TSTP Solution File: HAL002+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:53:53 EDT 2023
% Result : Theorem 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 147 ( 3 unt; 0 def)
% Number of atoms : 496 ( 114 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 567 ( 218 ~; 264 |; 50 &)
% ( 8 <=>; 26 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 214 (; 205 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f793,plain,
$false,
inference(avatar_sat_refutation,[],[f126,f189,f192,f411,f668,f679,f732,f792]) ).
fof(f792,plain,
( spl9_2
| spl9_6 ),
inference(avatar_contradiction_clause,[],[f791]) ).
fof(f791,plain,
( $false
| spl9_2
| spl9_6 ),
inference(subsumption_resolution,[],[f790,f738]) ).
fof(f738,plain,
( element(sK2(x,any1,any2),any1)
| spl9_2 ),
inference(resolution,[],[f737,f84]) ).
fof(f84,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
morphism(x,any1,any2),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',x_morphism) ).
fof(f737,plain,
( ! [X2,X3] :
( ~ morphism(x,X2,X3)
| element(sK2(x,X2,X3),X2) )
| spl9_2 ),
inference(resolution,[],[f124,f97]) ).
fof(f97,plain,
! [X2,X0,X1] :
( injection_2(X0)
| element(sK2(X0,X1,X2),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ( zero(X1) != sK2(X0,X1,X2)
& zero(X2) = apply(X0,sK2(X0,X1,X2))
& element(sK2(X0,X1,X2),X1) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f49,f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> ( zero(X1) != sK2(X0,X1,X2)
& zero(X2) = apply(X0,sK2(X0,X1,X2))
& element(sK2(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> zero(X1) = X3 )
& morphism(X0,X1,X2) )
=> injection_2(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',properties_for_injection_2) ).
fof(f124,plain,
( ~ injection_2(x)
| spl9_2 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f123,plain,
( spl9_2
<=> injection_2(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f790,plain,
( ~ element(sK2(x,any1,any2),any1)
| spl9_2
| spl9_6 ),
inference(subsumption_resolution,[],[f787,f183]) ).
fof(f183,plain,
( ~ element(zero(any1),any1)
| spl9_6 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f182,plain,
( spl9_6
<=> element(zero(any1),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f787,plain,
( element(zero(any1),any1)
| ~ element(sK2(x,any1,any2),any1)
| spl9_2 ),
inference(duplicate_literal_removal,[],[f786]) ).
fof(f786,plain,
( element(zero(any1),any1)
| ~ element(sK2(x,any1,any2),any1)
| ~ element(sK2(x,any1,any2),any1)
| spl9_2 ),
inference(superposition,[],[f93,f749]) ).
fof(f749,plain,
( zero(any1) = subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))
| spl9_2 ),
inference(resolution,[],[f738,f85]) ).
fof(f85,plain,
! [X0,X1] :
( ~ element(X1,X0)
| zero(X0) = subtract(X0,X1,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( zero(X0) = subtract(X0,X1,X1)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( element(X1,X0)
=> zero(X0) = subtract(X0,X1,X1) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X3] :
( element(X3,X1)
=> zero(X1) = subtract(X1,X3,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',subtract_to_0) ).
fof(f93,plain,
! [X2,X0,X1] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> element(subtract(X1,X4,X5),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',subtract_in_domain) ).
fof(f732,plain,
( spl9_1
| ~ spl9_5
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f731]) ).
fof(f731,plain,
( $false
| spl9_1
| ~ spl9_5
| ~ spl9_13 ),
inference(resolution,[],[f723,f84]) ).
fof(f723,plain,
( ! [X0] : ~ morphism(x,any1,X0)
| spl9_1
| ~ spl9_5
| ~ spl9_13 ),
inference(subsumption_resolution,[],[f722,f120]) ).
fof(f120,plain,
( ~ injection(x)
| spl9_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f119,plain,
( spl9_1
<=> injection(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f722,plain,
( ! [X0] :
( injection(x)
| ~ morphism(x,any1,X0) )
| spl9_1
| ~ spl9_5
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f721]) ).
fof(f721,plain,
( ! [X0] :
( sK3(x,any1) != sK3(x,any1)
| injection(x)
| ~ morphism(x,any1,X0) )
| spl9_1
| ~ spl9_5
| ~ spl9_13 ),
inference(superposition,[],[f103,f710]) ).
fof(f710,plain,
( sK3(x,any1) = sK4(x,any1)
| spl9_1
| ~ spl9_5
| ~ spl9_13 ),
inference(forward_demodulation,[],[f709,f222]) ).
fof(f222,plain,
( sK3(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ spl9_5 ),
inference(subsumption_resolution,[],[f221,f179]) ).
fof(f179,plain,
( element(sK3(x,any1),any1)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f178,plain,
( spl9_5
<=> element(sK3(x,any1),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f221,plain,
( sK3(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ element(sK3(x,any1),any1)
| ~ spl9_5 ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f218,plain,
( sK3(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ element(sK3(x,any1),any1)
| ~ element(sK3(x,any1),any1)
| ~ spl9_5 ),
inference(superposition,[],[f94,f199]) ).
fof(f199,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK3(x,any1))
| ~ spl9_5 ),
inference(resolution,[],[f179,f85]) ).
fof(f94,plain,
! [X2,X0,X1] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> subtract(X1,X4,subtract(X1,X4,X5)) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',subtract_cancellation) ).
fof(f709,plain,
( sK4(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| spl9_1
| ~ spl9_5
| ~ spl9_13 ),
inference(subsumption_resolution,[],[f708,f179]) ).
fof(f708,plain,
( sK4(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ element(sK3(x,any1),any1)
| spl9_1
| ~ spl9_13 ),
inference(subsumption_resolution,[],[f706,f426]) ).
fof(f426,plain,
( element(sK4(x,any1),any1)
| spl9_1 ),
inference(resolution,[],[f417,f84]) ).
fof(f417,plain,
( ! [X2,X3] :
( ~ morphism(x,X2,X3)
| element(sK4(x,X2),X2) )
| spl9_1 ),
inference(resolution,[],[f120,f101]) ).
fof(f101,plain,
! [X2,X0,X1] :
( injection(X0)
| element(sK4(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( injection(X0)
| ( sK3(X0,X1) != sK4(X0,X1)
& apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
& element(sK4(X0,X1),X1)
& element(sK3(X0,X1),X1) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f51,f67]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> ( sK3(X0,X1) != sK4(X0,X1)
& apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
& element(sK4(X0,X1),X1)
& element(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1,X2] :
( injection(X0)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( injection(X0)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( ! [X4,X5] :
( ( apply(X0,X4) = apply(X0,X5)
& element(X5,X1)
& element(X4,X1) )
=> X4 = X5 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',properties_for_injection) ).
fof(f706,plain,
( sK4(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ element(sK4(x,any1),any1)
| ~ element(sK3(x,any1),any1)
| ~ spl9_13 ),
inference(superposition,[],[f94,f663]) ).
fof(f663,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f661,plain,
( spl9_13
<=> zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f103,plain,
! [X2,X0,X1] :
( sK3(X0,X1) != sK4(X0,X1)
| injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f679,plain,
( spl9_1
| ~ spl9_5
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f678,plain,
( $false
| spl9_1
| ~ spl9_5
| spl9_14 ),
inference(subsumption_resolution,[],[f677,f179]) ).
fof(f677,plain,
( ~ element(sK3(x,any1),any1)
| spl9_1
| spl9_14 ),
inference(subsumption_resolution,[],[f676,f426]) ).
fof(f676,plain,
( ~ element(sK4(x,any1),any1)
| ~ element(sK3(x,any1),any1)
| spl9_14 ),
inference(resolution,[],[f667,f93]) ).
fof(f667,plain,
( ~ element(subtract(any1,sK3(x,any1),sK4(x,any1)),any1)
| spl9_14 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f665,plain,
( spl9_14
<=> element(subtract(any1,sK3(x,any1),sK4(x,any1)),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
fof(f668,plain,
( spl9_13
| ~ spl9_14
| spl9_1
| ~ spl9_2
| ~ spl9_5 ),
inference(avatar_split_clause,[],[f635,f178,f123,f119,f665,f661]) ).
fof(f635,plain,
( ~ element(subtract(any1,sK3(x,any1),sK4(x,any1)),any1)
| zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| spl9_1
| ~ spl9_2
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f631]) ).
fof(f631,plain,
( zero(any2) != zero(any2)
| ~ element(subtract(any1,sK3(x,any1),sK4(x,any1)),any1)
| zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| spl9_1
| ~ spl9_2
| ~ spl9_5 ),
inference(superposition,[],[f447,f627]) ).
fof(f627,plain,
( zero(any2) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1)))
| spl9_1
| ~ spl9_5 ),
inference(forward_demodulation,[],[f623,f441]) ).
fof(f441,plain,
( zero(any2) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| spl9_1 ),
inference(subsumption_resolution,[],[f438,f426]) ).
fof(f438,plain,
( zero(any2) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| ~ element(sK4(x,any1),any1)
| spl9_1 ),
inference(superposition,[],[f135,f433]) ).
fof(f433,plain,
( apply(x,sK3(x,any1)) = apply(x,sK4(x,any1))
| spl9_1 ),
inference(resolution,[],[f416,f84]) ).
fof(f416,plain,
( ! [X0,X1] :
( ~ morphism(x,X0,X1)
| apply(x,sK3(x,X0)) = apply(x,sK4(x,X0)) )
| spl9_1 ),
inference(resolution,[],[f120,f102]) ).
fof(f102,plain,
! [X2,X0,X1] :
( injection(X0)
| apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f135,plain,
! [X0] :
( zero(any2) = subtract(any2,apply(x,X0),apply(x,X0))
| ~ element(X0,any1) ),
inference(resolution,[],[f134,f85]) ).
fof(f134,plain,
! [X0] :
( element(apply(x,X0),any2)
| ~ element(X0,any1) ),
inference(resolution,[],[f86,f84]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1) ) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(X3,X1)
=> element(apply(X0,X3),X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',morphism) ).
fof(f623,plain,
( subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1))) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1)))
| spl9_1
| ~ spl9_5 ),
inference(resolution,[],[f620,f179]) ).
fof(f620,plain,
( ! [X0] :
( ~ element(X0,any1)
| apply(x,subtract(any1,X0,sK4(x,any1))) = subtract(any2,apply(x,X0),apply(x,sK3(x,any1))) )
| spl9_1 ),
inference(forward_demodulation,[],[f427,f433]) ).
fof(f427,plain,
( ! [X0] :
( ~ element(X0,any1)
| apply(x,subtract(any1,X0,sK4(x,any1))) = subtract(any2,apply(x,X0),apply(x,sK4(x,any1))) )
| spl9_1 ),
inference(resolution,[],[f426,f260]) ).
fof(f260,plain,
! [X0,X1] :
( ~ element(X0,any1)
| ~ element(X1,any1)
| apply(x,subtract(any1,X1,X0)) = subtract(any2,apply(x,X1),apply(x,X0)) ),
inference(resolution,[],[f88,f84]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| ~ element(X4,X1)
| ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X3,X4] :
( ( element(X4,X1)
& element(X3,X1) )
=> apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> apply(X0,subtract(X1,X4,X5)) = subtract(X2,apply(X0,X4),apply(X0,X5)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',subtract_distribution) ).
fof(f447,plain,
( ! [X0] :
( apply(x,X0) != zero(any2)
| ~ element(X0,any1)
| zero(any1) = X0 )
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f225,f125]) ).
fof(f125,plain,
( injection_2(x)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f225,plain,
! [X0] :
( apply(x,X0) != zero(any2)
| ~ element(X0,any1)
| zero(any1) = X0
| ~ injection_2(x) ),
inference(resolution,[],[f91,f84]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1)
| zero(X1) = X3
| ~ injection_2(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ! [X3] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ! [X3] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection_2(X0) )
=> ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> zero(X1) = X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',injection_properties_2) ).
fof(f411,plain,
( ~ spl9_1
| spl9_2
| ~ spl9_6 ),
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f410,plain,
( $false
| ~ spl9_1
| spl9_2
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f409,f84]) ).
fof(f409,plain,
( ~ morphism(x,any1,any2)
| ~ spl9_1
| spl9_2
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f408,f124]) ).
fof(f408,plain,
( injection_2(x)
| ~ morphism(x,any1,any2)
| ~ spl9_1
| spl9_2
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f407]) ).
fof(f407,plain,
( zero(any1) != zero(any1)
| injection_2(x)
| ~ morphism(x,any1,any2)
| ~ spl9_1
| spl9_2
| ~ spl9_6 ),
inference(superposition,[],[f99,f401]) ).
fof(f401,plain,
( zero(any1) = sK2(x,any1,any2)
| ~ spl9_1
| spl9_2
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f400,f354]) ).
fof(f354,plain,
( element(sK2(x,any1,any2),any1)
| spl9_2 ),
inference(resolution,[],[f352,f84]) ).
fof(f352,plain,
( ! [X2,X3] :
( ~ morphism(x,X2,X3)
| element(sK2(x,X2,X3),X2) )
| spl9_2 ),
inference(resolution,[],[f124,f97]) ).
fof(f400,plain,
( ~ element(sK2(x,any1,any2),any1)
| zero(any1) = sK2(x,any1,any2)
| ~ spl9_1
| spl9_2
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f398]) ).
fof(f398,plain,
( zero(any2) != zero(any2)
| ~ element(sK2(x,any1,any2),any1)
| zero(any1) = sK2(x,any1,any2)
| ~ spl9_1
| spl9_2
| ~ spl9_6 ),
inference(superposition,[],[f395,f366]) ).
fof(f366,plain,
( zero(any2) = apply(x,sK2(x,any1,any2))
| spl9_2 ),
inference(resolution,[],[f351,f84]) ).
fof(f351,plain,
( ! [X0,X1] :
( ~ morphism(x,X1,X0)
| zero(X0) = apply(x,sK2(x,X1,X0)) )
| spl9_2 ),
inference(resolution,[],[f124,f98]) ).
fof(f98,plain,
! [X2,X0,X1] :
( injection_2(X0)
| zero(X2) = apply(X0,sK2(X0,X1,X2))
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f395,plain,
( ! [X0] :
( apply(x,X0) != zero(any2)
| ~ element(X0,any1)
| zero(any1) = X0 )
| ~ spl9_1
| ~ spl9_6 ),
inference(forward_demodulation,[],[f391,f318]) ).
fof(f318,plain,
( zero(any2) = apply(x,zero(any1))
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f312,f184]) ).
fof(f184,plain,
( element(zero(any1),any1)
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f312,plain,
( zero(any2) = apply(x,zero(any1))
| ~ element(zero(any1),any1)
| ~ spl9_6 ),
inference(superposition,[],[f306,f135]) ).
fof(f306,plain,
( apply(x,zero(any1)) = subtract(any2,apply(x,zero(any1)),apply(x,zero(any1)))
| ~ spl9_6 ),
inference(forward_demodulation,[],[f302,f197]) ).
fof(f197,plain,
( zero(any1) = subtract(any1,zero(any1),zero(any1))
| ~ spl9_6 ),
inference(resolution,[],[f184,f85]) ).
fof(f302,plain,
( subtract(any2,apply(x,zero(any1)),apply(x,zero(any1))) = apply(x,subtract(any1,zero(any1),zero(any1)))
| ~ spl9_6 ),
inference(resolution,[],[f297,f184]) ).
fof(f297,plain,
( ! [X0] :
( ~ element(X0,any1)
| apply(x,subtract(any1,X0,zero(any1))) = subtract(any2,apply(x,X0),apply(x,zero(any1))) )
| ~ spl9_6 ),
inference(resolution,[],[f260,f184]) ).
fof(f391,plain,
( ! [X0] :
( apply(x,X0) != apply(x,zero(any1))
| ~ element(X0,any1)
| zero(any1) = X0 )
| ~ spl9_1
| ~ spl9_6 ),
inference(resolution,[],[f390,f184]) ).
fof(f390,plain,
( ! [X0,X1] :
( ~ element(X1,any1)
| apply(x,X0) != apply(x,X1)
| ~ element(X0,any1)
| X0 = X1 )
| ~ spl9_1 ),
inference(subsumption_resolution,[],[f250,f121]) ).
fof(f121,plain,
( injection(x)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f250,plain,
! [X0,X1] :
( apply(x,X0) != apply(x,X1)
| ~ element(X1,any1)
| ~ element(X0,any1)
| X0 = X1
| ~ injection(x) ),
inference(resolution,[],[f92,f84]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1)
| X3 = X4
| ~ injection(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X4,X5] :
( ( apply(X0,X4) = apply(X0,X5)
& element(X5,X1)
& element(X4,X1) )
=> X4 = X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',injection_properties) ).
fof(f99,plain,
! [X2,X0,X1] :
( zero(X1) != sK2(X0,X1,X2)
| injection_2(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f192,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_contradiction_clause,[],[f191]) ).
fof(f191,plain,
( $false
| ~ spl9_1
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f190,f121]) ).
fof(f190,plain,
( ~ injection(x)
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f83,f125]) ).
fof(f83,plain,
( ~ injection_2(x)
| ~ injection(x) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
( ( ~ injection_2(x)
| ~ injection(x) )
& ( injection_2(x)
| injection(x) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,plain,
( injection(x)
<~> injection_2(x) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852',my) ).
fof(f189,plain,
( spl9_1
| spl9_5 ),
inference(avatar_contradiction_clause,[],[f188]) ).
fof(f188,plain,
( $false
| spl9_1
| spl9_5 ),
inference(resolution,[],[f187,f84]) ).
fof(f187,plain,
( ! [X0] : ~ morphism(x,any1,X0)
| spl9_1
| spl9_5 ),
inference(resolution,[],[f180,f130]) ).
fof(f130,plain,
( ! [X0,X1] :
( element(sK3(x,X0),X0)
| ~ morphism(x,X0,X1) )
| spl9_1 ),
inference(resolution,[],[f100,f120]) ).
fof(f100,plain,
! [X2,X0,X1] :
( injection(X0)
| element(sK3(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f180,plain,
( ~ element(sK3(x,any1),any1)
| spl9_5 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f126,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f82,f123,f119]) ).
fof(f82,plain,
( injection_2(x)
| injection(x) ),
inference(cnf_transformation,[],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.13/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37 % Computer : n023.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Aug 28 02:48:25 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.Ipve3nKT4T/Vampire---4.8_18852
% 0.15/0.38 % (18959)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (18960)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.44 % (18965)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.44 % (18964)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.44 % (18963)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.22/0.44 % (18962)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.44 % (18961)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.44 % (18966)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.47 % (18965)First to succeed.
% 0.22/0.47 % (18965)Refutation found. Thanks to Tanya!
% 0.22/0.47 % SZS status Theorem for Vampire---4
% 0.22/0.47 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.47 % (18965)------------------------------
% 0.22/0.47 % (18965)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.47 % (18965)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.47 % (18965)Termination reason: Refutation
% 0.22/0.47
% 0.22/0.47 % (18965)Memory used [KB]: 5884
% 0.22/0.47 % (18965)Time elapsed: 0.035 s
% 0.22/0.47 % (18965)------------------------------
% 0.22/0.47 % (18965)------------------------------
% 0.22/0.47 % (18959)Success in time 0.094 s
% 0.22/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------