%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE135+1 : 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 : n016.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 11:40:25 AM UTC 2026
% Result : Theorem 8.66s 2.07s
% Output : Refutation 9.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 15
% Syntax : Number of formulae : 102 ( 75 unt; 0 def)
% Number of atoms : 129 ( 128 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 55 ( 28 ~; 22 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 124 ( 123 !; 1 ?)
% 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
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(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
fof(f28,axiom,
! [X0,X1,X2] :
( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2))
=> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence2) ).
fof(f29,conjecture,
! [X0] :
( divergence(X0) = zero
=> forward_diamond(star(X0),antidomain(X0)) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( divergence(X0) = zero
=> forward_diamond(star(X0),antidomain(X0)) = one ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
? [X0] :
( one != forward_diamond(star(X0),antidomain(X0))
& divergence(X0) = zero ),
inference(ennf_transformation,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f33,plain,
( one != forward_diamond(star(sK0),antidomain(sK0))
& zero = divergence(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f31]) ).
fof(f34,plain,
zero = divergence(sK0),
inference(cnf_transformation,[],[f33]) ).
fof(f35,plain,
one != forward_diamond(star(sK0),antidomain(sK0)),
inference(cnf_transformation,[],[f33]) ).
fof(f37,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f43,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f44,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f49,plain,
! [X2,X0,X1] :
( addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2))))
| addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f56,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f57,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f59,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f60,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f67,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f47,f47]) ).
fof(f69,plain,
one != antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(sK0)))))),
inference(definition_unfolding,[],[f35,f67]) ).
fof(f70,plain,
! [X2,X0,X1] :
( addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2))) != addition(antidomain(antidomain(X0)),addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2))))
| addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))) = addition(antidomain(antidomain(X0)),addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2))))))))) ),
inference(definition_unfolding,[],[f49,f67,f47,f47,f67,f47,f67,f47,f47,f47,f67,f47,f47]) ).
fof(f71,plain,
! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
inference(definition_unfolding,[],[f50,f67]) ).
fof(f72,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f42,f60]) ).
fof(f74,plain,
zero = antidomain(antidomain(multiplication(sK0,antidomain(antidomain(zero))))),
inference(superposition,[],[f71,f34]) ).
fof(f78,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f40,f60]) ).
fof(f79,plain,
! [X0] : one = addition(divergence(X0),antidomain(divergence(X0))),
inference(superposition,[],[f72,f71]) ).
fof(f80,plain,
one = addition(zero,antidomain(zero)),
inference(superposition,[],[f72,f74]) ).
fof(f82,plain,
one = addition(antidomain(multiplication(sK0,antidomain(antidomain(zero)))),zero),
inference(superposition,[],[f72,f74]) ).
fof(f83,plain,
one = addition(zero,antidomain(multiplication(sK0,antidomain(antidomain(zero))))),
inference(forward_demodulation,[],[f82,f60]) ).
fof(f85,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f80,f78]) ).
fof(f86,plain,
one = antidomain(multiplication(sK0,antidomain(antidomain(zero)))),
inference(forward_demodulation,[],[f83,f78]) ).
fof(f87,plain,
one = antidomain(multiplication(sK0,antidomain(one))),
inference(forward_demodulation,[],[f86,f85]) ).
fof(f88,plain,
zero = antidomain(antidomain(multiplication(sK0,antidomain(one)))),
inference(superposition,[],[f74,f85]) ).
fof(f90,plain,
zero = antidomain(one),
inference(forward_demodulation,[],[f88,f87]) ).
fof(f98,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f57,f37]) ).
fof(f103,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(X0),X1)) = multiplication(antidomain(X0),addition(X1,X0)),
inference(forward_demodulation,[],[f98,f60]) ).
fof(f107,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)),
inference(forward_demodulation,[],[f103,f78]) ).
fof(f114,plain,
! [X0,X1] :
( addition(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(zero)))))),antidomain(antidomain(X1))) != addition(antidomain(zero),addition(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(zero)))))),antidomain(antidomain(X1))))
| addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1)))))))) = addition(antidomain(zero),addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1))))))))) ),
inference(superposition,[],[f70,f74]) ).
fof(f125,plain,
! [X0,X1] :
( one != addition(antidomain(antidomain(X1)),one)
| addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))) = addition(antidomain(antidomain(X1)),addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))) ),
inference(superposition,[],[f70,f72]) ).
fof(f128,plain,
! [X0,X1] :
( one != addition(one,antidomain(antidomain(X1)))
| addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))) = addition(antidomain(antidomain(X1)),addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))) ),
inference(forward_demodulation,[],[f125,f60]) ).
fof(f134,plain,
! [X0,X1] :
( addition(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one))))),antidomain(antidomain(X1))) != addition(one,addition(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one))))),antidomain(antidomain(X1))))
| addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1)))))))) = addition(antidomain(zero),addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1))))))))) ),
inference(forward_demodulation,[],[f114,f85]) ).
fof(f140,plain,
! [X0,X1] :
( addition(antidomain(antidomain(multiplication(X0,antidomain(zero)))),antidomain(antidomain(X1))) != addition(one,addition(antidomain(antidomain(multiplication(X0,antidomain(zero)))),antidomain(antidomain(X1))))
| addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1)))))))) = addition(antidomain(zero),addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1))))))))) ),
inference(forward_demodulation,[],[f134,f90]) ).
fof(f146,plain,
! [X0,X1] :
( addition(antidomain(antidomain(multiplication(X0,one))),antidomain(antidomain(X1))) != addition(one,addition(antidomain(antidomain(multiplication(X0,one))),antidomain(antidomain(X1))))
| addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1)))))))) = addition(antidomain(zero),addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1))))))))) ),
inference(forward_demodulation,[],[f140,f85]) ).
fof(f150,plain,
! [X0,X1] :
( addition(antidomain(antidomain(X0)),antidomain(antidomain(X1))) != addition(one,addition(antidomain(antidomain(X0)),antidomain(antidomain(X1))))
| addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1)))))))) = addition(antidomain(zero),addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1))))))))) ),
inference(forward_demodulation,[],[f146,f44]) ).
fof(f154,plain,
! [X0,X1] :
( addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1)))))))) = addition(one,addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(X1)))))))))
| addition(antidomain(antidomain(X0)),antidomain(antidomain(X1))) != addition(one,addition(antidomain(antidomain(X0)),antidomain(antidomain(X1)))) ),
inference(forward_demodulation,[],[f150,f85]) ).
fof(f187,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[],[f56,f37]) ).
fof(f204,plain,
! [X0,X1] : multiplication(X1,X0) = multiplication(addition(antidomain(X0),X1),X0),
inference(forward_demodulation,[],[f187,f78]) ).
fof(f270,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f59,f58]) ).
fof(f330,plain,
! [X0] : multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)) = multiplication(antidomain(antidomain(antidomain(X0))),one),
inference(superposition,[],[f107,f72]) ).
fof(f340,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)),
inference(forward_demodulation,[],[f330,f44]) ).
fof(f356,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(superposition,[],[f204,f72]) ).
fof(f373,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f356,f43]) ).
fof(f423,plain,
! [X0] : one = addition(antidomain(X0),one),
inference(superposition,[],[f270,f72]) ).
fof(f424,plain,
! [X0] : one = addition(divergence(X0),one),
inference(superposition,[],[f270,f79]) ).
fof(f433,plain,
! [X0] : one = addition(one,divergence(X0)),
inference(forward_demodulation,[],[f424,f60]) ).
fof(f434,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f423,f60]) ).
fof(f444,plain,
! [X0,X1] : addition(one,X1) = addition(one,addition(divergence(X0),X1)),
inference(superposition,[],[f59,f433]) ).
fof(f454,plain,
! [X0,X1] : addition(one,X1) = addition(one,addition(antidomain(X0),X1)),
inference(superposition,[],[f59,f434]) ).
fof(f466,plain,
! [X0] : antidomain(X0) = antidomain(antidomain(antidomain(X0))),
inference(superposition,[],[f373,f340]) ).
fof(f496,plain,
one != antidomain(antidomain(multiplication(star(sK0),antidomain(sK0)))),
inference(superposition,[],[f69,f466]) ).
fof(f598,plain,
! [X0] :
( addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(zero))))))) = addition(one,addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(zero))))))))
| addition(antidomain(antidomain(X0)),antidomain(zero)) != addition(one,addition(antidomain(antidomain(X0)),antidomain(zero))) ),
inference(superposition,[],[f154,f74]) ).
fof(f619,plain,
! [X0] :
( addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(zero))))))) = addition(one,antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(zero)))))))
| addition(antidomain(antidomain(X0)),antidomain(zero)) != addition(one,addition(antidomain(antidomain(X0)),antidomain(zero))) ),
inference(forward_demodulation,[],[f598,f444]) ).
fof(f634,plain,
! [X0] :
( one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(zero)))))))
| addition(antidomain(antidomain(X0)),antidomain(zero)) != addition(one,addition(antidomain(antidomain(X0)),antidomain(zero))) ),
inference(forward_demodulation,[],[f619,f434]) ).
fof(f649,plain,
! [X0] :
( one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(zero)))))
| addition(antidomain(antidomain(X0)),antidomain(zero)) != addition(one,addition(antidomain(antidomain(X0)),antidomain(zero))) ),
inference(forward_demodulation,[],[f634,f466]) ).
fof(f664,plain,
! [X0] :
( one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),one))))
| addition(antidomain(antidomain(X0)),antidomain(zero)) != addition(one,addition(antidomain(antidomain(X0)),antidomain(zero))) ),
inference(forward_demodulation,[],[f649,f85]) ).
fof(f677,plain,
! [X0] :
( one = addition(divergence(X0),antidomain(antidomain(star(X0))))
| addition(antidomain(antidomain(X0)),antidomain(zero)) != addition(one,addition(antidomain(antidomain(X0)),antidomain(zero))) ),
inference(forward_demodulation,[],[f664,f44]) ).
fof(f685,plain,
! [X0] :
( addition(one,antidomain(zero)) != addition(antidomain(antidomain(X0)),antidomain(zero))
| one = addition(divergence(X0),antidomain(antidomain(star(X0)))) ),
inference(forward_demodulation,[],[f677,f454]) ).
fof(f691,plain,
! [X0] :
( addition(one,antidomain(zero)) != addition(antidomain(zero),antidomain(antidomain(X0)))
| one = addition(divergence(X0),antidomain(antidomain(star(X0)))) ),
inference(forward_demodulation,[],[f685,f60]) ).
fof(f697,plain,
! [X0] :
( addition(one,one) != addition(one,antidomain(antidomain(X0)))
| one = addition(divergence(X0),antidomain(antidomain(star(X0)))) ),
inference(forward_demodulation,[],[f691,f85]) ).
fof(f703,plain,
! [X0] :
( one != addition(one,one)
| one = addition(divergence(X0),antidomain(antidomain(star(X0)))) ),
inference(forward_demodulation,[],[f697,f434]) ).
fof(f708,plain,
! [X0] : one = addition(divergence(X0),antidomain(antidomain(star(X0)))),
inference(forward_subsumption_resolution,[],[f703,f58]) ).
fof(f726,plain,
one = addition(zero,antidomain(antidomain(star(sK0)))),
inference(superposition,[],[f708,f34]) ).
fof(f736,plain,
one = antidomain(antidomain(star(sK0))),
inference(forward_demodulation,[],[f726,f78]) ).
fof(f1932,plain,
! [X0] :
( one != addition(one,one)
| addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one)))))))))))) = addition(one,addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one))))))))))))) ),
inference(superposition,[],[f128,f736]) ).
fof(f1936,plain,
! [X0] : addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one)))))))))))) = addition(one,addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one))))))))))))),
inference(forward_subsumption_resolution,[],[f1932,f58]) ).
fof(f1951,plain,
! [X0] : addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one)))))))))))) = addition(one,antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one)))))))))))),
inference(forward_demodulation,[],[f1936,f444]) ).
fof(f1966,plain,
! [X0] : one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one)))))))))))),
inference(forward_demodulation,[],[f1951,f434]) ).
fof(f1980,plain,
! [X0] : one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(one)))))))))),
inference(forward_demodulation,[],[f1966,f466]) ).
fof(f1994,plain,
! [X0] : one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(multiplication(X0,antidomain(antidomain(one)))))))),
inference(forward_demodulation,[],[f1980,f466]) ).
fof(f1995,plain,
! [X0] : one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(multiplication(X0,antidomain(zero))))))),
inference(forward_demodulation,[],[f1994,f90]) ).
fof(f1996,plain,
! [X0] : one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(multiplication(X0,one)))))),
inference(forward_demodulation,[],[f1995,f85]) ).
fof(f1997,plain,
! [X0] : one = addition(divergence(X0),antidomain(antidomain(multiplication(star(X0),antidomain(X0))))),
inference(forward_demodulation,[],[f1996,f44]) ).
fof(f2337,plain,
one = addition(zero,antidomain(antidomain(multiplication(star(sK0),antidomain(sK0))))),
inference(superposition,[],[f1997,f34]) ).
fof(f2368,plain,
one = antidomain(antidomain(multiplication(star(sK0),antidomain(sK0)))),
inference(forward_demodulation,[],[f2337,f78]) ).
fof(f2373,plain,
$false,
inference(forward_subsumption_resolution,[],[f2368,f496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE135+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n016.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
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 13:17:02 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 8.66/2.07 % (2635443)Detected formulas, will run a generic FOF schedule.
% 8.66/2.07 % (2635453)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1736437375:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.66/2.07 % (2635450)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=2263296473:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.66/2.07 % (2635448)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=855503656:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.66/2.07 % (2635449)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=1165152745:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.66/2.07 % (2635452)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2034343871:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.66/2.07 % (2635451)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4148366969:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.66/2.07 % (2635454)dis-21_1_sil=8000:lcm=predicate:random_seed=4113589935: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)
% 8.66/2.07 % (2635454)Refutation not found, incomplete strategy
% 8.66/2.07 % (2635454)------------------------------
% 8.66/2.07 % (2635454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635454)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635454)Termination reason: Refutation not found, incomplete strategy
% 8.66/2.07 % (2635454)Time elapsed: 0.002 s
% 8.66/2.07 % (2635454)Peak memory usage: 88 MB
% 8.66/2.07 % (2635454)Instructions burned: 2 (million)
% 8.66/2.07 % (2635453)Instruction limit reached!
% 8.66/2.07 % (2635453)------------------------------
% 8.66/2.07 % (2635453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635453)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635453)Termination reason: Instruction limit
% 8.66/2.07 % (2635453)Termination phase: Saturation
% 8.66/2.07 % (2635453)Time elapsed: 0.045 s
% 8.66/2.07 % (2635453)Peak memory usage: 89 MB
% 8.66/2.07 % (2635453)Instructions burned: 140 (million)
% 8.66/2.07 % (2635451)Instruction limit reached!
% 8.66/2.07 % (2635451)------------------------------
% 8.66/2.07 % (2635451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635452)Instruction limit reached!
% 8.66/2.07 % (2635452)------------------------------
% 8.66/2.07 % (2635452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635452)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635451)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635452)Termination reason: Instruction limit
% 8.66/2.07 % (2635452)Termination phase: Saturation
% 8.66/2.07 % (2635451)Termination reason: Instruction limit
% 8.66/2.07 % (2635451)Termination phase: Saturation
% 8.66/2.07 % (2635452)Time elapsed: 0.070 s
% 8.66/2.07 % (2635451)Time elapsed: 0.069 s
% 8.66/2.07 % (2635452)Peak memory usage: 89 MB
% 8.66/2.07 % (2635451)Peak memory usage: 89 MB
% 8.66/2.07 % (2635451)Instructions burned: 111 (million)
% 8.66/2.07 % (2635452)Instructions burned: 121 (million)
% 8.66/2.07 % (2635462)lrs+10_1_sil=8000:sp=occurrence:random_seed=3993368031:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.66/2.07 % (2635463)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4098994027:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.66/2.07 % (2635464)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2206133999:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.66/2.07 % (2635462)Instruction limit reached!
% 8.66/2.07 % (2635462)------------------------------
% 8.66/2.07 % (2635462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635462)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635462)Termination reason: Instruction limit
% 8.66/2.07 % (2635462)Termination phase: Saturation
% 8.66/2.07 % (2635462)Time elapsed: 0.100 s
% 8.66/2.07 % (2635462)Peak memory usage: 92 MB
% 8.66/2.07 % (2635462)Instructions burned: 287 (million)
% 8.66/2.07 % (2635454)------------------------------
% 8.66/2.07 % (2635454)------------------------------
% 8.66/2.07 % (2635463)Instruction limit reached!
% 8.66/2.07 % (2635463)------------------------------
% 8.66/2.07 % (2635463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635463)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635463)Termination reason: Instruction limit
% 8.66/2.07 % (2635463)Termination phase: Saturation
% 8.66/2.07 % (2635463)Time elapsed: 0.084 s
% 8.66/2.07 % (2635463)Peak memory usage: 89 MB
% 8.66/2.07 % (2635463)Instructions burned: 158 (million)
% 8.66/2.07 % (2635468)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=744524036:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 8.66/2.07 % (2635468)Instruction limit reached!
% 8.66/2.07 % (2635468)------------------------------
% 8.66/2.07 % (2635468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635468)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635468)Termination reason: Instruction limit
% 8.66/2.07 % (2635468)Termination phase: Saturation
% 8.66/2.07 % (2635468)Time elapsed: 0.084 s
% 8.66/2.07 % (2635468)Peak memory usage: 92 MB
% 8.66/2.07 % (2635468)Instructions burned: 251 (million)
% 8.66/2.07 % (2635469)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2130663154:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.66/2.07 % (2635464)Instruction limit reached!
% 8.66/2.07 % (2635464)------------------------------
% 8.66/2.07 % (2635464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635464)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635464)Termination reason: Instruction limit
% 8.66/2.07 % (2635464)Termination phase: Saturation
% 8.66/2.07 % (2635464)Time elapsed: 0.198 s
% 8.66/2.07 % (2635464)Peak memory usage: 92 MB
% 8.66/2.07 % (2635464)Instructions burned: 325 (million)
% 8.66/2.07 % (2635470)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1560965630:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 8.66/2.07 % (2635472)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2623482757:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.66/2.07 % (2635472)Instruction limit reached!
% 8.66/2.07 % (2635472)------------------------------
% 8.66/2.07 % (2635472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635472)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635472)Termination reason: Instruction limit
% 8.66/2.07 % (2635472)Termination phase: Saturation
% 8.66/2.07 % (2635472)Time elapsed: 0.040 s
% 8.66/2.07 % (2635472)Peak memory usage: 90 MB
% 8.66/2.07 % (2635472)Instructions burned: 113 (million)
% 8.66/2.07 % (2635474)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=546401415:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 8.66/2.07 % (2635474)Refutation not found, incomplete strategy
% 8.66/2.07 % (2635474)------------------------------
% 8.66/2.07 % (2635474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635474)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635474)Termination reason: Refutation not found, incomplete strategy
% 8.66/2.07 % (2635474)Time elapsed: 0.001 s
% 8.66/2.07 % (2635474)Peak memory usage: 88 MB
% 8.66/2.07 % (2635474)Instructions burned: 1 (million)
% 8.66/2.07 % (2635469)Instruction limit reached!
% 8.66/2.07 % (2635469)------------------------------
% 8.66/2.07 % (2635469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635469)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635469)Termination reason: Instruction limit
% 8.66/2.07 % (2635469)Termination phase: Saturation
% 8.66/2.07 % (2635469)Time elapsed: 0.166 s
% 8.66/2.07 % (2635469)Peak memory usage: 91 MB
% 8.66/2.07 % (2635469)Instructions burned: 295 (million)
% 8.66/2.07 % (2635477)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4018837466:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.66/2.07 % (2635479)lrs+10_1_sil=8000:sp=occurrence:random_seed=4000289869:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.66/2.07 % (2635477)Instruction limit reached!
% 8.66/2.07 % (2635477)------------------------------
% 8.66/2.07 % (2635477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635477)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635477)Termination reason: Instruction limit
% 8.66/2.07 % (2635477)Termination phase: Saturation
% 8.66/2.07 % (2635477)Time elapsed: 0.061 s
% 8.66/2.07 % (2635477)Peak memory usage: 89 MB
% 8.66/2.07 % (2635477)Instructions burned: 115 (million)
% 8.66/2.07 % (2635474)------------------------------
% 8.66/2.07 % (2635474)------------------------------
% 8.66/2.07 % (2635449)First to succeed.
% 8.66/2.07 % (2635449)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2635443"
% 8.66/2.07 % (2635482)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2229030640:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 8.66/2.07 % (2635482)Refutation not found, incomplete strategy
% 8.66/2.07 % (2635482)------------------------------
% 8.66/2.07 % (2635482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.07 % (2635482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.07 % (2635482)CaDiCaL version: 2.1.3
% 8.66/2.07 % (2635482)Termination reason: Refutation not found, incomplete strategy
% 8.66/2.07 % (2635482)Time elapsed: 0.001 s
% 8.66/2.07 % (2635482)Peak memory usage: 88 MB
% 8.66/2.07 % (2635482)Instructions burned: 1 (million)
% 8.66/2.07 % (2635483)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=661639983:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 8.66/2.07 % (2635448)Also succeeded, but the first one will report.
% 8.66/2.07 % (2635449)Refutation found. Thanks to Tanya!
% 8.66/2.07 % SZS status Theorem for theBenchmark
% 8.66/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 9.12/2.27 % (2635449)------------------------------
% 9.12/2.27 % (2635449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.12/2.27 % (2635449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.12/2.27 % (2635449)CaDiCaL version: 2.1.3
% 9.12/2.27 % (2635449)Termination reason: Refutation
% 9.12/2.27 % (2635449)Time elapsed: 0.809 s
% 9.12/2.27 % (2635449)Peak memory usage: 131 MB
% 9.12/2.27 % (2635449)Instructions burned: 1223 (million)
% 9.12/2.27 % (2635449)------------------------------
% 9.12/2.27 % (2635449)------------------------------
% 9.12/2.27 % (2635443)Success in time 1.216 s
% 9.12/2.27 % Vampire exiting
%------------------------------------------------------------------------------