%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO429^1 : 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 : n001.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 08:47:40 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 464 ( 92 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 657 ( 105 ~; 68 |; 0 &; 425 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 6 con; 0-4 aty)
% ( 49 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 171 ( 142 ^; 29 !; 0 ?; 171 :)
% 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_b: $i > $i > $o ).
thf(func_def_33,type,
mbox_b: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_b: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
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(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_b @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',mbox_b) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ X0 ) ) ) )
= mdia_b ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',mdia_b) ).
thf(f35,axiom,
msymmetric @ rel_b,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mbox_b @ ( mdia_b @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mbox_b @ ( mdia_b @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f41,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f42,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f62,plain,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_b @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f63,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_b @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f72,plain,
msymmetric @ rel_b,
inference(rectify,[],[f35]) ).
thf(f73,plain,
( ( msymmetric @ rel_b )
= $true ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
~ ( mvalid @ ( mimplies @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mbox_b @ ( mdia_b @ p ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f75,plain,
( ( mvalid @ ( mimplies @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mbox_b @ ( mdia_b @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f74]) ).
thf(f81,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f82,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f85,plain,
( mdia_b
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f88,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f91,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f92,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f93,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f94,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mbox_b @ ( mdia_b @ p ) ) ) )
!= $true ),
inference(flattening,[],[f75]) ).
thf(f99,plain,
( mdia_b
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f115,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f116,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f118,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f124,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f127,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_b @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f130,plain,
( ( msymmetric @ rel_b )
= $true ),
inference(cnf_transformation,[],[f73]) ).
thf(f133,plain,
( ( mvalid @ ( mimplies @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mbox_b @ ( mdia_b @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f138,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,[],[f115,f124,f101]) ).
thf(f146,plain,
( mdia_b
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_b @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f99,f101,f127,f101]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_b ) ),
inference(definition_unfolding,[],[f130,f118]) ).
thf(f149,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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_b @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_b @ Y1 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_b @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_b @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f133,f116,f138,f146,f127,f127,f146]) ).
thf(f153,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_b @ Y1 @ Y2 ) ) )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_b @ Y1 @ Y2 ) ) )
| ~ ( rel_b @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f154,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_b @ Y1 @ Y2 ) ) )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_b @ Y1 @ Y2 ) ) )
| ~ ( rel_b @ Y0 @ Y1 ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ( rel_b @ sK0 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ( rel_b @ sK0 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ( rel_b @ sK0 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ( rel_b @ sK0 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ( rel_b @ sK0 @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_b @ sK1 @ Y0 ) ) )
| ~ ( rel_b @ sK0 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( ( ~ ( rel_b @ sK0 @ sK1 ) )
= $false ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_b @ sK1 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_b @ sK1 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_b @ sK1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( $true
= ( ~ ( p @ X1 )
| ~ ( rel_b @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) )
| ( ( ~ ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( ( p @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( rel_b @ sK0 @ sK1 )
= $true ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f169,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ( rel_b @ sK0 @ Y0 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f170,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ( rel_b @ sK0 @ Y0 ) ) )
= $false ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_b @ Y0 @ Y1 ) ) )
| ~ ( rel_b @ sK0 @ Y0 ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_b @ sK2 @ Y0 ) ) )
| ~ ( rel_b @ sK0 @ sK2 ) )
= $false ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( ~ ( rel_b @ sK0 @ sK2 ) )
= $false ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_b @ sK2 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_b @ sK2 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_b @ sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ( p @ X1 )
| ~ ( rel_b @ sK2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $true
= ( ~ ( rel_b @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( ( rel_b @ sK2 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( $true
= ( rel_b @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f181,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_b @ Y1 @ Y0 )
=> ( rel_b @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f182,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_b @ Y1 @ Y0 )
=> ( rel_b @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_b @ Y0 @ X1 )
=> ( rel_b @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( rel_b @ Y0 @ X1 )
=> ( rel_b @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( ( rel_b @ X2 @ X1 )
=> ( rel_b @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( ( rel_b @ X2 @ X1 )
= $false )
| ( ( rel_b @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f197,plain,
! [X0: $i] :
( ( $false
= ( p @ X0 ) )
| ( ( rel_b @ X0 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f186,f167]) ).
thf(f200,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p @ X0 ) )
| ( ( rel_b @ X0 @ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f179,f186]) ).
thf(f202,plain,
! [X0: $i] :
( ( ( rel_b @ X0 @ sK2 )
= $false )
| ( $true
= ( p @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f204,plain,
! [X0: $i] :
( ( ( rel_b @ X0 @ sK1 )
= $false )
| ( $false
= ( p @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f211,plain,
( ( $true
= ( p @ sK0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f180,f202]) ).
thf(f212,plain,
( $true
= ( p @ sK0 ) ),
inference(trivial_inequality_removal,[],[f211]) ).
thf(f223,plain,
( ( $true = $false )
| ( $false
= ( p @ sK0 ) ) ),
inference(constrained_superposition,[],[f168,f204]) ).
thf(f225,plain,
( $false
= ( p @ sK0 ) ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f230,plain,
$true = $false,
inference(forward_demodulation,[],[f225,f212]) ).
thf(f231,plain,
$false,
inference(trivial_inequality_removal,[],[f230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO429^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n001.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 16:57:22 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.22 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
% 0.19/0.29 % (1508167)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.29 % (1508174)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4083924146:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.29 % (1508174)Instruction limit reached!
% 0.19/0.29 % (1508174)------------------------------
% 0.19/0.29 % (1508174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1508174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1508174)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1508174)Termination reason: Instruction limit
% 0.19/0.29 % (1508174)Termination phase: Property scanning
% 0.19/0.29 % (1508174)Time elapsed: 0.001 s
% 0.19/0.29 % (1508174)Peak memory usage: 10 MB
% 0.19/0.29 % (1508174)Instructions burned: 4 (million)
% 0.19/0.29 % (1508172)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3625952358:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.29 % (1508175)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=3825231821: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)
% 0.19/0.29 % (1508176)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3342771724:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.29 % (1508180)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1322750236:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.29 % (1508180)Instruction limit reached!
% 0.19/0.29 % (1508180)------------------------------
% 0.19/0.29 % (1508180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1508180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1508180)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1508180)Termination reason: Instruction limit
% 0.19/0.29 % (1508180)Termination phase: Property scanning
% 0.19/0.29 % (1508180)Time elapsed: 0.001 s
% 0.19/0.29 % (1508180)Peak memory usage: 10 MB
% 0.19/0.29 % (1508180)Instructions burned: 3 (million)
% 0.19/0.29 % (1508172) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1508167-1508172"...
% 0.19/0.29 % (1508172)...printing done.
% 0.19/0.29 % (1508172)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (1508172)------------------------------
% 0.19/0.29 % (1508172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1508172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1508172)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1508172)Termination reason: Refutation
% 0.19/0.29 % (1508172)Time elapsed: 0.010 s
% 0.19/0.29 % (1508172)Peak memory usage: 12 MB
% 0.19/0.29 % (1508172)Instructions burned: 17 (million)
% 0.19/0.29 % (1508167)Success in time 0.055 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------