%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO068^4.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:48:52 AM UTC 2026
% Result : Theorem 0.12s 0.27s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 55 unt; 0 typ; 1 def)
% Number of atoms : 541 ( 119 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 730 ( 38 ~; 72 |; 0 &; 511 @)
% ( 1 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 75 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 38 usr; 5 con; 0-4 aty)
% ( 50 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 220 ( 0 sgn 62 !; 0 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
p0: $i > $o ).
thf(func_def_22,type,
p1: $i > $o ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_29,type,
vOR: $o > $o > $o ).
thf(func_def_30,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
sK1: $i > $i ).
thf(func_def_37,type,
sK2: $i > $i ).
thf(func_def_38,type,
sK3: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f14,axiom,
( iimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ p1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(f24,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f25,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
thf(f26,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f27,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f26]) ).
thf(f30,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f31,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f33,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f37,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f38,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f44,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f48,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f49,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f56,plain,
ivalid @ ( iatom @ p1 ),
inference(rectify,[],[f22]) ).
thf(f57,plain,
( ( ivalid @ ( iatom @ p1 ) )
= $true ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
inference(rectify,[],[f23]) ).
thf(f59,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(rectify,[],[f25]) ).
thf(f61,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(flattening,[],[f61]) ).
thf(f65,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f67,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f68,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f70,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f71,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f72,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f78,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f82,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f86,plain,
( ( ivalid @ ( iatom @ p1 ) )
= $true ),
inference(cnf_transformation,[],[f57]) ).
thf(f87,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f88,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(cnf_transformation,[],[f62]) ).
thf(f91,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,[],[f70,f68,f67]) ).
thf(f96,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f78,f91,f71,f71]) ).
thf(f100,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 ) ) ),
inference(definition_unfolding,[],[f86,f82,f72]) ).
thf(f101,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 > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ) ) ),
inference(definition_unfolding,[],[f87,f82,f96,f72,f96,f72,f72]) ).
thf(f102,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ),
inference(definition_unfolding,[],[f88,f82,f72]) ).
thf(f103,plain,
( $true
!= ( !! @ $i @ p0 ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
( $false
= ( p0 @ sK0 ) ),
inference(sigma_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f106,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( p1 @ ( sK1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( p1 @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f124,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f114]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( p1 @ ( sK3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( p1 @ ( sK3 @ X2 ) ) ) )
| ( $true
= ( p0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p1 @ ( sK3 @ X2 ) ) )
| ( $true
= ( p0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( $true
= ( !! @ $i @ p1 ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f133,plain,
! [X1: $i] :
( $true
= ( p1 @ X1 ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p1 @ ( sK3 @ X2 ) ) )
| ( $true
= ( p0 @ X3 ) ) ),
inference(forward_demodulation,[],[f130,f133]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p1 @ ( sK3 @ X2 ) ) )
| ( $true
= ( p0 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p0 @ X3 ) ) ),
inference(forward_demodulation,[],[f203,f133]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p0 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f204]) ).
thf(f210,definition,
( spl4_6
<=> ! [X3: $i] :
( $true
= ( p0 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f211,plain,
( ! [X3: $i] :
( $true
= ( p0 @ X3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f221,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p0 @ X0 ) ) ),
inference(equality_factoring,[],[f205]) ).
thf(f222,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f221]) ).
thf(f230,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p0 @ X0 ) ) ),
inference(forward_demodulation,[],[f222,f65]) ).
thf(f231,plain,
! [X0: $i] :
( $true
= ( p0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f234,plain,
( ( $true = $false )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f211,f104]) ).
thf(f238,plain,
( $false
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f234]) ).
thf(f239,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f238]) ).
thf(f240,plain,
spl4_6,
inference(avatar_split_clause,[],[f231,f210]) ).
cnf(s48,plain,
~ spl4_6,
inference(sat_conversion,[],[f239]) ).
cnf(s50,plain,
spl4_6,
inference(sat_conversion,[],[f240]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s48,s50]) ).
thf(f241,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO068^4.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.19 % Computer : n015.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 16:32:33 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.22 Running first-order model finding
% 0.12/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.27 % (3744927)Will run a generic schedule for satisfiability detection.
% 0.12/0.27 % (3744936)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2532040325:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.27 % (3744936)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.27 % (3744933)% WARNING: option uhcvi not known.
% 0.12/0.27 % (3744933)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1646939392:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.27 % (3744932)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4014432548_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.27 % (3744937)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3501099244:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.27 % (3744934)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1015452579:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.27 % (3744938)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2716629901:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.27 % (3744933)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.27 % (3744933)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.12/0.27 % Exception at run slice level
% 0.12/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.27 % (3744934) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3744927-3744934"...
% 0.12/0.27 % (3744937) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3744927-3744937"...
% 0.12/0.27 % (3744935)dis+10_1_sil=32000:sp=arity:random_seed=106217835:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.27 % (3744934)...printing done.
% 0.12/0.27 % (3744933) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3744927-3744933"...
% 0.12/0.27 % (3744937)...printing done.
% 0.12/0.27 % (3744934)Refutation found. Thanks to Tanya!
% 0.12/0.27 % SZS status Theorem for theBenchmark
% 0.12/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.28 % (3744934)------------------------------
% 0.12/0.28 % (3744934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.28 % (3744934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.28 % (3744934)CaDiCaL version: 2.1.3
% 0.12/0.28 % (3744934)Termination reason: Refutation
% 0.12/0.28 % (3744934)Time elapsed: 0.009 s
% 0.12/0.28 % (3744934)Peak memory usage: 13 MB
% 0.12/0.28 % (3744934)Instructions burned: 15 (million)
% 0.12/0.28 % (3744927)Success in time 0.048 s
% 0.12/0.28 % Vampire exiting
%------------------------------------------------------------------------------