%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE010+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 6.74s 2.02s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 95 ( 36 unt; 2 def)
% Number of atoms : 186 ( 57 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 166 ( 75 ~; 62 |; 20 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 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 : 89 ( 0 sgn 85 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f19,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0,X1] :
( ( ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,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,[],[f21]) ).
fof(f28,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f29,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)],[f22]) ).
fof(f30,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f28]) ).
fof(f35,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(f36,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,[],[f35]) ).
fof(f37,plain,
test(sK0),
inference(cnf_transformation,[],[f29]) ).
fof(f38,plain,
test(sK1),
inference(cnf_transformation,[],[f29]) ).
fof(f39,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,[],[f29]) ).
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(f43,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f44,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f46,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f50,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f60,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f64,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f50]) ).
fof(f65,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,[],[f39,f44]) ).
fof(f66,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,[],[f65,f44]) ).
fof(f67,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,[],[f66,f44]) ).
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)))))
| ~ 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,[],[f67,f40]) ).
fof(f69,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,[],[f68,f44]) ).
fof(f70,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,[],[f69,f44]) ).
fof(f71,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,[],[f70,f44]) ).
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)
| ~ 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,[],[f71,f40]) ).
fof(f74,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(f75,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,[],[f74]) ).
fof(f77,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(f78,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,[],[f77]) ).
fof(f79,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f72,f77,f74]) ).
fof(f80,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f55,f64]) ).
fof(f81,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f80,f44]) ).
fof(f82,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f81,f38]) ).
fof(f83,plain,
one = addition(sK0,c(sK0)),
inference(resolution,[],[f81,f37]) ).
fof(f107,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f43,f41]) ).
fof(f108,plain,
! [X0] : addition(sK0,addition(c(sK0),X0)) = addition(one,X0),
inference(superposition,[],[f43,f83]) ).
fof(f113,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f44,f43]) ).
fof(f117,plain,
! [X2,X3,X0,X1] : addition(multiplication(X1,addition(X3,X2)),X0) = addition(multiplication(X1,X3),addition(X0,multiplication(X1,X2))),
inference(superposition,[],[f107,f44]) ).
fof(f119,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,addition(X3,X2)),multiplication(X1,X2)) = addition(multiplication(X0,X3),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f107,f40]) ).
fof(f123,plain,
( ~ leq(one,addition(multiplication(c(sK0),addition(c(sK1),sK1)),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))))
| spl3_1 ),
inference(superposition,[],[f75,f107]) ).
fof(f132,plain,
( ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK0),addition(multiplication(c(sK0),addition(c(sK1),sK1)),multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f123,f113]) ).
fof(f139,plain,
( ~ leq(one,addition(multiplication(sK0,sK1),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(c(sK0),addition(c(sK1),sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f132,f113]) ).
fof(f143,plain,
( ~ leq(one,addition(multiplication(sK0,sK1),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(c(sK0),addition(sK1,c(sK1))))))
| spl3_1 ),
inference(forward_demodulation,[],[f139,f44]) ).
fof(f145,plain,
( ~ leq(one,addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),one))))
| spl3_1 ),
inference(forward_demodulation,[],[f143,f82]) ).
fof(f147,plain,
( ~ leq(one,addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),c(sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f145,f60]) ).
fof(f149,plain,
( ~ leq(one,addition(c(sK0),addition(multiplication(sK0,sK1),multiplication(one,sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f147,f113]) ).
fof(f151,plain,
( ~ leq(one,addition(c(sK0),addition(multiplication(sK0,sK1),sK0)))
| spl3_1 ),
inference(forward_demodulation,[],[f149,f59]) ).
fof(f153,plain,
( ~ leq(one,addition(sK0,addition(c(sK0),multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f151,f113]) ).
fof(f155,plain,
( ~ leq(one,addition(one,multiplication(sK0,sK1)))
| spl3_1 ),
inference(forward_demodulation,[],[f153,f108]) ).
fof(f159,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f43,f42]) ).
fof(f410,plain,
one = addition(sK1,one),
inference(superposition,[],[f159,f82]) ).
fof(f710,plain,
! [X0,X1] : addition(multiplication(X0,one),multiplication(X1,one)) = addition(multiplication(X0,sK1),multiplication(addition(X0,X1),one)),
inference(superposition,[],[f119,f410]) ).
fof(f716,plain,
! [X0,X1] : addition(multiplication(X0,one),multiplication(X1,one)) = addition(multiplication(X0,sK1),addition(X0,X1)),
inference(forward_demodulation,[],[f710,f60]) ).
fof(f720,plain,
! [X0,X1] : addition(multiplication(X0,one),multiplication(X1,one)) = addition(X0,addition(X1,multiplication(X0,sK1))),
inference(forward_demodulation,[],[f716,f113]) ).
fof(f722,plain,
! [X0,X1] : multiplication(addition(X0,X1),one) = addition(X0,addition(X1,multiplication(X0,sK1))),
inference(forward_demodulation,[],[f720,f40]) ).
fof(f723,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,multiplication(X0,sK1))),
inference(forward_demodulation,[],[f722,f60]) ).
fof(f800,plain,
( addition(one,multiplication(sK0,sK1)) != addition(one,addition(one,multiplication(sK0,sK1)))
| spl3_1 ),
inference(resolution,[],[f155,f46]) ).
fof(f802,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f800,f159]) ).
fof(f803,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f802]) ).
fof(f804,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,[],[f78,f113]) ).
fof(f805,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,[],[f804,f117]) ).
fof(f806,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,[],[f805,f113]) ).
fof(f807,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,[],[f806,f113]) ).
fof(f808,plain,
( ~ leq(addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),one))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f807,f82]) ).
fof(f809,plain,
( ~ leq(addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),c(sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f808,f60]) ).
fof(f810,plain,
( ~ leq(addition(c(sK0),addition(multiplication(sK0,sK1),multiplication(one,sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f809,f113]) ).
fof(f811,plain,
( ~ leq(addition(c(sK0),addition(multiplication(sK0,sK1),sK0)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f810,f59]) ).
fof(f812,plain,
( ~ leq(addition(sK0,addition(c(sK0),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f811,f113]) ).
fof(f813,plain,
( ~ leq(addition(sK0,c(sK0)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f812,f723]) ).
fof(f814,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f813,f83]) ).
fof(f880,plain,
( one != addition(one,one)
| spl3_2 ),
inference(resolution,[],[f814,f46]) ).
fof(f882,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f880,f42]) ).
fof(f883,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f882]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
spl3_1,
inference(sat_conversion,[],[f803]) ).
cnf(s5,plain,
spl3_2,
inference(sat_conversion,[],[f883]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s3]) ).
fof(f884,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 12:58:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.74/2.02 % (947934)Detected formulas, will run a generic FOF schedule.
% 6.74/2.02 % (947945)dis-21_1_sil=8000:lcm=predicate:random_seed=3111497458: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)
% 6.74/2.02 % (947945)Refutation not found, incomplete strategy
% 6.74/2.02 % (947945)------------------------------
% 6.74/2.02 % (947945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947945)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947945)Termination reason: Refutation not found, incomplete strategy
% 6.74/2.02 % (947945)Time elapsed: 0.002 s
% 6.74/2.02 % (947945)Peak memory usage: 88 MB
% 6.74/2.02 % (947945)Instructions burned: 2 (million)
% 6.74/2.02 % (947944)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1236673798:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.74/2.02 % (947943)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2550736074:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.74/2.02 % (947942)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2195560529:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.74/2.02 % (947939)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=3188488567:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.74/2.02 % (947941)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=2903981373:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.74/2.02 % (947940)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=2796910860:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.74/2.02 % (947942)Refutation not found, incomplete strategy
% 6.74/2.02 % (947942)------------------------------
% 6.74/2.02 % (947942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947942)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947942)Termination reason: Refutation not found, incomplete strategy
% 6.74/2.02 % (947942)Time elapsed: 0.002 s
% 6.74/2.02 % (947942)Peak memory usage: 88 MB
% 6.74/2.02 % (947942)Instructions burned: 1 (million)
% 6.74/2.02 % (947943)Instruction limit reached!
% 6.74/2.02 % (947943)------------------------------
% 6.74/2.02 % (947943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947943)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947943)Termination reason: Instruction limit
% 6.74/2.02 % (947943)Termination phase: Saturation
% 6.74/2.02 % (947943)Time elapsed: 0.068 s
% 6.74/2.02 % (947943)Peak memory usage: 89 MB
% 6.74/2.02 % (947943)Instructions burned: 121 (million)
% 6.74/2.02 % (947944)Instruction limit reached!
% 6.74/2.02 % (947944)------------------------------
% 6.74/2.02 % (947944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947944)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947944)Termination reason: Instruction limit
% 6.74/2.02 % (947944)Termination phase: Saturation
% 6.74/2.02 % (947944)Time elapsed: 0.079 s
% 6.74/2.02 % (947944)Peak memory usage: 90 MB
% 6.74/2.02 % (947944)Instructions burned: 139 (million)
% 6.74/2.02 % (947945)------------------------------
% 6.74/2.02 % (947945)------------------------------
% 6.74/2.02 % (947953)lrs+10_1_sil=8000:sp=occurrence:random_seed=3081883511:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.74/2.02 % (947955)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1465430389:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.74/2.02 % (947954)lrs+10_1_sil=32000:urr=on:br=off:random_seed=878814265:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.74/2.02 % (947942)------------------------------
% 6.74/2.02 % (947942)------------------------------
% 6.74/2.02 % (947954)Instruction limit reached!
% 6.74/2.02 % (947954)------------------------------
% 6.74/2.02 % (947954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947954)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947954)Termination reason: Instruction limit
% 6.74/2.02 % (947954)Termination phase: Saturation
% 6.74/2.02 % (947954)Time elapsed: 0.099 s
% 6.74/2.02 % (947954)Peak memory usage: 90 MB
% 6.74/2.02 % (947954)Instructions burned: 157 (million)
% 6.74/2.02 % (947955)Instruction limit reached!
% 6.74/2.02 % (947955)------------------------------
% 6.74/2.02 % (947955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947955)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947955)Termination reason: Instruction limit
% 6.74/2.02 % (947955)Termination phase: Saturation
% 6.74/2.02 % (947955)Time elapsed: 0.104 s
% 6.74/2.02 % (947955)Peak memory usage: 92 MB
% 6.74/2.02 % (947955)Instructions burned: 326 (million)
% 6.74/2.02 % (947953)Instruction limit reached!
% 6.74/2.02 % (947953)------------------------------
% 6.74/2.02 % (947953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947953)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947953)Termination reason: Instruction limit
% 6.74/2.02 % (947953)Termination phase: Saturation
% 6.74/2.02 % (947953)Time elapsed: 0.179 s
% 6.74/2.02 % (947953)Peak memory usage: 91 MB
% 6.74/2.02 % (947953)Instructions burned: 285 (million)
% 6.74/2.02 % (947959)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=173368887:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.74/2.02 % (947960)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=592280144:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.74/2.02 % (947961)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2784392645:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.74/2.02 % (947960)Instruction limit reached!
% 6.74/2.02 % (947960)------------------------------
% 6.74/2.02 % (947960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947960)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947960)Termination reason: Instruction limit
% 6.74/2.02 % (947960)Termination phase: Saturation
% 6.74/2.02 % (947960)Time elapsed: 0.096 s
% 6.74/2.02 % (947960)Peak memory usage: 90 MB
% 6.74/2.02 % (947960)Instructions burned: 297 (million)
% 6.74/2.02 % (947962)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4286829261:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.74/2.02 % (947959)Instruction limit reached!
% 6.74/2.02 % (947959)------------------------------
% 6.74/2.02 % (947959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947959)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947959)Termination reason: Instruction limit
% 6.74/2.02 % (947959)Termination phase: Saturation
% 6.74/2.02 % (947959)Time elapsed: 0.156 s
% 6.74/2.02 % (947959)Peak memory usage: 92 MB
% 6.74/2.02 % (947959)Instructions burned: 248 (million)
% 6.74/2.02 % (947962)Instruction limit reached!
% 6.74/2.02 % (947962)------------------------------
% 6.74/2.02 % (947962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947962)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947962)Termination reason: Instruction limit
% 6.74/2.02 % (947962)Termination phase: Saturation
% 6.74/2.02 % (947962)Time elapsed: 0.073 s
% 6.74/2.02 % (947962)Peak memory usage: 90 MB
% 6.74/2.02 % (947962)Instructions burned: 114 (million)
% 6.74/2.02 % (947966)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3496782199:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.74/2.02 % (947966)Instruction limit reached!
% 6.74/2.02 % (947966)------------------------------
% 6.74/2.02 % (947966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947966)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947966)Termination reason: Instruction limit
% 6.74/2.02 % (947966)Termination phase: Saturation
% 6.74/2.02 % (947966)Time elapsed: 0.028 s
% 6.74/2.02 % (947966)Peak memory usage: 88 MB
% 6.74/2.02 % (947966)Instructions burned: 130 (million)
% 6.74/2.02 % (947968)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3853546523:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.74/2.02 % (947940)First to succeed.
% 6.74/2.02 % (947940)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-947934"
% 6.74/2.02 % (947968)Instruction limit reached!
% 6.74/2.02 % (947968)------------------------------
% 6.74/2.02 % (947968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947968)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947968)Termination reason: Instruction limit
% 6.74/2.02 % (947968)Termination phase: Saturation
% 6.74/2.02 % (947968)Time elapsed: 0.065 s
% 6.74/2.02 % (947968)Peak memory usage: 89 MB
% 6.74/2.02 % (947968)Instructions burned: 114 (million)
% 6.74/2.02 % (947971)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1673168219:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.74/2.02 % (947971)Refutation not found, incomplete strategy
% 6.74/2.02 % (947971)------------------------------
% 6.74/2.02 % (947971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.02 % (947971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.02 % (947971)CaDiCaL version: 2.1.3
% 6.74/2.02 % (947971)Termination reason: Refutation not found, incomplete strategy
% 6.74/2.02 % (947971)Time elapsed: 0.001 s
% 6.74/2.02 % (947971)Peak memory usage: 88 MB
% 6.74/2.02 % (947971)Instructions burned: 2 (million)
% 6.74/2.02 % (947969)lrs+10_1_sil=8000:sp=occurrence:random_seed=2557446582:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.74/2.02 % (947939)Also succeeded, but the first one will report.
% 6.74/2.02 % (947973)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2826142508:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.74/2.02 % (947971)------------------------------
% 6.74/2.02 % (947971)------------------------------
% 6.74/2.02 % (947940)Refutation found. Thanks to Tanya!
% 6.74/2.02 % SZS status Theorem for theBenchmark
% 6.74/2.02 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/2.21 % (947940)------------------------------
% 0.15/2.21 % (947940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/2.21 % (947940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/2.21 % (947940)CaDiCaL version: 2.1.3
% 0.15/2.21 % (947940)Termination reason: Refutation
% 0.15/2.21 % (947940)Time elapsed: 0.714 s
% 0.15/2.21 % (947940)Peak memory usage: 129 MB
% 0.15/2.21 % (947940)Instructions burned: 1064 (million)
% 0.15/2.21 % (947940)------------------------------
% 0.15/2.21 % (947940)------------------------------
% 0.15/2.21 % (947934)Success in time 1.157 s
% 0.15/2.21 % Vampire exiting
%------------------------------------------------------------------------------