%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO576^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:50:27 AM UTC 2026
% Result : Theorem 0.55s 0.41s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of formulae : 122 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 874 ( 174 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1315 ( 180 ~; 157 |; 13 &; 855 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 79 ( 79 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 5 con; 0-4 aty)
% ( 98 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 284 ( 211 ^; 73 !; 0 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: 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,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $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,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
p: $i > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[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,
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_45,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(func_def_52,type,
sK0: $i > mu ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(func_def_56,type,
sK4: $i > $i ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.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/LCL015^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.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(f37,conjecture,
mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
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,[],[f3]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f50,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f63,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f64,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f69,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(f70,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,[],[f69]) ).
thf(f83,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f91,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f92,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f93,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f94,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f95,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f96,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f97,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f100,plain,
~ ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f100]) ).
thf(f102,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) )
!= $true ),
inference(flattening,[],[f101]) ).
thf(f107,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f114,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f123,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f126,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,[],[f70]) ).
thf(f133,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f137,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f138,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f139,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f140,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f97]) ).
thf(f142,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f147,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,[],[f114,f108,f107]) ).
thf(f154,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,[],[f138,f107,f137,f107]) ).
thf(f155,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f139,f123]) ).
thf(f156,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,[],[f140,f126]) ).
thf(f157,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 > $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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [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 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f142,f133,f147,f154,f137,f154,f137,f154,f137]) ).
thf(f158,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ $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 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ~ ( !! @ $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 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ 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,[],[f160]) ).
thf(f163,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ 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(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ 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(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ 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,[],[f164]) ).
thf(f166,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ 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,[],[f165]) ).
thf(f167,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,[],[f166]) ).
thf(f168,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( $true
= ( rel_s4 @ sK1 @ sK2 ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,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,[],[f167]) ).
thf(f171,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,[],[f170]) ).
thf(f172,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,[],[f171]) ).
thf(f173,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,[],[f172]) ).
thf(f174,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,[],[f173]) ).
thf(f175,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,[],[f174]) ).
thf(f176,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,[],[f175]) ).
thf(f177,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,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f182,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,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ ( sK3 @ X1 ) @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ ( sK3 @ X1 ) @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ ( sK3 @ X1 ) @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( p @ X2 ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f187,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK4 @ X1 ) )
| ( p @ ( sK4 @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $false
= ( p @ ( sK4 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK4 @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,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,[],[f156]) ).
thf(f198,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,[],[f197]) ).
thf(f199,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,[],[f198]) ).
thf(f200,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,[],[f199]) ).
thf(f201,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,[],[f200]) ).
thf(f202,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,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,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,[],[f203]) ).
thf(f205,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,[],[f204]) ).
thf(f206,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f207,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f275,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK1 @ ( sK3 @ X0 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X0 ) )
| ( $true
= ( p @ ( sK4 @ ( sK3 @ X0 ) ) ) ) ),
inference(constrained_superposition,[],[f196,f185]) ).
thf(f280,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ sK1 @ ( sK3 @ X0 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X0 ) )
| ( $true
= ( p @ ( sK4 @ ( sK3 @ X0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f275]) ).
thf(f562,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f169,f205]) ).
thf(f579,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f562]) ).
thf(f611,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f205,f579]) ).
thf(f620,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f611]) ).
thf(f939,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f180,f620]) ).
thf(f969,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f939]) ).
thf(f989,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f969,f208]) ).
thf(f990,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f989]) ).
thf(f1013,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) )
| ( $false
= ( rel_s4 @ sK1 @ sK1 ) ) ),
inference(constrained_superposition,[],[f194,f990]) ).
thf(f1018,plain,
( ( $false
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) )
| ( $false
= ( rel_s4 @ sK1 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f1013]) ).
thf(f1854,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) ) ),
inference(forward_demodulation,[],[f1018,f208]) ).
thf(f1855,plain,
( $false
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[],[f1854]) ).
thf(f3741,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK1 @ sK1 ) )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) ) ),
inference(constrained_superposition,[],[f990,f280]) ).
thf(f3742,plain,
( ( $false
= ( rel_s4 @ sK1 @ sK1 ) )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f3741]) ).
thf(f3761,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) ) ),
inference(forward_demodulation,[],[f3742,f208]) ).
thf(f3762,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $true
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f3761]) ).
thf(f3773,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) ) ),
inference(forward_demodulation,[],[f3762,f208]) ).
thf(f3774,plain,
( $true
= ( p @ ( sK4 @ ( sK3 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[],[f3773]) ).
thf(f3781,plain,
$true = $false,
inference(forward_demodulation,[],[f3774,f1855]) ).
thf(f3782,plain,
$false,
inference(trivial_inequality_removal,[],[f3781]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO576^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n006.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:16:40 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.55/0.41 % (1045182)Will run a generic schedule for satisfiability detection.
% 0.55/0.41 % (1045188)% WARNING: option uhcvi not known.
% 0.55/0.41 % (1045188)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3084002011:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.55/0.41 % (1045189)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=715617682:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.55/0.41 % (1045188)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.55/0.41 % (1045188)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.55/0.41 % (1045187)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2450601461_2999 on theBenchmark for (2999ds/0Mi)
% 0.55/0.41 % Exception at run slice level
% 0.55/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.55/0.41 % (1045190)dis+10_1_sil=32000:sp=arity:random_seed=1631068484:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.55/0.41 % (1045193)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2533159744:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.55/0.41 % (1045192)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2417296649:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.55/0.41 % (1045191)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2825656819:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.55/0.41 % (1045197)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=128014551:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.55/0.41 % (1045191)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.55/0.41 % Exception at run slice level
% 0.55/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.55/0.41 % (1045203)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2930473625:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.55/0.41 % (1045190)Instruction limit reached!
% 0.55/0.41 % (1045190)------------------------------
% 0.55/0.41 % (1045190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (1045190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (1045190)CaDiCaL version: 2.1.3
% 0.55/0.41 % (1045190)Termination reason: Instruction limit
% 0.55/0.41 % (1045190)Termination phase: Saturation
% 0.55/0.41 % (1045190)Time elapsed: 0.084 s
% 0.55/0.41 % (1045190)Peak memory usage: 12 MB
% 0.55/0.41 % (1045190)Instructions burned: 103 (million)
% 0.55/0.41 % (1045189) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1045182-1045189"...
% 0.55/0.41 % (1045205)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=2727678361:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.55/0.41 % (1045205)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.55/0.41 % (1045205)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.55/0.41 % (1045189)...printing done.
% 0.55/0.41 % (1045189)Refutation found. Thanks to Tanya!
% 0.55/0.41 % SZS status Theorem for theBenchmark
% 0.55/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.55/0.41 % (1045189)------------------------------
% 0.55/0.41 % (1045189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (1045189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (1045189)CaDiCaL version: 2.1.3
% 0.55/0.41 % (1045189)Termination reason: Refutation
% 0.55/0.41 % (1045189)Time elapsed: 0.120 s
% 0.55/0.41 % (1045189)Peak memory usage: 13 MB
% 0.55/0.41 % (1045189)Instructions burned: 242 (million)
% 0.55/0.41 % (1045182)Success in time 0.162 s
% 0.55/0.41 % Vampire exiting
%------------------------------------------------------------------------------