%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO402^1 : 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 : n013.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 08:49:52 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 20
% Syntax : Number of formulae : 194 ( 49 unt; 0 typ; 12 def)
% Number of atoms : 1403 ( 241 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1711 ( 353 ~; 378 |; 0 &; 903 @)
% ( 12 <=>; 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 : 70 ( 66 usr; 19 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_k: $i > $i > $o ).
thf(func_def_33,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_k: ( $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_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f34,conjecture,
mvalid @ ( mimplies @ ( mbox_k @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_k @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f38,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f39,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f41,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f45,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f79,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f80,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f87,plain,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f88,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f90,plain,
~ ( mvalid @ ( mimplies @ ( mbox_k @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f91,plain,
( ( mvalid @ ( mimplies @ ( mbox_k @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( ( mvalid @ ( mimplies @ ( mbox_k @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) ) )
!= $true ),
inference(flattening,[],[f91]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f96,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f97,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f98,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f100,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f124,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f126,plain,
( ( mvalid @ ( mimplies @ ( mbox_k @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_k @ p ) @ ( mbox_k @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f129,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,[],[f97,f95,f96,f95,f95]) ).
thf(f130,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,[],[f98,f96,f95]) ).
thf(f132,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,[],[f100,f129,f130,f130]) ).
thf(f139,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_k @ 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_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f126,f120,f130,f124,f132,f132,f124,f124]) ).
thf(f140,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f152,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f161,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK1 )
| ( q @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK1 )
| ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f185,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f186,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ( p @ sK2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f200,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ( p @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f203,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( q @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f206,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( q @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f208,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f209,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f211,definition,
( spl4_1
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f212,plain,
( ! [X2: $i] :
( ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f214,definition,
( spl4_2
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f215,plain,
( ! [X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f216,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f176,f214,f211]) ).
thf(f218,definition,
( spl4_3
<=> ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f220,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f221,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f183,f214,f218]) ).
thf(f223,definition,
( spl4_4
<=> ( $false
= ( q @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f225,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f226,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f184,f214,f223]) ).
thf(f228,definition,
( spl4_5
<=> ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f230,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,plain,
( spl4_1
| spl4_5 ),
inference(avatar_split_clause,[],[f196,f228,f211]) ).
thf(f233,definition,
( spl4_6
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f235,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f236,plain,
( spl4_1
| spl4_6 ),
inference(avatar_split_clause,[],[f198,f233,f211]) ).
thf(f238,definition,
( spl4_7
<=> ( $true
= ( rel_k @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f240,plain,
( ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f241,plain,
( spl4_7
| spl4_5 ),
inference(avatar_split_clause,[],[f206,f228,f238]) ).
thf(f243,definition,
( spl4_8
<=> ( $false
= ( q @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f245,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl4_8
| spl4_5 ),
inference(avatar_split_clause,[],[f204,f228,f243]) ).
thf(f247,plain,
( spl4_7
| spl4_6 ),
inference(avatar_split_clause,[],[f209,f233,f238]) ).
thf(f248,plain,
( spl4_8
| spl4_6 ),
inference(avatar_split_clause,[],[f207,f233,f243]) ).
thf(f249,plain,
( ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(constrained_superposition,[],[f215,f230]) ).
thf(f261,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ( $false
= ( q @ sK2 ) )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f159,f230]) ).
thf(f266,plain,
( ( $true
= ( p @ sK2 ) )
| ( $false
= ( q @ sK2 ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f261]) ).
thf(f268,definition,
( spl4_9
<=> ( $false
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f270,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f272,definition,
( spl4_10
<=> ( $true
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
thf(f274,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f276,plain,
( spl4_9
| spl4_10
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f266,f228,f272,f268]) ).
thf(f286,plain,
( ( $true = $false )
| ( $true
= ( q @ sK3 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(constrained_superposition,[],[f215,f240]) ).
thf(f287,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f286]) ).
thf(f293,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(constrained_superposition,[],[f287,f245]) ).
thf(f297,plain,
( $false
| ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f293]) ).
thf(f298,plain,
( ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f297]) ).
thf(f299,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f249]) ).
thf(f301,plain,
( ( $true = $false )
| ~ spl4_6
| ~ spl4_10 ),
inference(constrained_superposition,[],[f274,f235]) ).
thf(f305,plain,
( $false
| ~ spl4_6
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f301]) ).
thf(f306,plain,
( ~ spl4_6
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[],[f305]) ).
thf(f332,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(constrained_superposition,[],[f299,f270]) ).
thf(f336,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f332]) ).
thf(f337,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f336]) ).
thf(f341,plain,
( ( $true = $false )
| ( $true
= ( q @ sK1 ) )
| ( $false
= ( p @ sK1 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f220,f155]) ).
thf(f346,plain,
( ( $true
= ( q @ sK1 ) )
| ( $false
= ( p @ sK1 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f341]) ).
thf(f349,definition,
( spl4_11
<=> ( $false
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
thf(f351,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f349]) ).
thf(f353,definition,
( spl4_12
<=> ( $true
= ( q @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
thf(f355,plain,
( ( $true
= ( q @ sK1 ) )
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f357,plain,
( spl4_11
| spl4_12
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f346,f218,f353,f349]) ).
thf(f381,plain,
( ( $true = $false )
| ( $true
= ( p @ sK1 ) )
| ~ spl4_1
| ~ spl4_3 ),
inference(constrained_superposition,[],[f220,f212]) ).
thf(f382,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl4_1
| ~ spl4_5 ),
inference(constrained_superposition,[],[f230,f212]) ).
thf(f384,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f382]) ).
thf(f385,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl4_1
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f381]) ).
thf(f389,plain,
( spl4_10
| ~ spl4_1
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f384,f228,f211,f272]) ).
thf(f406,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_11 ),
inference(constrained_superposition,[],[f385,f351]) ).
thf(f410,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f406]) ).
thf(f411,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f410]) ).
thf(f414,plain,
( ( $true = $false )
| ~ spl4_4
| ~ spl4_12 ),
inference(constrained_superposition,[],[f355,f225]) ).
thf(f418,plain,
( $false
| ~ spl4_4
| ~ spl4_12 ),
inference(trivial_inequality_removal,[],[f414]) ).
thf(f419,plain,
( ~ spl4_4
| ~ spl4_12 ),
inference(avatar_contradiction_clause,[],[f418]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f216]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f221]) ).
cnf(s3,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f226]) ).
cnf(s4,plain,
( spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f231]) ).
cnf(s5,plain,
( spl4_1
| spl4_6 ),
inference(sat_conversion,[],[f236]) ).
cnf(s6,plain,
( spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f241]) ).
cnf(s7,plain,
( spl4_5
| spl4_8 ),
inference(sat_conversion,[],[f246]) ).
cnf(s8,plain,
( spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f247]) ).
cnf(s9,plain,
( spl4_6
| spl4_8 ),
inference(sat_conversion,[],[f248]) ).
cnf(s11,plain,
( ~ spl4_5
| spl4_9
| spl4_10 ),
inference(sat_conversion,[],[f276]) ).
cnf(s13,plain,
( ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f298]) ).
cnf(s15,plain,
( ~ spl4_6
| ~ spl4_10 ),
inference(sat_conversion,[],[f306]) ).
cnf(s17,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(sat_conversion,[],[f337]) ).
cnf(s19,plain,
( ~ spl4_3
| spl4_11
| spl4_12 ),
inference(sat_conversion,[],[f357]) ).
cnf(s20,plain,
( ~ spl4_1
| ~ spl4_5
| spl4_10 ),
inference(sat_conversion,[],[f389]) ).
cnf(s27,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_11 ),
inference(sat_conversion,[],[f411]) ).
cnf(s29,plain,
( ~ spl4_4
| ~ spl4_12 ),
inference(sat_conversion,[],[f419]) ).
cnf(s30,plain,
spl4_1,
inference(rat,[],[s11,s17,s15,s1,s4,s5]) ).
cnf(s31,plain,
( spl4_6
| ~ spl4_2 ),
inference(rat,[],[s13,s8,s9]) ).
cnf(s32,plain,
~ spl4_2,
inference(rat,[],[s13,s6,s7,s20,s15,s31,s30]) ).
cnf(s33,plain,
spl4_4,
inference(rat,[],[s3,s32]) ).
cnf(s34,plain,
spl4_3,
inference(rat,[],[s2,s32]) ).
cnf(s35,plain,
~ spl4_12,
inference(rat,[],[s29,s33]) ).
cnf(s36,plain,
~ spl4_11,
inference(rat,[],[s27,s30,s34]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s19,s35,s34,s36]) ).
thf(f420,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO402^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 16:50:06 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.07/0.25 % (2368302)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (2368313)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1637870095:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.25 % (2368308)% WARNING: option uhcvi not known.
% 0.07/0.25 % (2368313) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2368302-2368313"...
% 0.07/0.25 % (2368308)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3652031178:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.25 % (2368307)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3951601714_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.25 % (2368310)dis+10_1_sil=32000:sp=arity:random_seed=2751720999:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.25 % (2368311)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2063245785:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.25 % (2368312)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4032767255:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.25 % (2368308)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.25 % (2368313)...printing done.
% 0.07/0.25 % (2368311)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.25 % (2368313)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (2368313)------------------------------
% 0.07/0.25 % (2368313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (2368313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (2368313)CaDiCaL version: 2.1.3
% 0.07/0.25 % (2368313)Termination reason: Refutation
% 0.07/0.25 % (2368313)Time elapsed: 0.008 s
% 0.07/0.25 % (2368313)Peak memory usage: 13 MB
% 0.07/0.25 % (2368313)Instructions burned: 29 (million)
% 0.07/0.25 % (2368302)Success in time 0.044 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------