%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HAL001+2 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 10:18:52 AM UTC 2026
% Result : Theorem 9.59s 2.23s
% Output : Refutation 10.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 155 ( 45 unt; 7 def)
% Number of atoms : 528 ( 118 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 694 ( 321 ~; 318 |; 36 &)
% ( 10 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-3 aty)
% Number of variables : 215 ( 0 sgn 207 !; 8 ?)
% 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/theBenchmark.p',morphism) ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4] :
( ( exact(X0,X1)
& morphism(X0,X2,X3)
& morphism(X1,X3,X4) )
=> ! [X5] :
( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
<=> ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exact_properties) ).
fof(f8,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( commute(X0,X1,X2,X3)
& morphism(X0,X4,X5)
& morphism(X1,X5,X7)
& morphism(X2,X4,X6)
& morphism(X3,X6,X7) )
=> ! [X8] :
( element(X8,X4)
=> apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commute_properties) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( injection(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(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_injection_2) ).
fof(f16,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_morphism) ).
fof(f17,axiom,
morphism(beta,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_morphism) ).
fof(f18,axiom,
morphism(gamma,d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gamma_morphism) ).
fof(f19,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_morphism) ).
fof(f20,axiom,
morphism(f,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_morphism) ).
fof(f21,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
fof(f22,axiom,
morphism(h,c,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_morphism) ).
fof(f24,axiom,
injection(gamma),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gamma_injection) ).
fof(f27,axiom,
exact(alpha,beta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_beta_exact) ).
fof(f29,axiom,
commute(alpha,g,f,gamma),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_g_f_gamma_commute) ).
fof(f30,axiom,
commute(beta,h,g,delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
fof(f31,axiom,
injection(f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_injection) ).
fof(f32,axiom,
injection(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_injection) ).
fof(f33,conjecture,
injection(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_injection) ).
fof(f34,negated_conjecture,
~ injection(g),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ injection(g),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ! [X3] :
( X3 = zero(X1)
| ~ element(X3,X1)
| apply(X0,X3) != zero(X2) )
| ~ injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ! [X3] :
( X3 = zero(X1)
| ~ element(X3,X1)
| apply(X0,X3) != zero(X2) )
| ~ injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ? [X3] :
( zero(X1) != X3
& element(X3,X1)
& apply(X0,X3) = zero(X2) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ? [X3] :
( zero(X1) != X3
& element(X3,X1)
& apply(X0,X3) = zero(X2) ) ),
inference(flattening,[],[f38]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
<=> ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
<=> ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(flattening,[],[f43]) ).
fof(f45,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(f56,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8] :
( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ element(X8,X4) )
| ~ commute(X0,X1,X2,X3)
| ~ morphism(X0,X4,X5)
| ~ morphism(X1,X5,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X3,X6,X7) ),
inference(ennf_transformation,[],[f8]) ).
fof(f57,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8] :
( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ element(X8,X4) )
| ~ commute(X0,X1,X2,X3)
| ~ morphism(X0,X4,X5)
| ~ morphism(X1,X5,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X3,X6,X7) ),
inference(flattening,[],[f56]) ).
fof(f64,plain,
! [X0,X1,X2] :
( injection(X0)
| ~ morphism(X0,X1,X2)
| ( zero(X1) != sK0(X0,X1,X2)
& element(sK0(X0,X1,X2),X1)
& zero(X2) = apply(X0,sK0(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f39]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
| ! [X6] :
( ~ element(X6,X2)
| apply(X0,X6) != X5 ) )
& ( ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 )
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4) ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(nnf_transformation,[],[f44]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
| ! [X6] :
( ~ element(X6,X2)
| apply(X0,X6) != X5 ) )
& ( ? [X6] :
( element(X6,X2)
& apply(X0,X6) = X5 )
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4) ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
| ! [X6] :
( ~ element(X6,X2)
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( element(X7,X2)
& apply(X0,X7) = X5 )
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4) ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( element(X5,X3)
& apply(X1,X5) = zero(X4) )
| ! [X6] :
( ~ element(X6,X2)
| apply(X0,X6) != X5 ) )
& ( ( element(sK3(X0,X2,X5),X2)
& apply(X0,sK3(X0,X2,X5)) = X5 )
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4) ) )
| ~ exact(X0,X1)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X7,sK3(X0,X2,X5))],[f71]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3) != zero(X2)
| ~ element(X3,X1)
| zero(X1) = X3
| ~ injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection(X0)
| zero(X2) = apply(X0,sK0(X0,X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f79,plain,
! [X2,X0,X1] :
( element(sK0(X0,X1,X2),X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f80,plain,
! [X2,X0,X1] :
( zero(X1) != sK0(X0,X1,X2)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f81,plain,
morphism(alpha,a,b),
inference(cnf_transformation,[],[f16]) ).
fof(f82,plain,
morphism(beta,b,c),
inference(cnf_transformation,[],[f17]) ).
fof(f83,plain,
morphism(gamma,d,e),
inference(cnf_transformation,[],[f18]) ).
fof(f84,plain,
morphism(delta,e,r),
inference(cnf_transformation,[],[f19]) ).
fof(f85,plain,
morphism(f,a,d),
inference(cnf_transformation,[],[f20]) ).
fof(f86,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f21]) ).
fof(f87,plain,
morphism(h,c,r),
inference(cnf_transformation,[],[f22]) ).
fof(f89,plain,
injection(gamma),
inference(cnf_transformation,[],[f24]) ).
fof(f92,plain,
exact(alpha,beta),
inference(cnf_transformation,[],[f27]) ).
fof(f94,plain,
commute(alpha,g,f,gamma),
inference(cnf_transformation,[],[f29]) ).
fof(f95,plain,
commute(beta,h,g,delta),
inference(cnf_transformation,[],[f30]) ).
fof(f96,plain,
injection(f),
inference(cnf_transformation,[],[f31]) ).
fof(f97,plain,
injection(h),
inference(cnf_transformation,[],[f32]) ).
fof(f98,plain,
~ injection(g),
inference(cnf_transformation,[],[f35]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ exact(X0,X1)
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4)
| apply(X0,sK3(X0,X2,X5)) = X5
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(cnf_transformation,[],[f72]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ exact(X0,X1)
| ~ element(X5,X3)
| apply(X1,X5) != zero(X4)
| element(sK3(X0,X2,X5),X2)
| ~ morphism(X0,X2,X3)
| ~ morphism(X1,X3,X4) ),
inference(cnf_transformation,[],[f72]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,zero(X1)) = zero(X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f122,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ commute(X0,X1,X2,X3)
| ~ element(X8,X4)
| apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ morphism(X0,X4,X5)
| ~ morphism(X1,X5,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X3,X6,X7) ),
inference(cnf_transformation,[],[f57]) ).
fof(f132,plain,
( injection(g)
| zero(e) = apply(g,sK0(g,b,e)) ),
inference(resolution,[],[f78,f86]) ).
fof(f133,plain,
zero(e) = apply(g,sK0(g,b,e)),
inference(forward_subsumption_resolution,[],[f132,f98]) ).
fof(f138,definition,
( spl9_1
<=> element(sK0(g,b,e),b) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f139,plain,
( ~ element(sK0(g,b,e),b)
| spl9_1 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f145,plain,
( ~ morphism(g,b,e)
| injection(g)
| spl9_1 ),
inference(resolution,[],[f139,f79]) ).
fof(f147,plain,
( injection(g)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f145,f86]) ).
fof(f148,plain,
( $false
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f147,f98]) ).
fof(f149,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f148]) ).
fof(f166,plain,
! [X0] :
( element(apply(f,X0),d)
| ~ element(X0,a) ),
inference(resolution,[],[f85,f110]) ).
fof(f229,plain,
zero(r) = apply(delta,zero(e)),
inference(resolution,[],[f84,f109]) ).
fof(f258,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(beta,X1,X2)
| apply(h,apply(beta,X0)) = apply(delta,apply(g,X0))
| ~ element(X0,X1)
| ~ morphism(h,X2,X3)
| ~ morphism(g,X1,X4)
| ~ morphism(delta,X4,X3) ),
inference(resolution,[],[f122,f95]) ).
fof(f259,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(alpha,X1,X2)
| apply(g,apply(alpha,X0)) = apply(gamma,apply(f,X0))
| ~ element(X0,X1)
| ~ morphism(g,X2,X3)
| ~ morphism(f,X1,X4)
| ~ morphism(gamma,X4,X3) ),
inference(resolution,[],[f122,f94]) ).
fof(f260,plain,
! [X2,X0,X1] :
( apply(h,apply(beta,X0)) = apply(delta,apply(g,X0))
| ~ element(X0,b)
| ~ morphism(h,c,X1)
| ~ morphism(g,b,X2)
| ~ morphism(delta,X2,X1) ),
inference(resolution,[],[f82,f258]) ).
fof(f263,plain,
! [X0] :
( element(apply(beta,X0),c)
| ~ element(X0,b) ),
inference(resolution,[],[f82,f110]) ).
fof(f291,definition,
( spl9_24
<=> ! [X2,X1] :
( ~ morphism(h,c,X1)
| ~ morphism(g,b,X2)
| ~ morphism(delta,X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition]) ).
fof(f292,plain,
( ! [X2,X1] :
( ~ morphism(h,c,X1)
| ~ morphism(g,b,X2)
| ~ morphism(delta,X2,X1) )
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f294,definition,
( spl9_25
<=> ! [X0] :
( apply(h,apply(beta,X0)) = apply(delta,apply(g,X0))
| ~ element(X0,b) ) ),
introduced(definition,[new_symbols(definition,[spl9_25])],[avatar_definition]) ).
fof(f295,plain,
( ! [X0] :
( ~ element(X0,b)
| apply(h,apply(beta,X0)) = apply(delta,apply(g,X0)) )
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f296,plain,
( spl9_24
| spl9_25 ),
inference(avatar_split_clause,[],[f260,f294,f291]) ).
fof(f297,plain,
( $false
| ~ spl9_24 ),
inference(unit_resulting_resolution,[],[f292,f84,f86,f87]) ).
fof(f299,plain,
~ spl9_24,
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f344,plain,
! [X2,X0,X1] :
( apply(g,apply(alpha,X0)) = apply(gamma,apply(f,X0))
| ~ element(X0,a)
| ~ morphism(g,b,X1)
| ~ morphism(f,a,X2)
| ~ morphism(gamma,X2,X1) ),
inference(resolution,[],[f81,f259]) ).
fof(f346,plain,
zero(b) = apply(alpha,zero(a)),
inference(resolution,[],[f81,f109]) ).
fof(f365,definition,
( spl9_35
<=> ! [X2,X1] :
( ~ morphism(g,b,X1)
| ~ morphism(f,a,X2)
| ~ morphism(gamma,X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl9_35])],[avatar_definition]) ).
fof(f366,plain,
( ! [X2,X1] :
( ~ morphism(g,b,X1)
| ~ morphism(f,a,X2)
| ~ morphism(gamma,X2,X1) )
| ~ spl9_35 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f368,definition,
( spl9_36
<=> ! [X0] :
( apply(g,apply(alpha,X0)) = apply(gamma,apply(f,X0))
| ~ element(X0,a) ) ),
introduced(definition,[new_symbols(definition,[spl9_36])],[avatar_definition]) ).
fof(f369,plain,
( ! [X0] :
( ~ element(X0,a)
| apply(g,apply(alpha,X0)) = apply(gamma,apply(f,X0)) )
| ~ spl9_36 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f370,plain,
( spl9_35
| spl9_36 ),
inference(avatar_split_clause,[],[f344,f368,f365]) ).
fof(f371,plain,
( $false
| ~ spl9_35 ),
inference(unit_resulting_resolution,[],[f366,f83,f85,f86]) ).
fof(f373,plain,
~ spl9_35,
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f511,plain,
( element(sK0(g,b,e),b)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f514,plain,
( apply(h,apply(beta,sK0(g,b,e))) = apply(delta,apply(g,sK0(g,b,e)))
| ~ spl9_1
| ~ spl9_25 ),
inference(resolution,[],[f511,f295]) ).
fof(f517,plain,
( apply(delta,zero(e)) = apply(h,apply(beta,sK0(g,b,e)))
| ~ spl9_1
| ~ spl9_25 ),
inference(forward_demodulation,[],[f514,f133]) ).
fof(f519,plain,
( zero(r) = apply(h,apply(beta,sK0(g,b,e)))
| ~ spl9_1
| ~ spl9_25 ),
inference(forward_demodulation,[],[f517,f229]) ).
fof(f522,plain,
( ! [X0,X1] :
( zero(X0) != zero(r)
| ~ element(apply(beta,sK0(g,b,e)),X1)
| zero(X1) = apply(beta,sK0(g,b,e))
| ~ injection(h)
| ~ morphism(h,X1,X0) )
| ~ spl9_1
| ~ spl9_25 ),
inference(superposition,[],[f77,f519]) ).
fof(f523,plain,
( ! [X0,X1] :
( zero(X0) != zero(r)
| ~ element(apply(beta,sK0(g,b,e)),X1)
| zero(X1) = apply(beta,sK0(g,b,e))
| ~ morphism(h,X1,X0) )
| ~ spl9_1
| ~ spl9_25 ),
inference(forward_subsumption_resolution,[],[f522,f97]) ).
fof(f524,plain,
( ! [X0] :
( ~ element(apply(beta,sK0(g,b,e)),X0)
| zero(X0) = apply(beta,sK0(g,b,e))
| ~ morphism(h,X0,r) )
| ~ spl9_1
| ~ spl9_25 ),
inference(equality_resolution,[],[f523]) ).
fof(f525,plain,
( zero(c) = apply(beta,sK0(g,b,e))
| ~ morphism(h,c,r)
| ~ element(sK0(g,b,e),b)
| ~ spl9_1
| ~ spl9_25 ),
inference(resolution,[],[f524,f263]) ).
fof(f526,plain,
( zero(c) = apply(beta,sK0(g,b,e))
| ~ element(sK0(g,b,e),b)
| ~ spl9_1
| ~ spl9_25 ),
inference(forward_subsumption_resolution,[],[f525,f87]) ).
fof(f527,plain,
( zero(c) = apply(beta,sK0(g,b,e))
| ~ spl9_1
| ~ spl9_25 ),
inference(forward_subsumption_resolution,[],[f526,f511]) ).
fof(f636,plain,
! [X2,X3,X0,X1] :
( ~ morphism(beta,X1,X2)
| zero(X2) != apply(beta,X0)
| apply(alpha,sK3(alpha,X3,X0)) = X0
| ~ morphism(alpha,X3,X1)
| ~ element(X0,X1) ),
inference(resolution,[],[f105,f92]) ).
fof(f638,plain,
! [X0,X1] :
( ~ morphism(alpha,X1,b)
| apply(alpha,sK3(alpha,X1,X0)) = X0
| apply(beta,X0) != zero(c)
| ~ element(X0,b) ),
inference(resolution,[],[f636,f82]) ).
fof(f639,plain,
! [X0] :
( apply(beta,X0) != zero(c)
| apply(alpha,sK3(alpha,a,X0)) = X0
| ~ element(X0,b) ),
inference(resolution,[],[f638,f81]) ).
fof(f641,plain,
( zero(c) != zero(c)
| sK0(g,b,e) = apply(alpha,sK3(alpha,a,sK0(g,b,e)))
| ~ element(sK0(g,b,e),b)
| ~ spl9_1
| ~ spl9_25 ),
inference(superposition,[],[f639,f527]) ).
fof(f647,plain,
( sK0(g,b,e) = apply(alpha,sK3(alpha,a,sK0(g,b,e)))
| ~ element(sK0(g,b,e),b)
| ~ spl9_1
| ~ spl9_25 ),
inference(trivial_inequality_removal,[],[f641]) ).
fof(f664,plain,
( sK0(g,b,e) = apply(alpha,sK3(alpha,a,sK0(g,b,e)))
| ~ spl9_1
| ~ spl9_25 ),
inference(forward_subsumption_resolution,[],[f647,f511]) ).
fof(f1697,plain,
! [X2,X3,X0,X1] :
( ~ morphism(beta,X1,X2)
| zero(X2) != apply(beta,X0)
| element(sK3(alpha,X3,X0),X3)
| ~ morphism(alpha,X3,X1)
| ~ element(X0,X1) ),
inference(resolution,[],[f106,f92]) ).
fof(f1699,plain,
! [X0,X1] :
( ~ morphism(alpha,X1,b)
| element(sK3(alpha,X1,X0),X1)
| apply(beta,X0) != zero(c)
| ~ element(X0,b) ),
inference(resolution,[],[f1697,f82]) ).
fof(f1700,plain,
! [X0] :
( element(sK3(alpha,a,X0),a)
| apply(beta,X0) != zero(c)
| ~ element(X0,b) ),
inference(resolution,[],[f1699,f81]) ).
fof(f1703,plain,
( ! [X0] :
( apply(beta,X0) != zero(c)
| ~ element(X0,b)
| apply(g,apply(alpha,sK3(alpha,a,X0))) = apply(gamma,apply(f,sK3(alpha,a,X0))) )
| ~ spl9_36 ),
inference(resolution,[],[f1700,f369]) ).
fof(f1748,plain,
( zero(c) != zero(c)
| ~ element(sK0(g,b,e),b)
| apply(g,apply(alpha,sK3(alpha,a,sK0(g,b,e)))) = apply(gamma,apply(f,sK3(alpha,a,sK0(g,b,e))))
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(superposition,[],[f1703,f527]) ).
fof(f1754,plain,
( ~ element(sK0(g,b,e),b)
| apply(g,apply(alpha,sK3(alpha,a,sK0(g,b,e)))) = apply(gamma,apply(f,sK3(alpha,a,sK0(g,b,e))))
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(trivial_inequality_removal,[],[f1748]) ).
fof(f1761,plain,
( apply(g,apply(alpha,sK3(alpha,a,sK0(g,b,e)))) = apply(gamma,apply(f,sK3(alpha,a,sK0(g,b,e))))
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(forward_subsumption_resolution,[],[f1754,f511]) ).
fof(f1770,plain,
( apply(g,sK0(g,b,e)) = apply(gamma,apply(f,sK3(alpha,a,sK0(g,b,e))))
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(forward_demodulation,[],[f1761,f664]) ).
fof(f1775,plain,
( zero(e) = apply(gamma,apply(f,sK3(alpha,a,sK0(g,b,e))))
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(forward_demodulation,[],[f1770,f133]) ).
fof(f1785,plain,
( ! [X0,X1] :
( zero(X0) != zero(e)
| ~ element(apply(f,sK3(alpha,a,sK0(g,b,e))),X1)
| zero(X1) = apply(f,sK3(alpha,a,sK0(g,b,e)))
| ~ injection(gamma)
| ~ morphism(gamma,X1,X0) )
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(superposition,[],[f77,f1775]) ).
fof(f1786,plain,
( ! [X0,X1] :
( zero(X0) != zero(e)
| ~ element(apply(f,sK3(alpha,a,sK0(g,b,e))),X1)
| zero(X1) = apply(f,sK3(alpha,a,sK0(g,b,e)))
| ~ morphism(gamma,X1,X0) )
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(forward_subsumption_resolution,[],[f1785,f89]) ).
fof(f1790,plain,
( ! [X0] :
( ~ element(apply(f,sK3(alpha,a,sK0(g,b,e))),X0)
| zero(X0) = apply(f,sK3(alpha,a,sK0(g,b,e)))
| ~ morphism(gamma,X0,e) )
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(equality_resolution,[],[f1786]) ).
fof(f1791,plain,
( zero(d) = apply(f,sK3(alpha,a,sK0(g,b,e)))
| ~ morphism(gamma,d,e)
| ~ element(sK3(alpha,a,sK0(g,b,e)),a)
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(resolution,[],[f1790,f166]) ).
fof(f1792,plain,
( zero(d) = apply(f,sK3(alpha,a,sK0(g,b,e)))
| ~ element(sK3(alpha,a,sK0(g,b,e)),a)
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(forward_subsumption_resolution,[],[f1791,f83]) ).
fof(f1794,definition,
( spl9_99
<=> element(sK3(alpha,a,sK0(g,b,e)),a) ),
introduced(definition,[new_symbols(definition,[spl9_99])],[avatar_definition]) ).
fof(f1795,plain,
( ~ element(sK3(alpha,a,sK0(g,b,e)),a)
| spl9_99 ),
inference(avatar_component_clause,[],[f1794]) ).
fof(f1797,definition,
( spl9_100
<=> zero(d) = apply(f,sK3(alpha,a,sK0(g,b,e))) ),
introduced(definition,[new_symbols(definition,[spl9_100])],[avatar_definition]) ).
fof(f1798,plain,
( zero(d) = apply(f,sK3(alpha,a,sK0(g,b,e)))
| ~ spl9_100 ),
inference(avatar_component_clause,[],[f1797]) ).
fof(f1799,plain,
( ~ spl9_99
| spl9_100
| ~ spl9_1
| ~ spl9_25
| ~ spl9_36 ),
inference(avatar_split_clause,[],[f1792,f368,f294,f138,f1797,f1794]) ).
fof(f1804,plain,
( zero(c) != apply(beta,sK0(g,b,e))
| ~ element(sK0(g,b,e),b)
| spl9_99 ),
inference(resolution,[],[f1795,f1700]) ).
fof(f1809,plain,
( ~ element(sK0(g,b,e),b)
| ~ spl9_1
| ~ spl9_25
| spl9_99 ),
inference(forward_subsumption_resolution,[],[f1804,f527]) ).
fof(f1810,plain,
( $false
| ~ spl9_1
| ~ spl9_25
| spl9_99 ),
inference(forward_subsumption_resolution,[],[f1809,f511]) ).
fof(f1811,plain,
( ~ spl9_1
| ~ spl9_25
| spl9_99 ),
inference(avatar_contradiction_clause,[],[f1810]) ).
fof(f1817,plain,
( ! [X0,X1] :
( zero(X0) != zero(d)
| ~ element(sK3(alpha,a,sK0(g,b,e)),X1)
| zero(X1) = sK3(alpha,a,sK0(g,b,e))
| ~ injection(f)
| ~ morphism(f,X1,X0) )
| ~ spl9_100 ),
inference(superposition,[],[f77,f1798]) ).
fof(f1818,plain,
( ! [X0,X1] :
( zero(X0) != zero(d)
| ~ element(sK3(alpha,a,sK0(g,b,e)),X1)
| zero(X1) = sK3(alpha,a,sK0(g,b,e))
| ~ morphism(f,X1,X0) )
| ~ spl9_100 ),
inference(forward_subsumption_resolution,[],[f1817,f96]) ).
fof(f1825,plain,
( ! [X0] :
( ~ element(sK3(alpha,a,sK0(g,b,e)),X0)
| zero(X0) = sK3(alpha,a,sK0(g,b,e))
| ~ morphism(f,X0,d) )
| ~ spl9_100 ),
inference(equality_resolution,[],[f1818]) ).
fof(f1826,plain,
( zero(a) = sK3(alpha,a,sK0(g,b,e))
| ~ morphism(f,a,d)
| zero(c) != apply(beta,sK0(g,b,e))
| ~ element(sK0(g,b,e),b)
| ~ spl9_100 ),
inference(resolution,[],[f1825,f1700]) ).
fof(f1827,plain,
( zero(a) = sK3(alpha,a,sK0(g,b,e))
| zero(c) != apply(beta,sK0(g,b,e))
| ~ element(sK0(g,b,e),b)
| ~ spl9_100 ),
inference(forward_subsumption_resolution,[],[f1826,f85]) ).
fof(f1828,plain,
( zero(a) = sK3(alpha,a,sK0(g,b,e))
| ~ element(sK0(g,b,e),b)
| ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(forward_subsumption_resolution,[],[f1827,f527]) ).
fof(f1829,plain,
( zero(a) = sK3(alpha,a,sK0(g,b,e))
| ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(forward_subsumption_resolution,[],[f1828,f511]) ).
fof(f1834,plain,
( sK0(g,b,e) = apply(alpha,zero(a))
| ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(superposition,[],[f664,f1829]) ).
fof(f1838,plain,
( zero(b) = sK0(g,b,e)
| ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(forward_demodulation,[],[f1834,f346]) ).
fof(f1889,plain,
( zero(b) != zero(b)
| ~ morphism(g,b,e)
| injection(g)
| ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(superposition,[],[f80,f1838]) ).
fof(f1890,plain,
( ~ morphism(g,b,e)
| injection(g)
| ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(trivial_inequality_removal,[],[f1889]) ).
fof(f1892,plain,
( injection(g)
| ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(forward_subsumption_resolution,[],[f1890,f86]) ).
fof(f1909,plain,
( $false
| ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(forward_subsumption_resolution,[],[f1892,f98]) ).
fof(f1910,plain,
( ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(avatar_contradiction_clause,[],[f1909]) ).
cnf(s3,plain,
spl9_1,
inference(sat_conversion,[],[f149]) ).
cnf(s19,plain,
( spl9_24
| spl9_25 ),
inference(sat_conversion,[],[f296]) ).
cnf(s20,plain,
~ spl9_24,
inference(sat_conversion,[],[f299]) ).
cnf(s29,plain,
( spl9_35
| spl9_36 ),
inference(sat_conversion,[],[f370]) ).
cnf(s30,plain,
~ spl9_35,
inference(sat_conversion,[],[f373]) ).
cnf(s117,plain,
( ~ spl9_1
| ~ spl9_25
| ~ spl9_36
| ~ spl9_99
| spl9_100 ),
inference(sat_conversion,[],[f1799]) ).
cnf(s122,plain,
( ~ spl9_1
| ~ spl9_25
| spl9_99 ),
inference(sat_conversion,[],[f1811]) ).
cnf(s125,plain,
( ~ spl9_1
| ~ spl9_25
| ~ spl9_100 ),
inference(sat_conversion,[],[f1910]) ).
cnf(s132,plain,
spl9_36,
inference(rat,[],[s29,s30]) ).
cnf(s139,plain,
spl9_25,
inference(rat,[],[s19,s20]) ).
cnf(s141,plain,
~ spl9_100,
inference(rat,[],[s125,s139,s3]) ).
cnf(s142,plain,
spl9_99,
inference(rat,[],[s122,s139,s3]) ).
cnf(s143,plain,
$false,
inference(rat,[],[s117,s141,s139,s132,s142,s3]) ).
fof(f1920,plain,
$false,
inference(avatar_sat_refutation,[],[s143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HAL001+2 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n018.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 10:50:54 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.59/2.23 % (2153479)Detected formulas, will run a generic FOF schedule.
% 9.59/2.23 % (2153490)dis-21_1_sil=8000:lcm=predicate:random_seed=699605068:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 9.59/2.23 % (2153486)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3938066093:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.59/2.23 % (2153484)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4023005231:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.59/2.23 % (2153490)Instruction limit reached!
% 9.59/2.23 % (2153490)------------------------------
% 9.59/2.23 % (2153490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153490)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153490)Termination reason: Instruction limit
% 9.59/2.23 % (2153490)Termination phase: Saturation
% 9.59/2.23 % (2153490)Time elapsed: 0.039 s
% 9.59/2.23 % (2153490)Peak memory usage: 89 MB
% 9.59/2.23 % (2153490)Instructions burned: 132 (million)
% 9.59/2.23 % (2153485)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2635433361:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.59/2.23 % (2153488)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=381228889:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.59/2.23 % (2153487)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1689127743:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.59/2.23 % (2153489)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1316883039:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.59/2.23 % (2153487)Refutation not found, incomplete strategy
% 9.59/2.23 % (2153487)------------------------------
% 9.59/2.23 % (2153487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153487)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153487)Termination reason: Refutation not found, incomplete strategy
% 9.59/2.23 % (2153487)Time elapsed: 0.001 s
% 9.59/2.23 % (2153488)Refutation not found, incomplete strategy
% 9.59/2.23 % (2153488)------------------------------
% 9.59/2.23 % (2153488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153487)Peak memory usage: 87 MB
% 9.59/2.23 % (2153488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153488)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153488)Termination reason: Refutation not found, incomplete strategy
% 9.59/2.23 % (2153488)Time elapsed: 0.001 s
% 9.59/2.23 % (2153488)Peak memory usage: 87 MB
% 9.59/2.23 % (2153495)lrs+10_1_sil=8000:sp=occurrence:random_seed=1841034799:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.59/2.23 % (2153489)Instruction limit reached!
% 9.59/2.23 % (2153489)------------------------------
% 9.59/2.23 % (2153489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153489)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153489)Termination reason: Instruction limit
% 9.59/2.23 % (2153489)Termination phase: Saturation
% 9.59/2.23 % (2153489)Time elapsed: 0.097 s
% 9.59/2.23 % (2153489)Peak memory usage: 90 MB
% 9.59/2.23 % (2153489)Instructions burned: 139 (million)
% 9.59/2.23 % (2153495)Instruction limit reached!
% 9.59/2.23 % (2153495)------------------------------
% 9.59/2.23 % (2153495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153495)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153495)Termination reason: Instruction limit
% 9.59/2.23 % (2153495)Termination phase: Saturation
% 9.59/2.23 % (2153495)Time elapsed: 0.089 s
% 9.59/2.23 % (2153495)Peak memory usage: 91 MB
% 9.59/2.23 % (2153495)Instructions burned: 287 (million)
% 9.59/2.23 % (2153500)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1282272149:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.59/2.23 % (2153500)Refutation not found, incomplete strategy
% 9.59/2.23 % (2153500)------------------------------
% 9.59/2.23 % (2153500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153500)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153500)Termination reason: Refutation not found, incomplete strategy
% 9.59/2.23 % (2153500)Time elapsed: 0.002 s
% 9.59/2.23 % (2153500)Peak memory usage: 88 MB
% 9.59/2.23 % (2153500)Instructions burned: 1 (million)
% 9.59/2.23 % (2153487)------------------------------
% 9.59/2.23 % (2153487)------------------------------
% 9.59/2.23 % (2153488)------------------------------
% 9.59/2.23 % (2153488)------------------------------
% 9.59/2.23 % (2153501)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2238773477:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 9.59/2.23 % (2153501)Refutation not found, incomplete strategy
% 9.59/2.23 % (2153501)------------------------------
% 9.59/2.23 % (2153501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153501)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153501)Termination reason: Refutation not found, incomplete strategy
% 9.59/2.23 % (2153501)Time elapsed: 0.003 s
% 9.59/2.23 % (2153501)Peak memory usage: 88 MB
% 9.59/2.23 % (2153501)Instructions burned: 3 (million)
% 9.59/2.23 % (2153503)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=616373779:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 9.59/2.23 % (2153504)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2602767220:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 9.59/2.23 % (2153504)Refutation not found, incomplete strategy
% 9.59/2.23 % (2153504)------------------------------
% 9.59/2.23 % (2153504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153504)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153504)Termination reason: Refutation not found, incomplete strategy
% 9.59/2.23 % (2153504)Time elapsed: 0.002 s
% 9.59/2.23 % (2153504)Peak memory usage: 88 MB
% 9.59/2.23 % (2153504)Instructions burned: 2 (million)
% 9.59/2.23 % (2153503)Instruction limit reached!
% 9.59/2.23 % (2153503)------------------------------
% 9.59/2.23 % (2153503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153503)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153503)Termination reason: Instruction limit
% 9.59/2.23 % (2153503)Termination phase: Saturation
% 9.59/2.23 % (2153503)Time elapsed: 0.077 s
% 9.59/2.23 % (2153503)Peak memory usage: 92 MB
% 9.59/2.23 % (2153503)Instructions burned: 248 (million)
% 9.59/2.23 % (2153500)------------------------------
% 9.59/2.23 % (2153500)------------------------------
% 9.59/2.23 % (2153508)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3188973758:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.59/2.23 % (2153501)------------------------------
% 9.59/2.23 % (2153501)------------------------------
% 9.59/2.23 % (2153509)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=942380464:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 9.59/2.23 % (2153504)------------------------------
% 9.59/2.23 % (2153504)------------------------------
% 9.59/2.23 % (2153511)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3008793979:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 9.59/2.23 % (2153509)Instruction limit reached!
% 9.59/2.23 % (2153509)------------------------------
% 9.59/2.23 % (2153509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153509)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153509)Termination reason: Instruction limit
% 9.59/2.23 % (2153509)Termination phase: Saturation
% 9.59/2.23 % (2153509)Time elapsed: 0.081 s
% 9.59/2.23 % (2153509)Peak memory usage: 89 MB
% 9.59/2.23 % (2153509)Instructions burned: 114 (million)
% 9.59/2.23 % (2153511)Instruction limit reached!
% 9.59/2.23 % (2153511)------------------------------
% 9.59/2.23 % (2153511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153511)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153511)Termination reason: Instruction limit
% 9.59/2.23 % (2153511)Termination phase: Saturation
% 9.59/2.23 % (2153511)Time elapsed: 0.066 s
% 9.59/2.23 % (2153511)Peak memory usage: 89 MB
% 9.59/2.23 % (2153511)Instructions burned: 128 (million)
% 9.59/2.23 % (2153513)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=183616549:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.59/2.23 % (2153513)Refutation not found, incomplete strategy
% 9.59/2.23 % (2153513)------------------------------
% 9.59/2.23 % (2153513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153513)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153513)Termination reason: Refutation not found, incomplete strategy
% 9.59/2.23 % (2153513)Time elapsed: 0.001 s
% 9.59/2.23 % (2153513)Peak memory usage: 87 MB
% 9.59/2.23 % (2153515)lrs+10_1_sil=8000:sp=occurrence:random_seed=2981369807:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.59/2.23 % (2153516)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3987270334:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.59/2.23 % (2153516)Refutation not found, incomplete strategy
% 9.59/2.23 % (2153516)------------------------------
% 9.59/2.23 % (2153516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.59/2.23 % (2153516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.59/2.23 % (2153516)CaDiCaL version: 2.1.3
% 9.59/2.23 % (2153516)Termination reason: Refutation not found, incomplete strategy
% 9.59/2.23 % (2153516)Time elapsed: 0.002 s
% 9.59/2.23 % (2153516)Peak memory usage: 88 MB
% 9.59/2.23 % (2153516)Instructions burned: 2 (million)
% 9.59/2.23 % (2153485)First to succeed.
% 9.59/2.23 % (2153485)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2153479"
% 9.59/2.23 % (2153513)------------------------------
% 9.59/2.23 % (2153513)------------------------------
% 9.59/2.23 % (2153516)------------------------------
% 9.59/2.23 % (2153516)------------------------------
% 9.59/2.23 % (2153520)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3421459423:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 9.59/2.23 % (2153508)Also succeeded, but the first one will report.
% 9.59/2.23 % (2153485)Refutation found. Thanks to Tanya!
% 9.59/2.23 % SZS status Theorem for theBenchmark
% 9.59/2.23 % SZS output start Proof for theBenchmark
% See solution above
% 10.07/2.32 % (2153485)------------------------------
% 10.07/2.32 % (2153485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.07/2.32 % (2153485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.07/2.32 % (2153485)CaDiCaL version: 2.1.3
% 10.07/2.32 % (2153485)Termination reason: Refutation
% 10.07/2.32 % (2153485)Time elapsed: 0.949 s
% 10.07/2.32 % (2153485)Peak memory usage: 134 MB
% 10.07/2.32 % (2153485)Instructions burned: 1386 (million)
% 10.07/2.32 % (2153485)------------------------------
% 10.07/2.32 % (2153485)------------------------------
% 10.07/2.32 % (2153479)Success in time 1.347 s
% 10.07/2.32 % Vampire exiting
%------------------------------------------------------------------------------