%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE017+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 : n017.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 11:40:04 AM UTC 2026
% Result : Theorem 15.27s 3.24s
% Output : Refutation 15.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 126 ( 48 unt; 4 def)
% Number of atoms : 279 ( 88 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 247 ( 94 ~; 100 |; 39 &)
% ( 9 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 101 !; 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2) )
=> ( leq(X2,multiplication(X0,X1))
<=> ( leq(X2,X0)
& leq(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2) )
=> ( leq(X2,multiplication(X0,X1))
<=> ( leq(X2,X0)
& leq(X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ( leq(X2,multiplication(X0,X1))
<~> ( leq(X2,X0)
& leq(X2,X1) ) )
& test(X0)
& test(X1)
& test(X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ( leq(X2,multiplication(X0,X1))
<~> ( leq(X2,X0)
& leq(X2,X1) ) )
& test(X0)
& test(X1)
& test(X2) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f19]) ).
fof(f30,plain,
? [X0,X1,X2] :
( ( ~ leq(X2,X0)
| ~ leq(X2,X1)
| ~ leq(X2,multiplication(X0,X1)) )
& ( ( leq(X2,X0)
& leq(X2,X1) )
| leq(X2,multiplication(X0,X1)) )
& test(X0)
& test(X1)
& test(X2) ),
inference(nnf_transformation,[],[f22]) ).
fof(f31,plain,
? [X0,X1,X2] :
( ( ~ leq(X2,X0)
| ~ leq(X2,X1)
| ~ leq(X2,multiplication(X0,X1)) )
& ( ( leq(X2,X0)
& leq(X2,X1) )
| leq(X2,multiplication(X0,X1)) )
& test(X0)
& test(X1)
& test(X2) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
( ( ~ leq(sK3,sK1)
| ~ leq(sK3,sK2)
| ~ leq(sK3,multiplication(sK1,sK2)) )
& ( ( leq(sK3,sK1)
& leq(sK3,sK2) )
| leq(sK3,multiplication(sK1,sK2)) )
& test(sK1)
& test(sK2)
& test(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f31]) ).
fof(f33,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f34,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f41,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f44,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f48,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f56,plain,
test(sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
test(sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
( leq(sK3,sK2)
| leq(sK3,multiplication(sK1,sK2)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f59,plain,
( leq(sK3,sK1)
| leq(sK3,multiplication(sK1,sK2)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f60,plain,
( ~ leq(sK3,sK1)
| ~ leq(sK3,sK2)
| ~ leq(sK3,multiplication(sK1,sK2)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f52]) ).
fof(f62,definition,
sF4 = multiplication(sK1,sK2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f63,plain,
multiplication(sK1,sK2) = sF4,
inference(reorient_equations,[],[f62]) ).
fof(f64,plain,
( ~ leq(sK3,sK1)
| ~ leq(sK3,sK2)
| ~ leq(sK3,sF4) ),
inference(definition_folding,[],[f60,f63]) ).
fof(f65,plain,
( leq(sK3,sK1)
| leq(sK3,sF4) ),
inference(definition_folding,[],[f59,f63]) ).
fof(f66,plain,
( leq(sK3,sK2)
| leq(sK3,sF4) ),
inference(definition_folding,[],[f58,f63]) ).
fof(f68,definition,
( spl5_1
<=> leq(sK3,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f69,plain,
( ~ leq(sK3,sF4)
| spl5_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f70,plain,
( leq(sK3,sF4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f72,definition,
( spl5_2
<=> leq(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f73,plain,
( ~ leq(sK3,sK2)
| spl5_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f74,plain,
( leq(sK3,sK2)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f66,f72,f68]) ).
fof(f77,definition,
( spl5_3
<=> leq(sK3,sK1) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f78,plain,
( ~ leq(sK3,sK1)
| spl5_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( leq(sK3,sK1)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f65,f77,f68]) ).
fof(f81,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f64,f77,f72,f68]) ).
fof(f82,plain,
( sK2 = addition(sK3,sK2)
| ~ spl5_2 ),
inference(resolution,[],[f44,f74]) ).
fof(f83,plain,
( sK1 = addition(sK3,sK1)
| ~ spl5_3 ),
inference(resolution,[],[f44,f79]) ).
fof(f90,plain,
! [X0] :
( ~ test(X0)
| one = addition(c(X0),X0) ),
inference(resolution,[],[f48,f61]) ).
fof(f122,plain,
! [X0] : multiplication(addition(X0,sK1),sK2) = addition(multiplication(X0,sK2),sF4),
inference(superposition,[],[f41,f63]) ).
fof(f131,plain,
! [X2,X0,X1] :
( multiplication(X1,X2) != multiplication(addition(X0,X1),X2)
| leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(superposition,[],[f45,f41]) ).
fof(f149,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f34,f40]) ).
fof(f254,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,c(X0)) ),
inference(resolution,[],[f49,f61]) ).
fof(f320,plain,
one = addition(c(sK2),sK2),
inference(resolution,[],[f90,f56]) ).
fof(f321,plain,
one = addition(c(sK1),sK1),
inference(resolution,[],[f90,f57]) ).
fof(f356,plain,
one = addition(sK2,c(sK2)),
inference(superposition,[],[f33,f320]) ).
fof(f495,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,addition(X3,X2)),multiplication(X1,X2)) = addition(multiplication(X0,X3),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f149,f41]) ).
fof(f577,plain,
! [X0,X1] : addition(multiplication(X0,c(sK2)),multiplication(addition(X0,X1),sK2)) = addition(multiplication(X0,one),multiplication(X1,sK2)),
inference(superposition,[],[f495,f320]) ).
fof(f578,plain,
! [X0,X1] : addition(multiplication(X0,c(sK1)),multiplication(addition(X0,X1),sK1)) = addition(multiplication(X0,one),multiplication(X1,sK1)),
inference(superposition,[],[f495,f321]) ).
fof(f687,plain,
! [X0,X1] : addition(multiplication(X0,c(sK1)),multiplication(addition(X0,X1),sK1)) = addition(X0,multiplication(X1,sK1)),
inference(forward_demodulation,[],[f578,f38]) ).
fof(f688,plain,
! [X0,X1] : addition(multiplication(X0,c(sK2)),multiplication(addition(X0,X1),sK2)) = addition(X0,multiplication(X1,sK2)),
inference(forward_demodulation,[],[f577,f38]) ).
fof(f776,plain,
zero = multiplication(sK2,c(sK2)),
inference(resolution,[],[f254,f56]) ).
fof(f1672,plain,
( ! [X0] :
( multiplication(sK1,X0) != multiplication(sK1,X0)
| leq(multiplication(sK3,X0),multiplication(sK1,X0)) )
| ~ spl5_3 ),
inference(superposition,[],[f131,f83]) ).
fof(f1673,plain,
( ! [X0] :
( multiplication(sK2,X0) != multiplication(sK2,X0)
| leq(multiplication(sK3,X0),multiplication(sK2,X0)) )
| ~ spl5_2 ),
inference(superposition,[],[f131,f82]) ).
fof(f1681,plain,
( ! [X0] : leq(multiplication(sK3,X0),multiplication(sK2,X0))
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f1673]) ).
fof(f1682,plain,
( ! [X0] : leq(multiplication(sK3,X0),multiplication(sK1,X0))
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f1672]) ).
fof(f1740,plain,
( leq(multiplication(sK3,c(sK2)),zero)
| ~ spl5_2 ),
inference(superposition,[],[f1681,f776]) ).
fof(f1793,plain,
( zero = addition(multiplication(sK3,c(sK2)),zero)
| ~ spl5_2 ),
inference(resolution,[],[f1740,f44]) ).
fof(f1794,plain,
( zero = multiplication(sK3,c(sK2))
| ~ spl5_2 ),
inference(forward_demodulation,[],[f1793,f35]) ).
fof(f1800,plain,
( ! [X0] : addition(multiplication(sK3,X0),zero) = multiplication(sK3,addition(X0,c(sK2)))
| ~ spl5_2 ),
inference(superposition,[],[f40,f1794]) ).
fof(f1830,plain,
( ! [X0] : multiplication(sK3,X0) = multiplication(sK3,addition(X0,c(sK2)))
| ~ spl5_2 ),
inference(forward_demodulation,[],[f1800,f35]) ).
fof(f1839,plain,
( multiplication(sK3,sK2) = multiplication(sK3,one)
| ~ spl5_2 ),
inference(superposition,[],[f1830,f356]) ).
fof(f1869,plain,
( sK3 = multiplication(sK3,sK2)
| ~ spl5_2 ),
inference(forward_demodulation,[],[f1839,f38]) ).
fof(f1879,plain,
( leq(sK3,multiplication(sK1,sK2))
| ~ spl5_2
| ~ spl5_3 ),
inference(superposition,[],[f1682,f1869]) ).
fof(f1910,plain,
( leq(sK3,sF4)
| ~ spl5_2
| ~ spl5_3 ),
inference(forward_demodulation,[],[f1879,f63]) ).
fof(f1913,plain,
( $false
| spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f1910,f69]) ).
fof(f1914,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f1913]) ).
fof(f1915,plain,
( sF4 = addition(sK3,sF4)
| ~ spl5_1 ),
inference(resolution,[],[f70,f44]) ).
fof(f1916,plain,
( ! [X0] : addition(sF4,X0) = addition(sK3,addition(sF4,X0))
| ~ spl5_1 ),
inference(superposition,[],[f34,f1915]) ).
fof(f1955,plain,
( ! [X0] : addition(X0,sF4) = addition(sK3,addition(X0,sF4))
| ~ spl5_1 ),
inference(superposition,[],[f1916,f33]) ).
fof(f4039,plain,
! [X0] : addition(X0,multiplication(X0,sK2)) = addition(multiplication(X0,c(sK2)),multiplication(X0,sK2)),
inference(superposition,[],[f688,f36]) ).
fof(f4140,plain,
! [X0] : multiplication(X0,addition(c(sK2),sK2)) = addition(X0,multiplication(X0,sK2)),
inference(forward_demodulation,[],[f4039,f40]) ).
fof(f4177,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK2)),
inference(forward_demodulation,[],[f4140,f320]) ).
fof(f4205,plain,
! [X0] : addition(X0,multiplication(X0,sK2)) = X0,
inference(forward_demodulation,[],[f4177,f38]) ).
fof(f4241,plain,
sK1 = addition(sK1,sF4),
inference(superposition,[],[f4205,f63]) ).
fof(f4384,plain,
( sK1 = addition(sK3,sK1)
| ~ spl5_1 ),
inference(superposition,[],[f1955,f4241]) ).
fof(f4415,plain,
( sK1 != sK1
| leq(sK3,sK1)
| ~ spl5_1 ),
inference(superposition,[],[f45,f4384]) ).
fof(f4427,plain,
( leq(sK3,sK1)
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f4415]) ).
fof(f4432,plain,
( $false
| ~ spl5_1
| spl5_3 ),
inference(forward_subsumption_resolution,[],[f4427,f78]) ).
fof(f4433,plain,
( ~ spl5_1
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f4432]) ).
fof(f4721,plain,
! [X0] : addition(X0,multiplication(X0,sK1)) = addition(multiplication(X0,c(sK1)),multiplication(X0,sK1)),
inference(superposition,[],[f687,f36]) ).
fof(f4823,plain,
! [X0] : multiplication(X0,addition(c(sK1),sK1)) = addition(X0,multiplication(X0,sK1)),
inference(forward_demodulation,[],[f4721,f40]) ).
fof(f4854,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK1)),
inference(forward_demodulation,[],[f4823,f321]) ).
fof(f4876,plain,
! [X0] : addition(X0,multiplication(X0,sK1)) = X0,
inference(forward_demodulation,[],[f4854,f38]) ).
fof(f4901,plain,
one = addition(one,sK1),
inference(superposition,[],[f4876,f39]) ).
fof(f5013,plain,
multiplication(one,sK2) = addition(multiplication(one,sK2),sF4),
inference(superposition,[],[f122,f4901]) ).
fof(f5033,plain,
sK2 = addition(sK2,sF4),
inference(forward_demodulation,[],[f5013,f39]) ).
fof(f5046,plain,
( sK2 = addition(sK3,sK2)
| ~ spl5_1 ),
inference(superposition,[],[f1955,f5033]) ).
fof(f5118,plain,
( sK2 != sK2
| leq(sK3,sK2)
| ~ spl5_1 ),
inference(superposition,[],[f45,f5046]) ).
fof(f5131,plain,
( leq(sK3,sK2)
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f5118]) ).
fof(f5136,plain,
( $false
| ~ spl5_1
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f5131,f73]) ).
fof(f5137,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f5136]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f75]) ).
cnf(s2,plain,
( spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f80]) ).
cnf(s3,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f81]) ).
cnf(s28,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f1914]) ).
cnf(s44,plain,
( ~ spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f4433]) ).
cnf(s49,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f5137]) ).
cnf(s59,plain,
spl5_1,
inference(rat,[],[s28,s1,s2]) ).
cnf(s60,plain,
spl5_2,
inference(rat,[],[s49,s59]) ).
cnf(s61,plain,
spl5_3,
inference(rat,[],[s44,s59]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s3,s60,s61,s59]) ).
fof(f5143,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 % Computer : n017.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 12:54:35 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 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
% 14.93/3.20 % (2528289)Detected formulas, will run a generic FOF schedule.
% 14.93/3.20 % (2528297)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=1771780996:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 14.93/3.20 % (2528298)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=3100317592:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 14.93/3.20 % (2528296)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=1064767056:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 14.93/3.20 % (2528300)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3954075558:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 14.93/3.20 % (2528299)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2604602668:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 14.93/3.20 % (2528302)dis-21_1_sil=8000:lcm=predicate:random_seed=157238942: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)
% 14.93/3.20 % (2528301)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2736465939:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 14.93/3.20 % (2528299)Refutation not found, incomplete strategy
% 14.93/3.20 % (2528299)------------------------------
% 14.93/3.20 % (2528299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.20 % (2528299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.93/3.20 % (2528299)CaDiCaL version: 2.1.3
% 14.93/3.20 % (2528299)Termination reason: Refutation not found, incomplete strategy
% 14.93/3.20 % (2528299)Time elapsed: 0.002 s
% 14.93/3.20 % (2528299)Peak memory usage: 88 MB
% 14.93/3.20 % (2528302)Refutation not found, incomplete strategy
% 14.93/3.20 % (2528302)------------------------------
% 14.93/3.20 % (2528302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.20 % (2528302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.93/3.20 % (2528302)CaDiCaL version: 2.1.3
% 14.93/3.20 % (2528302)Termination reason: Refutation not found, incomplete strategy
% 14.93/3.20 % (2528302)Time elapsed: 0.005 s
% 14.93/3.20 % (2528302)Peak memory usage: 88 MB
% 14.93/3.20 % (2528302)Instructions burned: 3 (million)
% 14.93/3.20 % (2528300)Instruction limit reached!
% 14.93/3.20 % (2528300)------------------------------
% 14.93/3.20 % (2528300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.20 % (2528300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.93/3.20 % (2528300)CaDiCaL version: 2.1.3
% 14.93/3.20 % (2528300)Termination reason: Instruction limit
% 14.93/3.20 % (2528300)Termination phase: Saturation
% 14.93/3.20 % (2528300)Time elapsed: 0.115 s
% 14.93/3.20 % (2528300)Peak memory usage: 88 MB
% 14.93/3.20 % (2528300)Instructions burned: 120 (million)
% 14.93/3.20 % (2528301)Instruction limit reached!
% 14.93/3.20 % (2528301)------------------------------
% 14.93/3.20 % (2528301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.20 % (2528301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.93/3.20 % (2528301)CaDiCaL version: 2.1.3
% 14.93/3.20 % (2528301)Termination reason: Instruction limit
% 14.93/3.20 % (2528301)Termination phase: Saturation
% 14.93/3.20 % (2528301)Time elapsed: 0.133 s
% 14.93/3.20 % (2528301)Peak memory usage: 90 MB
% 14.93/3.20 % (2528301)Instructions burned: 140 (million)
% 14.93/3.20 % (2528310)lrs+10_1_sil=8000:sp=occurrence:random_seed=1873901797:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 14.93/3.20 % (2528302)------------------------------
% 14.93/3.20 % (2528302)------------------------------
% 14.93/3.20 % (2528299)------------------------------
% 14.93/3.20 % (2528299)------------------------------
% 14.93/3.20 % (2528311)lrs+10_1_sil=32000:urr=on:br=off:random_seed=725183138:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 14.93/3.20 % (2528311)Instruction limit reached!
% 14.93/3.20 % (2528311)------------------------------
% 14.93/3.20 % (2528311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.20 % (2528311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528311)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528311)Termination reason: Instruction limit
% 15.27/3.24 % (2528311)Termination phase: Saturation
% 15.27/3.24 % (2528311)Time elapsed: 0.130 s
% 15.27/3.24 % (2528311)Peak memory usage: 89 MB
% 15.27/3.24 % (2528311)Instructions burned: 157 (million)
% 15.27/3.24 % (2528313)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2873397406:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 15.27/3.24 % (2528310)Instruction limit reached!
% 15.27/3.24 % (2528310)------------------------------
% 15.27/3.24 % (2528310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528310)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528310)Termination reason: Instruction limit
% 15.27/3.24 % (2528310)Termination phase: Saturation
% 15.27/3.24 % (2528310)Time elapsed: 0.288 s
% 15.27/3.24 % (2528310)Peak memory usage: 91 MB
% 15.27/3.24 % (2528310)Instructions burned: 285 (million)
% 15.27/3.24 % (2528314)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=1600185378:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 15.27/3.24 % (2528313)Instruction limit reached!
% 15.27/3.24 % (2528313)------------------------------
% 15.27/3.24 % (2528313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528313)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528313)Termination reason: Instruction limit
% 15.27/3.24 % (2528313)Termination phase: Saturation
% 15.27/3.24 % (2528313)Time elapsed: 0.181 s
% 15.27/3.24 % (2528313)Peak memory usage: 93 MB
% 15.27/3.24 % (2528313)Instructions burned: 325 (million)
% 15.27/3.24 % (2528316)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1567726804:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 15.27/3.24 % (2528298)Refutation not found, incomplete strategy
% 15.27/3.24 % (2528298)------------------------------
% 15.27/3.24 % (2528298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528298)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528298)Termination reason: Refutation not found, incomplete strategy
% 15.27/3.24 % (2528298)Time elapsed: 0.930 s
% 15.27/3.24 % (2528298)Peak memory usage: 127 MB
% 15.27/3.24 % (2528298)Instructions burned: 892 (million)
% 15.27/3.24 % (2528314)Instruction limit reached!
% 15.27/3.24 % (2528314)------------------------------
% 15.27/3.24 % (2528314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528314)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528314)Termination reason: Instruction limit
% 15.27/3.24 % (2528314)Termination phase: Saturation
% 15.27/3.24 % (2528314)Time elapsed: 0.226 s
% 15.27/3.24 % (2528314)Peak memory usage: 91 MB
% 15.27/3.24 % (2528314)Instructions burned: 249 (million)
% 15.27/3.24 % (2528318)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=827930238:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 15.27/3.24 % (2528320)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2009591132:cts=off:i=113:fsr=off:ss=included:sgt=4_2988 on theBenchmark for (2988ds/113Mi)
% 15.27/3.24 % (2528316)Instruction limit reached!
% 15.27/3.24 % (2528316)------------------------------
% 15.27/3.24 % (2528316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528316)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528316)Termination reason: Instruction limit
% 15.27/3.24 % (2528316)Termination phase: Saturation
% 15.27/3.24 % (2528316)Time elapsed: 0.272 s
% 15.27/3.24 % (2528316)Peak memory usage: 89 MB
% 15.27/3.24 % (2528316)Instructions burned: 294 (million)
% 15.27/3.24 % (2528298)------------------------------
% 15.27/3.24 % (2528298)------------------------------
% 15.27/3.24 % (2528322)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3294229106:i=127:av=off:fsr=off:sup=off_2987 on theBenchmark for (2987ds/127Mi)
% 15.27/3.24 % (2528320)Instruction limit reached!
% 15.27/3.24 % (2528320)------------------------------
% 15.27/3.24 % (2528320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528320)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528320)Termination reason: Instruction limit
% 15.27/3.24 % (2528320)Termination phase: Saturation
% 15.27/3.24 % (2528320)Time elapsed: 0.122 s
% 15.27/3.24 % (2528320)Peak memory usage: 90 MB
% 15.27/3.24 % (2528320)Instructions burned: 113 (million)
% 15.27/3.24 % (2528325)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=148114092:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2985 on theBenchmark for (2985ds/114Mi)
% 15.27/3.24 % (2528325)Refutation not found, incomplete strategy
% 15.27/3.24 % (2528325)------------------------------
% 15.27/3.24 % (2528325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528325)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528325)Termination reason: Refutation not found, incomplete strategy
% 15.27/3.24 % (2528325)Time elapsed: 0.001 s
% 15.27/3.24 % (2528325)Peak memory usage: 88 MB
% 15.27/3.24 % (2528325)Instructions burned: 1 (million)
% 15.27/3.24 % (2528322)Instruction limit reached!
% 15.27/3.24 % (2528322)------------------------------
% 15.27/3.24 % (2528322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528322)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528322)Termination reason: Instruction limit
% 15.27/3.24 % (2528322)Termination phase: Saturation
% 15.27/3.24 % (2528322)Time elapsed: 0.087 s
% 15.27/3.24 % (2528322)Peak memory usage: 89 MB
% 15.27/3.24 % (2528322)Instructions burned: 127 (million)
% 15.27/3.24 % (2528326)lrs+10_1_sil=8000:sp=occurrence:random_seed=1816547818:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2985 on theBenchmark for (2985ds/907Mi)
% 15.27/3.24 % (2528328)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4078760804:i=437:sd=1:aac=none:ss=included_2984 on theBenchmark for (2984ds/437Mi)
% 15.27/3.24 % (2528328)Refutation not found, incomplete strategy
% 15.27/3.24 % (2528328)------------------------------
% 15.27/3.24 % (2528328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528328)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528328)Termination reason: Refutation not found, incomplete strategy
% 15.27/3.24 % (2528328)Time elapsed: 0.001 s
% 15.27/3.24 % (2528328)Peak memory usage: 88 MB
% 15.27/3.24 % (2528325)------------------------------
% 15.27/3.24 % (2528325)------------------------------
% 15.27/3.24 % (2528330)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1608142611:i=5202:ss=axioms:sgt=16_2984 on theBenchmark for (2984ds/5202Mi)
% 15.27/3.24 % (2528296)First to succeed.
% 15.27/3.24 % (2528296)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2528289"
% 15.27/3.24 % (2528336)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2413013643:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2982 on theBenchmark for (2982ds/134Mi)
% 15.27/3.24 % (2528336)Refutation not found, incomplete strategy
% 15.27/3.24 % (2528336)------------------------------
% 15.27/3.24 % (2528336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528336)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528336)Termination reason: Refutation not found, incomplete strategy
% 15.27/3.24 % (2528336)Time elapsed: 0.001 s
% 15.27/3.24 % (2528336)Peak memory usage: 89 MB
% 15.27/3.24 % (2528336)Instructions burned: 1 (million)
% 15.27/3.24 % (2528328)------------------------------
% 15.27/3.24 % (2528328)------------------------------
% 15.27/3.24 % (2528336)------------------------------
% 15.27/3.24 % (2528336)------------------------------
% 15.27/3.24 % (2528377)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2699611956:st=8:i=592:sd=3:ep=RST:ss=axioms_2980 on theBenchmark for (2980ds/592Mi)
% 15.27/3.24 % (2528377)Refutation not found, incomplete strategy
% 15.27/3.24 % (2528377)------------------------------
% 15.27/3.24 % (2528377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.27/3.24 % (2528377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.27/3.24 % (2528377)CaDiCaL version: 2.1.3
% 15.27/3.24 % (2528377)Termination reason: Refutation not found, incomplete strategy
% 15.27/3.24 % (2528377)Time elapsed: 0.002 s
% 15.27/3.24 % (2528377)Peak memory usage: 88 MB
% 15.27/3.24 % (2528377)Instructions burned: 1 (million)
% 15.27/3.24 % (2528392)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3754035973:st=3:i=13193:sd=3:ss=axioms_2979 on theBenchmark for (2979ds/13193Mi)
% 15.27/3.24 % (2528296)Refutation found. Thanks to Tanya!
% 15.27/3.24 % SZS status Theorem for theBenchmark
% 15.27/3.24 % SZS output start Proof for theBenchmark
% See solution above
% 15.96/3.43 % (2528296)------------------------------
% 15.96/3.43 % (2528296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.96/3.43 % (2528296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.96/3.43 % (2528296)CaDiCaL version: 2.1.3
% 15.96/3.43 % (2528296)Termination reason: Refutation
% 15.96/3.43 % (2528296)Time elapsed: 1.585 s
% 15.96/3.43 % (2528296)Peak memory usage: 137 MB
% 15.96/3.43 % (2528296)Instructions burned: 1643 (million)
% 15.96/3.43 % (2528296)------------------------------
% 15.96/3.43 % (2528296)------------------------------
% 15.96/3.43 % (2528289)Success in time 2.156 s
% 15.96/3.43 % Vampire exiting
%------------------------------------------------------------------------------