%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO435^1 : 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 : n017.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 08:49:57 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 15
% Syntax : Number of formulae : 140 ( 76 unt; 0 typ; 4 def)
% Number of atoms : 856 ( 159 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1301 ( 219 ~; 165 |; 13 &; 798 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 79 ( 79 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 57 usr; 9 con; 0-4 aty)
% ( 90 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 271 ( 0 sgn 68 !; 0 ?; 271 :)
% 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_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK3: $i > $i ).
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(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
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_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( mdia_s4
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) ),
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(f45,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f61,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f62,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f67,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f68,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
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_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f90,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f91,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f92,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f93,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f92]) ).
thf(f94,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f95,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f96,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) )
!= $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(f104,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f116,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f119,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f126,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f130,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f131,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f132,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f93]) ).
thf(f133,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f134,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
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(f146,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f131,f101,f130,f101]) ).
thf(f147,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f132,f116]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f133,f119]) ).
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_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f134,f126,f138,f130,f146,f130,f146,f130,f146]) ).
thf(f150,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y3 @ Y4 )
| ~ ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y3 @ Y4 )
| ~ ( p @ Y4 ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s4 @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK1 @ X1 ) )
| ~ ( p @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $false
= ( ~ ( p @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( p @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f167,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f168,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( $true
= ( rel_s4 @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f173,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK3 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ ( sK3 @ X1 ) @ X2 )
| ~ ( p @ X2 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X2 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ ( sK3 @ X1 ) @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ ( sK3 @ X1 ) @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ ( sK3 @ X1 ) @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( p @ X2 ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f190,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s4 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X1 ) )
| ( $true
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f199,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f235,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X0 ) )
| ( $false
= ( p @ ( sK1 @ ( sK3 @ X0 ) ) ) ) ),
inference(constrained_superposition,[],[f165,f188]) ).
thf(f238,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X0 ) )
| ( $false
= ( rel_s4 @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( p @ ( sK1 @ ( sK3 @ X0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f235]) ).
thf(f252,definition,
( spl4_6
<=> ( $false
= ( rel_s4 @ sK2 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f254,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f252]) ).
thf(f316,plain,
( ( $true = $false )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f200,f254]) ).
thf(f323,plain,
( $false
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f324,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f323]) ).
thf(f503,definition,
( spl4_11
<=> ( $false
= ( rel_s4 @ sK0 @ ( sK3 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
thf(f504,plain,
( ( $false
!= ( rel_s4 @ sK0 @ ( sK3 @ sK2 ) ) )
| spl4_11 ),
inference(avatar_component_clause,[],[f503]) ).
thf(f505,plain,
( ( $false
= ( rel_s4 @ sK0 @ ( sK3 @ sK2 ) ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f503]) ).
thf(f514,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X0 ) ) )
| ~ spl4_11 ),
inference(constrained_superposition,[],[f197,f505]) ).
thf(f515,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X0 ) ) )
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f531,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ~ spl4_11 ),
inference(constrained_superposition,[],[f515,f182]) ).
thf(f548,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f531]) ).
thf(f569,definition,
( spl4_13
<=> ( $false
= ( rel_s4 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
thf(f571,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f569]) ).
thf(f573,plain,
( spl4_6
| spl4_13
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f548,f503,f569,f252]) ).
thf(f744,plain,
( ( $true = $false )
| ~ spl4_13 ),
inference(constrained_superposition,[],[f571,f171]) ).
thf(f756,plain,
( $false
| ~ spl4_13 ),
inference(trivial_inequality_removal,[],[f744]) ).
thf(f757,plain,
~ spl4_13,
inference(avatar_contradiction_clause,[],[f756]) ).
thf(f777,plain,
( ( $false != $false )
| ( $true
= ( p @ ( sK1 @ ( sK3 @ sK2 ) ) ) )
| spl4_11 ),
inference(constrained_superposition,[],[f504,f166]) ).
thf(f778,plain,
( ( $false != $false )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $false
= ( p @ ( sK1 @ ( sK3 @ sK2 ) ) ) )
| spl4_11 ),
inference(constrained_superposition,[],[f504,f238]) ).
thf(f780,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $false
= ( p @ ( sK1 @ ( sK3 @ sK2 ) ) ) )
| spl4_11 ),
inference(trivial_inequality_removal,[],[f778]) ).
thf(f781,plain,
( ( $true
= ( p @ ( sK1 @ ( sK3 @ sK2 ) ) ) )
| spl4_11 ),
inference(trivial_inequality_removal,[],[f777]) ).
thf(f785,definition,
( spl4_14
<=> ( $false
= ( p @ ( sK1 @ ( sK3 @ sK2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
thf(f787,plain,
( ( $false
= ( p @ ( sK1 @ ( sK3 @ sK2 ) ) ) )
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f785]) ).
thf(f788,plain,
( spl4_14
| spl4_6
| spl4_11 ),
inference(avatar_split_clause,[],[f780,f503,f252,f785]) ).
thf(f789,plain,
( ( $true = $false )
| spl4_11
| ~ spl4_14 ),
inference(constrained_superposition,[],[f787,f781]) ).
thf(f795,plain,
( $false
| spl4_11
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f789]) ).
thf(f796,plain,
( spl4_11
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f795]) ).
cnf(s10,plain,
~ spl4_6,
inference(sat_conversion,[],[f324]) ).
cnf(s22,plain,
( spl4_6
| ~ spl4_11
| spl4_13 ),
inference(sat_conversion,[],[f573]) ).
cnf(s24,plain,
~ spl4_13,
inference(sat_conversion,[],[f757]) ).
cnf(s27,plain,
( spl4_6
| spl4_11
| spl4_14 ),
inference(sat_conversion,[],[f788]) ).
cnf(s29,plain,
( spl4_11
| ~ spl4_14 ),
inference(sat_conversion,[],[f796]) ).
cnf(s30,plain,
( spl4_6
| ~ spl4_11 ),
inference(rat,[],[s22,s24]) ).
cnf(s32,plain,
~ spl4_11,
inference(rat,[],[s30,s10]) ).
cnf(s33,plain,
~ spl4_14,
inference(rat,[],[s29,s32]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s27,s10,s33,s32]) ).
thf(f797,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO435^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:47:08 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.29 % (594746)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (594758)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2001032734:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (594758)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (594755)% WARNING: option uhcvi not known.
% 0.19/0.29 % (594754)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1931043011_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (594756)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2235636837:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (594755)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=690969909:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (594757)dis+10_1_sil=32000:sp=arity:random_seed=1803730236:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (594759)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1494232670:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (594760)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4260519987:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (594755)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (594755)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.29 % (594758)Instruction limit reached!
% 0.19/0.29 % (594758)------------------------------
% 0.19/0.29 % (594758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (594758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (594758)CaDiCaL version: 2.1.3
% 0.19/0.29 % (594758)Termination reason: Instruction limit
% 0.19/0.29 % (594758)Termination phase: Saturation
% 0.19/0.29 % (594758)Time elapsed: 0.028 s
% 0.19/0.29 % (594758)Peak memory usage: 12 MB
% 0.19/0.29 % (594758)Instructions burned: 117 (million)
% 0.19/0.29 % (594780)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2642002284:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.29 % (594760) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-594746-594760"...
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (594788)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3849417609:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (594760)...printing done.
% 0.19/0.29 % (594760)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (594760)------------------------------
% 0.19/0.29 % (594760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (594760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (594760)CaDiCaL version: 2.1.3
% 0.19/0.29 % (594760)Termination reason: Refutation
% 0.19/0.29 % (594760)Time elapsed: 0.032 s
% 0.19/0.29 % (594760)Peak memory usage: 13 MB
% 0.19/0.29 % (594760)Instructions burned: 60 (million)
% 0.19/0.29 % (594746)Success in time 0.058 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------