%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO458^2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:47:51 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 92 ( 62 unt; 0 typ; 3 def)
% Number of atoms : 526 ( 86 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 745 ( 154 ~; 112 |; 0 &; 447 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 56 usr; 8 con; 0-4 aty)
% ( 29 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 192 ( 0 sgn 12 !; 0 ?; 192 :)
% 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_d: $i > $i > $o ).
thf(func_def_33,type,
mbox_d: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_d: ( $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,
vOR: $o > $o > $o ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_54,type,
sK2: $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,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_d @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mbox_d) ).
thf(f35,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) @ ( mbox_d @ ( mequiv @ p @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) @ ( mbox_d @ ( mequiv @ p @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f37,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f38,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f45,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f62,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f63,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f69,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f70,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_d @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f72,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f87,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f89,plain,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) @ ( mbox_d @ ( mequiv @ p @ q ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f90,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) @ ( mbox_d @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f89]) ).
thf(f95,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) @ ( mbox_d @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(flattening,[],[f90]) ).
thf(f103,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f112,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f113,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f122,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) @ ( mbox_d @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f123,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f124,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f127,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f130,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f133,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f123,f112,f124,f112,f112]) ).
thf(f134,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f103,f124,f112]) ).
thf(f136,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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f130,f133,f134,f134]) ).
thf(f143,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f122,f113,f134,f133,f127,f127,f127,f136]) ).
thf(f145,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f146,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( $false
= ( ~ ( rel_d @ sK0 @ sK1 )
| ~ ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) )
| ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) )
| ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( $false
= ( ~ ( rel_d @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( $true
= ( rel_d @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) )
| ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f156,plain,
( ( ( ~ ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
= $true )
| ( ( ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( ( ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f159,plain,
( ( ( ~ ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) )
= $true )
| ( $false
= ( p @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( ( $false
= ( ( q @ sK1 )
| ~ ( p @ sK1 ) ) )
| ( $false
= ( p @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( $false
= ( q @ sK1 ) )
| ( $false
= ( p @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f169,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f170,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( ~ ( rel_d @ sK0 @ X1 )
| ( q @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) )
| ( $true
= ( q @ X1 ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f179,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( ~ ( rel_d @ sK0 @ X1 )
| ( p @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f188,definition,
( spl3_1
<=> ( $false
= ( q @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f190,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f192,definition,
( spl3_2
<=> ( $false
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f194,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f195,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f162,f192,f188]) ).
thf(f197,definition,
( spl3_3
<=> ( $true
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f198,plain,
( ( $true
!= ( p @ sK1 ) )
| spl3_3 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f199,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f205,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f199,f194]) ).
thf(f206,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f207,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f206]) ).
thf(f210,plain,
( ( $false = $true )
| ( $true
= ( q @ sK1 ) ) ),
inference(constrained_superposition,[],[f154,f177]) ).
thf(f212,plain,
( $true
= ( q @ sK1 ) ),
inference(trivial_inequality_removal,[],[f210]) ).
thf(f216,plain,
( ( $false = $true )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f212,f190]) ).
thf(f217,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f218,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f217]) ).
thf(f223,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f154,f182]) ).
thf(f225,plain,
( $true
= ( p @ sK1 ) ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f228,plain,
( $false
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f225,f198]) ).
thf(f229,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f228]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f195]) ).
cnf(s3,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f207]) ).
cnf(s5,plain,
~ spl3_1,
inference(sat_conversion,[],[f218]) ).
cnf(s8,plain,
spl3_3,
inference(sat_conversion,[],[f229]) ).
cnf(s9,plain,
~ spl3_2,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s5]) ).
thf(f230,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO458^2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 % Computer : n008.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 16:58:24 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 Running higher-order theorem proving
% 0.11/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.25 % (3427150)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.25 % (3427167)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2750716423:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.11/0.25 % (3427167) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3427150-3427167"...
% 0.11/0.25 % (3427173)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.11/0.25 % (3427173)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.11/0.25 % (3427167)...printing done.
% 0.11/0.25 % (3427169)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3316399184:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.11/0.25 % (3427167)Refutation found. Thanks to Tanya!
% 0.11/0.25 % SZS status Theorem for theBenchmark
% 0.11/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.26 % (3427167)------------------------------
% 0.11/0.26 % (3427167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.26 % (3427167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.26 % (3427167)CaDiCaL version: 2.1.3
% 0.11/0.26 % (3427167)Termination reason: Refutation
% 0.11/0.26 % (3427167)Time elapsed: 0.005 s
% 0.11/0.26 % (3427167)Peak memory usage: 13 MB
% 0.11/0.26 % (3427167)Instructions burned: 17 (million)
% 0.11/0.26 % (3427150)Success in time 0.041 s
% 0.11/0.26 % Vampire exiting
%------------------------------------------------------------------------------