%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO061^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:48:50 AM UTC 2026
% Result : Theorem 0.25s 0.32s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 87 ( 56 unt; 0 typ; 2 def)
% Number of atoms : 467 ( 96 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 545 ( 36 ~; 48 |; 0 &; 386 @)
% ( 2 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 38 usr; 7 con; 0-4 aty)
% ( 33 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 168 ( 0 sgn 28 !; 0 ?; 168 :)
% 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,
a: $i > $o ).
thf(func_def_22,type,
b: $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_37,type,
sK2: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(f23,conjecture,
ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f24,negated_conjecture,
~ ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f29,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f30,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f32,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f35,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f36,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f37,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f43,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f47,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f48,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f55,plain,
ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
inference(rectify,[],[f22]) ).
thf(f56,plain,
( ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) )
= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
~ ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) ),
inference(rectify,[],[f24]) ).
thf(f58,plain,
( ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) )
!= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) )
!= $true ),
inference(flattening,[],[f58]) ).
thf(f64,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f65,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f67,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f68,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f69,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f75,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f79,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f83,plain,
( ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) )
= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f84,plain,
( ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) )
!= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f87,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,[],[f67,f65,f64]) ).
thf(f92,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,[],[f75,f87,f68,f68]) ).
thf(f96,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
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) ) ),
inference(definition_unfolding,[],[f83,f79,f92,f69,f69]) ).
thf(f97,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
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) ) ),
inference(definition_unfolding,[],[f84,f79,f92,f69,f69]) ).
thf(f98,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f100]) ).
thf(f102,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f100]) ).
thf(f103,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ( a @ X1 ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f101]) ).
thf(f108,plain,
( $false
= ( ( irel @ sK0 @ sK1 )
=> ( b @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
( $false
= ( b @ sK1 ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( $true
= ( irel @ sK0 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f111,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f112,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( b @ X2 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( a @ ( sK2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( a @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( b @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( a @ ( sK2 @ X1 ) ) )
| ( $true
= ( b @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK2 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f152,plain,
( ( $true = $false )
| ( $false
= ( a @ ( sK2 @ sK0 ) ) )
| ( $true
= ( b @ sK1 ) ) ),
inference(constrained_superposition,[],[f110,f120]) ).
thf(f153,plain,
( ( $false
= ( a @ ( sK2 @ sK0 ) ) )
| ( $true
= ( b @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f158,plain,
( ( $true = $false )
| ( $false
= ( a @ ( sK2 @ sK0 ) ) ) ),
inference(forward_demodulation,[],[f153,f109]) ).
thf(f159,plain,
( $false
= ( a @ ( sK2 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f158]) ).
thf(f162,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( a @ ( sK2 @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f121,f106]) ).
thf(f175,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( a @ ( sK2 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f162]) ).
thf(f177,definition,
( spl3_1
<=> ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f178,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f180,definition,
( spl3_2
<=> ( $true
= ( a @ ( sK2 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f182,plain,
( ( $true
= ( a @ ( sK2 @ sK0 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f180]) ).
thf(f184,plain,
( spl3_2
| spl3_1 ),
inference(avatar_split_clause,[],[f175,f177,f180]) ).
thf(f256,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f159,f182]) ).
thf(f262,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f256]) ).
thf(f263,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f262]) ).
thf(f268,plain,
( ( $true = $false )
| ( $true
= ( b @ sK1 ) )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f178,f110]) ).
thf(f281,plain,
( ( $true
= ( b @ sK1 ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f288,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f281,f109]) ).
thf(f289,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f288]) ).
thf(f290,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f289]) ).
cnf(s2,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f184]) ).
cnf(s4,plain,
~ spl3_2,
inference(sat_conversion,[],[f263]) ).
cnf(s6,plain,
~ spl3_1,
inference(sat_conversion,[],[f290]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s4,s6]) ).
thf(f291,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO061^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.24 % Computer : n020.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 16:26:49 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.28 Running first-order model finding
% 0.11/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.32 % (1255067)Will run a generic schedule for satisfiability detection.
% 0.25/0.32 % (1255075)dis+10_1_sil=32000:sp=arity:random_seed=3426976069:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.32 % (1255072)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3847032221_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.32 % Exception at run slice level
% 0.25/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.32 % (1255073)% WARNING: option uhcvi not known.
% 0.25/0.32 % (1255075) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1255067-1255075"...
% 0.25/0.32 % (1255076)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1658699440:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.32 % (1255073)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=785315606:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.32 % (1255075)...printing done.
% 0.25/0.32 % (1255075)Refutation found. Thanks to Tanya!
% 0.25/0.32 % SZS status Theorem for theBenchmark
% 0.25/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.32 % (1255075)------------------------------
% 0.25/0.32 % (1255075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.32 % (1255075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.32 % (1255075)CaDiCaL version: 2.1.3
% 0.25/0.32 % (1255075)Termination reason: Refutation
% 0.25/0.32 % (1255075)Time elapsed: 0.011 s
% 0.25/0.32 % (1255075)Peak memory usage: 13 MB
% 0.25/0.32 % (1255075)Instructions burned: 20 (million)
% 0.25/0.32 % (1255067)Success in time 0.037 s
% 0.25/0.32 % Vampire exiting
%------------------------------------------------------------------------------