/0.33 % Vampire exiting
%------------------------------------------------------------------------------