%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE029+1 : TPTP v9.3.1. Released v4.0.0.
% 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 11:40:08 AM UTC 2026
% Result : Theorem 2.61s 1.28s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 166 ( 16 unt; 11 def)
% Number of atoms : 530 ( 47 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 601 ( 237 ~; 292 |; 51 &)
% ( 19 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 157 ( 0 sgn 145 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( leq(X2,X0)
& leq(X2,X1)
& ! [X3] :
( ( leq(X3,X0)
& leq(X3,X1) )
=> leq(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ismeet) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ismeetu(X2,X0,X1)
<=> ! [X3] :
( ( leq(X3,X0)
& leq(X3,X1) )
<=> leq(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ismeetu) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ismeet(X0,X1,X2)
<=> ismeetu(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ismeet(X0,X1,X2)
<=> ismeetu(X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( leq(X2,X0)
& leq(X2,X1)
& ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( leq(X2,X0)
& leq(X2,X1)
& ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) ) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ismeet(X0,X1,X2)
<~> ismeetu(X0,X1,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ismeet(X2,X0,X1)
| ~ leq(X2,X0)
| ~ leq(X2,X1)
| ? [X3] :
( ~ leq(X3,X2)
& leq(X3,X0)
& leq(X3,X1) ) )
& ( ( leq(X2,X0)
& leq(X2,X1)
& ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) ) )
| ~ ismeet(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ismeet(X2,X0,X1)
| ~ leq(X2,X0)
| ~ leq(X2,X1)
| ? [X3] :
( ~ leq(X3,X2)
& leq(X3,X0)
& leq(X3,X1) ) )
& ( ( leq(X2,X0)
& leq(X2,X1)
& ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) ) )
| ~ ismeet(X2,X0,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ismeet(X2,X0,X1)
| ~ leq(X2,X0)
| ~ leq(X2,X1)
| ? [X3] :
( ~ leq(X3,X2)
& leq(X3,X0)
& leq(X3,X1) ) )
& ( ( leq(X2,X0)
& leq(X2,X1)
& ! [X4] :
( leq(X4,X2)
| ~ leq(X4,X0)
| ~ leq(X4,X1) ) )
| ~ ismeet(X2,X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ismeet(X2,X0,X1)
| ~ leq(X2,X0)
| ~ leq(X2,X1)
| ( ~ leq(sK0(X0,X1,X2),X2)
& leq(sK0(X0,X1,X2),X0)
& leq(sK0(X0,X1,X2),X1) ) )
& ( ( leq(X2,X0)
& leq(X2,X1)
& ! [X4] :
( leq(X4,X2)
| ~ leq(X4,X0)
| ~ leq(X4,X1) ) )
| ~ ismeet(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ismeetu(X2,X0,X1)
| ? [X3] :
( ( ~ leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) )
& ( leq(X3,X2)
| ( leq(X3,X0)
& leq(X3,X1) ) ) ) )
& ( ! [X3] :
( ( ( leq(X3,X0)
& leq(X3,X1) )
| ~ leq(X3,X2) )
& ( leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ismeetu(X2,X0,X1)
| ? [X3] :
( ( ~ leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) )
& ( leq(X3,X2)
| ( leq(X3,X0)
& leq(X3,X1) ) ) ) )
& ( ! [X3] :
( ( ( leq(X3,X0)
& leq(X3,X1) )
| ~ leq(X3,X2) )
& ( leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ismeetu(X2,X0,X1)
| ? [X3] :
( ( ~ leq(X3,X2)
| ~ leq(X3,X0)
| ~ leq(X3,X1) )
& ( leq(X3,X2)
| ( leq(X3,X0)
& leq(X3,X1) ) ) ) )
& ( ! [X4] :
( ( ( leq(X4,X0)
& leq(X4,X1) )
| ~ leq(X4,X2) )
& ( leq(X4,X2)
| ~ leq(X4,X0)
| ~ leq(X4,X1) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ismeetu(X2,X0,X1)
| ( ( ~ leq(sK1(X0,X1,X2),X2)
| ~ leq(sK1(X0,X1,X2),X0)
| ~ leq(sK1(X0,X1,X2),X1) )
& ( leq(sK1(X0,X1,X2),X2)
| ( leq(sK1(X0,X1,X2),X0)
& leq(sK1(X0,X1,X2),X1) ) ) ) )
& ( ! [X4] :
( ( ( leq(X4,X0)
& leq(X4,X1) )
| ~ leq(X4,X2) )
& ( leq(X4,X2)
| ~ leq(X4,X0)
| ~ leq(X4,X1) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ~ ismeetu(X0,X1,X2)
| ~ ismeet(X0,X1,X2) )
& ( ismeetu(X0,X1,X2)
| ismeet(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f30,plain,
( ( ~ ismeetu(sK2,sK3,sK4)
| ~ ismeet(sK2,sK3,sK4) )
& ( ismeetu(sK2,sK3,sK4)
| ismeet(sK2,sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( leq(X4,X2)
| ~ leq(X4,X0)
| ~ leq(X4,X1)
| ~ ismeet(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X2,X0,X1] :
( leq(X2,X1)
| ~ ismeet(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X2,X0,X1] :
( leq(X2,X0)
| ~ ismeet(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X2,X0,X1] :
( leq(sK0(X0,X1,X2),X1)
| ~ leq(X2,X0)
| ~ leq(X2,X1)
| ismeet(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X2,X0,X1] :
( leq(sK0(X0,X1,X2),X0)
| ~ leq(X2,X0)
| ~ leq(X2,X1)
| ismeet(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ismeet(X2,X0,X1)
| ~ leq(X2,X0)
| ~ leq(X2,X1)
| ~ leq(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f50,plain,
! [X2,X0,X1,X4] :
( leq(X4,X2)
| ~ leq(X4,X0)
| ~ leq(X4,X1)
| ~ ismeetu(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X2,X0,X1,X4] :
( leq(X4,X1)
| ~ leq(X4,X2)
| ~ ismeetu(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X2,X0,X1,X4] :
( leq(X4,X0)
| ~ leq(X4,X2)
| ~ ismeetu(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
! [X2,X0,X1] :
( leq(sK1(X0,X1,X2),X2)
| ismeetu(X2,X0,X1)
| leq(sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X2,X0,X1] :
( leq(sK1(X0,X1,X2),X2)
| ismeetu(X2,X0,X1)
| leq(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ismeetu(X2,X0,X1)
| ~ leq(sK1(X0,X1,X2),X2)
| ~ leq(sK1(X0,X1,X2),X0)
| ~ leq(sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
( ismeetu(sK2,sK3,sK4)
| ismeet(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
( ~ ismeetu(sK2,sK3,sK4)
| ~ ismeet(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f30]) ).
fof(f59,definition,
( spl5_1
<=> ismeet(sK2,sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f60,plain,
( ~ ismeet(sK2,sK3,sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( ismeet(sK2,sK3,sK4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl5_2
<=> ismeetu(sK2,sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f64,plain,
( ~ ismeetu(sK2,sK3,sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( ismeetu(sK2,sK3,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f56,f63,f59]) ).
fof(f67,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f57,f63,f59]) ).
fof(f76,plain,
( ~ leq(sK2,sK3)
| ~ leq(sK2,sK4)
| ~ leq(sK0(sK3,sK4,sK2),sK2)
| spl5_1 ),
inference(resolution,[],[f49,f60]) ).
fof(f78,definition,
( spl5_3
<=> leq(sK0(sK3,sK4,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f80,plain,
( ~ leq(sK0(sK3,sK4,sK2),sK2)
| spl5_3 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl5_4
<=> leq(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f83,plain,
( leq(sK2,sK4)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( ~ leq(sK2,sK4)
| spl5_4 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f86,definition,
( spl5_5
<=> leq(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f87,plain,
( leq(sK2,sK3)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( ~ leq(sK2,sK3)
| spl5_5 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( ~ spl5_3
| ~ spl5_4
| ~ spl5_5
| spl5_1 ),
inference(avatar_split_clause,[],[f76,f59,f86,f82,f78]) ).
fof(f90,plain,
( ! [X0,X1] :
( ~ ismeetu(sK2,X0,X1)
| ~ leq(sK0(sK3,sK4,sK2),X1)
| ~ leq(sK0(sK3,sK4,sK2),X0) )
| spl5_3 ),
inference(resolution,[],[f80,f50]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( ~ ismeet(X1,X2,X3)
| ~ leq(X0,X2)
| ~ leq(X0,X3)
| addition(X0,X1) = X1 ),
inference(resolution,[],[f42,f44]) ).
fof(f107,plain,
! [X2,X0,X1] :
( addition(sK1(X0,X1,X2),X2) = X2
| ismeetu(X2,X0,X1)
| leq(sK1(X0,X1,X2),X0) ),
inference(resolution,[],[f42,f54]) ).
fof(f108,plain,
! [X2,X0,X1] :
( addition(sK1(X0,X1,X2),X2) = X2
| ismeetu(X2,X0,X1)
| leq(sK1(X0,X1,X2),X1) ),
inference(resolution,[],[f42,f53]) ).
fof(f109,plain,
! [X2,X0,X1] :
( leq(sK1(X0,X1,X2),X1)
| ismeetu(X2,X0,X1)
| addition(X2,sK1(X0,X1,X2)) = X2 ),
inference(forward_demodulation,[],[f108,f31]) ).
fof(f110,plain,
! [X2,X0,X1] :
( leq(sK1(X0,X1,X2),X0)
| ismeetu(X2,X0,X1)
| addition(X2,sK1(X0,X1,X2)) = X2 ),
inference(forward_demodulation,[],[f107,f31]) ).
fof(f120,definition,
( spl5_6
<=> leq(sK0(sK3,sK4,sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f122,plain,
( ~ leq(sK0(sK3,sK4,sK2),sK3)
| spl5_6 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f124,definition,
( spl5_7
<=> leq(sK0(sK3,sK4,sK2),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f126,plain,
( ~ leq(sK0(sK3,sK4,sK2),sK4)
| spl5_7 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f135,plain,
( ~ leq(sK2,sK3)
| ~ leq(sK2,sK4)
| ismeet(sK2,sK3,sK4)
| spl5_6 ),
inference(resolution,[],[f122,f48]) ).
fof(f141,plain,
( ! [X0] : ~ ismeet(sK2,X0,sK4)
| spl5_4 ),
inference(resolution,[],[f84,f45]) ).
fof(f144,plain,
( ! [X0,X1] :
( ~ ismeetu(X0,X1,sK4)
| ~ leq(sK2,X0) )
| spl5_4 ),
inference(resolution,[],[f84,f51]) ).
fof(f148,plain,
( ~ leq(sK2,sK2)
| ~ spl5_2
| spl5_4 ),
inference(resolution,[],[f144,f65]) ).
fof(f150,plain,
( sK2 != addition(sK2,sK2)
| ~ spl5_2
| spl5_4 ),
inference(resolution,[],[f148,f43]) ).
fof(f158,plain,
( $false
| ~ spl5_2
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f150,f34]) ).
fof(f159,plain,
( ~ spl5_2
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f158]) ).
fof(f161,plain,
( $false
| ~ spl5_1
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f61,f141]) ).
fof(f162,plain,
( ~ spl5_1
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f161]) ).
fof(f164,plain,
( spl5_1
| ~ spl5_4
| ~ spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f135,f120,f86,f82,f59]) ).
fof(f166,plain,
( sK4 = addition(sK2,sK4)
| ~ spl5_4 ),
inference(resolution,[],[f83,f42]) ).
fof(f167,plain,
( ~ leq(sK0(sK3,sK4,sK2),sK4)
| ~ leq(sK0(sK3,sK4,sK2),sK3)
| ~ spl5_2
| spl5_3 ),
inference(resolution,[],[f65,f90]) ).
fof(f174,plain,
( ! [X0,X1] :
( ~ ismeetu(X0,sK3,X1)
| ~ leq(sK2,X0) )
| spl5_5 ),
inference(resolution,[],[f88,f52]) ).
fof(f179,plain,
( ~ leq(sK2,sK2)
| ~ spl5_2
| spl5_5 ),
inference(resolution,[],[f174,f65]) ).
fof(f181,plain,
( sK2 != addition(sK2,sK2)
| ~ spl5_2
| spl5_5 ),
inference(resolution,[],[f179,f43]) ).
fof(f189,plain,
( $false
| ~ spl5_2
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f181,f34]) ).
fof(f190,plain,
( ~ spl5_2
| spl5_5 ),
inference(avatar_contradiction_clause,[],[f189]) ).
fof(f192,plain,
( ~ spl5_6
| ~ spl5_7
| ~ spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f167,f78,f63,f124,f120]) ).
fof(f193,plain,
( sK3 = addition(sK2,sK3)
| ~ spl5_5 ),
inference(resolution,[],[f87,f42]) ).
fof(f198,plain,
( ~ leq(sK2,sK3)
| ~ leq(sK2,sK4)
| ismeet(sK2,sK3,sK4)
| spl5_7 ),
inference(resolution,[],[f126,f47]) ).
fof(f207,plain,
( ~ leq(sK2,sK4)
| ismeet(sK2,sK3,sK4)
| ~ spl5_5
| spl5_7 ),
inference(forward_subsumption_resolution,[],[f198,f87]) ).
fof(f208,plain,
( ismeet(sK2,sK3,sK4)
| ~ spl5_4
| ~ spl5_5
| spl5_7 ),
inference(forward_subsumption_resolution,[],[f207,f83]) ).
fof(f209,plain,
( $false
| spl5_1
| ~ spl5_4
| ~ spl5_5
| spl5_7 ),
inference(forward_subsumption_resolution,[],[f208,f60]) ).
fof(f210,plain,
( spl5_1
| ~ spl5_4
| ~ spl5_5
| spl5_7 ),
inference(avatar_contradiction_clause,[],[f209]) ).
fof(f216,plain,
( ~ leq(sK1(sK3,sK4,sK2),sK2)
| ~ leq(sK1(sK3,sK4,sK2),sK3)
| ~ leq(sK1(sK3,sK4,sK2),sK4)
| spl5_2 ),
inference(resolution,[],[f64,f55]) ).
fof(f218,definition,
( spl5_8
<=> leq(sK1(sK3,sK4,sK2),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f219,plain,
( leq(sK1(sK3,sK4,sK2),sK4)
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f220,plain,
( ~ leq(sK1(sK3,sK4,sK2),sK4)
| spl5_8 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f222,definition,
( spl5_9
<=> leq(sK1(sK3,sK4,sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f224,plain,
( ~ leq(sK1(sK3,sK4,sK2),sK3)
| spl5_9 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl5_10
<=> leq(sK1(sK3,sK4,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f228,plain,
( ~ leq(sK1(sK3,sK4,sK2),sK2)
| spl5_10 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f229,plain,
( ~ spl5_8
| ~ spl5_9
| ~ spl5_10
| spl5_2 ),
inference(avatar_split_clause,[],[f216,f63,f226,f222,f218]) ).
fof(f230,plain,
( sK4 != addition(sK1(sK3,sK4,sK2),sK4)
| spl5_8 ),
inference(resolution,[],[f220,f43]) ).
fof(f237,plain,
( sK4 != addition(sK4,sK1(sK3,sK4,sK2))
| spl5_8 ),
inference(forward_demodulation,[],[f230,f31]) ).
fof(f266,plain,
( ! [X0] : addition(sK4,X0) = addition(sK2,addition(sK4,X0))
| ~ spl5_4 ),
inference(superposition,[],[f32,f166]) ).
fof(f267,plain,
( ! [X0] : addition(sK3,X0) = addition(sK2,addition(sK3,X0))
| ~ spl5_5 ),
inference(superposition,[],[f32,f193]) ).
fof(f280,plain,
( ! [X0] : addition(X0,sK4) = addition(sK2,addition(X0,sK4))
| ~ spl5_4 ),
inference(superposition,[],[f266,f31]) ).
fof(f301,plain,
( ! [X0] : addition(X0,sK3) = addition(sK2,addition(X0,sK3))
| ~ spl5_5 ),
inference(superposition,[],[f267,f31]) ).
fof(f406,plain,
( ! [X0] :
( ~ leq(X0,sK4)
| ~ leq(X0,sK3)
| sK2 = addition(X0,sK2) )
| ~ spl5_1 ),
inference(resolution,[],[f100,f61]) ).
fof(f423,plain,
( ismeetu(sK2,sK3,sK4)
| sK2 = addition(sK2,sK1(sK3,sK4,sK2))
| spl5_8 ),
inference(resolution,[],[f109,f220]) ).
fof(f428,plain,
( sK2 = addition(sK2,sK1(sK3,sK4,sK2))
| spl5_2
| spl5_8 ),
inference(forward_subsumption_resolution,[],[f423,f64]) ).
fof(f429,plain,
( ! [X0] : addition(sK2,addition(sK1(sK3,sK4,sK2),X0)) = addition(sK2,X0)
| spl5_2
| spl5_8 ),
inference(superposition,[],[f32,f428]) ).
fof(f460,plain,
( addition(sK2,sK4) = addition(sK1(sK3,sK4,sK2),sK4)
| spl5_2
| ~ spl5_4
| spl5_8 ),
inference(superposition,[],[f429,f280]) ).
fof(f470,plain,
( addition(sK2,sK4) = addition(sK4,sK1(sK3,sK4,sK2))
| spl5_2
| ~ spl5_4
| spl5_8 ),
inference(forward_demodulation,[],[f460,f31]) ).
fof(f479,plain,
( sK4 = addition(sK4,sK1(sK3,sK4,sK2))
| spl5_2
| ~ spl5_4
| spl5_8 ),
inference(forward_demodulation,[],[f470,f166]) ).
fof(f483,plain,
( $false
| spl5_2
| ~ spl5_4
| spl5_8 ),
inference(forward_subsumption_resolution,[],[f479,f237]) ).
fof(f484,plain,
( spl5_2
| ~ spl5_4
| spl5_8 ),
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f485,plain,
( ~ leq(sK1(sK3,sK4,sK2),sK3)
| sK2 = addition(sK1(sK3,sK4,sK2),sK2)
| ~ spl5_1
| ~ spl5_8 ),
inference(resolution,[],[f219,f406]) ).
fof(f488,plain,
( sK2 = addition(sK2,sK1(sK3,sK4,sK2))
| ~ leq(sK1(sK3,sK4,sK2),sK3)
| ~ spl5_1
| ~ spl5_8 ),
inference(forward_demodulation,[],[f485,f31]) ).
fof(f490,definition,
( spl5_11
<=> sK2 = addition(sK2,sK1(sK3,sK4,sK2)) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
fof(f492,plain,
( sK2 = addition(sK2,sK1(sK3,sK4,sK2))
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f493,plain,
( ~ spl5_9
| spl5_11
| ~ spl5_1
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f488,f218,f59,f490,f222]) ).
fof(f494,plain,
( ismeetu(sK2,sK3,sK4)
| sK2 = addition(sK2,sK1(sK3,sK4,sK2))
| spl5_9 ),
inference(resolution,[],[f224,f110]) ).
fof(f495,plain,
( sK3 != addition(sK1(sK3,sK4,sK2),sK3)
| spl5_9 ),
inference(resolution,[],[f224,f43]) ).
fof(f502,plain,
( sK3 != addition(sK3,sK1(sK3,sK4,sK2))
| spl5_9 ),
inference(forward_demodulation,[],[f495,f31]) ).
fof(f503,plain,
( sK2 = addition(sK2,sK1(sK3,sK4,sK2))
| spl5_2
| spl5_9 ),
inference(forward_subsumption_resolution,[],[f494,f64]) ).
fof(f504,plain,
( spl5_11
| spl5_2
| spl5_9 ),
inference(avatar_split_clause,[],[f503,f222,f63,f490]) ).
fof(f510,plain,
( ! [X0] : addition(sK2,addition(sK1(sK3,sK4,sK2),X0)) = addition(sK2,X0)
| ~ spl5_11 ),
inference(superposition,[],[f32,f492]) ).
fof(f551,plain,
( addition(sK2,sK3) = addition(sK1(sK3,sK4,sK2),sK3)
| ~ spl5_5
| ~ spl5_11 ),
inference(superposition,[],[f510,f301]) ).
fof(f563,plain,
( addition(sK2,sK3) = addition(sK3,sK1(sK3,sK4,sK2))
| ~ spl5_5
| ~ spl5_11 ),
inference(forward_demodulation,[],[f551,f31]) ).
fof(f572,plain,
( sK3 = addition(sK3,sK1(sK3,sK4,sK2))
| ~ spl5_5
| ~ spl5_11 ),
inference(forward_demodulation,[],[f563,f193]) ).
fof(f575,plain,
( $false
| ~ spl5_5
| spl5_9
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f572,f502]) ).
fof(f576,plain,
( ~ spl5_5
| spl5_9
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f575]) ).
fof(f580,plain,
( ! [X0] : ~ ismeet(sK2,sK3,X0)
| spl5_5 ),
inference(resolution,[],[f88,f46]) ).
fof(f585,plain,
( $false
| ~ spl5_1
| spl5_5 ),
inference(resolution,[],[f580,f61]) ).
fof(f587,plain,
( ~ spl5_1
| spl5_5 ),
inference(avatar_contradiction_clause,[],[f585]) ).
fof(f592,plain,
( sK2 != addition(sK1(sK3,sK4,sK2),sK2)
| spl5_10 ),
inference(resolution,[],[f228,f43]) ).
fof(f601,plain,
( sK2 != addition(sK2,sK1(sK3,sK4,sK2))
| spl5_10 ),
inference(forward_demodulation,[],[f592,f31]) ).
fof(f602,plain,
( $false
| spl5_10
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f601,f492]) ).
fof(f603,plain,
( spl5_10
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f602]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f66]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
( spl5_1
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(sat_conversion,[],[f89]) ).
cnf(s6,plain,
( ~ spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f159]) ).
cnf(s7,plain,
( ~ spl5_1
| spl5_4 ),
inference(sat_conversion,[],[f162]) ).
cnf(s9,plain,
( spl5_1
| ~ spl5_4
| ~ spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f164]) ).
cnf(s10,plain,
( ~ spl5_2
| spl5_5 ),
inference(sat_conversion,[],[f190]) ).
cnf(s11,plain,
( ~ spl5_2
| spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(sat_conversion,[],[f192]) ).
cnf(s12,plain,
( spl5_1
| ~ spl5_4
| ~ spl5_5
| spl5_7 ),
inference(sat_conversion,[],[f210]) ).
cnf(s15,plain,
( spl5_2
| ~ spl5_8
| ~ spl5_9
| ~ spl5_10 ),
inference(sat_conversion,[],[f229]) ).
cnf(s17,plain,
( spl5_2
| ~ spl5_4
| spl5_8 ),
inference(sat_conversion,[],[f484]) ).
cnf(s18,plain,
( ~ spl5_1
| ~ spl5_8
| ~ spl5_9
| spl5_11 ),
inference(sat_conversion,[],[f493]) ).
cnf(s19,plain,
( spl5_2
| spl5_9
| spl5_11 ),
inference(sat_conversion,[],[f504]) ).
cnf(s21,plain,
( ~ spl5_5
| spl5_9
| ~ spl5_11 ),
inference(sat_conversion,[],[f576]) ).
cnf(s22,plain,
( ~ spl5_1
| spl5_5 ),
inference(sat_conversion,[],[f587]) ).
cnf(s23,plain,
( spl5_10
| ~ spl5_11 ),
inference(sat_conversion,[],[f603]) ).
cnf(s24,plain,
spl5_1,
inference(rat,[],[s11,s3,s9,s12,s6,s10,s1]) ).
cnf(s25,plain,
spl5_5,
inference(rat,[],[s22,s24]) ).
cnf(s26,plain,
spl5_4,
inference(rat,[],[s7,s24]) ).
cnf(s27,plain,
~ spl5_2,
inference(rat,[],[s2,s24]) ).
cnf(s28,plain,
spl5_8,
inference(rat,[],[s17,s26,s27]) ).
cnf(s29,plain,
spl5_9,
inference(rat,[],[s19,s21,s27,s25]) ).
cnf(s30,plain,
spl5_11,
inference(rat,[],[s18,s28,s24,s29]) ).
cnf(s31,plain,
~ spl5_10,
inference(rat,[],[s15,s28,s27,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s23,s30,s31]) ).
fof(f604,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE029+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n018.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 13:06:24 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.61/1.28 % (2337252)Detected formulas, will run a generic FOF schedule.
% 2.61/1.28 % (2337259)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=1359908455:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.61/1.28 % (2337263)dis-21_1_sil=8000:lcm=predicate:random_seed=771809217: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)
% 2.61/1.28 % (2337257)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=2236518716:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.61/1.28 % (2337261)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1437951750:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.61/1.28 % (2337260)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2864270719:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.61/1.28 % (2337258)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=68177825:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.61/1.28 % (2337262)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2758877570:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.61/1.28 % (2337260)Refutation not found, incomplete strategy
% 2.61/1.28 % (2337260)------------------------------
% 2.61/1.28 % (2337260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.28 % (2337260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.28 % (2337260)CaDiCaL version: 2.1.3
% 2.61/1.28 % (2337260)Termination reason: Refutation not found, incomplete strategy
% 2.61/1.28 % (2337260)Time elapsed: 0.003 s
% 2.61/1.28 % (2337260)Peak memory usage: 88 MB
% 2.61/1.28 % (2337260)Instructions burned: 3 (million)
% 2.61/1.28 % (2337262)First to succeed.
% 2.61/1.28 % (2337262)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2337252"
% 2.61/1.28 % (2337261)Instruction limit reached!
% 2.61/1.28 % (2337261)------------------------------
% 2.61/1.28 % (2337261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.28 % (2337261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.28 % (2337261)CaDiCaL version: 2.1.3
% 2.61/1.28 % (2337261)Termination reason: Instruction limit
% 2.61/1.28 % (2337261)Termination phase: Saturation
% 2.61/1.28 % (2337261)Time elapsed: 0.068 s
% 2.61/1.28 % (2337261)Peak memory usage: 88 MB
% 2.61/1.28 % (2337261)Instructions burned: 119 (million)
% 2.61/1.28 % (2337263)Instruction limit reached!
% 2.61/1.28 % (2337263)------------------------------
% 2.61/1.28 % (2337263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.28 % (2337263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.28 % (2337263)CaDiCaL version: 2.1.3
% 2.61/1.28 % (2337263)Termination reason: Instruction limit
% 2.61/1.28 % (2337263)Termination phase: Saturation
% 2.61/1.28 % (2337263)Time elapsed: 0.071 s
% 2.61/1.28 % (2337263)Peak memory usage: 89 MB
% 2.61/1.28 % (2337263)Instructions burned: 130 (million)
% 2.61/1.28 % (2337271)lrs+10_1_sil=8000:sp=occurrence:random_seed=1344020669:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.61/1.28 % (2337272)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3594893483:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.61/1.28 % (2337272)Refutation not found, incomplete strategy
% 2.61/1.28 % (2337272)------------------------------
% 2.61/1.28 % (2337272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.28 % (2337272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.28 % (2337272)CaDiCaL version: 2.1.3
% 2.61/1.28 % (2337272)Termination reason: Refutation not found, incomplete strategy
% 2.61/1.28 % (2337272)Time elapsed: 0.002 s
% 2.61/1.28 % (2337272)Peak memory usage: 88 MB
% 2.61/1.28 % (2337272)Instructions burned: 1 (million)
% 2.61/1.28 % (2337260)------------------------------
% 2.61/1.28 % (2337260)------------------------------
% 2.61/1.28 % (2337262)Refutation found. Thanks to Tanya!
% 2.61/1.28 % SZS status Theorem for theBenchmark
% 2.61/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.38 % (2337262)------------------------------
% 3.50/1.38 % (2337262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (2337262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (2337262)CaDiCaL version: 2.1.3
% 3.50/1.38 % (2337262)Termination reason: Refutation
% 3.50/1.38 % (2337262)Time elapsed: 0.025 s
% 3.50/1.38 % (2337262)Peak memory usage: 90 MB
% 3.50/1.38 % (2337262)Instructions burned: 28 (million)
% 3.50/1.38 % (2337262)------------------------------
% 3.50/1.38 % (2337262)------------------------------
% 3.50/1.38 % (2337252)Success in time 0.431 s
% 3.50/1.38 % Vampire exiting
%------------------------------------------------------------------------------