%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO396^1 : 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 : n018.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 08:47:35 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 14
% Syntax : Number of formulae : 122 ( 47 unt; 0 typ; 5 def)
% Number of atoms : 943 ( 156 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1383 ( 356 ~; 252 |; 0 &; 713 @)
% ( 5 <=>; 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 : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 57 usr; 11 con; 0-4 aty)
% ( 57 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 251 ( 0 sgn 29 !; 0 ?; 251 :)
% 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_k: $i > $i > $o ).
thf(func_def_33,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
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,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
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,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_k ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ X0 ) ) ) )
= mdia_k ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^1.ax',mdia_k) ).
thf(f34,conjecture,
mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia_k @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia_k @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f38,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f40,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f48,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f49,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f52,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_k ),
inference(rectify,[],[f32]) ).
thf(f53,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f58,plain,
~ ( mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia_k @ p ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f59,plain,
( ( mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia_k @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f58]) ).
thf(f69,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f70,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f76,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f77,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f92,plain,
( ( mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia_k @ p ) ) ) )
!= $true ),
inference(flattening,[],[f59]) ).
thf(f98,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f104,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f111,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f114,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f116,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f118,plain,
( ( mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia_k @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f120,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f123,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f129,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,[],[f114,f111,f105,f111,f111]) ).
thf(f130,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,[],[f104,f105,f111]) ).
thf(f132,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,[],[f120,f129,f130,f130]) ).
thf(f138,plain,
( mdia_k
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_k @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f98,f111,f123,f111]) ).
thf(f139,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_k @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f118,f116,f132,f123,f130,f111,f111,f138]) ).
thf(f140,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ~ ( p @ sK1 )
| ~ ( p @ sK1 )
| ~ ( rel_k @ sK0 @ sK1 ) ) )
| ( $false
= ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( $false
= ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( ~ ( p @ sK1 )
| ~ ( p @ sK1 ) )
= $false )
| ( $false
= ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( ( ~ ( p @ sK1 ) )
= $false )
| ( $false
= ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f166,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f167,plain,
( ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( $true
= ( p @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( ( ~ ( p @ sK2 ) )
= $false )
| ( $true
= ( p @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f171,plain,
( ( $false
= ( ~ ( p @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f172,plain,
( ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( ( ~ ( p @ sK2 ) )
= $false )
| ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $true
= ( p @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f201,plain,
( ( $false
= ( ~ ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f219,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f220,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X2 )
| ~ ( rel_k @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( p @ X1 )
| ~ ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( p @ X1 )
| ~ ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( p @ X1 )
| ~ ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ~ ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( p @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( p @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( ( p @ X2 )
= $false )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( ( p @ X2 )
= $false )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $false )
| ( ( p @ X1 )
= $false )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( ( p @ X2 )
= $false )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( ( p @ X2 )
= $false )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( ( p @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f232]) ).
thf(f235,definition,
( spl4_1
<=> ( $true
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f237,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f235]) ).
thf(f239,definition,
( spl4_2
<=> ( $true
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f241,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f244,definition,
( spl4_3
<=> ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f246,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f248,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f169,f235,f239]) ).
thf(f249,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f170,f244,f235]) ).
thf(f251,definition,
( spl4_4
<=> ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f253,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f254,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f174,f239,f251]) ).
thf(f255,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f175,f251,f244]) ).
thf(f257,definition,
( spl4_5
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $false )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f258,plain,
( ! [X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( ( p @ X1 )
= $false ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f272,plain,
( spl4_5
| spl4_5 ),
inference(avatar_split_clause,[],[f233,f257,f257]) ).
thf(f273,plain,
( ( $true = $false )
| ( ( p @ sK2 )
= $false )
| ~ spl4_3
| ~ spl4_5 ),
inference(constrained_superposition,[],[f246,f258]) ).
thf(f275,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f278,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(constrained_superposition,[],[f241,f275]) ).
thf(f281,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f278]) ).
thf(f282,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f281]) ).
thf(f285,plain,
( ( ( p @ sK1 )
= $false )
| ( $true = $false )
| ~ spl4_4
| ~ spl4_5 ),
inference(constrained_superposition,[],[f258,f253]) ).
thf(f286,plain,
( ( ( p @ sK1 )
= $false )
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f285]) ).
thf(f289,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(constrained_superposition,[],[f237,f286]) ).
thf(f292,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f289]) ).
thf(f293,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f292]) ).
cnf(s3,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f249]) ).
cnf(s5,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f254]) ).
cnf(s6,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f255]) ).
cnf(s12,plain,
( spl4_5
| spl4_5 ),
inference(sat_conversion,[],[f272]) ).
cnf(s13,plain,
spl4_5,
inference(rat,[],[s12]) ).
cnf(s15,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f282]) ).
cnf(s17,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f293]) ).
cnf(s18,plain,
spl4_1,
inference(rat,[],[s15,s3,s4,s13]) ).
cnf(s19,plain,
~ spl4_4,
inference(rat,[],[s17,s13,s18]) ).
cnf(s20,plain,
spl4_3,
inference(rat,[],[s6,s19]) ).
cnf(s21,plain,
spl4_2,
inference(rat,[],[s5,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s15,s13,s20,s21]) ).
thf(f294,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO396^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:52:42 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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
% 0.22/0.31 % (338665)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (338670)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=107835583:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (338671)lrs+10_16_si=on:nwc=1.5:random_seed=2211119324:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (338670) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-338665-338670"...
% 0.22/0.31 % (338671) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-338665-338671"...
% 0.22/0.31 % (338672)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3501250400:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (338670)...printing done.
% 0.22/0.31 % (338671)...printing done.
% 0.22/0.31 % (338671)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (338671)------------------------------
% 0.22/0.31 % (338671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (338671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (338671)CaDiCaL version: 2.1.3
% 0.22/0.31 % (338671)Termination reason: Refutation
% 0.22/0.31 % (338671)Time elapsed: 0.011 s
% 0.22/0.31 % (338671)Peak memory usage: 13 MB
% 0.22/0.31 % (338671)Instructions burned: 20 (million)
% 0.22/0.31 % (338665)Success in time 0.044 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------