%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE010+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 2.43s 0.91s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 144 ( 58 unt; 2 def)
% Number of atoms : 249 ( 78 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 193 ( 88 ~; 84 |; 10 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 95 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,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,[],[f18]) ).
fof(f24,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,[],[f23]) ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f39,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f14]) ).
fof(f40,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f41,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1] :
( zero != multiplication(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X0,X1)
| complement(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f44,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f46,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,[],[f24]) ).
fof(f47,plain,
test(sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
test(sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f44]) ).
fof(f51,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(f53,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,[],[f51]) ).
fof(f55,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(f57,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,[],[f55]) ).
fof(f58,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f46,f55,f51]) ).
fof(f70,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(superposition,[],[f53,f25]) ).
fof(f71,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,[],[f70,f25]) ).
fof(f77,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,[],[f71,f25]) ).
fof(f84,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f36,f28]) ).
fof(f87,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f84]) ).
fof(f94,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK0(X0)) ),
inference(resolution,[],[f39,f38]) ).
fof(f95,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f39,f49]) ).
fof(f96,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f95,f25]) ).
fof(f98,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(sK0(X0),X0) ),
inference(resolution,[],[f40,f38]) ).
fof(f100,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,sK0(X0)) ),
inference(resolution,[],[f41,f38]) ).
fof(f111,plain,
one = addition(sK1,sK0(sK1)),
inference(resolution,[],[f94,f47]) ).
fof(f112,plain,
one = addition(sK2,sK0(sK2)),
inference(resolution,[],[f94,f48]) ).
fof(f155,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f96,f47]) ).
fof(f156,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f96,f48]) ).
fof(f182,plain,
zero = multiplication(sK0(sK2),sK2),
inference(resolution,[],[f98,f48]) ).
fof(f190,plain,
zero = multiplication(sK2,sK0(sK2)),
inference(resolution,[],[f100,f48]) ).
fof(f213,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,[],[f57,f25]) ).
fof(f224,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)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f213,f25]) ).
fof(f225,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))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f224,f25]) ).
fof(f567,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f26,f28]) ).
fof(f568,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f26,f25]) ).
fof(f579,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(sK0(sK1),X0)),
inference(superposition,[],[f26,f111]) ).
fof(f580,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(c(sK1),X0)),
inference(superposition,[],[f26,f155]) ).
fof(f581,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(sK0(sK2),X0)),
inference(superposition,[],[f26,f112]) ).
fof(f583,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))),
inference(superposition,[],[f26,f28]) ).
fof(f584,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(superposition,[],[f26,f25]) ).
fof(f599,plain,
addition(sK1,sK0(sK1)) = addition(one,sK0(sK1)),
inference(superposition,[],[f579,f28]) ).
fof(f600,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(X0,sK0(sK1))),
inference(superposition,[],[f579,f25]) ).
fof(f624,plain,
one = addition(one,sK0(sK1)),
inference(forward_demodulation,[],[f599,f111]) ).
fof(f882,plain,
addition(sK2,sK0(sK2)) = addition(one,sK0(sK2)),
inference(superposition,[],[f581,f28]) ).
fof(f883,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(X0,sK0(sK2))),
inference(superposition,[],[f581,f25]) ).
fof(f907,plain,
one = addition(one,sK0(sK2)),
inference(forward_demodulation,[],[f882,f112]) ).
fof(f1068,plain,
addition(sK1,one) = addition(one,one),
inference(superposition,[],[f600,f624]) ).
fof(f1078,plain,
one = addition(sK1,one),
inference(forward_demodulation,[],[f1068,f28]) ).
fof(f1082,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(one,X0)),
inference(superposition,[],[f26,f1078]) ).
fof(f1194,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f32,f30]) ).
fof(f1859,plain,
addition(sK2,one) = addition(one,one),
inference(superposition,[],[f883,f907]) ).
fof(f1871,plain,
one = addition(sK2,one),
inference(forward_demodulation,[],[f1859,f28]) ).
fof(f2205,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),multiplication(addition(sK2,c(sK2)),sK1)))),one)
| spl3_2 ),
inference(superposition,[],[f225,f33]) ).
fof(f2214,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),multiplication(one,sK1)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f2205,f156]) ).
fof(f2293,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f2214,f31]) ).
fof(f2296,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),addition(sK1,multiplication(sK1,sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f2293,f25]) ).
fof(f2405,plain,
( zero != zero
| one != addition(sK0(sK2),sK2)
| zero != multiplication(sK0(sK2),sK2)
| complement(sK2,sK0(sK2)) ),
inference(superposition,[],[f42,f190]) ).
fof(f2409,plain,
( one != addition(sK0(sK2),sK2)
| zero != multiplication(sK0(sK2),sK2)
| complement(sK2,sK0(sK2)) ),
inference(trivial_inequality_removal,[],[f2405]) ).
fof(f2441,plain,
( one != addition(sK0(sK2),sK2)
| complement(sK2,sK0(sK2)) ),
inference(forward_subsumption_resolution,[],[f2409,f182]) ).
fof(f2513,plain,
( one != addition(sK2,sK0(sK2))
| complement(sK2,sK0(sK2)) ),
inference(forward_demodulation,[],[f2441,f25]) ).
fof(f2601,plain,
complement(sK2,sK0(sK2)),
inference(forward_subsumption_resolution,[],[f2513,f112]) ).
fof(f2635,plain,
( ~ test(sK2)
| c(sK2) = sK0(sK2) ),
inference(resolution,[],[f2601,f43]) ).
fof(f2641,plain,
c(sK2) = sK0(sK2),
inference(forward_subsumption_resolution,[],[f2635,f48]) ).
fof(f3953,plain,
! [X0] : addition(one,X0) = addition(one,addition(sK1,X0)),
inference(superposition,[],[f568,f1078]) ).
fof(f5459,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(X0,one)),
inference(forward_demodulation,[],[f3953,f584]) ).
fof(f5715,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(addition(X0,one),addition(one,X0))),
inference(superposition,[],[f583,f5459]) ).
fof(f5720,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(one,addition(X0,addition(X0,one)))),
inference(forward_demodulation,[],[f5715,f584]) ).
fof(f5732,plain,
! [X0] : addition(one,X0) = addition(one,addition(X0,addition(X0,one))),
inference(forward_demodulation,[],[f5720,f1082]) ).
fof(f5738,plain,
! [X0] : addition(one,X0) = addition(one,addition(X0,one)),
inference(forward_demodulation,[],[f5732,f567]) ).
fof(f5832,plain,
! [X0] :
( addition(one,X0) != addition(X0,one)
| leq(one,addition(X0,one)) ),
inference(superposition,[],[f36,f5738]) ).
fof(f5843,plain,
! [X0] : leq(one,addition(X0,one)),
inference(forward_subsumption_resolution,[],[f5832,f25]) ).
fof(f5862,plain,
! [X0] : leq(one,addition(one,X0)),
inference(superposition,[],[f5843,f25]) ).
fof(f8630,plain,
( ~ leq(addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(sK1,addition(one,sK2)))),one)
| spl3_2 ),
inference(superposition,[],[f2296,f1194]) ).
fof(f8637,plain,
( ~ leq(addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,addition(one,sK2)),multiplication(c(sK1),c(sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8630,f584]) ).
fof(f8741,plain,
( ~ leq(addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,addition(one,sK2)),multiplication(c(sK1),sK0(sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8637,f2641]) ).
fof(f8807,plain,
( ~ leq(addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),sK0(sK2)),multiplication(sK1,addition(one,sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8741,f25]) ).
fof(f8839,plain,
( ~ leq(addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),sK0(sK2)),multiplication(sK1,addition(sK2,one)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8807,f25]) ).
fof(f8848,plain,
( ~ leq(addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),sK0(sK2)),multiplication(sK1,one))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8839,f1871]) ).
fof(f8854,plain,
( ~ leq(addition(multiplication(sK1,one),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),sK0(sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8848,f584]) ).
fof(f8857,plain,
( ~ leq(addition(multiplication(sK1,one),multiplication(c(sK1),addition(sK2,sK0(sK2)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8854,f32]) ).
fof(f8858,plain,
( ~ leq(addition(multiplication(sK1,one),multiplication(c(sK1),one)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8857,f112]) ).
fof(f8859,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),one),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8858,f33]) ).
fof(f8860,plain,
( ~ leq(addition(sK1,c(sK1)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f8859,f30]) ).
fof(f8861,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f8860,f155]) ).
fof(f8862,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f8861,f87]) ).
fof(f8863,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f8862]) ).
fof(f8865,plain,
( ~ leq(one,addition(multiplication(c(sK1),sK2),addition(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))),multiplication(c(sK1),c(sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f77,f584]) ).
fof(f8913,plain,
( ~ leq(one,addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8865,f25]) ).
fof(f8925,plain,
( ~ leq(one,addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,sK2),addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(c(sK1),c(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8913,f584]) ).
fof(f8930,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(c(sK1),c(sK2))),multiplication(c(sK1),sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f8925,f584]) ).
fof(f8935,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(c(sK1),sK2),addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(c(sK1),c(sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8930,f25]) ).
fof(f8942,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8935,f25]) ).
fof(f8947,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(c(sK1),sK2),addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),multiplication(c(sK1),c(sK2)))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8942,f584]) ).
fof(f8952,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(addition(multiplication(c(sK2),sK1),multiplication(c(sK1),c(sK2))),multiplication(c(sK1),sK2)))))
| spl3_1 ),
inference(forward_demodulation,[],[f8947,f584]) ).
fof(f8955,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK2),sK1),multiplication(c(sK1),c(sK2)))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8952,f25]) ).
fof(f8958,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(c(sK1),sK2),addition(multiplication(sK0(sK2),sK1),multiplication(c(sK1),sK0(sK2)))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8955,f2641]) ).
fof(f8961,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),addition(multiplication(c(sK1),sK0(sK2)),multiplication(c(sK1),sK2))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8958,f584]) ).
fof(f8964,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),sK0(sK2)))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8961,f25]) ).
fof(f8967,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),multiplication(c(sK1),addition(sK2,sK0(sK2)))))))
| spl3_1 ),
inference(forward_demodulation,[],[f8964,f32]) ).
fof(f8970,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),multiplication(c(sK1),one)))))
| spl3_1 ),
inference(forward_demodulation,[],[f8967,f112]) ).
fof(f8973,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),addition(multiplication(sK0(sK2),sK1),c(sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f8970,f30]) ).
fof(f8976,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(c(sK1),addition(multiplication(sK2,sK1),multiplication(sK0(sK2),sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f8973,f584]) ).
fof(f8979,plain,
( ~ leq(one,addition(c(sK1),addition(addition(multiplication(sK2,sK1),multiplication(sK0(sK2),sK1)),multiplication(sK1,sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f8976,f584]) ).
fof(f8982,plain,
( ~ leq(one,addition(c(sK1),addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),multiplication(sK0(sK2),sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f8979,f25]) ).
fof(f8985,plain,
( ~ leq(one,addition(c(sK1),addition(multiplication(sK1,sK2),multiplication(addition(sK2,sK0(sK2)),sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f8982,f33]) ).
fof(f8988,plain,
( ~ leq(one,addition(c(sK1),addition(multiplication(sK1,sK2),multiplication(one,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f8985,f112]) ).
fof(f8991,plain,
( ~ leq(one,addition(c(sK1),addition(multiplication(sK1,sK2),sK1)))
| spl3_1 ),
inference(forward_demodulation,[],[f8988,f31]) ).
fof(f8994,plain,
( ~ leq(one,addition(sK1,addition(c(sK1),multiplication(sK1,sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f8991,f584]) ).
fof(f8998,plain,
( ~ leq(one,addition(one,multiplication(sK1,sK2)))
| spl3_1 ),
inference(forward_demodulation,[],[f8994,f580]) ).
fof(f8999,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f8998,f5862]) ).
fof(f9000,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f8999]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f58]) ).
cnf(s139,plain,
spl3_2,
inference(sat_conversion,[],[f8863]) ).
cnf(s144,plain,
spl3_1,
inference(sat_conversion,[],[f9000]) ).
cnf(s153,plain,
$false,
inference(rat,[],[s1,s139,s144]) ).
fof(f9001,plain,
$false,
inference(avatar_sat_refutation,[],[s153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 27 12:58:30 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.23/0.50 Running first-order model finding
% 0.23/0.50 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.43/0.91 % (2014497)Will run a generic schedule for satisfiability detection.
% 2.43/0.91 % (2014504)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2396080268:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.43/0.91 % (2014503)% WARNING: option uhcvi not known.
% 2.43/0.91 % (2014502)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2203222795_2999 on theBenchmark for (2999ds/0Mi)
% 2.43/0.91 % (2014503)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2630259531:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.43/0.91 % (2014507)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3192494811:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.43/0.91 % (2014505)dis+10_1_sil=32000:sp=arity:random_seed=2286455329:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.43/0.91 % (2014506)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4227030484:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.43/0.91 % (2014508)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=118072705:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.43/0.91 % TRYING [1]
% 2.43/0.91 % TRYING [2]
% 2.43/0.91 % TRYING [3]
% 2.43/0.91 % TRYING [4]
% 2.43/0.91 % TRYING [5]
% 2.43/0.91 % (2014505)Instruction limit reached!
% 2.43/0.91 % (2014505)------------------------------
% 2.43/0.91 % (2014505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.91 % (2014505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.91 % (2014505)CaDiCaL version: 2.1.3
% 2.43/0.91 % (2014505)Termination reason: Instruction limit
% 2.43/0.91 % (2014505)Termination phase: Saturation
% 2.43/0.91 % (2014505)Time elapsed: 0.110 s
% 2.43/0.91 % (2014505)Peak memory usage: 13 MB
% 2.43/0.91 % (2014505)Instructions burned: 103 (million)
% 2.43/0.91 % (2014506)Instruction limit reached!
% 2.43/0.91 % (2014506)------------------------------
% 2.43/0.91 % (2014506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.91 % (2014506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.91 % (2014506)CaDiCaL version: 2.1.3
% 2.43/0.91 % (2014506)Termination reason: Instruction limit
% 2.43/0.91 % (2014506)Termination phase: Saturation
% 2.43/0.91 % (2014506)Time elapsed: 0.114 s
% 2.43/0.91 % (2014506)Peak memory usage: 13 MB
% 2.43/0.91 % (2014506)Instructions burned: 117 (million)
% 2.43/0.91 % (2014507)Instruction limit reached!
% 2.43/0.91 % (2014507)------------------------------
% 2.43/0.91 % (2014507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.91 % (2014507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.91 % (2014507)CaDiCaL version: 2.1.3
% 2.43/0.91 % (2014507)Termination reason: Instruction limit
% 2.43/0.91 % (2014507)Termination phase: Saturation
% 2.43/0.91 % (2014507)Time elapsed: 0.118 s
% 2.43/0.91 % (2014507)Peak memory usage: 12 MB
% 2.43/0.91 % (2014507)Instructions burned: 131 (million)
% 2.43/0.91 % (2014518)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=1527300053:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.43/0.91 % (2014516)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4246692026:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 2.43/0.91 % TRYING [6]
% 2.43/0.91 % (2014517)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=525334961:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.43/0.91 % TRYING [1]
% 2.43/0.91 % TRYING [2]
% 2.43/0.91 % TRYING [3]
% 2.43/0.91 % TRYING [4]
% 2.43/0.91 % (2014508)Instruction limit reached!
% 2.43/0.91 % (2014508)------------------------------
% 2.43/0.91 % (2014508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.91 % (2014508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.91 % (2014508)CaDiCaL version: 2.1.3
% 2.43/0.91 % (2014508)Termination reason: Instruction limit
% 2.43/0.91 % (2014508)Termination phase: Saturation
% 2.43/0.91 % (2014508)Time elapsed: 0.174 s
% 2.43/0.91 % (2014508)Peak memory usage: 13 MB
% 2.43/0.91 % (2014508)Instructions burned: 159 (million)
% 2.43/0.91 % TRYING [5]
% 2.43/0.91 % (2014524)ott-21_1_sil=16000:fs=off:random_seed=164449474:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 2.43/0.91 % (2014517)Instruction limit reached!
% 2.43/0.91 % (2014517)------------------------------
% 2.43/0.91 % (2014517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.91 % (2014517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.91 % (2014517)CaDiCaL version: 2.1.3
% 2.43/0.91 % (2014517)Termination reason: Instruction limit
% 2.43/0.91 % (2014517)Termination phase: Saturation
% 2.43/0.91 % (2014517)Time elapsed: 0.135 s
% 2.43/0.91 % (2014517)Peak memory usage: 13 MB
% 2.43/0.91 % (2014517)Instructions burned: 131 (million)
% 2.43/0.91 % (2014528)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4199355339:i=477:bd=all_2996 on theBenchmark for (2996ds/477Mi)
% 2.43/0.91 % TRYING [6]
% 2.43/0.91 % (2014524)Instruction limit reached!
% 2.43/0.91 % (2014524)------------------------------
% 2.43/0.91 % (2014524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.91 % (2014524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.91 % (2014524)CaDiCaL version: 2.1.3
% 2.43/0.91 % (2014524)Termination reason: Instruction limit
% 2.43/0.91 % (2014524)Termination phase: Saturation
% 2.43/0.91 % (2014524)Time elapsed: 0.144 s
% 2.43/0.91 % (2014524)Peak memory usage: 12 MB
% 2.43/0.91 % (2014524)Instructions burned: 180 (million)
% 2.43/0.91 % (2014518) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2014497-2014518"...
% 2.43/0.91 % (2014518)...printing done.
% 2.43/0.91 % TRYING [7]
% 2.43/0.91 % (2014518)Refutation found. Thanks to Tanya!
% 2.43/0.91 % SZS status Theorem for theBenchmark
% 2.43/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 2.43/0.92 % (2014518)------------------------------
% 2.43/0.92 % (2014518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.92 % (2014518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.92 % (2014518)CaDiCaL version: 2.1.3
% 2.43/0.92 % (2014518)Termination reason: Refutation
% 2.43/0.92 % (2014518)Time elapsed: 0.223 s
% 2.43/0.92 % (2014518)Peak memory usage: 15 MB
% 2.43/0.92 % (2014518)Instructions burned: 229 (million)
% 2.43/0.92 % (2014497)Success in time 0.406 s
% 2.43/0.92 % Vampire exiting
%------------------------------------------------------------------------------