%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV442^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:40:07 AM UTC 2026
% Result : Theorem 0.29s 0.40s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 310 ( 65 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 427 ( 23 ~; 16 |; 0 &; 321 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 63 usr; 7 con; 0-4 aty)
% ( 32 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 176 ( 164 ^; 11 !; 1 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
reli: $i > $i > $o ).
thf(func_def_21,type,
relr: $i > $i > $o ).
thf(func_def_22,type,
cs4_atom: ( $i > $o ) > $i > $o ).
thf(func_def_23,type,
cs4_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_24,type,
cs4_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_25,type,
cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_26,type,
cs4_true: $i > $o ).
thf(func_def_27,type,
cs4_false: $i > $o ).
thf(func_def_28,type,
cs4_all: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_29,type,
cs4_box: ( $i > $o ) > $i > $o ).
thf(func_def_30,type,
cs4_valid: ( $i > $o ) > $o ).
thf(func_def_31,type,
princ_inj: individuals > $i > $o ).
thf(func_def_32,type,
bl_atom: ( $i > $o ) > $i > $o ).
thf(func_def_33,type,
bl_princ: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
bl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
bl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_37,type,
bl_all: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_38,type,
bl_true: $i > $o ).
thf(func_def_39,type,
bl_false: $i > $o ).
thf(func_def_40,type,
bl_says: individuals > ( $i > $o ) > $i > $o ).
thf(func_def_41,type,
bl_valid: ( $i > $o ) > $o ).
thf(func_def_42,type,
loca: individuals ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vAND: $o > $o > $o ).
thf(func_def_52,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
vIMP: $o > $o > $o ).
thf(func_def_54,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
sK0: $i > $o ).
thf(func_def_60,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_61,type,
sK5: $i > ( $i > $o ) > $i ).
thf(func_def_62,type,
sK6: $i > ( $i > $o ) > $i ).
thf(func_def_63,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_64,type,
sK8: $i > ( $i > $o ) > $i ).
thf(func_def_65,type,
sK9: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( cs4_atom
= ( ^ [X0: $i > $o] : ( mbox @ reli @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_atom) ).
thf(f19,axiom,
( cs4_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ reli @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_impl) ).
thf(f30,axiom,
( bl_atom
= ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_atom) ).
thf(f34,axiom,
( bl_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( cs4_impl @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_impl) ).
thf(f39,axiom,
bl_valid = mvalid,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_valid_def) ).
thf(f41,conjecture,
! [X0: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_id) ).
thf(f42,negated_conjecture,
~ ! [X0: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f45,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f46,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f48,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f51,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f53,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f61,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f62,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f69,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f72,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f86,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f90,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f95,plain,
~ ! [X0: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) ),
inference(rectify,[],[f42]) ).
thf(f96,plain,
~ ! [X0: $i > $o] :
( ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
? [X0: $i > $o] :
( ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[],[f96]) ).
thf(f98,plain,
( $true
!= ( bl_valid @ ( bl_impl @ ( bl_atom @ sK0 ) @ ( bl_atom @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f97]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f104,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f106,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f110,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f114,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f117,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f128,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f132,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f137,plain,
mvalid = bl_valid,
inference(cnf_transformation,[],[f39]) ).
thf(f139,plain,
( $true
!= ( bl_valid @ ( bl_impl @ ( bl_atom @ sK0 ) @ ( bl_atom @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f142,plain,
( mimpl
= ( ^ [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,[],[f104,f102,f101]) ).
thf(f144,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ reli
@ Y0 ) ) ),
inference(definition_unfolding,[],[f114,f106]) ).
thf(f147,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ ( ^ [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 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f117,f106,f142]) ).
thf(f153,plain,
( bl_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f128,f144]) ).
thf(f157,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f132,f147]) ).
thf(f160,plain,
( bl_valid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f137,f110]) ).
thf(f169,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 )
@ sK0 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 )
@ sK0 ) ) ) ),
inference(definition_unfolding,[],[f139,f160,f157,f153,f153]) ).
thf(f170,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( $false
= ( ( reli @ sK1 @ sK2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f179,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( $true
= ( ( reli @ sK2 @ X1 )
=> ( sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( reli @ sK2 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f184,plain,
( $false
= ( ( reli @ sK2 @ sK3 )
=> ( sK0 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( $false
= ( sK0 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( $true
= ( reli @ sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f280,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(constrained_superposition,[],[f186,f182]) ).
thf(f281,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f283,plain,
$false = $true,
inference(forward_demodulation,[],[f281,f185]) ).
thf(f284,plain,
$false,
inference(trivial_inequality_removal,[],[f283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV442^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.29 % Computer : n014.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 16:04:15 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.29/0.34 Running first-order model finding
% 0.29/0.34 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
% 0.29/0.40 % (2853174)Will run a generic schedule for satisfiability detection.
% 0.29/0.40 % (2853181)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3116421977:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.29/0.40 % (2853180)% WARNING: option uhcvi not known.
% 0.29/0.40 % (2853181) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2853174-2853181"...
% 0.29/0.40 % (2853181)...printing done.
% 0.29/0.40 % (2853181)Refutation found. Thanks to Tanya!
% 0.29/0.40 % SZS status Theorem for theBenchmark
% 0.29/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.40 % (2853181)------------------------------
% 0.29/0.40 % (2853181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.40 % (2853181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.40 % (2853181)CaDiCaL version: 2.1.3
% 0.29/0.40 % (2853181)Termination reason: Refutation
% 0.29/0.40 % (2853181)Time elapsed: 0.009 s
% 0.29/0.40 % (2853181)Peak memory usage: 12 MB
% 0.29/0.40 % (2853181)Instructions burned: 18 (million)
% 0.29/0.40 % (2853174)Success in time 0.044 s
% 0.29/0.40 % Vampire exiting
%------------------------------------------------------------------------------