%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO423^1 : 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 : n014.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 08:47:39 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 114 ( 48 unt; 0 typ; 5 def)
% Number of atoms : 901 ( 193 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 1245 ( 238 ~; 234 |; 0 &; 716 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 129 ( 129 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 60 usr; 10 con; 0-4 aty)
% ( 47 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 312 ( 0 sgn 68 !; 2 ?; 312 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vNOT: $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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK2: $i > $i ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(func_def_56,type,
sK4: $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] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
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(f20,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_d @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_d ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mbox_d) ).
thf(f34,axiom,
mserial @ rel_d,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',a1) ).
thf(f35,conjecture,
mvalid @ ( mnot @ ( mbox_d @ ( mand @ ( mbox_d @ ( mand @ p @ q ) ) @ ( mbox_d @ ( mimplies @ p @ ( mnot @ q ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mnot @ ( mbox_d @ ( mand @ ( mbox_d @ ( mand @ p @ q ) ) @ ( mbox_d @ ( mimplies @ p @ ( mnot @ q ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_d @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_d ),
inference(rectify,[],[f32]) ).
thf(f40,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f58,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f59,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f61,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f62,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
inference(rectify,[],[f20]) ).
thf(f63,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
~ ( mvalid @ ( mnot @ ( mbox_d @ ( mand @ ( mbox_d @ ( mand @ p @ q ) ) @ ( mbox_d @ ( mimplies @ p @ ( mnot @ q ) ) ) ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f65,plain,
( ( mvalid @ ( mnot @ ( mbox_d @ ( mand @ ( mbox_d @ ( mand @ p @ q ) ) @ ( mbox_d @ ( mimplies @ p @ ( mnot @ q ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f64]) ).
thf(f68,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f69,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f73,plain,
mserial @ rel_d,
inference(rectify,[],[f34]) ).
thf(f74,plain,
( ( mserial @ rel_d )
= $true ),
inference(fool_elimination,[],[f73]) ).
thf(f91,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f92,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f95,plain,
( ( mvalid @ ( mnot @ ( mbox_d @ ( mand @ ( mbox_d @ ( mand @ p @ q ) ) @ ( mbox_d @ ( mimplies @ p @ ( mnot @ q ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f65]) ).
thf(f106,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f114,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f115,plain,
( ( mvalid @ ( mnot @ ( mbox_d @ ( mand @ ( mbox_d @ ( mand @ p @ q ) ) @ ( mbox_d @ ( mimplies @ p @ ( mnot @ q ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f116,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f118,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f120,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f121,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f126,plain,
( ( mserial @ rel_d )
= $true ),
inference(cnf_transformation,[],[f74]) ).
thf(f130,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
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] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f114,f120,f106,f120,f120]) ).
thf(f134,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,[],[f116,f106,f120]) ).
thf(f143,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ 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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ q ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f115,f121,f120,f118,f133,f118,f133,f118,f134,f120]) ).
thf(f144,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ rel_d )
= $true ),
inference(definition_unfolding,[],[f126,f130]) ).
thf(f145,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ 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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ q ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f146,plain,
sF0 != $true,
inference(definition_folding,[],[f143,f145]) ).
thf(f147,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( rel_d @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f148,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( ?? @ $i @ ( rel_d @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( ( ?? @ $i @ ( rel_d @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( rel_d @ X1 @ ( sK1 @ X1 ) )
= $true ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( sF0 = $true )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ 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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ q ) ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f145]) ).
thf(f196,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( p @ Y2 )
| ~ ( q @ Y2 ) )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( q @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f197,plain,
( ( ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( p @ Y2 )
| ~ ( q @ Y2 ) )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( q @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
@ sK5 )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( q @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) )
| ~ ( rel_d @ sK5 @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( q @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) )
| ~ ( rel_d @ sK5 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( q @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) )
| ~ ( rel_d @ sK5 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_d @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_d @ X1 @ Y0 ) ) ) )
| ~ ( rel_d @ sK5 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( ( ~ ( rel_d @ sK5 @ X1 ) )
= $true )
| ( sF0 = $true )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_d @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_d @ X1 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( sF0 = $true )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_d @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_d @ X1 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_d @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_d @ X1 @ Y0 ) ) ) )
= $false )
| ( ( rel_d @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_d @ X1 @ Y0 ) ) ) )
= $false )
| ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_d @ X1 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f207,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_d @ X1 @ Y0 ) ) )
= $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ~ ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_d @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ~ ( p @ X2 )
| ~ ( q @ X2 ) )
| ~ ( rel_d @ X1 @ X2 ) )
= $true )
| ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ~ ( p @ X2 )
| ~ ( q @ X2 ) ) )
= $true )
| ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ~ ( rel_d @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ~ ( rel_d @ X1 @ X2 ) )
= $true )
| ( ( ~ ( p @ X2 )
| ~ ( q @ X2 ) )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ~ ( p @ X2 )
| ~ ( q @ X2 ) )
= $false )
| ( ( rel_d @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X1: $i] :
( ( ( rel_d @ X1 @ X2 )
= $false )
| ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ~ ( q @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( rel_d @ X1 @ X2 )
= $false )
| ( ( ~ ( p @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( p @ X2 )
= $true )
| ( sF0 = $true )
| ( ( rel_d @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( rel_d @ X1 @ X2 )
= $false )
| ( ( q @ X2 )
= $true )
| ( ( rel_d @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f217,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_d @ X1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_d @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( p @ X2 )
| ~ ( q @ X2 )
| ~ ( rel_d @ X1 @ X2 ) )
= $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ~ ( p @ X2 )
| ~ ( q @ X2 ) )
= $true )
| ( ( ~ ( rel_d @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( q @ X2 ) )
= $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ~ ( p @ X2 ) )
= $true )
| ( sF0 = $true )
| ( ( ~ ( rel_d @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( ~ ( rel_d @ X1 @ X2 ) )
= $true )
| ( ( ~ ( p @ X2 ) )
= $true )
| ( ( q @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( rel_d @ X1 @ X2 )
= $false )
| ( sF0 = $true )
| ( ( ~ ( p @ X2 ) )
= $true )
| ( ( q @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( p @ X2 )
= $false )
| ( ( rel_d @ X1 @ X2 )
= $false )
| ( ( q @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f258,definition,
( spl6_9
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f262,definition,
( spl6_10
<=> ! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( rel_d @ X1 @ X2 )
= $false )
| ( ( p @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
thf(f263,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( p @ X2 )
= $true )
| ( ( rel_d @ X1 @ X2 )
= $false ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f264,plain,
( spl6_9
| spl6_10 ),
inference(avatar_split_clause,[],[f215,f262,f258]) ).
thf(f266,definition,
( spl6_11
<=> ! [X2: $i,X1: $i] :
( ( ( rel_d @ X1 @ X2 )
= $false )
| ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( q @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
thf(f267,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( q @ X2 )
= $true )
| ( ( rel_d @ X1 @ X2 )
= $false ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f268,plain,
( spl6_11
| spl6_9 ),
inference(avatar_split_clause,[],[f216,f258,f266]) ).
thf(f270,definition,
( spl6_12
<=> ! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( q @ X2 )
= $false )
| ( ( rel_d @ X1 @ X2 )
= $false )
| ( ( p @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition]) ).
thf(f271,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_d @ sK5 @ X1 )
= $false )
| ( ( p @ X2 )
= $false )
| ( ( q @ X2 )
= $false )
| ( ( rel_d @ X1 @ X2 )
= $false ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f272,plain,
( spl6_12
| spl6_9 ),
inference(avatar_split_clause,[],[f224,f258,f270]) ).
thf(f273,plain,
~ spl6_9,
inference(avatar_split_clause,[],[f146,f258]) ).
thf(f286,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( p @ X0 )
= $true )
| ( ( rel_d @ ( sK1 @ sK5 ) @ X0 )
= $false ) )
| ~ spl6_10 ),
inference(constrained_superposition,[],[f263,f150]) ).
thf(f292,plain,
( ! [X0: $i] :
( ( ( rel_d @ ( sK1 @ sK5 ) @ X0 )
= $false )
| ( ( p @ X0 )
= $true ) )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f286]) ).
thf(f307,plain,
( ( ( p @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $true )
| ( $true = $false )
| ~ spl6_10 ),
inference(constrained_superposition,[],[f150,f292]) ).
thf(f308,plain,
( ( ( p @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $true )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f307]) ).
thf(f311,plain,
( ! [X0: $i] :
( ( ( p @ X0 )
= $false )
| ( ( rel_d @ ( sK1 @ sK5 ) @ X0 )
= $false )
| ( $true = $false )
| ( ( q @ X0 )
= $false ) )
| ~ spl6_12 ),
inference(constrained_superposition,[],[f271,f150]) ).
thf(f317,plain,
( ! [X0: $i] :
( ( ( rel_d @ ( sK1 @ sK5 ) @ X0 )
= $false )
| ( ( q @ X0 )
= $false )
| ( ( p @ X0 )
= $false ) )
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f311]) ).
thf(f321,plain,
( ( ( p @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $false )
| ( ( q @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $false )
| ( $true = $false )
| ~ spl6_12 ),
inference(constrained_superposition,[],[f150,f317]) ).
thf(f322,plain,
( ( ( p @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $false )
| ( ( q @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $false )
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f325,plain,
( ( $true = $false )
| ( ( q @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $false )
| ~ spl6_10
| ~ spl6_12 ),
inference(forward_demodulation,[],[f322,f308]) ).
thf(f326,plain,
( ( ( q @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $false )
| ~ spl6_10
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f331,plain,
( ! [X0: $i] :
( ( ( rel_d @ ( sK1 @ sK5 ) @ X0 )
= $false )
| ( $true
= ( q @ X0 ) )
| ( $true = $false ) )
| ~ spl6_11 ),
inference(constrained_superposition,[],[f267,f150]) ).
thf(f335,plain,
( ! [X0: $i] :
( ( ( rel_d @ ( sK1 @ sK5 ) @ X0 )
= $false )
| ( $true
= ( q @ X0 ) ) )
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f331]) ).
thf(f339,plain,
( ( $true = $false )
| ( ( q @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $true )
| ~ spl6_11 ),
inference(constrained_superposition,[],[f335,f150]) ).
thf(f343,plain,
( ( ( q @ ( sK1 @ ( sK1 @ sK5 ) ) )
= $true )
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f339]) ).
thf(f348,plain,
( ( $true = $false )
| ~ spl6_10
| ~ spl6_11
| ~ spl6_12 ),
inference(forward_demodulation,[],[f343,f326]) ).
thf(f349,plain,
( $false
| ~ spl6_10
| ~ spl6_11
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f350,plain,
( ~ spl6_10
| ~ spl6_11
| ~ spl6_12 ),
inference(avatar_contradiction_clause,[],[f349]) ).
cnf(s8,plain,
( spl6_9
| spl6_10 ),
inference(sat_conversion,[],[f264]) ).
cnf(s9,plain,
( spl6_9
| spl6_11 ),
inference(sat_conversion,[],[f268]) ).
cnf(s10,plain,
( spl6_9
| spl6_12 ),
inference(sat_conversion,[],[f272]) ).
cnf(s11,plain,
~ spl6_9,
inference(sat_conversion,[],[f273]) ).
cnf(s14,plain,
( ~ spl6_10
| ~ spl6_11
| ~ spl6_12 ),
inference(sat_conversion,[],[f350]) ).
cnf(s15,plain,
spl6_12,
inference(rat,[],[s10,s11]) ).
cnf(s16,plain,
spl6_11,
inference(rat,[],[s9,s11]) ).
cnf(s17,plain,
~ spl6_10,
inference(rat,[],[s14,s15,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s8,s17,s11]) ).
thf(f351,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO423^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:51:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.27 % (2922657)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (2922668)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (2922668)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
% 0.21/0.27 % (2922668)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3738464090:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.27 % (2922668) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2922657-2922668"...
% 0.21/0.27 % (2922662)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1518400268:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (2922663)lrs+10_16_si=on:nwc=1.5:random_seed=648122237:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (2922664)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3715881420:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (2922668)...printing done.
% 0.21/0.27 % (2922665)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1563648961:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.27 % (2922666)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2221362172:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (2922667)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1090111371:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (2922668)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (2922668)------------------------------
% 0.21/0.27 % (2922668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2922668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2922668)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2922668)Termination reason: Refutation
% 0.21/0.27 % (2922668)Time elapsed: 0.007 s
% 0.21/0.27 % (2922668)Peak memory usage: 13 MB
% 0.21/0.27 % (2922668)Instructions burned: 24 (million)
% 0.21/0.27 % (2922657)Success in time 0.036 s
% 0.21/0.27 % Vampire exiting
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