%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO422^1 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:39 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 375 ( 80 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 482 ( 81 ~; 70 |; 0 &; 309 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 52 usr; 5 con; 0-4 aty)
% ( 16 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 136 ( 111 ^; 23 !; 2 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_d: $i > $i > $o ).
thf(func_def_33,type,
mbox_d: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_d: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sK1: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f20,axiom,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_d @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mbox_d) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ X0 ) ) ) )
= mdia_d ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mdia_d) ).
thf(f34,axiom,
mserial @ rel_d,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',a1) ).
thf(f35,conjecture,
mvalid @ ( mdia_d @ ( mimplies @ ( mimplies @ ( mimplies @ p @ q ) @ p ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mdia_d @ ( mimplies @ ( mimplies @ ( mimplies @ p @ q ) @ p ) @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f42,plain,
( mdia_d
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f51,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f52,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f54,plain,
mserial @ rel_d,
inference(rectify,[],[f34]) ).
thf(f55,plain,
( ( mserial @ rel_d )
= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f20]) ).
thf(f57,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f61,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f62,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f70,plain,
~ ( mvalid @ ( mdia_d @ ( mimplies @ ( mimplies @ ( mimplies @ p @ q ) @ p ) @ p ) ) ),
inference(rectify,[],[f36]) ).
thf(f71,plain,
( ( mvalid @ ( mdia_d @ ( mimplies @ ( mimplies @ ( mimplies @ p @ q ) @ p ) @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f70]) ).
thf(f72,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f73,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f78,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f83,plain,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_d @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f84,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f95,plain,
( ( mvalid @ ( mdia_d @ ( mimplies @ ( mimplies @ ( mimplies @ p @ q ) @ p ) @ p ) ) )
!= $true ),
inference(flattening,[],[f71]) ).
thf(f97,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f100,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f102,plain,
( mdia_d
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f107,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f119,plain,
( ( mvalid @ ( mdia_d @ ( mimplies @ ( mimplies @ ( mimplies @ p @ q ) @ p ) @ p ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f124,plain,
( ( mserial @ rel_d )
= $true ),
inference(cnf_transformation,[],[f55]) ).
thf(f126,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f127,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f128,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f134,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,[],[f126,f128,f97]) ).
thf(f142,plain,
( mdia_d
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_d @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f102,f97,f100,f97]) ).
thf(f143,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [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_d @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [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 > $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 > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ p
@ q )
@ p )
@ p ) ) ) ),
inference(definition_unfolding,[],[f119,f107,f142,f134,f134,f134]) ).
thf(f144,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ rel_d ) ),
inference(definition_unfolding,[],[f124,f127]) ).
thf(f145,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( p @ Y1 )
| ~ ( ( p @ Y1 )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f146,plain,
( ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( p @ Y1 )
| ~ ( ( p @ Y1 )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ~ ( ( p @ Y0 )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ~ ( rel_d @ sK0 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ~ ( ( p @ Y0 )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ~ ( rel_d @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ~ ( ( p @ Y0 )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ~ ( rel_d @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( ~ ( ( p @ X1 )
| ~ ( ( p @ X1 )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
| ~ ( rel_d @ sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( ( ~ ( ( p @ X1 )
| ~ ( ( p @ X1 )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) )
= $true )
| ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( $false
= ( ( p @ X1 )
| ~ ( ( p @ X1 )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) )
| ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) )
| ( $false
= ( ~ ( ( p @ X1 )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) )
| ( ( p @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( ( p @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ( p @ X1 )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) )
| ( $false
= ( rel_d @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f157,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( ( p @ X1 )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( ( ( q @ X1 )
| ~ ( p @ X1 ) )
= $false )
| ( $false
= ( rel_d @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( ~ ( p @ X1 ) ) )
| ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f163,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f162]) ).
thf(f164,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( rel_d @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f165,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( rel_d @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( $true
= ( ?? @ $i @ ( rel_d @ X1 ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( $true
= ( rel_d @ X1 @ ( sK1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( p @ ( sK1 @ sK0 ) ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f167,f155]) ).
thf(f170,plain,
( $false
= ( p @ ( sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f172,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK1 @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f163,f167]) ).
thf(f174,plain,
( $true
= ( p @ ( sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f176,plain,
$true = $false,
inference(forward_demodulation,[],[f174,f170]) ).
thf(f177,plain,
$false,
inference(trivial_inequality_removal,[],[f176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO422^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n008.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 16:51:54 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.29 % (3417663)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (3417672)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=897390973: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)
% 0.20/0.29 % (3417669)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4098020952:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (3417670)lrs+10_16_si=on:nwc=1.5:random_seed=742924918:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (3417671)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3371686910:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (3417673)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1556233535:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (3417674)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2138424575:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (3417671)Instruction limit reached!
% 0.20/0.29 % (3417671)------------------------------
% 0.20/0.29 % (3417671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3417671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3417671)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3417671)Termination reason: Instruction limit
% 0.20/0.29 % (3417671)Termination phase: Property scanning
% 0.20/0.29 % (3417671)Time elapsed: 0.003 s
% 0.20/0.29 % (3417671)Peak memory usage: 10 MB
% 0.20/0.29 % (3417671)Instructions burned: 5 (million)
% 0.20/0.29 % (3417670) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3417663-3417670"...
% 0.20/0.29 % (3417669) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3417663-3417669"...
% 0.20/0.29 % (3417669)...printing done.
% 0.20/0.29 % (3417670)...printing done.
% 0.20/0.29 % (3417670)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (3417670)------------------------------
% 0.20/0.30 % (3417670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3417670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3417670)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3417670)Termination reason: Refutation
% 0.20/0.30 % (3417670)Time elapsed: 0.007 s
% 0.20/0.30 % (3417670)Peak memory usage: 12 MB
% 0.20/0.30 % (3417670)Instructions burned: 13 (million)
% 0.20/0.30 % (3417663)Success in time 0.055 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------