%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE103+1 : 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 : n002.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 11:40:20 AM UTC 2026
% Result : Theorem 23.32s 5.08s
% Output : Refutation 27.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 24
% Syntax : Number of formulae : 204 ( 200 unt; 0 def)
% Number of atoms : 208 ( 207 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 261 ( 258 !; 3 ?)
% 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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
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(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
fof(f18,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain2) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain4) ).
fof(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).
fof(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_diamond) ).
fof(f25,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_box) ).
fof(f26,axiom,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_box) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( addition(forward_box(X0,domain(X1)),domain(X2)) = one
=> addition(domain(X1),backward_box(X0,domain(X2))) = one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(forward_box(X0,domain(X1)),domain(X2)) = one
=> addition(domain(X1),backward_box(X0,domain(X2))) = one ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( one != addition(domain(X1),backward_box(X0,domain(X2)))
& addition(forward_box(X0,domain(X1)),domain(X2)) = one ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( one != addition(domain(sK1),backward_box(sK0,domain(sK2)))
& one = addition(forward_box(sK0,domain(sK1)),domain(sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
fof(f31,plain,
one = addition(forward_box(sK0,domain(sK1)),domain(sK2)),
inference(cnf_transformation,[],[f30]) ).
fof(f32,plain,
one != addition(domain(sK1),backward_box(sK0,domain(sK2))),
inference(cnf_transformation,[],[f30]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f41,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] : backward_box(X0,X1) = c(backward_diamond(X0,c(X1))),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f50,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f52,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f14]) ).
fof(f53,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f54,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f55,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f57,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f58,plain,
! [X0] : c(X0) = antidomain(antidomain(antidomain(X0))),
inference(definition_unfolding,[],[f44,f45]) ).
fof(f59,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f54,f49,f49]) ).
fof(f60,plain,
! [X0,X1] : backward_box(X0,X1) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X0)))))),
inference(definition_unfolding,[],[f47,f58,f59,f58]) ).
fof(f62,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f42,f45,f45]) ).
fof(f63,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(antidomain(X1))))))))))),
inference(definition_unfolding,[],[f46,f58,f62,f58]) ).
fof(f64,plain,
one != addition(antidomain(antidomain(sK1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2))))))),sK0))))))),
inference(definition_unfolding,[],[f32,f45,f60,f45]) ).
fof(f65,plain,
one = addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1))))))))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f31,f63,f45,f45]) ).
fof(f66,plain,
one = addition(antidomain(antidomain(sK2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1)))))))))))))),
inference(forward_demodulation,[],[f65,f37]) ).
fof(f73,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(superposition,[],[f39,f37]) ).
fof(f74,plain,
! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0))),
inference(superposition,[],[f38,f37]) ).
fof(f76,plain,
zero = antidomain(one),
inference(superposition,[],[f41,f53]) ).
fof(f78,plain,
one = addition(antidomain(zero),zero),
inference(superposition,[],[f39,f76]) ).
fof(f79,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f78,f57]) ).
fof(f81,plain,
zero = coantidomain(one),
inference(superposition,[],[f40,f51]) ).
fof(f83,plain,
one = addition(coantidomain(zero),zero),
inference(superposition,[],[f38,f81]) ).
fof(f84,plain,
one = coantidomain(zero),
inference(forward_demodulation,[],[f83,f57]) ).
fof(f88,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[],[f33,f53]) ).
fof(f91,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),zero),
inference(superposition,[],[f33,f51]) ).
fof(f92,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(superposition,[],[f33,f53]) ).
fof(f99,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[],[f92,f57]) ).
fof(f100,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[],[f91,f57]) ).
fof(f108,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(superposition,[],[f99,f39]) ).
fof(f117,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f108,f40]) ).
fof(f145,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f37,f57]) ).
fof(f146,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f34,f41]) ).
fof(f151,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[],[f34,f53]) ).
fof(f153,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,coantidomain(X0))),
inference(superposition,[],[f34,f51]) ).
fof(f157,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f34,f53]) ).
fof(f170,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)),
inference(forward_demodulation,[],[f157,f57]) ).
fof(f174,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,coantidomain(X0))),
inference(forward_demodulation,[],[f153,f57]) ).
fof(f176,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[],[f151,f145]) ).
fof(f183,plain,
! [X2,X0,X1] : multiplication(antidomain(multiplication(X1,X2)),multiplication(X0,X2)) = multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f170,f33]) ).
fof(f213,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(X0),X1)),multiplication(antidomain(antidomain(X0)),X1)) = multiplication(antidomain(multiplication(antidomain(X0),X1)),multiplication(one,X1)),
inference(superposition,[],[f183,f39]) ).
fof(f214,plain,
! [X0,X1] : multiplication(antidomain(multiplication(coantidomain(X0),X1)),multiplication(coantidomain(coantidomain(X0)),X1)) = multiplication(antidomain(multiplication(coantidomain(X0),X1)),multiplication(one,X1)),
inference(superposition,[],[f183,f38]) ).
fof(f225,plain,
! [X0,X1] : multiplication(antidomain(multiplication(coantidomain(X0),X1)),multiplication(coantidomain(coantidomain(X0)),X1)) = multiplication(antidomain(multiplication(coantidomain(X0),X1)),X1),
inference(forward_demodulation,[],[f214,f40]) ).
fof(f226,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(X0),X1)),multiplication(antidomain(antidomain(X0)),X1)) = multiplication(antidomain(multiplication(antidomain(X0),X1)),X1),
inference(forward_demodulation,[],[f213,f40]) ).
fof(f241,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f36,f35]) ).
fof(f245,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f36,f34]) ).
fof(f348,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,coantidomain(coantidomain(X0))),
inference(superposition,[],[f174,f38]) ).
fof(f364,plain,
! [X0] : multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(forward_demodulation,[],[f348,f41]) ).
fof(f384,plain,
! [X0] : multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)) = multiplication(antidomain(antidomain(antidomain(X0))),one),
inference(superposition,[],[f176,f39]) ).
fof(f401,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)),
inference(forward_demodulation,[],[f384,f41]) ).
fof(f407,plain,
! [X0] : antidomain(X0) = antidomain(antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f401,f117]) ).
fof(f420,plain,
one = addition(antidomain(antidomain(sK2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(sK1)))))))))))),
inference(superposition,[],[f66,f407]) ).
fof(f421,plain,
one != addition(antidomain(antidomain(sK1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(sK2))))),sK0))))))),
inference(superposition,[],[f64,f407]) ).
fof(f430,plain,
one != addition(antidomain(antidomain(sK1)),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(sK2))))),sK0))))),
inference(forward_demodulation,[],[f421,f407]) ).
fof(f431,plain,
one = addition(antidomain(antidomain(sK2)),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(sK1)))))))))),
inference(forward_demodulation,[],[f420,f407]) ).
fof(f443,plain,
one != addition(antidomain(antidomain(sK1)),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(sK2))),sK0))))),
inference(forward_demodulation,[],[f430,f407]) ).
fof(f444,plain,
one = addition(antidomain(antidomain(sK2)),antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(sK1)))))))),
inference(forward_demodulation,[],[f431,f407]) ).
fof(f455,plain,
one = addition(antidomain(antidomain(sK2)),antidomain(multiplication(sK0,antidomain(antidomain(antidomain(sK1)))))),
inference(forward_demodulation,[],[f444,f407]) ).
fof(f463,plain,
one = addition(antidomain(antidomain(sK2)),antidomain(multiplication(sK0,antidomain(sK1)))),
inference(forward_demodulation,[],[f455,f407]) ).
fof(f520,plain,
! [X0] : multiplication(antidomain(X0),coantidomain(antidomain(antidomain(X0)))) = multiplication(one,coantidomain(antidomain(antidomain(X0)))),
inference(superposition,[],[f100,f73]) ).
fof(f527,plain,
! [X0] : coantidomain(antidomain(antidomain(X0))) = multiplication(antidomain(X0),coantidomain(antidomain(antidomain(X0)))),
inference(forward_demodulation,[],[f520,f40]) ).
fof(f544,plain,
! [X0] : one = addition(antidomain(X0),one),
inference(superposition,[],[f241,f73]) ).
fof(f559,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f544,f37]) ).
fof(f714,plain,
multiplication(one,antidomain(sK2)) = addition(zero,multiplication(antidomain(multiplication(sK0,antidomain(sK1))),antidomain(sK2))),
inference(superposition,[],[f88,f463]) ).
fof(f761,plain,
multiplication(one,antidomain(sK2)) = multiplication(antidomain(multiplication(sK0,antidomain(sK1))),antidomain(sK2)),
inference(forward_demodulation,[],[f714,f145]) ).
fof(f780,plain,
antidomain(sK2) = multiplication(antidomain(multiplication(sK0,antidomain(sK1))),antidomain(sK2)),
inference(forward_demodulation,[],[f761,f40]) ).
fof(f1008,plain,
! [X0,X1] : multiplication(zero,X1) = multiplication(antidomain(X0),multiplication(X0,X1)),
inference(superposition,[],[f48,f53]) ).
fof(f1060,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(X0,X1)),
inference(forward_demodulation,[],[f1008,f55]) ).
fof(f1281,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,[],[f245,f33]) ).
fof(f1501,plain,
! [X2,X0,X1] : addition(multiplication(X0,coantidomain(coantidomain(X1))),multiplication(addition(X0,X2),coantidomain(X1))) = addition(multiplication(X0,one),multiplication(X2,coantidomain(X1))),
inference(superposition,[],[f1281,f38]) ).
fof(f1580,plain,
! [X2,X0,X1] : addition(multiplication(antidomain(antidomain(X0)),addition(X1,X2)),multiplication(antidomain(X0),X2)) = addition(multiplication(antidomain(antidomain(X0)),X1),multiplication(one,X2)),
inference(superposition,[],[f1281,f39]) ).
fof(f1639,plain,
! [X2,X0,X1] : addition(multiplication(antidomain(antidomain(X0)),X1),X2) = addition(multiplication(antidomain(antidomain(X0)),addition(X1,X2)),multiplication(antidomain(X0),X2)),
inference(forward_demodulation,[],[f1580,f40]) ).
fof(f1705,plain,
! [X2,X0,X1] : addition(multiplication(X0,coantidomain(coantidomain(X1))),multiplication(addition(X0,X2),coantidomain(X1))) = addition(X0,multiplication(X2,coantidomain(X1))),
inference(forward_demodulation,[],[f1501,f41]) ).
fof(f1731,plain,
! [X2,X0,X1] : addition(multiplication(antidomain(antidomain(X0)),X1),X2) = addition(multiplication(antidomain(X0),X2),multiplication(antidomain(antidomain(X0)),addition(X1,X2))),
inference(forward_demodulation,[],[f1639,f37]) ).
fof(f1822,plain,
! [X0,X1] : addition(X0,multiplication(X0,coantidomain(X1))) = addition(multiplication(X0,coantidomain(coantidomain(X1))),multiplication(X0,coantidomain(X1))),
inference(superposition,[],[f1705,f35]) ).
fof(f1896,plain,
! [X0,X1] : addition(X0,multiplication(X0,coantidomain(X1))) = addition(multiplication(X0,coantidomain(X1)),multiplication(X0,coantidomain(coantidomain(X1)))),
inference(forward_demodulation,[],[f1822,f37]) ).
fof(f1928,plain,
! [X0,X1] : addition(X0,multiplication(X0,coantidomain(X1))) = multiplication(X0,addition(coantidomain(X1),coantidomain(coantidomain(X1)))),
inference(forward_demodulation,[],[f1896,f34]) ).
fof(f1948,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[],[f1928,f74]) ).
fof(f1962,plain,
! [X0,X1] : multiplication(X0,one) = multiplication(X0,addition(one,coantidomain(X1))),
inference(forward_demodulation,[],[f1948,f146]) ).
fof(f1972,plain,
! [X0,X1] : multiplication(X0,addition(one,coantidomain(X1))) = X0,
inference(forward_demodulation,[],[f1962,f41]) ).
fof(f2273,plain,
! [X2,X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(multiplication(X0,X1))),X2)) = addition(coantidomain(multiplication(X0,multiplication(X1,X2))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(X0,X1))),X2))),
inference(superposition,[],[f50,f48]) ).
fof(f2300,plain,
! [X0,X1] : multiplication(multiplication(coantidomain(coantidomain(X0)),X1),coantidomain(multiplication(X0,X1))) = multiplication(multiplication(coantidomain(coantidomain(X0)),X1),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(superposition,[],[f174,f50]) ).
fof(f2316,plain,
! [X0,X1] : zero = multiplication(multiplication(coantidomain(coantidomain(X0)),X1),coantidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f2300,f51]) ).
fof(f2336,plain,
! [X0,X1] : zero = multiplication(coantidomain(coantidomain(X0)),multiplication(X1,coantidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f2316,f48]) ).
fof(f2355,plain,
addition(antidomain(multiplication(sK0,antidomain(sK1))),antidomain(sK2)) = multiplication(antidomain(multiplication(sK0,antidomain(sK1))),addition(one,antidomain(sK2))),
inference(superposition,[],[f146,f780]) ).
fof(f2366,plain,
addition(antidomain(multiplication(sK0,antidomain(sK1))),antidomain(sK2)) = multiplication(antidomain(multiplication(sK0,antidomain(sK1))),one),
inference(forward_demodulation,[],[f2355,f559]) ).
fof(f2372,plain,
antidomain(multiplication(sK0,antidomain(sK1))) = addition(antidomain(multiplication(sK0,antidomain(sK1))),antidomain(sK2)),
inference(forward_demodulation,[],[f2366,f41]) ).
fof(f2376,plain,
antidomain(multiplication(sK0,antidomain(sK1))) = addition(antidomain(sK2),antidomain(multiplication(sK0,antidomain(sK1)))),
inference(forward_demodulation,[],[f2372,f37]) ).
fof(f2378,plain,
multiplication(antidomain(multiplication(sK0,antidomain(sK1))),multiplication(sK0,antidomain(sK1))) = multiplication(antidomain(sK2),multiplication(sK0,antidomain(sK1))),
inference(superposition,[],[f99,f2376]) ).
fof(f2396,plain,
zero = multiplication(antidomain(sK2),multiplication(sK0,antidomain(sK1))),
inference(forward_demodulation,[],[f2378,f53]) ).
fof(f2534,plain,
! [X0,X1] : addition(multiplication(antidomain(antidomain(X0)),one),antidomain(X1)) = addition(multiplication(antidomain(X0),antidomain(X1)),multiplication(antidomain(antidomain(X0)),one)),
inference(superposition,[],[f1731,f559]) ).
fof(f2539,plain,
! [X0,X1] : addition(multiplication(antidomain(antidomain(X0)),antidomain(X1)),antidomain(antidomain(X1))) = addition(multiplication(antidomain(X0),antidomain(antidomain(X1))),multiplication(antidomain(antidomain(X0)),one)),
inference(superposition,[],[f1731,f73]) ).
fof(f2573,plain,
! [X0,X1] : addition(multiplication(antidomain(antidomain(X0)),antidomain(X1)),antidomain(antidomain(X1))) = addition(multiplication(antidomain(antidomain(X0)),one),multiplication(antidomain(X0),antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f2539,f37]) ).
fof(f2578,plain,
! [X0,X1] : addition(antidomain(antidomain(X0)),antidomain(X1)) = addition(multiplication(antidomain(X0),antidomain(X1)),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f2534,f41]) ).
fof(f2622,plain,
! [X0,X1] : addition(multiplication(antidomain(antidomain(X0)),antidomain(X1)),antidomain(antidomain(X1))) = addition(antidomain(antidomain(X0)),multiplication(antidomain(X0),antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f2573,f41]) ).
fof(f2627,plain,
! [X0,X1] : addition(antidomain(antidomain(X0)),multiplication(antidomain(X0),antidomain(X1))) = addition(antidomain(antidomain(X0)),antidomain(X1)),
inference(forward_demodulation,[],[f2578,f37]) ).
fof(f2651,plain,
! [X0,X1] : addition(antidomain(antidomain(X0)),multiplication(antidomain(X0),antidomain(antidomain(X1)))) = addition(antidomain(antidomain(X1)),multiplication(antidomain(antidomain(X0)),antidomain(X1))),
inference(forward_demodulation,[],[f2622,f37]) ).
fof(f2668,plain,
! [X0,X1] : addition(antidomain(antidomain(X1)),multiplication(antidomain(antidomain(X0)),antidomain(X1))) = addition(antidomain(antidomain(X0)),antidomain(antidomain(X1))),
inference(forward_demodulation,[],[f2651,f2627]) ).
fof(f2842,plain,
! [X0] : multiplication(coantidomain(X0),coantidomain(coantidomain(coantidomain(X0)))) = multiplication(one,coantidomain(coantidomain(coantidomain(X0)))),
inference(superposition,[],[f100,f74]) ).
fof(f2845,plain,
! [X0,X1] : multiplication(antidomain(multiplication(coantidomain(coantidomain(X0)),X1)),multiplication(coantidomain(X0),X1)) = multiplication(antidomain(multiplication(coantidomain(coantidomain(X0)),X1)),multiplication(one,X1)),
inference(superposition,[],[f183,f74]) ).
fof(f2847,plain,
! [X0] : one = addition(coantidomain(X0),one),
inference(superposition,[],[f241,f74]) ).
fof(f2858,plain,
! [X0] : one = addition(one,coantidomain(X0)),
inference(forward_demodulation,[],[f2847,f37]) ).
fof(f2860,plain,
! [X0,X1] : multiplication(antidomain(multiplication(coantidomain(coantidomain(X0)),X1)),multiplication(coantidomain(X0),X1)) = multiplication(antidomain(multiplication(coantidomain(coantidomain(X0)),X1)),X1),
inference(forward_demodulation,[],[f2845,f40]) ).
fof(f2863,plain,
! [X0] : coantidomain(coantidomain(coantidomain(X0))) = multiplication(coantidomain(X0),coantidomain(coantidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f2842,f40]) ).
fof(f2871,plain,
! [X0] : coantidomain(X0) = coantidomain(coantidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f2863,f364]) ).
fof(f3732,plain,
! [X0] : multiplication(antidomain(X0),addition(one,coantidomain(antidomain(antidomain(X0))))) = addition(antidomain(X0),coantidomain(antidomain(antidomain(X0)))),
inference(superposition,[],[f146,f527]) ).
fof(f3743,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),coantidomain(antidomain(antidomain(X0)))),
inference(forward_demodulation,[],[f3732,f1972]) ).
fof(f3806,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,antidomain(antidomain(X1)))),
inference(superposition,[],[f99,f52]) ).
fof(f3828,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f3806,f53]) ).
fof(f3945,plain,
! [X0,X1] : zero = multiplication(antidomain(zero),multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1))))),
inference(superposition,[],[f3828,f1060]) ).
fof(f4036,plain,
! [X0,X1] : zero = multiplication(one,multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[],[f3945,f79]) ).
fof(f4065,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f4036,f40]) ).
fof(f4277,plain,
! [X0,X1] : multiplication(antidomain(zero),multiplication(antidomain(antidomain(X0)),antidomain(antidomain(multiplication(X0,X1))))) = multiplication(antidomain(zero),antidomain(antidomain(multiplication(X0,X1)))),
inference(superposition,[],[f226,f4065]) ).
fof(f4326,plain,
! [X0,X1] : multiplication(one,multiplication(antidomain(antidomain(X0)),antidomain(antidomain(multiplication(X0,X1))))) = multiplication(one,antidomain(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f4277,f79]) ).
fof(f4360,plain,
! [X0,X1] : antidomain(antidomain(multiplication(X0,X1))) = multiplication(one,multiplication(antidomain(antidomain(X0)),antidomain(antidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[],[f4326,f40]) ).
fof(f4381,plain,
! [X0,X1] : antidomain(antidomain(multiplication(X0,X1))) = multiplication(antidomain(antidomain(X0)),antidomain(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f4360,f40]) ).
fof(f5052,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),multiplication(X0,coantidomain(zero))),
inference(superposition,[],[f2336,f53]) ).
fof(f5153,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),multiplication(X0,one)),
inference(forward_demodulation,[],[f5052,f84]) ).
fof(f5190,plain,
! [X0] : zero = multiplication(coantidomain(coantidomain(antidomain(X0))),X0),
inference(forward_demodulation,[],[f5153,f41]) ).
fof(f5541,plain,
! [X0] : multiplication(antidomain(zero),X0) = multiplication(antidomain(zero),multiplication(coantidomain(coantidomain(coantidomain(antidomain(X0)))),X0)),
inference(superposition,[],[f225,f5190]) ).
fof(f5624,plain,
! [X0] : multiplication(antidomain(zero),X0) = multiplication(antidomain(zero),multiplication(coantidomain(antidomain(X0)),X0)),
inference(forward_demodulation,[],[f5541,f2871]) ).
fof(f5641,plain,
! [X0] : multiplication(one,X0) = multiplication(one,multiplication(coantidomain(antidomain(X0)),X0)),
inference(forward_demodulation,[],[f5624,f79]) ).
fof(f5649,plain,
! [X0] : multiplication(one,X0) = multiplication(coantidomain(antidomain(X0)),X0),
inference(forward_demodulation,[],[f5641,f40]) ).
fof(f5652,plain,
! [X0] : multiplication(coantidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f5649,f40]) ).
fof(f5655,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(coantidomain(antidomain(X0)),antidomain(antidomain(X0))),
inference(superposition,[],[f5652,f407]) ).
fof(f6025,plain,
! [X0,X1] : addition(antidomain(antidomain(X0)),antidomain(antidomain(antidomain(multiplication(X0,X1))))) = addition(antidomain(antidomain(antidomain(multiplication(X0,X1)))),antidomain(antidomain(multiplication(X0,X1)))),
inference(superposition,[],[f2668,f4381]) ).
fof(f6076,plain,
! [X0,X1] : addition(antidomain(antidomain(X0)),antidomain(antidomain(antidomain(multiplication(X0,X1))))) = addition(antidomain(antidomain(multiplication(X0,X1))),antidomain(antidomain(antidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[],[f6025,f37]) ).
fof(f6114,plain,
! [X0,X1] : one = addition(antidomain(antidomain(X0)),antidomain(antidomain(antidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[],[f6076,f73]) ).
fof(f6140,plain,
! [X0,X1] : one = addition(antidomain(antidomain(X0)),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f6114,f407]) ).
fof(f9639,plain,
! [X0] : antidomain(antidomain(X0)) = addition(antidomain(antidomain(X0)),coantidomain(antidomain(X0))),
inference(superposition,[],[f3743,f407]) ).
fof(f9755,plain,
! [X0] : addition(coantidomain(antidomain(X0)),antidomain(antidomain(X0))) = multiplication(coantidomain(antidomain(X0)),addition(one,antidomain(antidomain(X0)))),
inference(superposition,[],[f146,f5655]) ).
fof(f9785,plain,
! [X0] : multiplication(coantidomain(antidomain(X0)),one) = addition(coantidomain(antidomain(X0)),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f9755,f559]) ).
fof(f9804,plain,
! [X0] : multiplication(coantidomain(antidomain(X0)),one) = addition(antidomain(antidomain(X0)),coantidomain(antidomain(X0))),
inference(forward_demodulation,[],[f9785,f37]) ).
fof(f9813,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(coantidomain(antidomain(X0)),one),
inference(forward_demodulation,[],[f9804,f9639]) ).
fof(f9815,plain,
! [X0] : antidomain(antidomain(X0)) = coantidomain(antidomain(X0)),
inference(forward_demodulation,[],[f9813,f41]) ).
fof(f9845,plain,
one != addition(antidomain(antidomain(sK1)),antidomain(coantidomain(coantidomain(multiplication(coantidomain(antidomain(antidomain(sK2))),sK0))))),
inference(superposition,[],[f443,f9815]) ).
fof(f9907,plain,
one != addition(antidomain(antidomain(sK1)),antidomain(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(sK2))),sK0))))),
inference(forward_demodulation,[],[f9845,f9815]) ).
fof(f9925,plain,
one != addition(antidomain(antidomain(sK1)),antidomain(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))))),
inference(forward_demodulation,[],[f9907,f407]) ).
fof(f14990,plain,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))),antidomain(sK1))) = addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))),antidomain(sK1)))),
inference(superposition,[],[f2273,f2396]) ).
fof(f15248,plain,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))),antidomain(sK1))) = addition(one,coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))),antidomain(sK1)))),
inference(forward_demodulation,[],[f14990,f84]) ).
fof(f15429,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))),antidomain(sK1))),
inference(forward_demodulation,[],[f15248,f2858]) ).
fof(f15864,plain,
zero = multiplication(multiplication(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))),antidomain(sK1)),one),
inference(superposition,[],[f51,f15429]) ).
fof(f15920,plain,
zero = multiplication(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))),antidomain(sK1)),
inference(forward_demodulation,[],[f15864,f41]) ).
fof(f15998,plain,
multiplication(antidomain(zero),antidomain(sK1)) = multiplication(antidomain(zero),multiplication(coantidomain(multiplication(antidomain(sK2),sK0)),antidomain(sK1))),
inference(superposition,[],[f2860,f15920]) ).
fof(f16073,plain,
multiplication(one,antidomain(sK1)) = multiplication(one,multiplication(coantidomain(multiplication(antidomain(sK2),sK0)),antidomain(sK1))),
inference(forward_demodulation,[],[f15998,f79]) ).
fof(f16102,plain,
multiplication(one,antidomain(sK1)) = multiplication(coantidomain(multiplication(antidomain(sK2),sK0)),antidomain(sK1)),
inference(forward_demodulation,[],[f16073,f40]) ).
fof(f16121,plain,
antidomain(sK1) = multiplication(coantidomain(multiplication(antidomain(sK2),sK0)),antidomain(sK1)),
inference(forward_demodulation,[],[f16102,f40]) ).
fof(f16260,plain,
multiplication(coantidomain(multiplication(antidomain(sK2),sK0)),addition(one,antidomain(sK1))) = addition(coantidomain(multiplication(antidomain(sK2),sK0)),antidomain(sK1)),
inference(superposition,[],[f146,f16121]) ).
fof(f16300,plain,
multiplication(coantidomain(multiplication(antidomain(sK2),sK0)),addition(one,antidomain(sK1))) = addition(antidomain(sK1),coantidomain(multiplication(antidomain(sK2),sK0))),
inference(forward_demodulation,[],[f16260,f37]) ).
fof(f16319,plain,
multiplication(coantidomain(multiplication(antidomain(sK2),sK0)),one) = addition(antidomain(sK1),coantidomain(multiplication(antidomain(sK2),sK0))),
inference(forward_demodulation,[],[f16300,f559]) ).
fof(f16329,plain,
coantidomain(multiplication(antidomain(sK2),sK0)) = addition(antidomain(sK1),coantidomain(multiplication(antidomain(sK2),sK0))),
inference(forward_demodulation,[],[f16319,f41]) ).
fof(f16335,plain,
multiplication(coantidomain(multiplication(antidomain(sK2),sK0)),coantidomain(coantidomain(multiplication(antidomain(sK2),sK0)))) = multiplication(antidomain(sK1),coantidomain(coantidomain(multiplication(antidomain(sK2),sK0)))),
inference(superposition,[],[f100,f16329]) ).
fof(f16357,plain,
zero = multiplication(antidomain(sK1),coantidomain(coantidomain(multiplication(antidomain(sK2),sK0)))),
inference(forward_demodulation,[],[f16335,f51]) ).
fof(f16525,plain,
multiplication(antidomain(zero),coantidomain(coantidomain(multiplication(antidomain(sK2),sK0)))) = multiplication(antidomain(zero),multiplication(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))))),
inference(superposition,[],[f226,f16357]) ).
fof(f16592,plain,
multiplication(one,coantidomain(coantidomain(multiplication(antidomain(sK2),sK0)))) = multiplication(one,multiplication(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))))),
inference(forward_demodulation,[],[f16525,f79]) ).
fof(f16617,plain,
multiplication(one,coantidomain(coantidomain(multiplication(antidomain(sK2),sK0)))) = multiplication(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(antidomain(sK2),sK0)))),
inference(forward_demodulation,[],[f16592,f40]) ).
fof(f16634,plain,
coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))) = multiplication(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(antidomain(sK2),sK0)))),
inference(forward_demodulation,[],[f16617,f40]) ).
fof(f16760,plain,
one = addition(antidomain(antidomain(antidomain(antidomain(sK1)))),antidomain(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))))),
inference(superposition,[],[f6140,f16634]) ).
fof(f16761,plain,
one = addition(antidomain(antidomain(sK1)),antidomain(coantidomain(coantidomain(multiplication(antidomain(sK2),sK0))))),
inference(forward_demodulation,[],[f16760,f407]) ).
fof(f16788,plain,
$false,
inference(forward_subsumption_resolution,[],[f16761,f9925]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE103+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n002.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 27 13:13:06 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.53 Running first-order theorem proving
% 0.26/0.53 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
% 22.50/4.40 % (3517712)Detected formulas, will run a generic FOF schedule.
% 22.50/4.40 % (3517719)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=1387687735:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 22.50/4.40 % (3517718)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=1079022949:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 22.50/4.40 % (3517717)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=2447553203:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 22.50/4.40 % (3517721)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=858427316:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 22.50/4.40 % (3517720)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2352366534:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 22.50/4.40 % (3517723)dis-21_1_sil=8000:lcm=predicate:random_seed=255939074: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)
% 22.50/4.40 % (3517722)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=775378576:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 22.50/4.40 % (3517723)Refutation not found, incomplete strategy
% 22.50/4.40 % (3517723)------------------------------
% 22.50/4.40 % (3517723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 22.50/4.40 % (3517723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.50/4.40 % (3517723)CaDiCaL version: 2.1.3
% 22.50/4.40 % (3517723)Termination reason: Refutation not found, incomplete strategy
% 22.50/4.40 % (3517723)Time elapsed: 0.003 s
% 22.50/4.40 % (3517723)Peak memory usage: 88 MB
% 22.50/4.40 % (3517723)Instructions burned: 1 (million)
% 22.50/4.40 % (3517721)Instruction limit reached!
% 22.50/4.40 % (3517721)------------------------------
% 22.50/4.40 % (3517721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 22.50/4.40 % (3517721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.50/4.40 % (3517721)CaDiCaL version: 2.1.3
% 22.50/4.40 % (3517721)Termination reason: Instruction limit
% 22.50/4.40 % (3517721)Termination phase: Saturation
% 22.50/4.40 % (3517721)Time elapsed: 0.105 s
% 22.50/4.40 % (3517721)Peak memory usage: 89 MB
% 22.50/4.40 % (3517721)Instructions burned: 119 (million)
% 22.50/4.40 % (3517720)Instruction limit reached!
% 22.50/4.40 % (3517720)------------------------------
% 22.50/4.40 % (3517720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 22.50/4.40 % (3517720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.50/4.40 % (3517720)CaDiCaL version: 2.1.3
% 22.50/4.40 % (3517720)Termination reason: Instruction limit
% 22.50/4.40 % (3517720)Termination phase: Saturation
% 22.50/4.40 % (3517720)Time elapsed: 0.121 s
% 22.50/4.40 % (3517720)Peak memory usage: 89 MB
% 22.50/4.40 % (3517720)Instructions burned: 109 (million)
% 22.50/4.40 % (3517722)Instruction limit reached!
% 22.50/4.40 % (3517722)------------------------------
% 22.50/4.40 % (3517722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 22.50/4.40 % (3517722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.50/4.40 % (3517722)CaDiCaL version: 2.1.3
% 22.50/4.40 % (3517722)Termination reason: Instruction limit
% 22.50/4.40 % (3517722)Termination phase: Saturation
% 22.50/4.40 % (3517722)Time elapsed: 0.138 s
% 22.50/4.40 % (3517722)Peak memory usage: 89 MB
% 22.50/4.40 % (3517722)Instructions burned: 139 (million)
% 22.50/4.40 % (3517748)lrs+10_1_sil=8000:sp=occurrence:random_seed=4149332596:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 22.50/4.40 % (3517723)------------------------------
% 22.50/4.40 % (3517723)------------------------------
% 22.50/4.40 % (3517749)lrs+10_1_sil=32000:urr=on:br=off:random_seed=369661851:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 22.50/4.40 % (3517750)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2916674195:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 22.50/4.40 % (3517749)Instruction limit reached!
% 22.50/4.40 % (3517749)------------------------------
% 22.50/4.40 % (3517749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517749)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517749)Termination reason: Instruction limit
% 23.32/5.08 % (3517749)Termination phase: Saturation
% 23.32/5.08 % (3517749)Time elapsed: 0.145 s
% 23.32/5.08 % (3517749)Peak memory usage: 90 MB
% 23.32/5.08 % (3517749)Instructions burned: 157 (million)
% 23.32/5.08 % (3517748)Instruction limit reached!
% 23.32/5.08 % (3517748)------------------------------
% 23.32/5.08 % (3517748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517748)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517748)Termination reason: Instruction limit
% 23.32/5.08 % (3517748)Termination phase: Saturation
% 23.32/5.08 % (3517748)Time elapsed: 0.268 s
% 23.32/5.08 % (3517748)Peak memory usage: 91 MB
% 23.32/5.08 % (3517748)Instructions burned: 288 (million)
% 23.32/5.08 % (3517753)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=1888428918:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 23.32/5.08 % (3517750)Instruction limit reached!
% 23.32/5.08 % (3517750)------------------------------
% 23.32/5.08 % (3517750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517750)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517750)Termination reason: Instruction limit
% 23.32/5.08 % (3517750)Termination phase: Saturation
% 23.32/5.08 % (3517750)Time elapsed: 0.326 s
% 23.32/5.08 % (3517750)Peak memory usage: 92 MB
% 23.32/5.08 % (3517750)Instructions burned: 325 (million)
% 23.32/5.08 % (3517753)Instruction limit reached!
% 23.32/5.08 % (3517753)------------------------------
% 23.32/5.08 % (3517753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517753)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517753)Termination reason: Instruction limit
% 23.32/5.08 % (3517753)Termination phase: Saturation
% 23.32/5.08 % (3517753)Time elapsed: 0.132 s
% 23.32/5.08 % (3517753)Peak memory usage: 91 MB
% 23.32/5.08 % (3517753)Instructions burned: 249 (million)
% 23.32/5.08 % (3517755)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1147027575:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 23.32/5.08 % (3517757)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1218169768:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 23.32/5.08 % (3517758)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3220654656:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 23.32/5.08 % (3517759)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=906901716:i=127:av=off:fsr=off:sup=off_2988 on theBenchmark for (2988ds/127Mi)
% 23.32/5.08 % (3517758)Instruction limit reached!
% 23.32/5.08 % (3517758)------------------------------
% 23.32/5.08 % (3517758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517758)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517758)Termination reason: Instruction limit
% 23.32/5.08 % (3517758)Termination phase: Saturation
% 23.32/5.08 % (3517758)Time elapsed: 0.060 s
% 23.32/5.08 % (3517758)Peak memory usage: 90 MB
% 23.32/5.08 % (3517758)Instructions burned: 114 (million)
% 23.32/5.08 % (3517759)Refutation not found, incomplete strategy
% 23.32/5.08 % (3517759)------------------------------
% 23.32/5.08 % (3517759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517759)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517759)Termination reason: Refutation not found, incomplete strategy
% 23.32/5.08 % (3517759)Time elapsed: 0.002 s
% 23.32/5.08 % (3517759)Peak memory usage: 88 MB
% 23.32/5.08 % (3517759)Instructions burned: 1 (million)
% 23.32/5.08 % (3517755)Instruction limit reached!
% 23.32/5.08 % (3517755)------------------------------
% 23.32/5.08 % (3517755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517755)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517755)Termination reason: Instruction limit
% 23.32/5.08 % (3517755)Termination phase: Saturation
% 23.32/5.08 % (3517755)Time elapsed: 0.267 s
% 23.32/5.08 % (3517755)Peak memory usage: 90 MB
% 23.32/5.08 % (3517755)Instructions burned: 294 (million)
% 23.32/5.08 % (3517764)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=135660283:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2986 on theBenchmark for (2986ds/114Mi)
% 23.32/5.08 % (3517764)Instruction limit reached!
% 23.32/5.08 % (3517764)------------------------------
% 23.32/5.08 % (3517764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517764)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517764)Termination reason: Instruction limit
% 23.32/5.08 % (3517764)Termination phase: Saturation
% 23.32/5.08 % (3517764)Time elapsed: 0.053 s
% 23.32/5.08 % (3517764)Peak memory usage: 88 MB
% 23.32/5.08 % (3517764)Instructions burned: 115 (million)
% 23.32/5.08 % (3517765)lrs+10_1_sil=8000:sp=occurrence:random_seed=2160437386:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2985 on theBenchmark for (2985ds/907Mi)
% 23.32/5.08 % (3517759)------------------------------
% 23.32/5.08 % (3517759)------------------------------
% 23.32/5.08 % (3517767)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1878537694:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 23.32/5.08 % (3517769)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2958836193:i=5202:ss=axioms:sgt=16_2982 on theBenchmark for (2982ds/5202Mi)
% 23.32/5.08 % (3517767)Instruction limit reached!
% 23.32/5.08 % (3517767)------------------------------
% 23.32/5.08 % (3517767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517767)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517767)Termination reason: Instruction limit
% 23.32/5.08 % (3517767)Termination phase: Saturation
% 23.32/5.08 % (3517767)Time elapsed: 0.199 s
% 23.32/5.08 % (3517767)Peak memory usage: 91 MB
% 23.32/5.08 % (3517767)Instructions burned: 437 (million)
% 23.32/5.08 % (3517772)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1481411849:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2978 on theBenchmark for (2978ds/134Mi)
% 23.32/5.08 % (3517772)Refutation not found, incomplete strategy
% 23.32/5.08 % (3517772)------------------------------
% 23.32/5.08 % (3517772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517772)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517772)Termination reason: Refutation not found, incomplete strategy
% 23.32/5.08 % (3517772)Time elapsed: 0.004 s
% 23.32/5.08 % (3517772)Peak memory usage: 89 MB
% 23.32/5.08 % (3517772)Instructions burned: 1 (million)
% 23.32/5.08 % (3517765)Instruction limit reached!
% 23.32/5.08 % (3517765)------------------------------
% 23.32/5.08 % (3517765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517765)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517765)Termination reason: Instruction limit
% 23.32/5.08 % (3517765)Termination phase: Saturation
% 23.32/5.08 % (3517765)Time elapsed: 0.851 s
% 23.32/5.08 % (3517765)Peak memory usage: 97 MB
% 23.32/5.08 % (3517765)Instructions burned: 907 (million)
% 23.32/5.08 % (3517772)------------------------------
% 23.32/5.08 % (3517772)------------------------------
% 23.32/5.08 % (3517774)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1046764454:st=8:i=592:sd=3:ep=RST:ss=axioms_2973 on theBenchmark for (2973ds/592Mi)
% 23.32/5.08 % (3517776)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3178455258:st=3:i=13193:sd=3:ss=axioms_2971 on theBenchmark for (2971ds/13193Mi)
% 23.32/5.08 % (3517774)Instruction limit reached!
% 23.32/5.08 % (3517774)------------------------------
% 23.32/5.08 % (3517774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517774)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517774)Termination reason: Instruction limit
% 23.32/5.08 % (3517774)Termination phase: Saturation
% 23.32/5.08 % (3517774)Time elapsed: 0.310 s
% 23.32/5.08 % (3517774)Peak memory usage: 96 MB
% 23.32/5.08 % (3517774)Instructions burned: 593 (million)
% 23.32/5.08 % (3517718)First to succeed.
% 23.32/5.08 % (3517718)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3517712"
% 23.32/5.08 % (3517778)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=4101874171:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2968 on theBenchmark for (2968ds/125Mi)
% 23.32/5.08 % (3517778)Instruction limit reached!
% 23.32/5.08 % (3517778)------------------------------
% 23.32/5.08 % (3517778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517778)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517778)Termination reason: Instruction limit
% 23.32/5.08 % (3517778)Termination phase: Saturation
% 23.32/5.08 % (3517778)Time elapsed: 0.124 s
% 23.32/5.08 % (3517778)Peak memory usage: 90 MB
% 23.32/5.08 % (3517778)Instructions burned: 125 (million)
% 23.32/5.08 % (3517757)Instruction limit reached!
% 23.32/5.08 % (3517757)------------------------------
% 23.32/5.08 % (3517757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.32/5.08 % (3517757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.32/5.08 % (3517757)CaDiCaL version: 2.1.3
% 23.32/5.08 % (3517757)Termination reason: Instruction limit
% 23.32/5.08 % (3517757)Termination phase: Saturation
% 23.32/5.08 % (3517757)Time elapsed: 2.464 s
% 23.32/5.08 % (3517757)Peak memory usage: 143 MB
% 23.32/5.08 % (3517757)Instructions burned: 2350 (million)
% 23.32/5.08 % (3517718)Refutation found. Thanks to Tanya!
% 23.32/5.08 % SZS status Theorem for theBenchmark
% 23.32/5.08 % SZS output start Proof for theBenchmark
% See solution above
% 27.88/5.46 % (3517718)------------------------------
% 27.88/5.46 % (3517718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 27.88/5.46 % (3517718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.88/5.46 % (3517718)CaDiCaL version: 2.1.3
% 27.88/5.46 % (3517718)Termination reason: Refutation
% 27.88/5.46 % (3517718)Time elapsed: 3.094 s
% 27.88/5.46 % (3517718)Peak memory usage: 148 MB
% 27.88/5.46 % (3517718)Instructions burned: 2886 (million)
% 27.88/5.46 % (3517718)------------------------------
% 27.88/5.46 % (3517718)------------------------------
% 27.88/5.46 % (3517712)Success in time 3.837 s
% 27.88/5.46 % Vampire exiting
%------------------------------------------------------------------------------