%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO437^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:49:58 AM UTC 2026
% Result : Theorem 0.08s 0.19s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 21
% Syntax : Number of formulae : 197 ( 93 unt; 0 typ; 9 def)
% Number of atoms : 1420 ( 264 equ; 0 cnn)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 1935 ( 341 ~; 368 |; 13 &;1122 @)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 148 ( 148 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 64 usr; 15 con; 0-4 aty)
% ( 70 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 349 ( 0 sgn 78 !; 0 ?; 349 :)
% 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,
q: $i > $o ).
thf(func_def_37,type,
r: $i > $o ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vAND: $o > $o > $o ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK1: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f45,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(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(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 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) )
!= $true ),
inference(flattening,[],[f97]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f103,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f104,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f106,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(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(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 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f137,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f103,f101,f102,f101,f101]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f104,f102,f101]) ).
thf(f140,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f106,f137,f138,f138]) ).
thf(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 > $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 > $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 ) )
@ r ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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 > $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] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ r ) ) ) ) ) ),
inference(definition_unfolding,[],[f134,f126,f138,f130,f138,f130,f140,f130,f138,f130,f140,f130]) ).
thf(f150,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( ~ ( ~ ( p @ Y2 )
| ( q @ Y2 ) )
| ~ ( ~ ( q @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ( r @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( ~ ( ~ ( p @ Y2 )
| ( q @ Y2 ) )
| ~ ( ~ ( q @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) ) ) ) ),
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 )
| ( q @ Y2 ) )
| ~ ( ~ ( q @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ( r @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( ~ ( ~ ( p @ Y2 )
| ( q @ Y2 ) )
| ~ ( ~ ( q @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) ) )
@ 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 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ),
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 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( r @ Y0 ) ) ) ) ),
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 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( r @ Y0 ) ) ) ),
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 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( r @ Y0 ) )
@ 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 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( r @ X1 ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( r @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK1 @ X1 ) )
| ~ ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) )
| ~ ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) )
| ~ ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( r @ X1 ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) )
| ~ ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( p @ ( sK1 @ X1 ) ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( q @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( q @ ( sK1 @ X1 ) ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( q @ ( sK1 @ X1 ) ) )
| ( $false
= ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( q @ ( sK1 @ X1 ) ) )
| ( $false
= ( ~ ( p @ ( sK1 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( q @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( p @ ( sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( p @ ( sK1 @ X1 ) ) )
| ( $false
= ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f178,plain,
! [X1: $i] :
( ( $false
= ( q @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( p @ ( sK1 @ X1 ) ) )
| ( $true
= ( r @ X1 ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f181,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f182,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( $true
= ( rel_s4 @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f187,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f188,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f204,plain,
( $false
= ( ~ ( rel_s4 @ sK2 @ sK3 )
| ( r @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
( $false
= ( r @ sK3 ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( $false
= ( ~ ( rel_s4 @ sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f207,plain,
( $true
= ( rel_s4 @ sK2 @ sK3 ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,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(f209,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,[],[f208]) ).
thf(f210,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,[],[f209]) ).
thf(f211,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,[],[f210]) ).
thf(f212,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,[],[f211]) ).
thf(f213,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,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,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,[],[f214]) ).
thf(f216,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,[],[f215]) ).
thf(f217,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f218,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f269,definition,
( spl4_6
<=> ( $false
= ( rel_s4 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f271,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f476,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f207,f216]) ).
thf(f499,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f476]) ).
thf(f567,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $true
= ( r @ sK3 ) ) ),
inference(constrained_superposition,[],[f499,f178]) ).
thf(f568,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $true
= ( r @ sK3 ) )
| ( $true
= ( p @ ( sK1 @ sK3 ) ) ) ),
inference(constrained_superposition,[],[f499,f176]) ).
thf(f578,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f216,f499]) ).
thf(f581,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f578]) ).
thf(f591,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $true
= ( r @ sK3 ) )
| ( $true
= ( p @ ( sK1 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[],[f568]) ).
thf(f592,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $true
= ( r @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f567]) ).
thf(f597,definition,
( spl4_20
<=> ( $true
= ( p @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_20])],[avatar_definition]) ).
thf(f599,plain,
( ( $true
= ( p @ ( sK1 @ sK3 ) ) )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f597]) ).
thf(f601,definition,
( spl4_21
<=> ( $true
= ( r @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_21])],[avatar_definition]) ).
thf(f603,plain,
( ( $true
= ( r @ sK3 ) )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f601]) ).
thf(f605,definition,
( spl4_22
<=> ( $true
= ( q @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition]) ).
thf(f607,plain,
( ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f605]) ).
thf(f610,definition,
( spl4_23
<=> ( $false
= ( p @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_23])],[avatar_definition]) ).
thf(f612,plain,
( ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ~ spl4_23 ),
inference(avatar_component_clause,[],[f610]) ).
thf(f614,definition,
( spl4_24
<=> ( $false
= ( q @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_24])],[avatar_definition]) ).
thf(f616,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f614]) ).
thf(f618,plain,
( spl4_20
| spl4_21
| spl4_22
| spl4_6 ),
inference(avatar_split_clause,[],[f591,f269,f605,f601,f597]) ).
thf(f619,plain,
( spl4_21
| spl4_23
| spl4_24
| spl4_6 ),
inference(avatar_split_clause,[],[f592,f269,f614,f610,f601]) ).
thf(f634,plain,
( ( $true = $false )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f271,f185]) ).
thf(f646,plain,
( $false
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f634]) ).
thf(f647,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f646]) ).
thf(f650,plain,
( ( $true = $false )
| ~ spl4_21 ),
inference(constrained_superposition,[],[f603,f205]) ).
thf(f654,plain,
( $false
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f650]) ).
thf(f655,plain,
~ spl4_21,
inference(avatar_contradiction_clause,[],[f654]) ).
thf(f659,plain,
( ( $true = $false )
| ~ spl4_20
| ~ spl4_23 ),
inference(constrained_superposition,[],[f612,f599]) ).
thf(f665,plain,
( $false
| ~ spl4_20
| ~ spl4_23 ),
inference(trivial_inequality_removal,[],[f659]) ).
thf(f666,plain,
( ~ spl4_20
| ~ spl4_23 ),
inference(avatar_contradiction_clause,[],[f665]) ).
thf(f977,definition,
( spl4_26
<=> ( $false
= ( rel_s4 @ sK2 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_26])],[avatar_definition]) ).
thf(f979,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ~ spl4_26 ),
inference(avatar_component_clause,[],[f977]) ).
thf(f1156,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ sK0 @ sK3 ) )
| ( $true
= ( r @ sK3 ) ) ),
inference(constrained_superposition,[],[f581,f166]) ).
thf(f1245,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ sK0 @ sK3 ) )
| ( $true
= ( r @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f1156]) ).
thf(f1252,definition,
( spl4_27
<=> ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_27])],[avatar_definition]) ).
thf(f1253,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) )
| ~ spl4_27 ),
inference(avatar_component_clause,[],[f1252]) ).
thf(f1255,definition,
( spl4_28
<=> ( $false
= ( rel_s4 @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_28])],[avatar_definition]) ).
thf(f1257,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK3 ) )
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f1255]) ).
thf(f1259,plain,
( spl4_21
| spl4_28
| spl4_27 ),
inference(avatar_split_clause,[],[f1245,f1252,f1255,f601]) ).
thf(f1283,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( p @ ( sK1 @ sK3 ) ) )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_27 ),
inference(constrained_superposition,[],[f1253,f202]) ).
thf(f1332,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( p @ ( sK1 @ sK3 ) ) )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_27 ),
inference(trivial_inequality_removal,[],[f1283]) ).
thf(f1365,plain,
( spl4_24
| spl4_20
| spl4_26
| ~ spl4_27 ),
inference(avatar_split_clause,[],[f1332,f1252,f977,f597,f614]) ).
thf(f1384,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl4_28 ),
inference(constrained_superposition,[],[f499,f1257]) ).
thf(f1385,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl4_28 ),
inference(trivial_inequality_removal,[],[f1384]) ).
thf(f1396,plain,
( spl4_6
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f1385,f1255,f269]) ).
thf(f1398,plain,
( ( $true = $false )
| ~ spl4_26 ),
inference(constrained_superposition,[],[f979,f219]) ).
thf(f1422,plain,
( $false
| ~ spl4_26 ),
inference(trivial_inequality_removal,[],[f1398]) ).
thf(f1423,plain,
~ spl4_26,
inference(avatar_contradiction_clause,[],[f1422]) ).
thf(f1740,plain,
( ( $true = $false )
| ~ spl4_22
| ~ spl4_24 ),
inference(constrained_superposition,[],[f607,f616]) ).
thf(f1741,plain,
( $false
| ~ spl4_22
| ~ spl4_24 ),
inference(trivial_inequality_removal,[],[f1740]) ).
thf(f1742,plain,
( ~ spl4_22
| ~ spl4_24 ),
inference(avatar_contradiction_clause,[],[f1741]) ).
thf(f1818,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ~ spl4_27 ),
inference(constrained_superposition,[],[f1253,f198]) ).
thf(f1881,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ~ spl4_27 ),
inference(trivial_inequality_removal,[],[f1818]) ).
thf(f1889,plain,
( spl4_23
| spl4_22
| spl4_26
| ~ spl4_27 ),
inference(avatar_split_clause,[],[f1881,f1252,f977,f605,f610]) ).
cnf(s21,plain,
( spl4_6
| spl4_20
| spl4_21
| spl4_22 ),
inference(sat_conversion,[],[f618]) ).
cnf(s22,plain,
( spl4_6
| spl4_21
| spl4_23
| spl4_24 ),
inference(sat_conversion,[],[f619]) ).
cnf(s26,plain,
~ spl4_6,
inference(sat_conversion,[],[f647]) ).
cnf(s30,plain,
~ spl4_21,
inference(sat_conversion,[],[f655]) ).
cnf(s32,plain,
( ~ spl4_20
| ~ spl4_23 ),
inference(sat_conversion,[],[f666]) ).
cnf(s38,plain,
( spl4_21
| spl4_27
| spl4_28 ),
inference(sat_conversion,[],[f1259]) ).
cnf(s43,plain,
( spl4_20
| spl4_24
| spl4_26
| ~ spl4_27 ),
inference(sat_conversion,[],[f1365]) ).
cnf(s47,plain,
( spl4_6
| ~ spl4_28 ),
inference(sat_conversion,[],[f1396]) ).
cnf(s52,plain,
~ spl4_26,
inference(sat_conversion,[],[f1423]) ).
cnf(s53,plain,
( ~ spl4_22
| ~ spl4_24 ),
inference(sat_conversion,[],[f1742]) ).
cnf(s58,plain,
( spl4_22
| spl4_23
| spl4_26
| ~ spl4_27 ),
inference(sat_conversion,[],[f1889]) ).
cnf(s60,plain,
( spl4_20
| spl4_24
| ~ spl4_27 ),
inference(rat,[],[s43,s52]) ).
cnf(s64,plain,
~ spl4_28,
inference(rat,[],[s47,s26]) ).
cnf(s65,plain,
spl4_27,
inference(rat,[],[s38,s30,s64]) ).
cnf(s67,plain,
( spl4_23
| spl4_24 ),
inference(rat,[],[s22,s30,s26]) ).
cnf(s68,plain,
( spl4_20
| spl4_22 ),
inference(rat,[],[s21,s30,s26]) ).
cnf(s75,plain,
spl4_20,
inference(rat,[],[s53,s68,s60,s65]) ).
cnf(s76,plain,
~ spl4_23,
inference(rat,[],[s32,s75]) ).
cnf(s77,plain,
spl4_22,
inference(rat,[],[s58,s65,s52,s76]) ).
cnf(s78,plain,
spl4_24,
inference(rat,[],[s67,s76]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s53,s78,s77]) ).
thf(f1890,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO437^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 16:51:19 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.12 Running first-order model finding
% 0.08/0.12 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % (371153)Will run a generic schedule for satisfiability detection.
% 0.08/0.19 % (371170)% WARNING: option uhcvi not known.
% 0.08/0.19 % (371170)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1107306357:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.19 % (371169)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3519853391_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.19 % (371171)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2035932067:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.19 % (371174)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2029883084:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.19 % (371172)dis+10_1_sil=32000:sp=arity:random_seed=2836818755:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.19 % (371173)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4203764864:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.19 % (371176)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=158145180:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.19 % (371170)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.19 % (371173)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.19 % Exception at run slice level% (371170)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.19
% 0.08/0.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.19 % (371191)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1138809226:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.08/0.19 % Exception at run slice level
% 0.08/0.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.19 % (371172)Instruction limit reached!
% 0.08/0.19 % (371172)------------------------------
% 0.08/0.19 % (371172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (371201)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=197546291:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.19 % (371172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (371172)CaDiCaL version: 2.1.3
% 0.08/0.19 % (371172)Termination reason: Instruction limit
% 0.08/0.19 % (371172)Termination phase: Saturation
% 0.08/0.19 % (371172)Time elapsed: 0.024 s
% 0.08/0.19 % (371172)Peak memory usage: 12 MB
% 0.08/0.19 % (371172)Instructions burned: 106 (million)
% 0.08/0.19 % (371173)Instruction limit reached!
% 0.08/0.19 % (371173)------------------------------
% 0.08/0.19 % (371173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (371173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (371173)CaDiCaL version: 2.1.3
% 0.08/0.19 % (371173)Termination reason: Instruction limit
% 0.08/0.19 % (371173)Termination phase: Saturation
% 0.08/0.19 % (371173)Time elapsed: 0.026 s
% 0.08/0.19 % (371173)Peak memory usage: 12 MB
% 0.08/0.19 % (371173)Instructions burned: 117 (million)
% 0.08/0.19 % (371174)Instruction limit reached!
% 0.08/0.19 % (371174)------------------------------
% 0.08/0.19 % (371174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (371174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (371174)CaDiCaL version: 2.1.3
% 0.08/0.19 % (371174)Termination reason: Instruction limit
% 0.08/0.19 % (371174)Termination phase: Saturation
% 0.08/0.19 % (371174)Time elapsed: 0.030 s
% 0.08/0.19 % (371174)Peak memory usage: 12 MB
% 0.08/0.19 % (371174)Instructions burned: 134 (million)
% 0.08/0.19 % (371208)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2796083475:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.08/0.19 % (371176) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-371153-371176"...
% 0.08/0.19 % (371208)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.19 % (371210)ott-21_1_sil=16000:fs=off:random_seed=708878948:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.08/0.19 % (371208)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.19 % (371176)...printing done.
% 0.08/0.19 % (371176)Refutation found. Thanks to Tanya!
% 0.08/0.19 % SZS status Theorem for theBenchmark
% 0.08/0.19 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.20 % (371176)------------------------------
% 0.08/0.20 % (371176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.20 % (371176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.20 % (371176)CaDiCaL version: 2.1.3
% 0.08/0.20 % (371176)Termination reason: Refutation
% 0.08/0.20 % (371176)Time elapsed: 0.038 s
% 0.08/0.20 % (371176)Peak memory usage: 13 MB
% 0.08/0.20 % (371176)Instructions burned: 151 (million)
% 0.08/0.20 % (371153)Success in time 0.068 s
% 0.08/0.20 % Vampire exiting
%------------------------------------------------------------------------------