%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HAL002+1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 : Tue Sep 29 10:18:53 AM UTC 2026
% Result : Theorem 0.15s 0.52s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 149 ( 10 unt; 6 def)
% Number of atoms : 435 ( 112 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 461 ( 175 ~; 231 |; 31 &)
% ( 8 <=>; 15 =>; 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 : 186 ( 0 sgn 180 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ( ! [X3] :
( element(X3,X1)
=> element(apply(X0,X3),X2) )
& apply(X0,zero(X1)) = zero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( injection(X0)
& morphism(X0,X1,X2) )
=> ! [X3,X4] :
( ( element(X3,X1)
& element(X4,X1)
& apply(X0,X3) = apply(X0,X4) )
=> X3 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',injection_properties) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& ! [X3,X4] :
( ( element(X3,X1)
& element(X4,X1)
& apply(X0,X3) = apply(X0,X4) )
=> X3 = X4 ) )
=> injection(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_injection) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( element(X1,X0)
& element(X2,X0) )
=> element(subtract(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
fof(f11,axiom,
! [X0,X1] :
( element(X1,X0)
=> subtract(X0,X1,X1) = zero(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_to_0) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( element(X1,X0)
& element(X2,X0) )
=> subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).
fof(f13,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X3,X4] :
( ( element(X3,X1)
& element(X4,X1) )
=> apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( injection_2(X0)
& morphism(X0,X1,X2) )
=> ! [X3] :
( ( element(X3,X1)
& apply(X0,X3) = zero(X2) )
=> X3 = zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injection_properties_2) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& ! [X3] :
( ( element(X3,X1)
& apply(X0,X3) = zero(X2) )
=> X3 = zero(X1) ) )
=> injection_2(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_injection_2) ).
fof(f16,axiom,
morphism(x,any1,any2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_morphism) ).
fof(f17,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',my) ).
fof(f18,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1) )
& apply(X0,zero(X1)) = zero(X2) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| ~ element(X3,X1)
| ~ element(X4,X1)
| apply(X0,X3) != apply(X0,X4) )
| ~ injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| ~ element(X3,X1)
| ~ element(X4,X1)
| apply(X0,X3) != apply(X0,X4) )
| ~ injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ? [X3,X4] :
( X3 != X4
& element(X3,X1)
& element(X4,X1)
& apply(X0,X3) = apply(X0,X4) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ? [X3,X4] :
( X3 != X4
& element(X3,X1)
& element(X4,X1)
& apply(X0,X3) = apply(X0,X4) ) ),
inference(flattening,[],[f22]) ).
fof(f36,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f37,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( subtract(X0,X1,X1) = zero(X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f39,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f40,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X3,X1)
| ~ element(X4,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X3,X1)
| ~ element(X4,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ! [X3] :
( X3 = zero(X1)
| ~ element(X3,X1)
| apply(X0,X3) != zero(X2) )
| ~ injection_2(X0)
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ! [X3] :
( X3 = zero(X1)
| ~ element(X3,X1)
| apply(X0,X3) != zero(X2) )
| ~ injection_2(X0)
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ~ morphism(X0,X1,X2)
| ? [X3] :
( zero(X1) != X3
& element(X3,X1)
& apply(X0,X3) = zero(X2) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f46,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ~ morphism(X0,X1,X2)
| ? [X3] :
( zero(X1) != X3
& element(X3,X1)
& apply(X0,X3) = zero(X2) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
( injection(x)
<~> injection_2(x) ),
inference(ennf_transformation,[],[f18]) ).
fof(f48,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ( sK0(X0,X1) != sK1(X0,X1)
& element(sK0(X0,X1),X1)
& element(sK1(X0,X1),X1)
& apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1)),skolemize(X4,sK1(X0,X1))],[f23]) ).
fof(f60,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ~ morphism(X0,X1,X2)
| ( zero(X1) != sK8(X0,X1,X2)
& element(sK8(X0,X1,X2),X1)
& zero(X2) = apply(X0,sK8(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f46]) ).
fof(f61,plain,
( ( ~ injection_2(x)
| ~ injection(x) )
& ( injection_2(x)
| injection(x) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,zero(X1)) = zero(X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4] :
( ~ injection(X0)
| ~ element(X3,X1)
| ~ element(X4,X1)
| apply(X0,X3) != apply(X0,X4)
| X3 = X4
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection(X0)
| apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection(X0)
| element(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection(X0)
| element(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection(X0)
| sK0(X0,X1) != sK1(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f86,plain,
! [X0,X1] :
( ~ element(X1,X0)
| subtract(X0,X1,X1) = zero(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ element(X1,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4] :
( ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ injection_2(X0)
| ~ element(X3,X1)
| apply(X0,X3) != zero(X2)
| zero(X1) = X3
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection_2(X0)
| zero(X2) = apply(X0,sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection_2(X0)
| element(sK8(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection_2(X0)
| zero(X1) != sK8(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f93,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[],[f16]) ).
fof(f94,plain,
( injection_2(x)
| injection(x) ),
inference(cnf_transformation,[],[f61]) ).
fof(f95,plain,
( ~ injection_2(x)
| ~ injection(x) ),
inference(cnf_transformation,[],[f61]) ).
fof(f97,definition,
( spl9_1
<=> injection(x) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f98,plain,
( ~ injection(x)
| spl9_1 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( injection(x)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl9_2
<=> injection_2(x) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f102,plain,
( ~ injection_2(x)
| spl9_2 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( injection_2(x)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f94,f101,f97]) ).
fof(f105,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f95,f101,f97]) ).
fof(f106,plain,
apply(x,zero(any1)) = zero(any2),
inference(resolution,[],[f62,f93]) ).
fof(f107,plain,
( injection(x)
| element(sK1(x,any1),any1) ),
inference(resolution,[],[f66,f93]) ).
fof(f108,plain,
( element(sK1(x,any1),any1)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f107,f98]) ).
fof(f109,plain,
( zero(any1) = subtract(any1,sK1(x,any1),sK1(x,any1))
| spl9_1 ),
inference(resolution,[],[f108,f86]) ).
fof(f110,plain,
( injection(x)
| element(sK0(x,any1),any1) ),
inference(resolution,[],[f67,f93]) ).
fof(f111,plain,
( element(sK0(x,any1),any1)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f110,f98]) ).
fof(f112,plain,
( zero(any1) = subtract(any1,sK0(x,any1),sK0(x,any1))
| spl9_1 ),
inference(resolution,[],[f111,f86]) ).
fof(f126,plain,
( subtract(any1,sK1(x,any1),sK1(x,any1)) = subtract(any1,sK0(x,any1),sK0(x,any1))
| spl9_1 ),
inference(superposition,[],[f109,f112]) ).
fof(f128,plain,
( ! [X0] :
( ~ element(X0,any1)
| element(subtract(any1,sK0(x,any1),X0),any1) )
| spl9_1 ),
inference(resolution,[],[f85,f111]) ).
fof(f130,plain,
( injection_2(x)
| element(sK8(x,any1,any2),any1) ),
inference(resolution,[],[f91,f93]) ).
fof(f137,plain,
( injection(x)
| sK1(x,any1) != sK0(x,any1) ),
inference(resolution,[],[f68,f93]) ).
fof(f139,plain,
( injection_2(x)
| zero(any1) != sK8(x,any1,any2) ),
inference(resolution,[],[f92,f93]) ).
fof(f154,plain,
( injection_2(x)
| zero(any2) = apply(x,sK8(x,any1,any2)) ),
inference(resolution,[],[f90,f93]) ).
fof(f162,plain,
( injection(x)
| apply(x,sK1(x,any1)) = apply(x,sK0(x,any1)) ),
inference(resolution,[],[f65,f93]) ).
fof(f178,plain,
( element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1)
| spl9_1 ),
inference(resolution,[],[f128,f108]) ).
fof(f182,plain,
( ! [X2,X0,X1] :
( ~ element(X0,X1)
| zero(X2) != apply(x,X0)
| zero(X1) = X0
| ~ morphism(x,X1,X2) )
| ~ spl9_2 ),
inference(resolution,[],[f89,f103]) ).
fof(f357,plain,
( ! [X0] :
( zero(X0) != apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| zero(any1) = subtract(any1,sK0(x,any1),sK1(x,any1))
| ~ morphism(x,any1,X0) )
| spl9_1
| ~ spl9_2 ),
inference(resolution,[],[f182,f178]) ).
fof(f376,plain,
( ! [X0] :
( subtract(any1,sK1(x,any1),sK1(x,any1)) = subtract(any1,sK0(x,any1),sK1(x,any1))
| zero(X0) != apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| ~ morphism(x,any1,X0) )
| spl9_1
| ~ spl9_2 ),
inference(forward_demodulation,[],[f357,f109]) ).
fof(f389,plain,
( ! [X0] :
( subtract(any1,sK0(x,any1),sK0(x,any1)) = subtract(any1,sK0(x,any1),sK1(x,any1))
| zero(X0) != apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| ~ morphism(x,any1,X0) )
| spl9_1
| ~ spl9_2 ),
inference(forward_demodulation,[],[f376,f126]) ).
fof(f416,definition,
( spl9_10
<=> ! [X0] :
( zero(X0) != apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| ~ morphism(x,any1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
fof(f417,plain,
( ! [X0] :
( ~ morphism(x,any1,X0)
| zero(X0) != apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f419,definition,
( spl9_11
<=> subtract(any1,sK0(x,any1),sK0(x,any1)) = subtract(any1,sK0(x,any1),sK1(x,any1)) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f421,plain,
( subtract(any1,sK0(x,any1),sK0(x,any1)) = subtract(any1,sK0(x,any1),sK1(x,any1))
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f422,plain,
( spl9_10
| spl9_11
| spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f389,f101,f97,f419,f416]) ).
fof(f466,plain,
( element(sK8(x,any1,any2),any1)
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f130,f102]) ).
fof(f467,plain,
( zero(any1) != sK8(x,any1,any2)
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f139,f102]) ).
fof(f468,plain,
( zero(any2) = apply(x,sK8(x,any1,any2))
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f154,f102]) ).
fof(f469,plain,
( apply(x,zero(any1)) = apply(x,sK8(x,any1,any2))
| spl9_2 ),
inference(forward_demodulation,[],[f468,f106]) ).
fof(f470,plain,
( ! [X2,X3,X0,X1] :
( ~ element(X0,X1)
| ~ element(X2,X1)
| apply(x,X0) != apply(x,X2)
| X0 = X2
| ~ morphism(x,X1,X3) )
| ~ spl9_1 ),
inference(resolution,[],[f99,f64]) ).
fof(f475,plain,
( ! [X0] :
( ~ element(X0,any1)
| element(subtract(any1,sK8(x,any1,any2),X0),any1) )
| spl9_2 ),
inference(resolution,[],[f466,f85]) ).
fof(f476,plain,
( zero(any1) = subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2))
| spl9_2 ),
inference(resolution,[],[f466,f86]) ).
fof(f481,plain,
( ! [X0,X1] :
( ~ element(X0,any1)
| apply(x,sK8(x,any1,any2)) != apply(x,X0)
| sK8(x,any1,any2) = X0
| ~ morphism(x,any1,X1) )
| ~ spl9_1
| spl9_2 ),
inference(resolution,[],[f470,f466]) ).
fof(f482,plain,
( ! [X0,X1] :
( apply(x,zero(any1)) != apply(x,X0)
| ~ element(X0,any1)
| sK8(x,any1,any2) = X0
| ~ morphism(x,any1,X1) )
| ~ spl9_1
| spl9_2 ),
inference(forward_demodulation,[],[f481,f469]) ).
fof(f484,definition,
( spl9_19
<=> ! [X1] : ~ morphism(x,any1,X1) ),
introduced(definition,[new_symbols(definition,[spl9_19])],[avatar_definition]) ).
fof(f485,plain,
( ! [X1] : ~ morphism(x,any1,X1)
| ~ spl9_19 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f487,definition,
( spl9_20
<=> ! [X0] :
( apply(x,zero(any1)) != apply(x,X0)
| sK8(x,any1,any2) = X0
| ~ element(X0,any1) ) ),
introduced(definition,[new_symbols(definition,[spl9_20])],[avatar_definition]) ).
fof(f488,plain,
( ! [X0] :
( ~ element(X0,any1)
| sK8(x,any1,any2) = X0
| apply(x,zero(any1)) != apply(x,X0) )
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f489,plain,
( spl9_19
| spl9_20
| ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f482,f101,f97,f487,f484]) ).
fof(f490,plain,
( $false
| ~ spl9_19 ),
inference(resolution,[],[f485,f93]) ).
fof(f491,plain,
~ spl9_19,
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f519,plain,
( element(subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)),any1)
| spl9_2 ),
inference(resolution,[],[f475,f466]) ).
fof(f520,plain,
( element(zero(any1),any1)
| spl9_2 ),
inference(forward_demodulation,[],[f519,f476]) ).
fof(f576,plain,
( zero(any1) = sK8(x,any1,any2)
| apply(x,zero(any1)) != apply(x,zero(any1))
| spl9_2
| ~ spl9_20 ),
inference(resolution,[],[f488,f520]) ).
fof(f580,plain,
( zero(any1) = sK8(x,any1,any2)
| spl9_2
| ~ spl9_20 ),
inference(trivial_inequality_removal,[],[f576]) ).
fof(f599,plain,
( $false
| spl9_2
| ~ spl9_20 ),
inference(forward_subsumption_resolution,[],[f580,f467]) ).
fof(f600,plain,
( spl9_2
| ~ spl9_20 ),
inference(avatar_contradiction_clause,[],[f599]) ).
fof(f601,plain,
( element(sK1(x,any1),any1)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f107,f98]) ).
fof(f602,plain,
( element(sK0(x,any1),any1)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f110,f98]) ).
fof(f603,plain,
( sK1(x,any1) != sK0(x,any1)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f137,f98]) ).
fof(f604,plain,
( apply(x,sK1(x,any1)) = apply(x,sK0(x,any1))
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f162,f98]) ).
fof(f612,plain,
( zero(any1) = subtract(any1,sK1(x,any1),sK1(x,any1))
| spl9_1 ),
inference(resolution,[],[f601,f86]) ).
fof(f614,plain,
( ! [X2,X0,X1] :
( ~ element(X1,any1)
| apply(X0,subtract(any1,sK1(x,any1),X1)) = subtract(X2,apply(X0,sK1(x,any1)),apply(X0,X1))
| ~ morphism(X0,any1,X2) )
| spl9_1 ),
inference(resolution,[],[f601,f88]) ).
fof(f632,plain,
( zero(any1) = subtract(any1,sK0(x,any1),sK0(x,any1))
| spl9_1 ),
inference(resolution,[],[f602,f86]) ).
fof(f633,plain,
( ! [X0] :
( ~ element(X0,any1)
| subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0)) = X0 )
| spl9_1 ),
inference(resolution,[],[f602,f87]) ).
fof(f634,plain,
( ! [X2,X0,X1] :
( ~ element(X1,any1)
| apply(X0,subtract(any1,sK0(x,any1),X1)) = subtract(X2,apply(X0,sK0(x,any1)),apply(X0,X1))
| ~ morphism(X0,any1,X2) )
| spl9_1 ),
inference(resolution,[],[f602,f88]) ).
fof(f698,plain,
( subtract(any1,sK1(x,any1),sK1(x,any1)) = subtract(any1,sK0(x,any1),sK0(x,any1))
| spl9_1 ),
inference(superposition,[],[f612,f632]) ).
fof(f746,plain,
( sK0(x,any1) = subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))
| spl9_1 ),
inference(resolution,[],[f633,f602]) ).
fof(f747,plain,
( sK1(x,any1) = subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1)))
| spl9_1 ),
inference(resolution,[],[f633,f601]) ).
fof(f748,plain,
( sK1(x,any1) = subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1)))
| spl9_1
| ~ spl9_11 ),
inference(forward_demodulation,[],[f747,f421]) ).
fof(f750,plain,
( sK1(x,any1) = sK0(x,any1)
| spl9_1
| ~ spl9_11 ),
inference(forward_demodulation,[],[f748,f746]) ).
fof(f751,plain,
( $false
| spl9_1
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f750,f603]) ).
fof(f752,plain,
( spl9_1
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f751]) ).
fof(f784,plain,
( ! [X0,X1] :
( apply(X0,subtract(any1,sK1(x,any1),sK1(x,any1))) = subtract(X1,apply(X0,sK1(x,any1)),apply(X0,sK1(x,any1)))
| ~ morphism(X0,any1,X1) )
| spl9_1 ),
inference(resolution,[],[f614,f601]) ).
fof(f785,plain,
( ! [X0,X1] :
( ~ morphism(X0,any1,X1)
| apply(X0,subtract(any1,sK0(x,any1),sK0(x,any1))) = subtract(X1,apply(X0,sK1(x,any1)),apply(X0,sK1(x,any1))) )
| spl9_1 ),
inference(forward_demodulation,[],[f784,f698]) ).
fof(f798,plain,
( ! [X0,X1] :
( ~ morphism(X0,any1,X1)
| apply(X0,subtract(any1,sK0(x,any1),sK1(x,any1))) = subtract(X1,apply(X0,sK0(x,any1)),apply(X0,sK1(x,any1))) )
| spl9_1 ),
inference(resolution,[],[f634,f601]) ).
fof(f1447,plain,
( subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))
| spl9_1 ),
inference(resolution,[],[f785,f93]) ).
fof(f1448,plain,
( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) = subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1)))
| spl9_1 ),
inference(forward_demodulation,[],[f1447,f604]) ).
fof(f1628,plain,
( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| spl9_1 ),
inference(resolution,[],[f798,f93]) ).
fof(f1629,plain,
( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| spl9_1 ),
inference(forward_demodulation,[],[f1628,f604]) ).
fof(f1630,plain,
( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| spl9_1 ),
inference(forward_demodulation,[],[f1629,f1448]) ).
fof(f1698,plain,
( zero(any2) != apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| ~ spl9_10 ),
inference(resolution,[],[f417,f93]) ).
fof(f1699,plain,
( zero(any2) != apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))
| spl9_1
| ~ spl9_10 ),
inference(forward_demodulation,[],[f1698,f1630]) ).
fof(f1700,plain,
( apply(x,zero(any1)) != apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))
| spl9_1
| ~ spl9_10 ),
inference(forward_demodulation,[],[f1699,f106]) ).
fof(f1701,plain,
( apply(x,subtract(any1,sK1(x,any1),sK1(x,any1))) != apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))
| spl9_1
| ~ spl9_10 ),
inference(forward_demodulation,[],[f1700,f612]) ).
fof(f1702,plain,
( apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))) != apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))
| spl9_1
| ~ spl9_10 ),
inference(forward_demodulation,[],[f1701,f698]) ).
fof(f1703,plain,
( $false
| spl9_1
| ~ spl9_10 ),
inference(trivial_inequality_removal,[],[f1702]) ).
fof(f1704,plain,
( spl9_1
| ~ spl9_10 ),
inference(avatar_contradiction_clause,[],[f1703]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f105]) ).
cnf(s7,plain,
( spl9_1
| ~ spl9_2
| spl9_10
| spl9_11 ),
inference(sat_conversion,[],[f422]) ).
cnf(s17,plain,
( ~ spl9_1
| spl9_2
| spl9_19
| spl9_20 ),
inference(sat_conversion,[],[f489]) ).
cnf(s18,plain,
~ spl9_19,
inference(sat_conversion,[],[f491]) ).
cnf(s26,plain,
( spl9_2
| ~ spl9_20 ),
inference(sat_conversion,[],[f600]) ).
cnf(s29,plain,
( spl9_1
| ~ spl9_11 ),
inference(sat_conversion,[],[f752]) ).
cnf(s77,plain,
( spl9_1
| ~ spl9_10 ),
inference(sat_conversion,[],[f1704]) ).
cnf(s78,plain,
( ~ spl9_1
| spl9_2
| spl9_20 ),
inference(rat,[],[s17,s18]) ).
cnf(s79,plain,
( spl9_1
| spl9_11
| spl9_10 ),
inference(rat,[],[s1,s7]) ).
cnf(s80,plain,
spl9_1,
inference(rat,[],[s79,s29,s77]) ).
cnf(s81,plain,
~ spl9_2,
inference(rat,[],[s2,s80]) ).
cnf(s84,plain,
~ spl9_20,
inference(rat,[],[s26,s81]) ).
cnf(s86,plain,
$false,
inference(rat,[],[s78,s80,s84,s81]) ).
fof(f1705,plain,
$false,
inference(avatar_sat_refutation,[],[s86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HAL002+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 % Computer : n004.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 27 10:48:37 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.42 Running first-order model finding
% 0.09/0.42 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
% 0.15/0.52 % (3333468)Will run a generic schedule for satisfiability detection.
% 0.15/0.52 % (3333474)% WARNING: option uhcvi not known.
% 0.15/0.52 % (3333473)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2696340155_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.52 % (3333477)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1510039328:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.52 % (3333474)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2569687529:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.52 % (3333476)dis+10_1_sil=32000:sp=arity:random_seed=640227698:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.52 % (3333475)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1089695651:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.52 % (3333478)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1401201094:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.52 % TRYING [1]
% 0.15/0.52 % TRYING [2]
% 0.15/0.52 % (3333479)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2414693462:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.52 % TRYING [3]
% 0.15/0.52 % TRYING [4]
% 0.15/0.52 % (3333478) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3333468-3333478"...
% 0.15/0.52 % (3333478)...printing done.
% 0.15/0.52 % (3333478)Refutation found. Thanks to Tanya!
% 0.15/0.52 % SZS status Theorem for theBenchmark
% 0.15/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.52 % (3333478)------------------------------
% 0.15/0.52 % (3333478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.52 % (3333478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.52 % (3333478)CaDiCaL version: 2.1.3
% 0.15/0.52 % (3333478)Termination reason: Refutation
% 0.15/0.52 % (3333478)Time elapsed: 0.046 s
% 0.15/0.52 % (3333478)Peak memory usage: 13 MB
% 0.15/0.52 % (3333478)Instructions burned: 81 (million)
% 0.15/0.52 % (3333468)Success in time 0.089 s
% 0.15/0.52 % Vampire exiting
%------------------------------------------------------------------------------