%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE010+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 11:40:37 AM UTC 2026
% Result : Theorem 1.79s 0.88s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 20
% Syntax : Number of formulae : 233 ( 75 unt; 5 def)
% Number of atoms : 461 ( 133 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 417 ( 189 ~; 201 |; 11 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 116 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(f18,axiom,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
fof(f19,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f22,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X0)
| ~ test(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
| ~ test(X0)
| ~ test(X1) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
? [X0,X1] :
( ( ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f30,plain,
? [X0,X1] :
( ( ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(flattening,[],[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(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f14]) ).
fof(f46,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f47,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f48,plain,
! [X0,X1] :
( zero != multiplication(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X0,X1)
| complement(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f49,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f51,plain,
! [X0] :
( test(X0)
| zero = c(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f53,plain,
! [X0,X1] :
( ~ test(X1)
| ~ test(X0)
| c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
( ~ leq(addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2)))) ),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
test(sK1),
inference(cnf_transformation,[],[f30]) ).
fof(f56,plain,
test(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f50]) ).
fof(f59,definition,
( spl3_1
<=> leq(one,addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f61,plain,
( ~ leq(one,addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))))
| spl3_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl3_2
<=> leq(addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f65,plain,
( ~ leq(addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one)
| spl3_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f54,f63,f59]) ).
fof(f69,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f31,f33]) ).
fof(f96,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f42,f34]) ).
fof(f101,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f96]) ).
fof(f103,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK0(X0)) ),
inference(resolution,[],[f45,f44]) ).
fof(f104,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f45,f57]) ).
fof(f105,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f104,f31]) ).
fof(f106,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(sK0(X0),X0) ),
inference(resolution,[],[f46,f44]) ).
fof(f108,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,sK0(X0)) ),
inference(resolution,[],[f47,f44]) ).
fof(f109,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(c(X0),X0) ),
inference(resolution,[],[f47,f57]) ).
fof(f119,plain,
one = addition(sK1,sK0(sK1)),
inference(resolution,[],[f103,f55]) ).
fof(f120,plain,
one = addition(sK2,sK0(sK2)),
inference(resolution,[],[f103,f56]) ).
fof(f137,definition,
( spl3_6
<=> one = sK1 ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f138,plain,
( one = sK1
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( one != sK1
| spl3_6 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f157,definition,
( spl3_10
<=> one = sK2 ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f158,plain,
( one = sK2
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( one != sK2
| spl3_10 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f163,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f105,f55]) ).
fof(f164,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f105,f56]) ).
fof(f189,plain,
zero = multiplication(sK0(sK1),sK1),
inference(resolution,[],[f106,f55]) ).
fof(f190,plain,
zero = multiplication(sK0(sK2),sK2),
inference(resolution,[],[f106,f56]) ).
fof(f197,plain,
zero = multiplication(sK1,sK0(sK1)),
inference(resolution,[],[f108,f55]) ).
fof(f198,plain,
zero = multiplication(sK2,sK0(sK2)),
inference(resolution,[],[f108,f56]) ).
fof(f201,plain,
zero = multiplication(c(sK1),sK1),
inference(resolution,[],[f109,f55]) ).
fof(f597,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f32,f34]) ).
fof(f598,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f32,f31]) ).
fof(f609,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(sK0(sK1),X0)),
inference(superposition,[],[f32,f119]) ).
fof(f610,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(c(sK1),X0)),
inference(superposition,[],[f32,f163]) ).
fof(f611,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(sK0(sK2),X0)),
inference(superposition,[],[f32,f120]) ).
fof(f614,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(superposition,[],[f32,f31]) ).
fof(f621,plain,
! [X2,X0,X1] :
( leq(addition(X0,X1),X2)
| addition(X0,addition(X1,X2)) != X2 ),
inference(superposition,[],[f42,f32]) ).
fof(f629,plain,
addition(sK1,sK0(sK1)) = addition(one,sK0(sK1)),
inference(superposition,[],[f609,f34]) ).
fof(f630,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(X0,sK0(sK1))),
inference(superposition,[],[f609,f31]) ).
fof(f654,plain,
one = addition(one,sK0(sK1)),
inference(forward_demodulation,[],[f629,f119]) ).
fof(f953,plain,
addition(sK2,sK0(sK2)) = addition(one,sK0(sK2)),
inference(superposition,[],[f611,f34]) ).
fof(f954,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(X0,sK0(sK2))),
inference(superposition,[],[f611,f31]) ).
fof(f978,plain,
one = addition(one,sK0(sK2)),
inference(forward_demodulation,[],[f953,f120]) ).
fof(f1080,plain,
! [X0] : multiplication(sK0(sK1),addition(sK1,X0)) = addition(zero,multiplication(sK0(sK1),X0)),
inference(superposition,[],[f38,f189]) ).
fof(f1116,plain,
! [X0] : addition(multiplication(sK1,X0),zero) = multiplication(sK1,addition(X0,sK0(sK1))),
inference(superposition,[],[f38,f197]) ).
fof(f1138,plain,
! [X0] : multiplication(sK1,X0) = multiplication(sK1,addition(X0,sK0(sK1))),
inference(forward_demodulation,[],[f1116,f33]) ).
fof(f1174,plain,
! [X0] : multiplication(sK0(sK1),X0) = multiplication(sK0(sK1),addition(sK1,X0)),
inference(forward_demodulation,[],[f1080,f69]) ).
fof(f1416,plain,
multiplication(sK1,one) = multiplication(sK1,sK1),
inference(superposition,[],[f1138,f119]) ).
fof(f1425,plain,
sK1 = multiplication(sK1,sK1),
inference(forward_demodulation,[],[f1416,f36]) ).
fof(f2067,plain,
! [X0] :
( ~ test(X0)
| c(multiplication(X0,sK2)) = addition(c(X0),c(sK2)) ),
inference(resolution,[],[f53,f56]) ).
fof(f2081,plain,
addition(sK1,one) = addition(one,one),
inference(superposition,[],[f630,f654]) ).
fof(f2091,plain,
one = addition(sK1,one),
inference(forward_demodulation,[],[f2081,f34]) ).
fof(f2095,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(one,X0)),
inference(superposition,[],[f32,f2091]) ).
fof(f2113,plain,
! [X0] : addition(X0,one) = addition(sK1,addition(X0,one)),
inference(superposition,[],[f2095,f31]) ).
fof(f2197,plain,
( zero != zero
| one != addition(sK0(sK1),sK1)
| zero != multiplication(sK0(sK1),sK1)
| complement(sK1,sK0(sK1)) ),
inference(superposition,[],[f48,f197]) ).
fof(f2209,plain,
( zero != zero
| one != addition(sK0(sK2),sK2)
| zero != multiplication(sK0(sK2),sK2)
| complement(sK2,sK0(sK2)) ),
inference(superposition,[],[f48,f198]) ).
fof(f2213,plain,
( one != addition(sK0(sK2),sK2)
| zero != multiplication(sK0(sK2),sK2)
| complement(sK2,sK0(sK2)) ),
inference(trivial_inequality_removal,[],[f2209]) ).
fof(f2218,plain,
( one != addition(sK0(sK1),sK1)
| zero != multiplication(sK0(sK1),sK1)
| complement(sK1,sK0(sK1)) ),
inference(trivial_inequality_removal,[],[f2197]) ).
fof(f2246,plain,
( one != addition(sK0(sK2),sK2)
| complement(sK2,sK0(sK2)) ),
inference(forward_subsumption_resolution,[],[f2213,f190]) ).
fof(f2258,plain,
( one != addition(sK0(sK1),sK1)
| complement(sK1,sK0(sK1)) ),
inference(forward_subsumption_resolution,[],[f2218,f189]) ).
fof(f2321,plain,
( one != addition(sK2,sK0(sK2))
| complement(sK2,sK0(sK2)) ),
inference(forward_demodulation,[],[f2246,f31]) ).
fof(f2343,plain,
( one != addition(sK1,sK0(sK1))
| complement(sK1,sK0(sK1)) ),
inference(forward_demodulation,[],[f2258,f31]) ).
fof(f2422,plain,
complement(sK2,sK0(sK2)),
inference(forward_subsumption_resolution,[],[f2321,f120]) ).
fof(f2436,plain,
complement(sK1,sK0(sK1)),
inference(forward_subsumption_resolution,[],[f2343,f119]) ).
fof(f2476,plain,
( ~ test(sK2)
| c(sK2) = sK0(sK2) ),
inference(resolution,[],[f2422,f49]) ).
fof(f2482,plain,
c(sK2) = sK0(sK2),
inference(forward_subsumption_resolution,[],[f2476,f56]) ).
fof(f2536,plain,
( ~ test(sK1)
| c(sK1) = sK0(sK1) ),
inference(resolution,[],[f2436,f49]) ).
fof(f2542,plain,
c(sK1) = sK0(sK1),
inference(forward_subsumption_resolution,[],[f2536,f55]) ).
fof(f3726,plain,
! [X0] :
( c(multiplication(X0,sK2)) = addition(c(X0),sK0(sK2))
| ~ test(X0) ),
inference(forward_demodulation,[],[f2067,f2482]) ).
fof(f3727,plain,
! [X0] :
( ~ test(X0)
| c(multiplication(X0,sK2)) = addition(sK0(sK2),c(X0)) ),
inference(forward_demodulation,[],[f3726,f31]) ).
fof(f3813,plain,
multiplication(sK0(sK1),one) = multiplication(sK0(sK1),sK0(sK1)),
inference(superposition,[],[f1174,f119]) ).
fof(f3834,plain,
sK0(sK1) = multiplication(sK0(sK1),sK0(sK1)),
inference(forward_demodulation,[],[f3813,f36]) ).
fof(f4478,plain,
addition(sK0(sK2),c(sK1)) = c(multiplication(sK1,sK2)),
inference(resolution,[],[f3727,f55]) ).
fof(f4481,plain,
addition(sK0(sK2),sK0(sK1)) = c(multiplication(sK1,sK2)),
inference(forward_demodulation,[],[f4478,f2542]) ).
fof(f4489,plain,
addition(sK0(sK1),sK0(sK2)) = c(multiplication(sK1,sK2)),
inference(forward_demodulation,[],[f4481,f31]) ).
fof(f4665,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f61,f31]) ).
fof(f4735,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f4665,f31]) ).
fof(f4753,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))))))
| spl3_1 ),
inference(forward_demodulation,[],[f4735,f31]) ).
fof(f4762,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),multiplication(addition(sK2,c(sK2)),sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f4753,f39]) ).
fof(f4765,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),multiplication(one,sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f4762,f164]) ).
fof(f4768,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f4765,f37]) ).
fof(f4771,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(sK1,multiplication(sK1,sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f4768,f31]) ).
fof(f4774,plain,
( ~ leq(one,addition(multiplication(sK0(sK1),c(sK2)),addition(multiplication(sK0(sK1),sK2),addition(sK1,multiplication(sK1,sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f4771,f2542]) ).
fof(f4778,plain,
( ~ leq(one,addition(multiplication(sK0(sK1),sK0(sK2)),addition(multiplication(sK0(sK1),sK2),addition(sK1,multiplication(sK1,sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f4774,f2482]) ).
fof(f5034,plain,
( sK1 = sK2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f158,f138]) ).
fof(f5204,plain,
( ~ leq(addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),sK1)
| spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f65,f138]) ).
fof(f5217,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2))),sK1)
| spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f5204,f31]) ).
fof(f5231,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)))),sK1)
| spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f5217,f31]) ).
fof(f5243,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))))),sK1)
| spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f5231,f31]) ).
fof(f5253,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),multiplication(addition(sK2,c(sK2)),sK1)))),sK1)
| spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f5243,f39]) ).
fof(f5263,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),multiplication(one,sK1)))),sK1)
| spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f5253,f164]) ).
fof(f5273,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),sK1))),sK1)
| spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f5263,f37]) ).
fof(f5283,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(sK1,multiplication(sK1,sK2)))),sK1)
| spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f5273,f31]) ).
fof(f5294,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK1)),addition(multiplication(c(sK1),sK1),addition(sK1,multiplication(sK1,sK1)))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5283,f5034]) ).
fof(f5304,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK1)),addition(multiplication(c(sK1),sK1),addition(sK1,sK1))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5294,f1425]) ).
fof(f5312,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK1)),addition(addition(sK1,sK1),multiplication(c(sK1),sK1))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5304,f31]) ).
fof(f5320,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK1)),addition(sK1,addition(sK1,multiplication(c(sK1),sK1)))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5312,f32]) ).
fof(f5330,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK1)),addition(sK1,addition(sK1,zero))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5320,f201]) ).
fof(f5336,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK1)),addition(sK1,sK1)),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5330,f33]) ).
fof(f5342,plain,
( ~ leq(addition(addition(sK1,sK1),multiplication(c(sK1),c(sK1))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5336,f31]) ).
fof(f5350,plain,
( ~ leq(addition(sK1,addition(sK1,multiplication(c(sK1),c(sK1)))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5342,f32]) ).
fof(f5355,plain,
( ~ leq(addition(sK1,addition(sK1,multiplication(sK0(sK1),sK0(sK1)))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5350,f2542]) ).
fof(f5358,plain,
( ~ leq(addition(sK1,addition(sK1,sK0(sK1))),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5355,f3834]) ).
fof(f5361,plain,
( ~ leq(addition(one,sK1),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5358,f630]) ).
fof(f5364,plain,
( ~ leq(addition(sK1,one),sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5361,f31]) ).
fof(f5367,plain,
( ~ leq(one,sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5364,f2091]) ).
fof(f5368,plain,
( ~ leq(sK1,sK1)
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_demodulation,[],[f5367,f138]) ).
fof(f5369,plain,
( $false
| spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(forward_subsumption_resolution,[],[f5368,f101]) ).
fof(f5370,plain,
( spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(avatar_contradiction_clause,[],[f5369]) ).
fof(f6202,definition,
( spl3_149
<=> test(multiplication(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_149])],[avatar_definition]) ).
fof(f6203,plain,
( test(multiplication(sK1,sK2))
| ~ spl3_149 ),
inference(avatar_component_clause,[],[f6202]) ).
fof(f6204,plain,
( ~ test(multiplication(sK1,sK2))
| spl3_149 ),
inference(avatar_component_clause,[],[f6202]) ).
fof(f6379,plain,
! [X0] : addition(one,X0) = addition(sK0(sK1),addition(sK1,X0)),
inference(superposition,[],[f598,f119]) ).
fof(f6521,plain,
( zero = c(multiplication(sK1,sK2))
| spl3_149 ),
inference(resolution,[],[f6204,f51]) ).
fof(f6522,plain,
( zero = addition(sK0(sK1),sK0(sK2))
| spl3_149 ),
inference(superposition,[],[f6521,f4489]) ).
fof(f6528,plain,
( addition(sK2,zero) = addition(one,sK0(sK1))
| spl3_149 ),
inference(superposition,[],[f954,f6522]) ).
fof(f6534,plain,
( addition(sK1,zero) = addition(one,sK0(sK2))
| spl3_149 ),
inference(superposition,[],[f609,f6522]) ).
fof(f6543,plain,
( one = addition(sK1,zero)
| spl3_149 ),
inference(forward_demodulation,[],[f6534,f978]) ).
fof(f6549,plain,
( one = addition(sK2,zero)
| spl3_149 ),
inference(forward_demodulation,[],[f6528,f654]) ).
fof(f6553,plain,
( one = sK1
| spl3_149 ),
inference(forward_demodulation,[],[f6543,f33]) ).
fof(f6554,plain,
( one = sK2
| spl3_149 ),
inference(forward_demodulation,[],[f6549,f33]) ).
fof(f6555,plain,
( $false
| spl3_6
| spl3_149 ),
inference(forward_subsumption_resolution,[],[f6553,f139]) ).
fof(f6556,plain,
( spl3_6
| spl3_149 ),
inference(avatar_contradiction_clause,[],[f6555]) ).
fof(f6557,plain,
( $false
| spl3_10
| spl3_149 ),
inference(forward_subsumption_resolution,[],[f6554,f159]) ).
fof(f6558,plain,
( spl3_10
| spl3_149 ),
inference(avatar_contradiction_clause,[],[f6557]) ).
fof(f6561,plain,
( one = addition(multiplication(sK1,sK2),sK0(multiplication(sK1,sK2)))
| ~ spl3_149 ),
inference(resolution,[],[f6203,f103]) ).
fof(f6919,plain,
! [X0] : addition(one,X0) = addition(sK0(sK1),addition(one,X0)),
inference(superposition,[],[f597,f6379]) ).
fof(f7114,plain,
! [X0] : addition(X0,one) = addition(sK0(sK1),addition(X0,one)),
inference(superposition,[],[f6919,f31]) ).
fof(f8661,plain,
! [X0] : addition(sK1,addition(X0,one)) = addition(one,addition(X0,one)),
inference(superposition,[],[f609,f7114]) ).
fof(f8672,plain,
! [X0] : addition(X0,one) = addition(one,addition(X0,one)),
inference(forward_demodulation,[],[f8661,f2113]) ).
fof(f8728,plain,
! [X0] :
( addition(X0,one) != addition(X0,one)
| leq(one,addition(X0,one)) ),
inference(superposition,[],[f42,f8672]) ).
fof(f8733,plain,
! [X0] : leq(one,addition(X0,one)),
inference(trivial_inequality_removal,[],[f8728]) ).
fof(f8752,plain,
! [X0] : leq(one,addition(one,X0)),
inference(superposition,[],[f8733,f31]) ).
fof(f9158,plain,
( ~ leq(one,addition(multiplication(sK0(sK1),sK0(sK2)),addition(multiplication(sK1,sK2),addition(multiplication(sK0(sK1),sK2),sK1))))
| spl3_1 ),
inference(superposition,[],[f4778,f614]) ).
fof(f9261,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(addition(multiplication(sK0(sK1),sK2),sK1),multiplication(sK0(sK1),sK0(sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f9158,f614]) ).
fof(f9432,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK0(sK1),sK0(sK2)),addition(multiplication(sK0(sK1),sK2),sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f9261,f31]) ).
fof(f9521,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK0(sK1),sK2),addition(sK1,multiplication(sK0(sK1),sK0(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f9432,f614]) ).
fof(f9564,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(sK1,addition(multiplication(sK0(sK1),sK0(sK2)),multiplication(sK0(sK1),sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f9521,f614]) ).
fof(f9588,plain,
( ~ leq(one,addition(sK1,addition(addition(multiplication(sK0(sK1),sK0(sK2)),multiplication(sK0(sK1),sK2)),multiplication(sK1,sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f9564,f614]) ).
fof(f9597,plain,
( ~ leq(one,addition(sK1,addition(multiplication(sK1,sK2),addition(multiplication(sK0(sK1),sK0(sK2)),multiplication(sK0(sK1),sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f9588,f31]) ).
fof(f9600,plain,
( ~ leq(one,addition(sK1,addition(multiplication(sK1,sK2),addition(multiplication(sK0(sK1),sK2),multiplication(sK0(sK1),sK0(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f9597,f31]) ).
fof(f9603,plain,
( ~ leq(one,addition(sK1,addition(multiplication(sK1,sK2),multiplication(sK0(sK1),addition(sK2,sK0(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f9600,f38]) ).
fof(f9607,plain,
( ~ leq(one,addition(sK1,addition(multiplication(sK1,sK2),multiplication(sK0(sK1),one))))
| spl3_1 ),
inference(forward_demodulation,[],[f9603,f120]) ).
fof(f9609,plain,
( ~ leq(one,addition(sK1,addition(multiplication(sK1,sK2),sK0(sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f9607,f36]) ).
fof(f9611,plain,
( ~ leq(one,addition(one,multiplication(sK1,sK2)))
| spl3_1 ),
inference(forward_demodulation,[],[f9609,f630]) ).
fof(f9614,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f9611,f8752]) ).
fof(f9615,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f9614]) ).
fof(f9618,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f65,f31]) ).
fof(f9625,plain,
( ~ leq(addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9618,f614]) ).
fof(f9632,plain,
( ~ leq(addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9625,f614]) ).
fof(f9639,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))),multiplication(c(sK1),sK2))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9632,f614]) ).
fof(f9646,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9639,f31]) ).
fof(f9653,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(c(sK1),sK2),addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),multiplication(c(sK1),c(sK2)))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9646,f614]) ).
fof(f9660,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(addition(multiplication(c(sK2),sK1),multiplication(c(sK1),c(sK2))),multiplication(c(sK1),sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9653,f614]) ).
fof(f9667,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK2),sK1),multiplication(c(sK1),c(sK2)))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9660,f31]) ).
fof(f9674,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(c(sK1),sK2),addition(multiplication(sK0(sK2),sK1),multiplication(c(sK1),sK0(sK2)))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9667,f2482]) ).
fof(f9681,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),addition(multiplication(c(sK1),sK0(sK2)),multiplication(c(sK1),sK2))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9674,f614]) ).
fof(f9688,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),sK0(sK2)))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9681,f31]) ).
fof(f9695,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),multiplication(c(sK1),addition(sK2,sK0(sK2)))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9688,f38]) ).
fof(f9699,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),multiplication(c(sK1),one)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9695,f120]) ).
fof(f9702,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),c(sK1)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9699,f36]) ).
fof(f9705,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(c(sK1),addition(multiplication(sK2,sK1),multiplication(sK0(sK2),sK1)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9702,f614]) ).
fof(f9708,plain,
( ~ leq(addition(c(sK1),addition(addition(multiplication(sK2,sK1),multiplication(sK0(sK2),sK1)),multiplication(sK1,sK2))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9705,f614]) ).
fof(f9711,plain,
( ~ leq(addition(c(sK1),addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),multiplication(sK0(sK2),sK1)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9708,f31]) ).
fof(f9714,plain,
( ~ leq(addition(c(sK1),addition(multiplication(sK1,sK2),multiplication(addition(sK2,sK0(sK2)),sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9711,f39]) ).
fof(f9717,plain,
( ~ leq(addition(c(sK1),addition(multiplication(sK1,sK2),multiplication(one,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9714,f120]) ).
fof(f9720,plain,
( ~ leq(addition(c(sK1),addition(multiplication(sK1,sK2),sK1)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9717,f37]) ).
fof(f9723,plain,
( ~ leq(addition(sK1,addition(c(sK1),multiplication(sK1,sK2))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9720,f614]) ).
fof(f9726,plain,
( ~ leq(addition(one,multiplication(sK1,sK2)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f9723,f610]) ).
fof(f19197,plain,
( one != addition(one,addition(multiplication(sK1,sK2),one))
| spl3_2 ),
inference(resolution,[],[f621,f9726]) ).
fof(f19344,plain,
( one != addition(one,addition(one,multiplication(sK1,sK2)))
| spl3_2 ),
inference(forward_demodulation,[],[f19197,f614]) ).
fof(f19377,plain,
( one != addition(one,multiplication(sK1,sK2))
| spl3_2 ),
inference(forward_demodulation,[],[f19344,f597]) ).
fof(f22353,plain,
( one = addition(multiplication(sK1,sK2),one)
| ~ spl3_149 ),
inference(superposition,[],[f597,f6561]) ).
fof(f22369,plain,
( one = addition(one,multiplication(sK1,sK2))
| ~ spl3_149 ),
inference(forward_demodulation,[],[f22353,f31]) ).
fof(f22390,plain,
( $false
| spl3_2
| ~ spl3_149 ),
inference(forward_subsumption_resolution,[],[f22369,f19377]) ).
fof(f22391,plain,
( spl3_2
| ~ spl3_149 ),
inference(avatar_contradiction_clause,[],[f22390]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f66]) ).
cnf(s239,plain,
( spl3_2
| ~ spl3_6
| ~ spl3_10 ),
inference(sat_conversion,[],[f5370]) ).
cnf(s260,plain,
( spl3_6
| spl3_149 ),
inference(sat_conversion,[],[f6556]) ).
cnf(s261,plain,
( spl3_10
| spl3_149 ),
inference(sat_conversion,[],[f6558]) ).
cnf(s298,plain,
spl3_1,
inference(sat_conversion,[],[f9615]) ).
cnf(s317,plain,
( spl3_2
| ~ spl3_149 ),
inference(sat_conversion,[],[f22391]) ).
cnf(s330,plain,
~ spl3_2,
inference(rat,[],[s1,s298]) ).
cnf(s331,plain,
~ spl3_149,
inference(rat,[],[s317,s330]) ).
cnf(s333,plain,
spl3_10,
inference(rat,[],[s261,s331]) ).
cnf(s334,plain,
spl3_6,
inference(rat,[],[s260,s331]) ).
cnf(s341,plain,
$false,
inference(rat,[],[s239,s330,s333,s334]) ).
fof(f22393,plain,
$false,
inference(avatar_sat_refutation,[],[s341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n006.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 12:58:10 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.79/0.88 % (2959919)Will run a generic schedule for satisfiability detection.
% 1.79/0.88 % (2959931)% WARNING: option uhcvi not known.
% 1.79/0.88 % (2959931)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2380355116:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.79/0.88 % (2959930)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2209546880_2999 on theBenchmark for (2999ds/0Mi)
% 1.79/0.88 % (2959934)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2733144910:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.79/0.88 % (2959932)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2137329794:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.79/0.88 % (2959933)dis+10_1_sil=32000:sp=arity:random_seed=1512224342:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.79/0.88 % (2959935)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=744687800:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.79/0.88 % (2959937)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3440591823:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.79/0.88 % TRYING [1]
% 1.79/0.88 % TRYING [2]
% 1.79/0.88 % TRYING [3]
% 1.79/0.88 % TRYING [4]
% 1.79/0.88 % TRYING [5]
% 1.79/0.88 % (2959933)Instruction limit reached!
% 1.79/0.88 % (2959933)------------------------------
% 1.79/0.88 % (2959933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2959933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2959933)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2959933)Termination reason: Instruction limit
% 1.79/0.88 % (2959933)Termination phase: Saturation
% 1.79/0.88 % (2959933)Time elapsed: 0.059 s
% 1.79/0.88 % (2959933)Peak memory usage: 12 MB
% 1.79/0.88 % (2959933)Instructions burned: 103 (million)
% 1.79/0.88 % (2959934)Instruction limit reached!
% 1.79/0.88 % (2959934)------------------------------
% 1.79/0.88 % (2959934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2959934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2959934)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2959934)Termination reason: Instruction limit
% 1.79/0.88 % (2959934)Termination phase: Saturation
% 1.79/0.88 % (2959934)Time elapsed: 0.069 s
% 1.79/0.88 % (2959934)Peak memory usage: 13 MB
% 1.79/0.88 % (2959934)Instructions burned: 116 (million)
% 1.79/0.88 % (2959935)Instruction limit reached!
% 1.79/0.88 % (2959935)------------------------------
% 1.79/0.88 % (2959935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2959935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2959935)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2959935)Termination reason: Instruction limit
% 1.79/0.88 % (2959935)Termination phase: Saturation
% 1.79/0.88 % (2959935)Time elapsed: 0.070 s
% 1.79/0.88 % (2959935)Peak memory usage: 12 MB
% 1.79/0.88 % (2959935)Instructions burned: 131 (million)
% 1.79/0.88 % TRYING [6]
% 1.79/0.88 % (2959969)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=977727502:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.79/0.88 % TRYING [1]
% 1.79/0.88 % TRYING [2]
% 1.79/0.88 % (2959972)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1977335920:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.79/0.88 % TRYING [3]
% 1.79/0.88 % (2959974)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3373796601:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.79/0.88 % TRYING [4]
% 1.79/0.88 % (2959937)Instruction limit reached!
% 1.79/0.88 % (2959937)------------------------------
% 1.79/0.88 % (2959937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2959937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2959937)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2959937)Termination reason: Instruction limit
% 1.79/0.88 % (2959937)Termination phase: Saturation
% 1.79/0.88 % (2959937)Time elapsed: 0.103 s
% 1.79/0.88 % (2959937)Peak memory usage: 13 MB
% 1.79/0.88 % (2959937)Instructions burned: 161 (million)
% 1.79/0.88 % TRYING [5]
% 1.79/0.88 % (2959992)ott-21_1_sil=16000:fs=off:random_seed=3845249366:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.79/0.88 % (2959972)Instruction limit reached!
% 1.79/0.88 % (2959972)------------------------------
% 1.79/0.88 % (2959972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2959972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2959972)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2959972)Termination reason: Instruction limit
% 1.79/0.88 % (2959972)Termination phase: Saturation
% 1.79/0.88 % (2959972)Time elapsed: 0.085 s
% 1.79/0.88 % (2959972)Peak memory usage: 13 MB
% 1.79/0.88 % (2959972)Instructions burned: 131 (million)
% 1.79/0.88 % TRYING [6]
% 1.79/0.88 % (2960013)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=844023763:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.79/0.88 % (2959992)Instruction limit reached!
% 1.79/0.88 % (2959992)------------------------------
% 1.79/0.88 % (2959992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2959992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2959992)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2959992)Termination reason: Instruction limit
% 1.79/0.88 % (2959992)Termination phase: Saturation
% 1.79/0.88 % (2959992)Time elapsed: 0.078 s
% 1.79/0.88 % (2959992)Peak memory usage: 12 MB
% 1.79/0.88 % (2959992)Instructions burned: 180 (million)
% 1.79/0.88 % TRYING [7]
% 1.79/0.88 % (2960021)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2994606333:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.79/0.88 % TRYING [1]
% 1.79/0.88 % TRYING [2]
% 1.79/0.88 % TRYING [3]
% 1.79/0.88 % TRYING [4]
% 1.79/0.88 % TRYING [5]
% 1.79/0.88 % TRYING [7]
% 1.79/0.88 % (2959969)Instruction limit reached!
% 1.79/0.88 % (2959969)------------------------------
% 1.79/0.88 % (2959969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2959969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2959969)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2959969)Termination reason: Instruction limit
% 1.79/0.88 % (2959969)Termination phase: Finite model building constraint generation
% 1.79/0.88 % (2959969)Time elapsed: 0.298 s
% 1.79/0.88 % (2959969)Peak memory usage: 32 MB
% 1.79/0.88 % (2959969)Instructions burned: 718 (million)
% 1.79/0.88 % TRYING [6]
% 1.79/0.88 % (2959974) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2959919-2959974"...
% 1.79/0.88 % (2959974)...printing done.
% 1.79/0.88 % (2959974)Refutation found. Thanks to Tanya!
% 1.79/0.88 % SZS status Theorem for theBenchmark
% 1.79/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 1.79/0.89 % (2959974)------------------------------
% 1.79/0.89 % (2959974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.89 % (2959974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.89 % (2959974)CaDiCaL version: 2.1.3
% 1.79/0.89 % (2959974)Termination reason: Refutation
% 1.79/0.89 % (2959974)Time elapsed: 0.307 s
% 1.79/0.89 % (2959974)Peak memory usage: 17 MB
% 1.79/0.89 % (2959974)Instructions burned: 559 (million)
% 1.79/0.89 % (2959919)Success in time 0.445 s
% 1.79/0.89 % Vampire exiting
%------------------------------------------------------------------------------