%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE011+2 : 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 : n005.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 6.78s 2.04s
% Output : Refutation 8.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 124 ( 40 unt; 4 def)
% Number of atoms : 256 ( 90 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 226 ( 94 ~; 100 |; 20 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 94 !; 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
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(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
fof(f17,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,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(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( ( ~ leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( ( ~ leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f22,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
( ( ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))))
| ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,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)],[f20]) ).
fof(f24,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(f25,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,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f22]) ).
fof(f31,plain,
test(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
test(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
( ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))))
| ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f26]) ).
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,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
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(f46,plain,
! [X0] :
( test(X0)
| zero = c(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f47,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f27]) ).
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(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1))))
| ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(forward_demodulation,[],[f33,f45]) ).
fof(f58,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))))
| ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(forward_demodulation,[],[f57,f45]) ).
fof(f59,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0)))) ),
inference(forward_demodulation,[],[f58,f45]) ).
fof(f60,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0)))) ),
inference(forward_demodulation,[],[f59,f45]) ).
fof(f62,definition,
( spl3_1
<=> leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0)))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f63,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))))
| spl3_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,definition,
( spl3_2
<=> leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))),one) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f66,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))),one)
| spl3_2 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f67,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f60,f65,f62]) ).
fof(f68,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f34,f56]) ).
fof(f69,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f68,f45]) ).
fof(f70,plain,
one = addition(sK0,c(sK0)),
inference(resolution,[],[f69,f31]) ).
fof(f71,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f69,f32]) ).
fof(f86,plain,
( addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))) != addition(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))))
| spl3_1 ),
inference(resolution,[],[f39,f63]) ).
fof(f87,plain,
( addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0))) != addition(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f86,f71]) ).
fof(f88,plain,
( addition(multiplication(c(sK0),c(sK1)),addition(multiplication(one,sK0),multiplication(addition(sK0,c(sK0)),sK1))) != addition(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(one,sK0),multiplication(addition(sK0,c(sK0)),sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f87,f45]) ).
fof(f89,plain,
( addition(multiplication(c(sK0),c(sK1)),addition(multiplication(one,sK0),multiplication(one,sK1))) != addition(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(one,sK0),multiplication(one,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f88,f70]) ).
fof(f90,plain,
( addition(multiplication(c(sK0),c(sK1)),multiplication(one,addition(sK0,sK1))) != addition(one,addition(multiplication(c(sK0),c(sK1)),multiplication(one,addition(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f89,f41]) ).
fof(f91,plain,
( addition(multiplication(one,addition(sK0,sK1)),multiplication(c(sK0),c(sK1))) != addition(one,addition(multiplication(one,addition(sK0,sK1)),multiplication(c(sK0),c(sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f90,f45]) ).
fof(f92,plain,
( addition(addition(sK0,sK1),multiplication(c(sK0),c(sK1))) != addition(one,addition(addition(sK0,sK1),multiplication(c(sK0),c(sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f91,f53]) ).
fof(f93,plain,
( addition(sK0,addition(sK1,multiplication(c(sK0),c(sK1)))) != addition(one,addition(sK0,addition(sK1,multiplication(c(sK0),c(sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f92,f44]) ).
fof(f107,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f45,f44]) ).
fof(f114,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(f122,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,[],[f114,f40]) ).
fof(f155,plain,
! [X2,X3,X0,X1] : addition(multiplication(X1,addition(X2,X3)),multiplication(X0,X3)) = addition(multiplication(X1,X2),multiplication(addition(X0,X1),X3)),
inference(superposition,[],[f122,f45]) ).
fof(f217,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f44,f42]) ).
fof(f320,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,addition(X1,X2))),
inference(superposition,[],[f217,f107]) ).
fof(f326,plain,
one = addition(sK1,one),
inference(superposition,[],[f217,f71]) ).
fof(f546,plain,
! [X0,X1] : addition(multiplication(X0,one),multiplication(X1,one)) = addition(multiplication(X0,sK1),multiplication(addition(X0,X1),one)),
inference(superposition,[],[f122,f326]) ).
fof(f552,plain,
! [X0,X1] : addition(multiplication(X0,one),multiplication(X1,one)) = addition(multiplication(X0,sK1),addition(X0,X1)),
inference(forward_demodulation,[],[f546,f54]) ).
fof(f556,plain,
! [X0,X1] : addition(multiplication(X0,one),multiplication(X1,one)) = addition(X0,addition(X1,multiplication(X0,sK1))),
inference(forward_demodulation,[],[f552,f107]) ).
fof(f558,plain,
! [X0,X1] : multiplication(addition(X0,X1),one) = addition(X0,addition(X1,multiplication(X0,sK1))),
inference(forward_demodulation,[],[f556,f40]) ).
fof(f559,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,multiplication(X0,sK1))),
inference(forward_demodulation,[],[f558,f54]) ).
fof(f724,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f45,f43]) ).
fof(f897,plain,
! [X0] :
( one = addition(X0,c(X0))
| zero = c(X0) ),
inference(resolution,[],[f46,f69]) ).
fof(f902,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0))))
| zero = c(sK1)
| spl3_1 ),
inference(superposition,[],[f63,f897]) ).
fof(f934,plain,
( ~ leq(one,addition(multiplication(one,sK0),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK0,c(sK0)),sK1))))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f902,f107]) ).
fof(f955,plain,
( ~ leq(one,addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(c(sK1),sK1)),multiplication(sK0,sK1))))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f934,f155]) ).
fof(f957,plain,
( ~ leq(one,addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),addition(c(sK1),sK1)))))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f955,f107]) ).
fof(f959,plain,
( ~ leq(one,addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),addition(sK1,c(sK1))))))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f957,f45]) ).
fof(f961,plain,
( ~ leq(one,addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),one))))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f959,f71]) ).
fof(f963,plain,
( ~ leq(one,addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),c(sK0))))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f961,f54]) ).
fof(f965,plain,
( ~ leq(one,addition(c(sK0),addition(multiplication(sK0,sK1),multiplication(one,sK0))))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f963,f107]) ).
fof(f967,plain,
( ~ leq(one,addition(c(sK0),addition(multiplication(sK0,sK1),sK0)))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f965,f53]) ).
fof(f968,plain,
( ~ leq(one,addition(sK0,addition(c(sK0),multiplication(sK0,sK1))))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f967,f107]) ).
fof(f969,plain,
( ~ leq(one,addition(sK0,c(sK0)))
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f968,f559]) ).
fof(f970,plain,
( ~ leq(one,one)
| zero = c(sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f969,f70]) ).
fof(f972,definition,
( spl3_9
<=> zero = c(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f973,plain,
( zero = c(sK1)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f972]) ).
fof(f975,definition,
( spl3_10
<=> leq(one,one) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f976,plain,
( ~ leq(one,one)
| spl3_10 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f977,plain,
( spl3_9
| ~ spl3_10
| spl3_1 ),
inference(avatar_split_clause,[],[f970,f62,f975,f972]) ).
fof(f979,plain,
( one != addition(one,one)
| spl3_10 ),
inference(resolution,[],[f976,f39]) ).
fof(f981,plain,
( $false
| spl3_10 ),
inference(forward_subsumption_resolution,[],[f979,f42]) ).
fof(f982,plain,
spl3_10,
inference(avatar_contradiction_clause,[],[f981]) ).
fof(f984,plain,
( one = addition(sK1,zero)
| ~ spl3_9 ),
inference(superposition,[],[f71,f973]) ).
fof(f998,plain,
( one = addition(zero,sK1)
| ~ spl3_9 ),
inference(forward_demodulation,[],[f984,f45]) ).
fof(f1005,plain,
( one = sK1
| ~ spl3_9 ),
inference(forward_demodulation,[],[f998,f724]) ).
fof(f1081,plain,
( addition(sK0,addition(sK1,multiplication(c(sK0),c(sK1)))) != addition(sK1,addition(sK0,addition(sK1,multiplication(c(sK0),c(sK1)))))
| spl3_1
| ~ spl3_9 ),
inference(superposition,[],[f93,f1005]) ).
fof(f1093,plain,
( $false
| spl3_1
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f1081,f320]) ).
fof(f1094,plain,
( spl3_1
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[],[f1093]) ).
fof(f1353,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f66,f71]) ).
fof(f1354,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK0,c(sK0)),sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1353,f107]) ).
fof(f1355,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(c(sK1),sK1)),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1354,f155]) ).
fof(f1356,plain,
( ~ leq(addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),addition(c(sK1),sK1)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1355,f107]) ).
fof(f1357,plain,
( ~ leq(addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),addition(sK1,c(sK1))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1356,f45]) ).
fof(f1358,plain,
( ~ leq(addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),multiplication(c(sK0),one))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1357,f71]) ).
fof(f1359,plain,
( ~ leq(addition(multiplication(sK0,sK1),addition(multiplication(one,sK0),c(sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1358,f54]) ).
fof(f1360,plain,
( ~ leq(addition(c(sK0),addition(multiplication(sK0,sK1),multiplication(one,sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1359,f107]) ).
fof(f1361,plain,
( ~ leq(addition(c(sK0),addition(multiplication(sK0,sK1),sK0)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1360,f53]) ).
fof(f1362,plain,
( ~ leq(addition(sK0,addition(c(sK0),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1361,f107]) ).
fof(f1363,plain,
( ~ leq(addition(sK0,c(sK0)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f1362,f559]) ).
fof(f1364,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f1363,f70]) ).
fof(f1365,plain,
( ~ spl3_10
| spl3_2 ),
inference(avatar_split_clause,[],[f1364,f65,f975]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s6,plain,
( spl3_1
| spl3_9
| ~ spl3_10 ),
inference(sat_conversion,[],[f977]) ).
cnf(s8,plain,
spl3_10,
inference(sat_conversion,[],[f982]) ).
cnf(s11,plain,
( spl3_1
| ~ spl3_9 ),
inference(sat_conversion,[],[f1094]) ).
cnf(s14,plain,
( spl3_2
| ~ spl3_10 ),
inference(sat_conversion,[],[f1365]) ).
cnf(s15,plain,
spl3_2,
inference(rat,[],[s14,s8]) ).
cnf(s16,plain,
( spl3_1
| spl3_9 ),
inference(rat,[],[s6,s8]) ).
cnf(s17,plain,
~ spl3_1,
inference(rat,[],[s1,s15]) ).
cnf(s18,plain,
~ spl3_9,
inference(rat,[],[s11,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s16,s18,s17]) ).
fof(f1366,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE011+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n005.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 12:58:17 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 6.78/2.04 % (3970733)Detected formulas, will run a generic FOF schedule.
% 6.78/2.04 % (3970742)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=368417806:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.78/2.04 % (3970741)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2623263385:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.78/2.04 % (3970741)Refutation not found, incomplete strategy
% 6.78/2.04 % (3970741)------------------------------
% 6.78/2.04 % (3970741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970741)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970741)Termination reason: Refutation not found, incomplete strategy
% 6.78/2.04 % (3970741)Time elapsed: 0.002 s
% 6.78/2.04 % (3970741)Peak memory usage: 88 MB
% 6.78/2.04 % (3970741)Instructions burned: 1 (million)
% 6.78/2.04 % (3970738)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=3338428583:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.78/2.04 % (3970740)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=2172480235:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.78/2.04 % (3970739)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=3033095844:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.78/2.04 % (3970742)Instruction limit reached!
% 6.78/2.04 % (3970742)------------------------------
% 6.78/2.04 % (3970742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970742)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970742)Termination reason: Instruction limit
% 6.78/2.04 % (3970742)Termination phase: Saturation
% 6.78/2.04 % (3970742)Time elapsed: 0.037 s
% 6.78/2.04 % (3970742)Peak memory usage: 88 MB
% 6.78/2.04 % (3970742)Instructions burned: 120 (million)
% 6.78/2.04 % (3970744)dis-21_1_sil=8000:lcm=predicate:random_seed=1649287942: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)
% 6.78/2.04 % (3970743)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=154737763:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.78/2.04 % (3970744)Refutation not found, incomplete strategy
% 6.78/2.04 % (3970744)------------------------------
% 6.78/2.04 % (3970744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970744)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970744)Termination reason: Refutation not found, incomplete strategy
% 6.78/2.04 % (3970744)Time elapsed: 0.003 s
% 6.78/2.04 % (3970744)Peak memory usage: 88 MB
% 6.78/2.04 % (3970744)Instructions burned: 2 (million)
% 6.78/2.04 % (3970743)Instruction limit reached!
% 6.78/2.04 % (3970743)------------------------------
% 6.78/2.04 % (3970743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970743)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970743)Termination reason: Instruction limit
% 6.78/2.04 % (3970743)Termination phase: Saturation
% 6.78/2.04 % (3970743)Time elapsed: 0.081 s
% 6.78/2.04 % (3970743)Peak memory usage: 90 MB
% 6.78/2.04 % (3970743)Instructions burned: 141 (million)
% 6.78/2.04 % (3970750)lrs+10_1_sil=8000:sp=occurrence:random_seed=126454229:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.78/2.04 % (3970750)Instruction limit reached!
% 6.78/2.04 % (3970750)------------------------------
% 6.78/2.04 % (3970750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970750)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970750)Termination reason: Instruction limit
% 6.78/2.04 % (3970750)Termination phase: Saturation
% 6.78/2.04 % (3970750)Time elapsed: 0.096 s
% 6.78/2.04 % (3970750)Peak memory usage: 91 MB
% 6.78/2.04 % (3970750)Instructions burned: 285 (million)
% 6.78/2.04 % (3970741)------------------------------
% 6.78/2.04 % (3970741)------------------------------
% 6.78/2.04 % (3970744)------------------------------
% 6.78/2.04 % (3970744)------------------------------
% 6.78/2.04 % (3970753)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3188298841:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.78/2.04 % (3970755)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3573309662:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 6.78/2.04 % (3970753)Instruction limit reached!
% 6.78/2.04 % (3970753)------------------------------
% 6.78/2.04 % (3970753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970753)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970753)Termination reason: Instruction limit
% 6.78/2.04 % (3970753)Termination phase: Saturation
% 6.78/2.04 % (3970753)Time elapsed: 0.103 s
% 6.78/2.04 % (3970753)Peak memory usage: 90 MB
% 6.78/2.04 % (3970753)Instructions burned: 158 (million)
% 6.78/2.04 % (3970756)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=4069804500:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.78/2.04 % (3970758)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4225678446:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.78/2.04 % (3970755)Instruction limit reached!
% 6.78/2.04 % (3970755)------------------------------
% 6.78/2.04 % (3970755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970755)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970755)Termination reason: Instruction limit
% 6.78/2.04 % (3970755)Termination phase: Saturation
% 6.78/2.04 % (3970755)Time elapsed: 0.102 s
% 6.78/2.04 % (3970755)Peak memory usage: 91 MB
% 6.78/2.04 % (3970755)Instructions burned: 326 (million)
% 6.78/2.04 % (3970760)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2921581230:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.78/2.04 % (3970756)Instruction limit reached!
% 6.78/2.04 % (3970756)------------------------------
% 6.78/2.04 % (3970756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970756)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970756)Termination reason: Instruction limit
% 6.78/2.04 % (3970756)Termination phase: Saturation
% 6.78/2.04 % (3970756)Time elapsed: 0.160 s
% 6.78/2.04 % (3970756)Peak memory usage: 91 MB
% 6.78/2.04 % (3970756)Instructions burned: 249 (million)
% 6.78/2.04 % (3970763)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=618498795:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.78/2.04 % (3970763)Instruction limit reached!
% 6.78/2.04 % (3970763)------------------------------
% 6.78/2.04 % (3970763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970763)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970763)Termination reason: Instruction limit
% 6.78/2.04 % (3970763)Termination phase: Saturation
% 6.78/2.04 % (3970763)Time elapsed: 0.039 s
% 6.78/2.04 % (3970763)Peak memory usage: 90 MB
% 6.78/2.04 % (3970763)Instructions burned: 116 (million)
% 6.78/2.04 % (3970758)Instruction limit reached!
% 6.78/2.04 % (3970758)------------------------------
% 6.78/2.04 % (3970758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970758)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970758)Termination reason: Instruction limit
% 6.78/2.04 % (3970758)Termination phase: Saturation
% 6.78/2.04 % (3970758)Time elapsed: 0.185 s
% 6.78/2.04 % (3970758)Peak memory usage: 90 MB
% 6.78/2.04 % (3970758)Instructions burned: 294 (million)
% 6.78/2.04 % (3970766)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2053125632:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.78/2.04 % (3970767)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2434241691:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.78/2.04 % (3970739)First to succeed.
% 6.78/2.04 % (3970739)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3970733"
% 6.78/2.04 % (3970767)Instruction limit reached!
% 6.78/2.04 % (3970767)------------------------------
% 6.78/2.04 % (3970767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970767)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970767)Termination reason: Instruction limit
% 6.78/2.04 % (3970767)Termination phase: Saturation
% 6.78/2.04 % (3970767)Time elapsed: 0.037 s
% 6.78/2.04 % (3970767)Peak memory usage: 89 MB
% 6.78/2.04 % (3970767)Instructions burned: 117 (million)
% 6.78/2.04 % (3970768)lrs+10_1_sil=8000:sp=occurrence:random_seed=3241376846:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.78/2.04 % (3970766)Instruction limit reached!
% 6.78/2.04 % (3970766)------------------------------
% 6.78/2.04 % (3970766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.04 % (3970766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.04 % (3970766)CaDiCaL version: 2.1.3
% 6.78/2.04 % (3970766)Termination reason: Instruction limit
% 6.78/2.04 % (3970766)Termination phase: Saturation
% 6.78/2.04 % (3970766)Time elapsed: 0.063 s
% 6.78/2.04 % (3970766)Peak memory usage: 89 MB
% 6.78/2.04 % (3970766)Instructions burned: 127 (million)
% 6.78/2.04 % (3970771)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=693067547:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.78/2.04 % (3970773)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=130744623:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.78/2.04 % (3970739)Refutation found. Thanks to Tanya!
% 6.78/2.04 % SZS status Theorem for theBenchmark
% 6.78/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 8.89/2.23 % (3970739)------------------------------
% 8.89/2.23 % (3970739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.89/2.23 % (3970739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.89/2.23 % (3970739)CaDiCaL version: 2.1.3
% 8.89/2.23 % (3970739)Termination reason: Refutation
% 8.89/2.23 % (3970739)Time elapsed: 0.748 s
% 8.89/2.23 % (3970739)Peak memory usage: 129 MB
% 8.89/2.23 % (3970739)Instructions burned: 1117 (million)
% 8.89/2.23 % (3970739)------------------------------
% 8.89/2.23 % (3970739)------------------------------
% 8.89/2.23 % (3970733)Success in time 1.169 s
% 8.89/2.23 % Vampire exiting
%------------------------------------------------------------------------------