%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO458^6 : 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 : 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 08:47:51 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 85 ( 61 unt; 0 typ; 2 def)
% Number of atoms : 502 ( 83 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 727 ( 147 ~; 105 |; 0 &; 444 @)
% ( 2 <=>; 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 : 58 ( 54 usr; 7 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_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
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,
( 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,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mbox_s5 @ ( mequiv @ p @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mbox_s5 @ ( mequiv @ p @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f40,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f42,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f53,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f54,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f70,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f77,plain,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mbox_s5 @ ( mequiv @ p @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f78,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mbox_s5 @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f80,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f95,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f96,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mbox_s5 @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(flattening,[],[f78]) ).
thf(f105,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f108,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f111,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mbox_s5 @ ( mequiv @ p @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f118,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f124,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f130,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f133,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f137,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f141,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,[],[f130,f133,f118,f133,f133]) ).
thf(f142,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,[],[f137,f118,f133]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f124,f141,f142,f142]) ).
thf(f152,plain,
( ( ^ [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 > $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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f111,f105,f142,f141,f108,f108,f108,f144]) ).
thf(f167,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f168,plain,
( ( ^ [Y0: $i] :
( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f176,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f182,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f187,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( ~ ( ~ ( p @ sK1 )
| ( q @ sK1 ) )
| ~ ( ~ ( q @ sK1 )
| ( p @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
( ( ~ ( ~ ( ~ ( p @ sK1 )
| ( q @ sK1 ) )
| ~ ( ~ ( q @ sK1 )
| ( p @ sK1 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( ~ ( rel_s5 @ sK0 @ sK1 ) )
= $false ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f190,plain,
( ( rel_s5 @ sK0 @ sK1 )
= $true ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( ~ ( ~ ( p @ sK1 )
| ( q @ sK1 ) )
| ~ ( ~ ( q @ sK1 )
| ( p @ sK1 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f192,plain,
( ( ( ~ ( ~ ( p @ sK1 )
| ( q @ sK1 ) ) )
= $true )
| ( ( ~ ( ~ ( q @ sK1 )
| ( p @ sK1 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( ( ~ ( p @ sK1 )
| ( q @ sK1 ) )
= $false )
| ( ( ~ ( ~ ( q @ sK1 )
| ( p @ sK1 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( ( ~ ( ~ ( q @ sK1 )
| ( p @ sK1 ) ) )
= $true )
| ( ( q @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f202,plain,
( ( $false
= ( ~ ( q @ sK1 )
| ( p @ sK1 ) ) )
| ( ( q @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f203,plain,
( ( ( p @ sK1 )
= $false )
| ( ( q @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f222,definition,
( spl2_3
<=> ( ( p @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f224,plain,
( ( ( p @ sK1 )
= $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f226,definition,
( spl2_4
<=> ( ( q @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f228,plain,
( ( ( q @ sK1 )
= $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f229,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f203,f226,f222]) ).
thf(f230,plain,
( ( ( p @ sK1 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f180,f190]) ).
thf(f233,plain,
( ( p @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f237,plain,
( ( $false = $true )
| ~ spl2_3 ),
inference(forward_demodulation,[],[f233,f224]) ).
thf(f238,plain,
( $false
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f239,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f238]) ).
thf(f246,plain,
( ( $false = $true )
| ( ( q @ sK1 )
= $true ) ),
inference(constrained_superposition,[],[f185,f190]) ).
thf(f249,plain,
( ( q @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f253,plain,
( ( $false = $true )
| ~ spl2_4 ),
inference(forward_demodulation,[],[f249,f228]) ).
thf(f254,plain,
( $false
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f253]) ).
thf(f255,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f254]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f229]) ).
cnf(s4,plain,
~ spl2_3,
inference(sat_conversion,[],[f239]) ).
cnf(s9,plain,
~ spl2_4,
inference(sat_conversion,[],[f255]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s4]) ).
thf(f256,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO458^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:57:40 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.29 % (1018157)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (1018162)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1169422156:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (1018162) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1018157-1018162"...
% 0.22/0.29 % (1018168)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (1018168)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
% 0.22/0.29 % (1018162)...printing done.
% 0.22/0.29 % (1018162)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (1018162)------------------------------
% 0.22/0.29 % (1018162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1018162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1018162)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1018162)Termination reason: Refutation
% 0.22/0.29 % (1018162)Time elapsed: 0.005 s
% 0.22/0.29 % (1018162)Peak memory usage: 13 MB
% 0.22/0.29 % (1018162)Instructions burned: 18 (million)
% 0.22/0.29 % (1018157)Success in time 0.036 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------