%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO464^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:47:56 AM UTC 2026
% Result : Theorem 0.20s 0.35s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 70 unt; 0 typ; 0 def)
% Number of atoms : 560 ( 96 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 917 ( 177 ~; 102 |; 0 &; 568 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 6 con; 0-4 aty)
% ( 60 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 220 ( 190 ^; 30 !; 0 ?; 220 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vIMP: $o > $o > $o ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db2:
!>[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_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) )
= mdia_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mbox_s5 @ ( mand @ p @ q ) ) @ ( mbox_s5 @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mand @ p @ q ) ) @ ( mbox_s5 @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f40,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f43,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f44,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f46,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f50,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f53,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f54,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f57,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f58,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f63,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mand @ p @ q ) ) @ ( mbox_s5 @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f64,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mand @ p @ q ) ) @ ( mbox_s5 @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f96,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f97,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mand @ p @ q ) ) @ ( mbox_s5 @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f64]) ).
thf(f102,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f104,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f110,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f112,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mand @ p @ q ) ) @ ( mbox_s5 @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f121,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f126,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f132,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f54]) ).
thf(f134,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f135,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f138,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f138,f121,f126,f121,f121]) ).
thf(f142,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,[],[f102,f126,f121]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f135,f121,f134,f121]) ).
thf(f151,plain,
( $true
!= ( ^ [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] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ 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 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f112,f104,f142,f134,f141,f134,f134,f142,f150,f150]) ).
thf(f153,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f132,f110]) ).
thf(f167,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f168,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( q @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( q @ Y1 )
| ~ ( p @ Y1 ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f174,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( q @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( q @ Y1 )
| ~ ( p @ Y1 ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK1 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK1 @ Y0 ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) )
| ~ ( rel_s5 @ sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f187,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( ~ ( q @ X1 )
| ~ ( rel_s5 @ sK2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK2 @ X1 ) )
= $true )
| ( ( ~ ( q @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK2 @ X1 )
= $false )
| ( ( ~ ( q @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK2 @ X1 )
= $false )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f202,plain,
( ( rel_s5 @ sK1 @ sK2 )
= $true ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f203,plain,
( ( rel_s5 @ sK0 @ sK1 )
= $true ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f204,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f205,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( $true
= ( ~ ( ~ ( q @ X1 )
| ~ ( p @ X1 ) )
| ~ ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( ~ ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( ~ ( q @ X1 )
| ~ ( p @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f211,plain,
! [X1: $i] :
( ( $false
= ( ~ ( q @ X1 ) ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f212,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f214,plain,
( ( $false = $true )
| ( ( q @ sK1 )
= $true ) ),
inference(constrained_superposition,[],[f212,f203]) ).
thf(f216,plain,
( ( q @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f214]) ).
thf(f240,plain,
! [X0: $i] :
( ( $false
= ( q @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK2 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f172,f193]) ).
thf(f248,plain,
! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK2 ) )
| ( $false
= ( q @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f240]) ).
thf(f266,plain,
( ( $false
= ( q @ sK1 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f202,f248]) ).
thf(f268,plain,
( $false
= ( q @ sK1 ) ),
inference(trivial_inequality_removal,[],[f266]) ).
thf(f273,plain,
$false = $true,
inference(forward_demodulation,[],[f268,f216]) ).
thf(f274,plain,
$false,
inference(trivial_inequality_removal,[],[f273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO464^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n026.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 17:02:27 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.26 Running higher-order theorem proving
% 0.20/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.35 % (873587)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (873593)lrs+10_16_si=on:nwc=1.5:random_seed=3791843354:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (873596)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2684497152:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (873594)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=417354327:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (873597)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2556937111:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (873595)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=3549992018: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)
% 0.20/0.35 % (873594)Instruction limit reached!
% 0.20/0.35 % (873594)------------------------------
% 0.20/0.35 % (873594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (873594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (873594)CaDiCaL version: 2.1.3
% 0.20/0.35 % (873594)Termination reason: Instruction limit
% 0.20/0.35 % (873594)Termination phase: Function definition elimination
% 0.20/0.35 % (873594)Time elapsed: 0.003 s
% 0.20/0.35 % (873594)Peak memory usage: 10 MB
% 0.20/0.35 % (873594)Instructions burned: 6 (million)
% 0.20/0.35 % (873593)Instruction limit reached!
% 0.20/0.35 % (873593)------------------------------
% 0.20/0.35 % (873593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (873593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (873593)CaDiCaL version: 2.1.3
% 0.20/0.35 % (873593)Termination reason: Instruction limit
% 0.20/0.35 % (873593)Termination phase: Saturation
% 0.20/0.35 % (873593)Time elapsed: 0.009 s
% 0.20/0.35 % (873593)Peak memory usage: 12 MB
% 0.20/0.35 % (873593)Instructions burned: 18 (million)
% 0.20/0.35 % (873598)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (873598)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
% 0.20/0.35 % (873596)Instruction limit reached!
% 0.20/0.35 % (873596)------------------------------
% 0.20/0.35 % (873596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (873596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (873596)CaDiCaL version: 2.1.3
% 0.20/0.35 % (873596)Termination reason: Instruction limit
% 0.20/0.35 % (873596)Termination phase: Saturation
% 0.20/0.35 % (873596)Time elapsed: 0.014 s
% 0.20/0.35 % (873596)Peak memory usage: 11 MB
% 0.20/0.35 % (873596)Instructions burned: 25 (million)
% 0.20/0.35 % (873592)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=389671109:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (873598)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=2350389363:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (873604)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3945686631:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (873592) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-873587-873592"...
% 0.20/0.35 % (873604)Instruction limit reached!
% 0.20/0.35 % (873604)------------------------------
% 0.20/0.35 % (873604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (873604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (873604)CaDiCaL version: 2.1.3
% 0.20/0.35 % (873604)Termination reason: Instruction limit
% 0.20/0.35 % (873604)Termination phase: Property scanning
% 0.20/0.35 % (873604)Time elapsed: 0.003 s
% 0.20/0.35 % (873604)Peak memory usage: 10 MB
% 0.20/0.35 % (873604)Instructions burned: 7 (million)
% 0.20/0.35 % (873605)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3870614208:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.35 % (873592)...printing done.
% 0.20/0.35 % (873606)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (873592)Refutation found. Thanks to Tanya!
% 0.20/0.35 % SZS status Theorem for theBenchmark
% 0.20/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.35 % (873592)------------------------------
% 0.20/0.35 % (873592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (873592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (873592)CaDiCaL version: 2.1.3
% 0.20/0.35 % (873592)Termination reason: Refutation
% 0.20/0.35 % (873592)Time elapsed: 0.011 s
% 0.20/0.35 % (873592)Peak memory usage: 12 MB
% 0.20/0.35 % (873592)Instructions burned: 21 (million)
% 0.20/0.35 % (873587)Success in time 0.068 s
% 0.20/0.35 % Vampire exiting
%------------------------------------------------------------------------------