%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE009+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 : n002.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 11:40:36 AM UTC 2026
% Result : Theorem 0.14s 0.48s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 170 ( 42 unt; 5 def)
% Number of atoms : 340 ( 96 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 293 ( 123 ~; 143 |; 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 : 102 ( 0 sgn 97 !; 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(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(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(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(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(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(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(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(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(f41,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[],[f13]) ).
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(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(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(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(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f60,plain,
( leq(one,addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( ~ leq(one,addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(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(multiplication(sK1,sK2),multiplication(sK1,c(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(multiplication(sK1,sK2),multiplication(sK1,c(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(f67,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f61,f31]) ).
fof(f68,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f67,f31]) ).
fof(f69,plain,
( ~ leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(sK1,addition(sK2,c(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f68,f38]) ).
fof(f71,plain,
! [X0] :
( test(c(X0))
| ~ test(X0) ),
inference(resolution,[],[f57,f43]) ).
fof(f76,plain,
( addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(sK1,addition(sK2,c(sK2))))) != addition(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(sK1,addition(sK2,c(sK2))))))
| spl3_1 ),
inference(resolution,[],[f42,f69]) ).
fof(f77,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK0(X0)) ),
inference(resolution,[],[f45,f44]) ).
fof(f78,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f45,f57]) ).
fof(f79,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f78,f31]) ).
fof(f85,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,c(X0)) ),
inference(resolution,[],[f46,f57]) ).
fof(f93,plain,
one = addition(sK1,sK0(sK1)),
inference(resolution,[],[f77,f55]) ).
fof(f96,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f32,f34]) ).
fof(f108,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f31,f32]) ).
fof(f111,plain,
! [X0] : addition(sK1,addition(sK0(sK1),X0)) = addition(one,X0),
inference(superposition,[],[f32,f93]) ).
fof(f142,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f32,f38]) ).
fof(f161,plain,
addition(sK1,sK0(sK1)) = addition(one,sK0(sK1)),
inference(superposition,[],[f111,f34]) ).
fof(f163,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(X0,sK0(sK1))),
inference(superposition,[],[f111,f31]) ).
fof(f166,plain,
one = addition(one,sK0(sK1)),
inference(forward_demodulation,[],[f161,f93]) ).
fof(f173,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f39,f37]) ).
fof(f219,plain,
! [X0] :
( ~ test(X0)
| c(multiplication(X0,sK1)) = addition(c(X0),c(sK1)) ),
inference(resolution,[],[f53,f55]) ).
fof(f223,plain,
! [X0] :
( ~ test(X0)
| c(multiplication(sK1,X0)) = addition(c(sK1),c(X0)) ),
inference(resolution,[],[f53,f55]) ).
fof(f236,plain,
addition(one,one) = addition(sK1,one),
inference(superposition,[],[f163,f166]) ).
fof(f240,plain,
one = addition(sK1,one),
inference(forward_demodulation,[],[f236,f34]) ).
fof(f251,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(one,X0)),
inference(superposition,[],[f32,f240]) ).
fof(f305,plain,
c(multiplication(sK1,sK1)) = addition(c(sK1),c(sK1)),
inference(resolution,[],[f219,f55]) ).
fof(f308,plain,
c(sK1) = c(multiplication(sK1,sK1)),
inference(forward_demodulation,[],[f305,f34]) ).
fof(f310,plain,
( test(c(sK1))
| ~ test(multiplication(sK1,sK1)) ),
inference(superposition,[],[f71,f308]) ).
fof(f313,definition,
( spl3_3
<=> test(multiplication(sK1,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f315,plain,
( ~ test(multiplication(sK1,sK1))
| spl3_3 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f322,definition,
( spl3_5
<=> test(c(sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f324,plain,
( test(c(sK1))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f325,plain,
( ~ spl3_3
| spl3_5 ),
inference(avatar_split_clause,[],[f310,f322,f313]) ).
fof(f332,plain,
( zero = c(multiplication(sK1,sK1))
| spl3_3 ),
inference(resolution,[],[f315,f51]) ).
fof(f339,plain,
( zero = c(sK1)
| spl3_3 ),
inference(superposition,[],[f308,f332]) ).
fof(f366,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f79,f55]) ).
fof(f367,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f79,f56]) ).
fof(f368,plain,
( one = addition(sK1,zero)
| spl3_3 ),
inference(forward_demodulation,[],[f366,f339]) ).
fof(f369,plain,
( one = sK1
| spl3_3 ),
inference(forward_demodulation,[],[f368,f33]) ).
fof(f416,plain,
( addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(sK1,addition(sK2,c(sK2))))) != addition(sK1,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(sK1,addition(sK2,c(sK2))))))
| spl3_1
| spl3_3 ),
inference(superposition,[],[f76,f369]) ).
fof(f421,plain,
( addition(multiplication(c(sK1),addition(c(sK2),sK2)),multiplication(sK1,addition(sK2,c(sK2)))) != addition(sK1,addition(multiplication(c(sK1),addition(c(sK2),sK2)),multiplication(sK1,addition(sK2,c(sK2)))))
| spl3_1
| spl3_3 ),
inference(forward_demodulation,[],[f416,f142]) ).
fof(f423,plain,
( addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),addition(c(sK2),sK2))) != addition(sK1,addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),addition(c(sK2),sK2))))
| spl3_1
| spl3_3 ),
inference(forward_demodulation,[],[f421,f31]) ).
fof(f425,plain,
( addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),addition(sK2,c(sK2)))) != addition(sK1,addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),addition(sK2,c(sK2)))))
| spl3_1
| spl3_3 ),
inference(forward_demodulation,[],[f423,f31]) ).
fof(f427,plain,
( multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))) != addition(sK1,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| spl3_1
| spl3_3 ),
inference(forward_demodulation,[],[f425,f39]) ).
fof(f429,plain,
( multiplication(addition(sK1,c(sK1)),one) != addition(sK1,multiplication(addition(sK1,c(sK1)),one))
| spl3_1
| spl3_3 ),
inference(forward_demodulation,[],[f427,f367]) ).
fof(f431,plain,
( addition(sK1,c(sK1)) != addition(sK1,addition(sK1,c(sK1)))
| spl3_1
| spl3_3 ),
inference(forward_demodulation,[],[f429,f36]) ).
fof(f433,plain,
( $false
| spl3_1
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f431,f96]) ).
fof(f434,plain,
( spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f439,plain,
zero = multiplication(sK1,c(sK1)),
inference(resolution,[],[f85,f55]) ).
fof(f446,plain,
( one = addition(c(sK1),c(c(sK1)))
| ~ spl3_5 ),
inference(resolution,[],[f324,f79]) ).
fof(f455,plain,
( addition(c(sK1),c(c(sK1))) = c(multiplication(sK1,c(sK1)))
| ~ spl3_5 ),
inference(resolution,[],[f324,f223]) ).
fof(f457,plain,
( c(zero) = addition(c(sK1),c(c(sK1)))
| ~ spl3_5 ),
inference(forward_demodulation,[],[f455,f439]) ).
fof(f463,plain,
( one = c(zero)
| ~ spl3_5 ),
inference(forward_demodulation,[],[f457,f446]) ).
fof(f542,definition,
( spl3_6
<=> test(zero) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f543,plain,
( test(zero)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f544,plain,
( ~ test(zero)
| spl3_6 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f593,plain,
( zero = c(zero)
| spl3_6 ),
inference(resolution,[],[f544,f51]) ).
fof(f791,plain,
( zero = one
| ~ spl3_5
| spl3_6 ),
inference(superposition,[],[f463,f593]) ).
fof(f805,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X2),addition(X3,multiplication(X0,X1))) = addition(X3,multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f108,f38]) ).
fof(f890,plain,
( addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),c(sK2)))) != addition(one,addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),c(sK2)))))
| spl3_1 ),
inference(superposition,[],[f76,f108]) ).
fof(f891,plain,
( ~ leq(one,addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),c(sK2)))))
| spl3_1 ),
inference(superposition,[],[f69,f108]) ).
fof(f899,plain,
( ~ leq(one,addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),multiplication(sK1,addition(sK2,c(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f891,f31]) ).
fof(f900,plain,
( addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),multiplication(sK1,addition(sK2,c(sK2))))) != addition(one,addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),multiplication(sK1,addition(sK2,c(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f890,f31]) ).
fof(f965,plain,
( ~ leq(one,addition(multiplication(c(sK1),addition(sK2,c(sK2))),multiplication(sK1,addition(sK2,c(sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f899,f142]) ).
fof(f966,plain,
( addition(multiplication(c(sK1),addition(sK2,c(sK2))),multiplication(sK1,addition(sK2,c(sK2)))) != addition(one,addition(multiplication(c(sK1),addition(sK2,c(sK2))),multiplication(sK1,addition(sK2,c(sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f900,f142]) ).
fof(f1003,plain,
( ~ leq(one,multiplication(addition(c(sK1),sK1),addition(sK2,c(sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f965,f39]) ).
fof(f1004,plain,
( multiplication(addition(c(sK1),sK1),addition(sK2,c(sK2))) != addition(one,multiplication(addition(c(sK1),sK1),addition(sK2,c(sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f966,f39]) ).
fof(f1029,plain,
( ~ leq(one,multiplication(addition(c(sK1),sK1),one))
| spl3_1 ),
inference(forward_demodulation,[],[f1003,f367]) ).
fof(f1030,plain,
( multiplication(addition(c(sK1),sK1),one) != addition(one,multiplication(addition(c(sK1),sK1),one))
| spl3_1 ),
inference(forward_demodulation,[],[f1004,f367]) ).
fof(f1042,plain,
( ~ leq(one,addition(c(sK1),sK1))
| spl3_1 ),
inference(forward_demodulation,[],[f1029,f36]) ).
fof(f1043,plain,
( multiplication(addition(c(sK1),sK1),one) != multiplication(addition(one,addition(c(sK1),sK1)),one)
| spl3_1 ),
inference(forward_demodulation,[],[f1030,f173]) ).
fof(f1051,plain,
( ~ leq(one,addition(sK1,c(sK1)))
| spl3_1 ),
inference(forward_demodulation,[],[f1042,f31]) ).
fof(f1052,plain,
( multiplication(addition(c(sK1),sK1),one) != addition(one,addition(c(sK1),sK1))
| spl3_1 ),
inference(forward_demodulation,[],[f1043,f36]) ).
fof(f1057,plain,
( ~ leq(one,one)
| spl3_1 ),
inference(forward_demodulation,[],[f1051,f366]) ).
fof(f1058,plain,
( multiplication(addition(c(sK1),sK1),one) != addition(sK1,addition(one,c(sK1)))
| spl3_1 ),
inference(forward_demodulation,[],[f1052,f108]) ).
fof(f1060,plain,
( ~ leq(zero,zero)
| spl3_1
| ~ spl3_5
| spl3_6 ),
inference(forward_demodulation,[],[f1057,f791]) ).
fof(f1065,plain,
( zero != addition(zero,zero)
| spl3_1
| ~ spl3_5
| spl3_6 ),
inference(resolution,[],[f1060,f42]) ).
fof(f1066,plain,
( $false
| spl3_1
| ~ spl3_5
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f1065,f34]) ).
fof(f1067,plain,
( spl3_1
| ~ spl3_5
| spl3_6 ),
inference(avatar_contradiction_clause,[],[f1066]) ).
fof(f1068,plain,
( leq(one,addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f60,f32]) ).
fof(f1070,plain,
( leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK1,c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2))))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1068,f32]) ).
fof(f1072,plain,
( leq(one,addition(multiplication(sK1,addition(sK2,c(sK2))),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1070,f142]) ).
fof(f1074,plain,
( leq(one,addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),sK2))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1072,f108]) ).
fof(f1076,plain,
( leq(one,addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),addition(sK2,c(sK2)))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1074,f805]) ).
fof(f1078,plain,
( leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1076,f39]) ).
fof(f1080,plain,
( leq(one,multiplication(addition(sK1,c(sK1)),one))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1078,f367]) ).
fof(f1082,plain,
( leq(one,addition(sK1,c(sK1)))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1080,f36]) ).
fof(f1084,plain,
( leq(one,one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1082,f366]) ).
fof(f1096,plain,
( ~ leq(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f65,f32]) ).
fof(f1101,plain,
( ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK1,c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1096,f32]) ).
fof(f1102,plain,
( ~ leq(addition(multiplication(sK1,addition(sK2,c(sK2))),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1101,f142]) ).
fof(f1103,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),sK2))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1102,f108]) ).
fof(f1104,plain,
( ~ leq(addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),addition(sK2,c(sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1103,f805]) ).
fof(f1105,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1104,f39]) ).
fof(f1106,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),one),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1105,f367]) ).
fof(f1107,plain,
( ~ leq(addition(sK1,c(sK1)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1106,f36]) ).
fof(f1108,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f1107,f366]) ).
fof(f1109,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f1108,f1084]) ).
fof(f1110,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f1109]) ).
fof(f1113,plain,
( multiplication(addition(c(sK1),sK1),one) != addition(one,c(sK1))
| spl3_1 ),
inference(forward_demodulation,[],[f1058,f251]) ).
fof(f1116,plain,
( addition(c(sK1),sK1) != addition(one,c(sK1))
| spl3_1 ),
inference(forward_demodulation,[],[f1113,f36]) ).
fof(f1119,plain,
( addition(sK1,c(sK1)) != addition(one,c(sK1))
| spl3_1 ),
inference(forward_demodulation,[],[f1116,f31]) ).
fof(f1122,plain,
( one != addition(one,c(sK1))
| spl3_1 ),
inference(forward_demodulation,[],[f1119,f366]) ).
fof(f1196,plain,
( c(multiplication(zero,sK1)) = addition(c(zero),c(sK1))
| ~ spl3_6 ),
inference(resolution,[],[f543,f219]) ).
fof(f1203,plain,
( c(multiplication(zero,sK1)) = addition(one,c(sK1))
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_demodulation,[],[f1196,f463]) ).
fof(f1217,plain,
( c(zero) = addition(one,c(sK1))
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_demodulation,[],[f1203,f41]) ).
fof(f1229,plain,
( one = addition(one,c(sK1))
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_demodulation,[],[f1217,f463]) ).
fof(f1234,plain,
( $false
| spl3_1
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f1229,f1122]) ).
fof(f1235,plain,
( spl3_1
| ~ spl3_5
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f1234]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f66]) ).
cnf(s3,plain,
( ~ spl3_3
| spl3_5 ),
inference(sat_conversion,[],[f325]) ).
cnf(s4,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f434]) ).
cnf(s9,plain,
( spl3_1
| ~ spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f1067]) ).
cnf(s11,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f1110]) ).
cnf(s13,plain,
( spl3_1
| ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f1235]) ).
cnf(s14,plain,
( ~ spl3_5
| spl3_1 ),
inference(rat,[],[s9,s13]) ).
cnf(s15,plain,
spl3_1,
inference(rat,[],[s14,s3,s4]) ).
cnf(s16,plain,
spl3_2,
inference(rat,[],[s11,s15]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s16,s15]) ).
fof(f1237,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:00:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.14/0.48 % (3513054)Will run a generic schedule for satisfiability detection.
% 0.14/0.48 % (3513059)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1830176914_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.48 % TRYING [1]
% 0.14/0.48 % TRYING [2]
% 0.14/0.48 % TRYING [3]
% 0.14/0.48 % (3513060)% WARNING: option uhcvi not known.
% 0.14/0.48 % TRYING [4]
% 0.14/0.48 % (3513060)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3191719385:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.48 % (3513061)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3228392131:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.48 % (3513062)dis+10_1_sil=32000:sp=arity:random_seed=180352811:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.48 % (3513064)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1838655544:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.48 % (3513063)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2626354658:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.48 % (3513065)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=825855358:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.48 % TRYING [5]
% 0.14/0.48 % (3513063) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3513054-3513063"...
% 0.14/0.48 % (3513063)...printing done.
% 0.14/0.48 % (3513063)Refutation found. Thanks to Tanya!
% 0.14/0.48 % SZS status Theorem for theBenchmark
% 0.14/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.49 % (3513063)------------------------------
% 0.14/0.49 % (3513063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.49 % (3513063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.49 % (3513063)CaDiCaL version: 2.1.3
% 0.14/0.49 % (3513063)Termination reason: Refutation
% 0.14/0.49 % (3513063)Time elapsed: 0.028 s
% 0.14/0.49 % (3513063)Peak memory usage: 13 MB
% 0.14/0.49 % (3513063)Instructions burned: 44 (million)
% 0.14/0.49 % (3513054)Success in time 0.073 s
% 0.14/0.49 % Vampire exiting
%------------------------------------------------------------------------------