%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO409^1 : 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 : n015.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 08:49:53 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 18
% Syntax : Number of formulae : 190 ( 51 unt; 0 typ; 9 def)
% Number of atoms : 1851 ( 295 equ; 0 cnn)
% Maximal formula atoms : 11 ( 9 avg)
% Number of connectives : 2426 ( 576 ~; 538 |; 0 &;1201 @)
% ( 9 <=>; 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 : 112 ( 112 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 63 usr; 16 con; 0-4 aty)
% ( 102 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 337 ( 0 sgn 51 !; 0 ?; 337 :)
% 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(f33,axiom,
( mdia_k
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^1.ax',mdia_k) ).
thf(f34,conjecture,
mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_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(f89,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f90,plain,
~ ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f91,plain,
( ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_k @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_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(f125,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f126,plain,
( ( mvalid @ ( mequiv @ ( mdia_k @ ( mor @ p @ q ) ) @ ( mor @ ( mdia_k @ p ) @ ( mdia_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(f138,plain,
( mdia_k
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f125,f95,f124,f95]) ).
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 > $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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f126,f120,f132,f138,f96,f96,f138,f138]) ).
thf(f140,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( ( p @ Y1 )
| ( q @ 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 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( ( p @ Y1 )
| ( q @ 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 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ 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 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ 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 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,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 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,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 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ sK2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( ( p @ sK2 )
| ( q @ sK2 ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ~ ( q @ sK1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( ( p @ sK2 )
| ( q @ sK2 ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( ( p @ sK2 )
| ( q @ sK2 ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( ( p @ sK2 )
| ( q @ sK2 ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( ( p @ sK2 )
| ( q @ sK2 ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f171,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ( p @ sK2 )
| ( q @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f172,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( ~ ( p @ sK3 ) ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $true
= ( p @ sK3 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f177,plain,
( ( $true
= ( q @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( ( p @ sK2 )
| ( q @ sK2 ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f178,plain,
( ( $true
= ( q @ sK1 ) )
| ( $false
= ( ~ ( ( p @ sK2 )
| ( q @ sK2 ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( q @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f185,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( ( p @ sK2 )
| ( q @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f186,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( p @ sK3 ) ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( ~ ( p @ sK3 ) ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $true
= ( p @ sK3 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f243,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f244,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f270,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f271,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f272,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f275]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f276]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f281]) ).
thf(f287,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f270]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( ( p @ Y0 )
| ( q @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( q @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f291]) ).
thf(f298,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f299,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f303,definition,
( spl7_1
<=> ( $true
= ( rel_k @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f305,plain,
( ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f307,definition,
( spl7_2
<=> ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f309,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f307]) ).
thf(f311,definition,
( spl7_3
<=> ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f313,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f311]) ).
thf(f314,plain,
( spl7_1
| spl7_2
| spl7_3 ),
inference(avatar_split_clause,[],[f169,f311,f307,f303]) ).
thf(f316,definition,
( spl7_4
<=> ( $true
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f318,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f319,plain,
( spl7_4
| spl7_2
| spl7_3 ),
inference(avatar_split_clause,[],[f170,f311,f307,f316]) ).
thf(f321,definition,
( spl7_5
<=> ( $true
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f323,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f325,definition,
( spl7_6
<=> ( $true
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f327,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f325]) ).
thf(f328,plain,
( spl7_5
| spl7_1
| spl7_6
| spl7_3 ),
inference(avatar_split_clause,[],[f175,f311,f325,f303,f321]) ).
thf(f329,plain,
( spl7_5
| spl7_4
| spl7_6
| spl7_3 ),
inference(avatar_split_clause,[],[f176,f311,f325,f316,f321]) ).
thf(f331,definition,
( spl7_7
<=> ( $true
= ( q @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f333,plain,
( ( $true
= ( q @ sK1 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f331]) ).
thf(f334,plain,
( spl7_1
| spl7_2
| spl7_7 ),
inference(avatar_split_clause,[],[f183,f331,f307,f303]) ).
thf(f335,plain,
( spl7_4
| spl7_2
| spl7_7 ),
inference(avatar_split_clause,[],[f184,f331,f307,f316]) ).
thf(f336,plain,
( spl7_5
| spl7_1
| spl7_6
| spl7_7 ),
inference(avatar_split_clause,[],[f189,f331,f325,f303,f321]) ).
thf(f337,plain,
( spl7_5
| spl7_4
| spl7_6
| spl7_7 ),
inference(avatar_split_clause,[],[f190,f331,f325,f316,f321]) ).
thf(f343,definition,
( spl7_9
<=> ! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f344,plain,
( ! [X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f343]) ).
thf(f358,definition,
( spl7_12
<=> ! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
thf(f359,plain,
( ! [X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( q @ X1 ) ) )
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f384,plain,
( spl7_9
| spl7_9 ),
inference(avatar_split_clause,[],[f282,f343,f343]) ).
thf(f387,plain,
( spl7_12
| spl7_12 ),
inference(avatar_split_clause,[],[f301,f358,f358]) ).
thf(f397,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ~ spl7_2
| ~ spl7_9 ),
inference(constrained_superposition,[],[f309,f344]) ).
thf(f398,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl7_2
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f403,plain,
( ( $true = $false )
| ( $false
= ( q @ sK2 ) )
| ~ spl7_2
| ~ spl7_12 ),
inference(constrained_superposition,[],[f309,f359]) ).
thf(f404,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl7_2
| ~ spl7_12 ),
inference(trivial_inequality_removal,[],[f403]) ).
thf(f407,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_5
| ~ spl7_9 ),
inference(constrained_superposition,[],[f398,f323]) ).
thf(f413,plain,
( $false
| ~ spl7_2
| ~ spl7_5
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f407]) ).
thf(f414,plain,
( ~ spl7_2
| ~ spl7_5
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f413]) ).
thf(f416,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_6
| ~ spl7_12 ),
inference(constrained_superposition,[],[f404,f327]) ).
thf(f422,plain,
( $false
| ~ spl7_2
| ~ spl7_6
| ~ spl7_12 ),
inference(trivial_inequality_removal,[],[f416]) ).
thf(f423,plain,
( ~ spl7_2
| ~ spl7_6
| ~ spl7_12 ),
inference(avatar_contradiction_clause,[],[f422]) ).
thf(f427,plain,
( ( $true = $false )
| ( $false
= ( q @ sK1 ) )
| ~ spl7_3
| ~ spl7_12 ),
inference(constrained_superposition,[],[f359,f313]) ).
thf(f430,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl7_3
| ~ spl7_12 ),
inference(trivial_inequality_removal,[],[f427]) ).
thf(f435,plain,
( ( $true = $false )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_12 ),
inference(constrained_superposition,[],[f430,f333]) ).
thf(f441,plain,
( $false
| ~ spl7_3
| ~ spl7_7
| ~ spl7_12 ),
inference(trivial_inequality_removal,[],[f435]) ).
thf(f442,plain,
( ~ spl7_3
| ~ spl7_7
| ~ spl7_12 ),
inference(avatar_contradiction_clause,[],[f441]) ).
thf(f447,plain,
( ( $true = $false )
| ( $false
= ( p @ sK3 ) )
| ~ spl7_1
| ~ spl7_9 ),
inference(constrained_superposition,[],[f344,f305]) ).
thf(f448,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl7_1
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f447]) ).
thf(f452,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_9 ),
inference(constrained_superposition,[],[f448,f318]) ).
thf(f458,plain,
( $false
| ~ spl7_1
| ~ spl7_4
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f452]) ).
thf(f459,plain,
( ~ spl7_1
| ~ spl7_4
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f458]) ).
cnf(s1,plain,
( spl7_1
| spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f314]) ).
cnf(s2,plain,
( spl7_2
| spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f319]) ).
cnf(s3,plain,
( spl7_1
| spl7_3
| spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f328]) ).
cnf(s4,plain,
( spl7_3
| spl7_4
| spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f329]) ).
cnf(s5,plain,
( spl7_1
| spl7_2
| spl7_7 ),
inference(sat_conversion,[],[f334]) ).
cnf(s6,plain,
( spl7_2
| spl7_4
| spl7_7 ),
inference(sat_conversion,[],[f335]) ).
cnf(s7,plain,
( spl7_1
| spl7_5
| spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f336]) ).
cnf(s8,plain,
( spl7_4
| spl7_5
| spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f337]) ).
cnf(s21,plain,
( spl7_9
| spl7_9 ),
inference(sat_conversion,[],[f384]) ).
cnf(s22,plain,
spl7_9,
inference(rat,[],[s21]) ).
cnf(s25,plain,
( spl7_12
| spl7_12 ),
inference(sat_conversion,[],[f387]) ).
cnf(s26,plain,
spl7_12,
inference(rat,[],[s25]) ).
cnf(s28,plain,
( ~ spl7_2
| ~ spl7_5
| ~ spl7_9 ),
inference(sat_conversion,[],[f414]) ).
cnf(s30,plain,
( ~ spl7_2
| ~ spl7_6
| ~ spl7_12 ),
inference(sat_conversion,[],[f423]) ).
cnf(s32,plain,
( ~ spl7_3
| ~ spl7_7
| ~ spl7_12 ),
inference(sat_conversion,[],[f442]) ).
cnf(s34,plain,
( ~ spl7_1
| ~ spl7_4
| ~ spl7_9 ),
inference(sat_conversion,[],[f459]) ).
cnf(s35,plain,
( spl7_2
| spl7_1 ),
inference(rat,[],[s32,s1,s5,s26]) ).
cnf(s36,plain,
( spl7_5
| spl7_6
| spl7_1 ),
inference(rat,[],[s32,s3,s7,s26]) ).
cnf(s37,plain,
spl7_1,
inference(rat,[],[s36,s28,s30,s35,s22,s26]) ).
cnf(s38,plain,
~ spl7_4,
inference(rat,[],[s34,s22,s37]) ).
cnf(s39,plain,
spl7_7,
inference(rat,[],[s8,s28,s30,s6,s38,s22,s26]) ).
cnf(s40,plain,
~ spl7_3,
inference(rat,[],[s32,s26,s39]) ).
cnf(s41,plain,
spl7_2,
inference(rat,[],[s2,s38,s40]) ).
cnf(s42,plain,
~ spl7_6,
inference(rat,[],[s30,s26,s41]) ).
cnf(s43,plain,
~ spl7_5,
inference(rat,[],[s28,s22,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s4,s40,s38,s42,s43]) ).
thf(f460,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO409^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:54:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.27 % (3790169)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (3790175)% WARNING: option uhcvi not known.
% 0.20/0.27 % (3790175)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1174303217:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (3790175)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (3790175)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.27 % (3790175) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3790169-3790175"...
% 0.20/0.27 % (3790174)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4275783668_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (3790177)dis+10_1_sil=32000:sp=arity:random_seed=3210149737:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (3790175)...printing done.
% 0.20/0.27 % (3790175)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (3790175)------------------------------
% 0.20/0.27 % (3790175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (3790175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (3790175)CaDiCaL version: 2.1.3
% 0.20/0.27 % (3790175)Termination reason: Refutation
% 0.20/0.27 % (3790175)Time elapsed: 0.009 s
% 0.20/0.27 % (3790175)Peak memory usage: 13 MB
% 0.20/0.27 % (3790175)Instructions burned: 30 (million)
% 0.20/0.27 % (3790169)Success in time 0.035 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------