%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE010+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:40:02 AM UTC 2026
% Result : Theorem 5.73s 1.87s
% Output : Refutation 7.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 108 ( 38 unt; 2 def)
% Number of atoms : 208 ( 76 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 184 ( 84 ~; 71 |; 19 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/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(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(f21,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,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f19]) ).
fof(f24,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f25,plain,
( ( ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))))
| ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one) )
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f24]) ).
fof(f32,plain,
test(sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f33,plain,
test(sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
( ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))))
| ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f47,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f54,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f56,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f47]) ).
fof(f57,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1))))
| ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(forward_demodulation,[],[f34,f45]) ).
fof(f58,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)))))
| ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(forward_demodulation,[],[f57,f45]) ).
fof(f59,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))))))
| ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(forward_demodulation,[],[f58,f45]) ).
fof(f60,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))))
| ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(forward_demodulation,[],[f59,f40]) ).
fof(f61,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))))) ),
inference(forward_demodulation,[],[f60,f45]) ).
fof(f62,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))))) ),
inference(forward_demodulation,[],[f61,f45]) ).
fof(f63,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))))) ),
inference(forward_demodulation,[],[f62,f45]) ).
fof(f64,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))))) ),
inference(forward_demodulation,[],[f63,f40]) ).
fof(f66,definition,
( spl3_1
<=> leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f68,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))))
| spl3_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f70,definition,
( spl3_2
<=> leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f72,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one)
| spl3_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f64,f70,f66]) ).
fof(f83,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f35,f56]) ).
fof(f84,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f83,f45]) ).
fof(f89,plain,
( addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))) != addition(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))))
| spl3_1 ),
inference(resolution,[],[f39,f68]) ).
fof(f93,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f44,f42]) ).
fof(f106,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f45,f44]) ).
fof(f133,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f40,f53]) ).
fof(f174,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f44,f41]) ).
fof(f210,plain,
one = addition(sK0,c(sK0)),
inference(resolution,[],[f84,f32]) ).
fof(f211,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f84,f33]) ).
fof(f214,plain,
! [X0] : addition(one,X0) = addition(sK0,addition(c(sK0),X0)),
inference(superposition,[],[f44,f210]) ).
fof(f219,plain,
( addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(one,sK0)))) != addition(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(one,sK0)))))
| spl3_1 ),
inference(superposition,[],[f89,f211]) ).
fof(f223,plain,
( addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK0,sK1),multiplication(one,sK0)),multiplication(c(sK0),c(sK1)))) != addition(one,addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK0,sK1),multiplication(one,sK0)),multiplication(c(sK0),c(sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f219,f106]) ).
fof(f225,plain,
( addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),addition(multiplication(sK0,sK1),multiplication(one,sK0)))) != addition(one,addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),addition(multiplication(sK0,sK1),multiplication(one,sK0)))))
| spl3_1 ),
inference(forward_demodulation,[],[f223,f45]) ).
fof(f227,plain,
( addition(multiplication(c(sK0),addition(sK1,c(sK1))),addition(multiplication(sK0,sK1),multiplication(one,sK0))) != addition(one,addition(multiplication(c(sK0),addition(sK1,c(sK1))),addition(multiplication(sK0,sK1),multiplication(one,sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f225,f174]) ).
fof(f229,plain,
( addition(addition(multiplication(sK0,sK1),multiplication(one,sK0)),multiplication(c(sK0),addition(sK1,c(sK1)))) != addition(one,addition(addition(multiplication(sK0,sK1),multiplication(one,sK0)),multiplication(c(sK0),addition(sK1,c(sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f227,f45]) ).
fof(f231,plain,
( addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),addition(sK1,c(sK1))))) != addition(one,addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),addition(sK1,c(sK1))))))
| spl3_1 ),
inference(forward_demodulation,[],[f229,f44]) ).
fof(f233,plain,
( addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(sK1,c(sK1))),multiplication(sK0,sK1))) != addition(one,addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(sK1,c(sK1))),multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f231,f106]) ).
fof(f235,plain,
( addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(sK1,c(sK1))))) != addition(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(sK1,c(sK1))))))
| spl3_1 ),
inference(forward_demodulation,[],[f233,f45]) ).
fof(f237,plain,
( addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),one))) != addition(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),one))))
| spl3_1 ),
inference(forward_demodulation,[],[f235,f211]) ).
fof(f239,plain,
( addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),c(sK0))) != addition(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),c(sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f237,f54]) ).
fof(f241,plain,
( addition(c(sK0),addition(multiplication(one,sK0),multiplication(sK0,sK1))) != addition(one,addition(c(sK0),addition(multiplication(one,sK0),multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f239,f106]) ).
fof(f243,plain,
( addition(c(sK0),addition(sK0,multiplication(sK0,sK1))) != addition(one,addition(c(sK0),addition(sK0,multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f241,f53]) ).
fof(f245,plain,
( addition(sK0,addition(multiplication(sK0,sK1),c(sK0))) != addition(one,addition(sK0,addition(multiplication(sK0,sK1),c(sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f243,f106]) ).
fof(f247,plain,
( addition(sK0,addition(c(sK0),multiplication(sK0,sK1))) != addition(one,addition(sK0,addition(c(sK0),multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f245,f45]) ).
fof(f249,plain,
( addition(one,multiplication(sK0,sK1)) != addition(one,addition(one,multiplication(sK0,sK1)))
| spl3_1 ),
inference(forward_demodulation,[],[f247,f214]) ).
fof(f250,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f249,f93]) ).
fof(f251,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f253,plain,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)),multiplication(c(sK0),c(sK1)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f72,f106]) ).
fof(f255,plain,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f253,f45]) ).
fof(f257,plain,
( ~ leq(addition(multiplication(c(sK0),addition(sK1,c(sK1))),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f255,f174]) ).
fof(f259,plain,
( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK0),addition(multiplication(c(sK0),addition(sK1,c(sK1))),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f257,f106]) ).
fof(f261,plain,
( ~ leq(addition(multiplication(sK0,sK1),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(c(sK0),addition(sK1,c(sK1))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f259,f106]) ).
fof(f263,plain,
( ~ leq(addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),one))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f261,f211]) ).
fof(f265,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),one),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f263,f106]) ).
fof(f267,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),one))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f265,f45]) ).
fof(f269,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),c(sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f267,f54]) ).
fof(f271,plain,
( ~ leq(addition(c(sK0),addition(multiplication(one,sK0),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f269,f106]) ).
fof(f273,plain,
( ~ leq(addition(c(sK0),addition(sK0,multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f271,f53]) ).
fof(f275,plain,
( ~ leq(addition(sK0,addition(multiplication(sK0,sK1),c(sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f273,f106]) ).
fof(f277,plain,
( ~ leq(addition(sK0,addition(c(sK0),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f275,f45]) ).
fof(f279,plain,
( ~ leq(addition(one,multiplication(sK0,sK1)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f277,f214]) ).
fof(f292,plain,
( one != addition(addition(one,multiplication(sK0,sK1)),one)
| spl3_2 ),
inference(resolution,[],[f279,f39]) ).
fof(f293,plain,
( one != addition(one,addition(one,multiplication(sK0,sK1)))
| spl3_2 ),
inference(forward_demodulation,[],[f292,f45]) ).
fof(f294,plain,
( one != addition(one,multiplication(sK0,sK1))
| spl3_2 ),
inference(forward_demodulation,[],[f293,f93]) ).
fof(f384,plain,
one = addition(sK0,one),
inference(superposition,[],[f93,f210]) ).
fof(f386,plain,
one = addition(sK1,one),
inference(superposition,[],[f93,f211]) ).
fof(f395,plain,
one = addition(one,sK1),
inference(forward_demodulation,[],[f386,f45]) ).
fof(f397,plain,
one = addition(one,sK0),
inference(forward_demodulation,[],[f384,f45]) ).
fof(f407,plain,
! [X0] : addition(one,X0) = addition(one,addition(sK1,X0)),
inference(superposition,[],[f44,f395]) ).
fof(f793,plain,
! [X0] : multiplication(one,X0) = addition(X0,multiplication(sK0,X0)),
inference(superposition,[],[f133,f397]) ).
fof(f852,plain,
! [X0] : addition(X0,multiplication(sK0,X0)) = X0,
inference(forward_demodulation,[],[f793,f53]) ).
fof(f5323,plain,
addition(one,multiplication(sK0,sK1)) = addition(one,sK1),
inference(superposition,[],[f407,f852]) ).
fof(f5383,plain,
one = addition(one,multiplication(sK0,sK1)),
inference(forward_demodulation,[],[f5323,f395]) ).
fof(f5411,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f5383,f294]) ).
fof(f5412,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f5411]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f73]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f251]) ).
cnf(s9,plain,
spl3_2,
inference(sat_conversion,[],[f5412]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s2]) ).
fof(f5426,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 13:04:00 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.73/1.87 % (3555079)Detected formulas, will run a generic FOF schedule.
% 5.73/1.87 % (3555190)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1165414959:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.73/1.87 % (3555188)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3518720923:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.73/1.87 % (3555185)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1665577303:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.73/1.87 % (3555186)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3785000591:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.73/1.87 % (3555191)dis-21_1_sil=8000:lcm=predicate:random_seed=567442746:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.73/1.87 % (3555187)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3519847623:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.73/1.87 % (3555188)Refutation not found, incomplete strategy
% 5.73/1.87 % (3555188)------------------------------
% 5.73/1.87 % (3555188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555188)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555188)Termination reason: Refutation not found, incomplete strategy
% 5.73/1.87 % (3555188)Time elapsed: 0.002 s
% 5.73/1.87 % (3555188)Peak memory usage: 88 MB
% 5.73/1.87 % (3555188)Instructions burned: 1 (million)
% 5.73/1.87 % (3555191)Refutation not found, incomplete strategy
% 5.73/1.87 % (3555191)------------------------------
% 5.73/1.87 % (3555191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555191)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555191)Termination reason: Refutation not found, incomplete strategy
% 5.73/1.87 % (3555191)Time elapsed: 0.002 s
% 5.73/1.87 % (3555191)Peak memory usage: 88 MB
% 5.73/1.87 % (3555191)Instructions burned: 2 (million)
% 5.73/1.87 % (3555190)Instruction limit reached!
% 5.73/1.87 % (3555190)------------------------------
% 5.73/1.87 % (3555190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555190)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555190)Termination reason: Instruction limit
% 5.73/1.87 % (3555190)Termination phase: Saturation
% 5.73/1.87 % (3555190)Time elapsed: 0.044 s
% 5.73/1.87 % (3555190)Peak memory usage: 90 MB
% 5.73/1.87 % (3555190)Instructions burned: 140 (million)
% 5.73/1.87 % (3555189)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=391755185:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.73/1.87 % (3555189)Instruction limit reached!
% 5.73/1.87 % (3555189)------------------------------
% 5.73/1.87 % (3555189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555189)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555189)Termination reason: Instruction limit
% 5.73/1.87 % (3555189)Termination phase: Saturation
% 5.73/1.87 % (3555189)Time elapsed: 0.066 s
% 5.73/1.87 % (3555189)Peak memory usage: 89 MB
% 5.73/1.87 % (3555189)Instructions burned: 120 (million)
% 5.73/1.87 % (3555202)lrs+10_1_sil=8000:sp=occurrence:random_seed=4217387425:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.73/1.87 % (3555202)Instruction limit reached!
% 5.73/1.87 % (3555202)------------------------------
% 5.73/1.87 % (3555202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555202)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555202)Termination reason: Instruction limit
% 5.73/1.87 % (3555202)Termination phase: Saturation
% 5.73/1.87 % (3555202)Time elapsed: 0.096 s
% 5.73/1.87 % (3555202)Peak memory usage: 91 MB
% 5.73/1.87 % (3555202)Instructions burned: 287 (million)
% 5.73/1.87 % (3555191)------------------------------
% 5.73/1.87 % (3555191)------------------------------
% 5.73/1.87 % (3555188)------------------------------
% 5.73/1.87 % (3555188)------------------------------
% 5.73/1.87 % (3555213)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2136734159:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.73/1.87 % (3555217)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2752366350:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.73/1.87 % (3555215)lrs+1011_1_sil=32000:sp=occurrence:random_seed=728941327:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 5.73/1.87 % (3555213)Instruction limit reached!
% 5.73/1.87 % (3555213)------------------------------
% 5.73/1.87 % (3555213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555213)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555213)Termination reason: Instruction limit
% 5.73/1.87 % (3555213)Termination phase: Saturation
% 5.73/1.87 % (3555213)Time elapsed: 0.100 s
% 5.73/1.87 % (3555213)Peak memory usage: 90 MB
% 5.73/1.87 % (3555213)Instructions burned: 158 (million)
% 5.73/1.87 % (3555216)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1667328289:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.73/1.87 % (3555217)Instruction limit reached!
% 5.73/1.87 % (3555217)------------------------------
% 5.73/1.87 % (3555217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555217)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555217)Termination reason: Instruction limit
% 5.73/1.87 % (3555217)Termination phase: Saturation
% 5.73/1.87 % (3555217)Time elapsed: 0.093 s
% 5.73/1.87 % (3555217)Peak memory usage: 90 MB
% 5.73/1.87 % (3555217)Instructions burned: 296 (million)
% 5.73/1.87 % (3555215)First to succeed.
% 5.73/1.87 % (3555215)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3555079"
% 5.73/1.87 % (3555221)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3005085172:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.73/1.87 % (3555216)Instruction limit reached!
% 5.73/1.87 % (3555216)------------------------------
% 5.73/1.87 % (3555216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555216)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555216)Termination reason: Instruction limit
% 5.73/1.87 % (3555216)Termination phase: Saturation
% 5.73/1.87 % (3555216)Time elapsed: 0.156 s
% 5.73/1.87 % (3555216)Peak memory usage: 91 MB
% 5.73/1.87 % (3555216)Instructions burned: 248 (million)
% 5.73/1.87 % (3555223)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2224780035:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.73/1.87 % (3555223)Instruction limit reached!
% 5.73/1.87 % (3555223)------------------------------
% 5.73/1.87 % (3555223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.87 % (3555223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.87 % (3555223)CaDiCaL version: 2.1.3
% 5.73/1.87 % (3555223)Termination reason: Instruction limit
% 5.73/1.87 % (3555223)Termination phase: Saturation
% 5.73/1.87 % (3555223)Time elapsed: 0.045 s
% 5.73/1.87 % (3555223)Peak memory usage: 90 MB
% 5.73/1.87 % (3555223)Instructions burned: 114 (million)
% 5.73/1.87 % (3555215)Refutation found. Thanks to Tanya!
% 5.73/1.87 % SZS status Theorem for theBenchmark
% 5.73/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 7.63/2.17 % (3555215)------------------------------
% 7.63/2.17 % (3555215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.17 % (3555215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.17 % (3555215)CaDiCaL version: 2.1.3
% 7.63/2.17 % (3555215)Termination reason: Refutation
% 7.63/2.17 % (3555215)Time elapsed: 0.102 s
% 7.63/2.17 % (3555215)Peak memory usage: 91 MB
% 7.63/2.17 % (3555215)Instructions burned: 171 (million)
% 7.63/2.17 % (3555215)------------------------------
% 7.63/2.17 % (3555215)------------------------------
% 7.63/2.17 % (3555079)Success in time 0.98 s
% 7.63/2.17 % Vampire exiting
%------------------------------------------------------------------------------