%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE102+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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:40:20 AM UTC 2026
% Result : Theorem 29.35s 5.72s
% Output : Refutation 34.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 80
% Number of leaves : 21
% Syntax : Number of formulae : 328 ( 324 unt; 0 def)
% Number of atoms : 332 ( 331 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 541 ( 538 !; 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(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(f27,conjecture,
! [X0,X1,X2] :
( multiplication(domain(X1),backward_diamond(X0,domain(X2))) = zero
=> multiplication(forward_diamond(X0,domain(X1)),domain(X2)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( multiplication(domain(X1),backward_diamond(X0,domain(X2))) = zero
=> multiplication(forward_diamond(X0,domain(X1)),domain(X2)) = zero ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( zero != multiplication(forward_diamond(X0,domain(X1)),domain(X2))
& multiplication(domain(X1),backward_diamond(X0,domain(X2))) = zero ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( zero != multiplication(forward_diamond(sK0,domain(sK1)),domain(sK2))
& zero = multiplication(domain(sK1),backward_diamond(sK0,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,
zero = multiplication(domain(sK1),backward_diamond(sK0,domain(sK2))),
inference(cnf_transformation,[],[f30]) ).
fof(f32,plain,
zero != multiplication(forward_diamond(sK0,domain(sK1)),domain(sK2)),
inference(cnf_transformation,[],[f30]) ).
fof(f33,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f35,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f37,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f45,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f47,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f48,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(f49,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f50,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(f51,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f52,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f53,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f54,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f55,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f56,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f57,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f45,f46,f46]) ).
fof(f62,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f39,f42,f42]) ).
fof(f64,plain,
zero != multiplication(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f32,f62,f42,f42]) ).
fof(f65,plain,
zero = multiplication(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0)))),
inference(definition_unfolding,[],[f31,f42,f59,f42]) ).
fof(f66,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f49,f55]) ).
fof(f67,plain,
! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f47,f55]) ).
fof(f69,plain,
zero = coantidomain(one),
inference(superposition,[],[f33,f56]) ).
fof(f70,plain,
! [X0] : multiplication(antidomain(antidomain(sK1)),addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0))),X0)) = addition(zero,multiplication(antidomain(antidomain(sK1)),X0)),
inference(superposition,[],[f52,f65]) ).
fof(f71,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[],[f52,f34]) ).
fof(f72,plain,
! [X0,X1] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(zero,multiplication(X0,X1)),
inference(superposition,[],[f52,f33]) ).
fof(f74,plain,
! [X0] : multiplication(antidomain(antidomain(sK1)),addition(X0,coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0))))) = addition(multiplication(antidomain(antidomain(sK1)),X0),zero),
inference(superposition,[],[f52,f65]) ).
fof(f75,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f52,f34]) ).
fof(f84,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(X0),X1)) = multiplication(antidomain(X0),addition(X1,X0)),
inference(forward_demodulation,[],[f75,f55]) ).
fof(f85,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(sK1)),X0)) = multiplication(antidomain(antidomain(sK1)),addition(X0,coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0))))),
inference(forward_demodulation,[],[f74,f55]) ).
fof(f90,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f55,f37]) ).
fof(f91,plain,
! [X0,X1] : multiplication(X0,multiplication(coantidomain(X0),X1)) = multiplication(zero,X1),
inference(superposition,[],[f38,f33]) ).
fof(f95,plain,
! [X0,X1] : multiplication(zero,X1) = multiplication(antidomain(X0),multiplication(X0,X1)),
inference(superposition,[],[f38,f34]) ).
fof(f102,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(X0,X1)),
inference(forward_demodulation,[],[f95,f35]) ).
fof(f105,plain,
! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X0),X1)),
inference(forward_demodulation,[],[f91,f35]) ).
fof(f113,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f51,f56]) ).
fof(f115,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[],[f51,f34]) ).
fof(f116,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(multiplication(X0,coantidomain(X1)),zero),
inference(superposition,[],[f51,f33]) ).
fof(f120,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(addition(X0,antidomain(X1)),X1),
inference(superposition,[],[f51,f34]) ).
fof(f129,plain,
! [X0,X1] : addition(zero,multiplication(X0,X1)) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[],[f120,f55]) ).
fof(f132,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = addition(zero,multiplication(X0,coantidomain(X1))),
inference(forward_demodulation,[],[f116,f55]) ).
fof(f133,plain,
! [X0,X1] : multiplication(X1,X0) = multiplication(addition(antidomain(X0),X1),X0),
inference(forward_demodulation,[],[f115,f90]) ).
fof(f136,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[],[f129,f90]) ).
fof(f138,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X1)) = multiplication(X0,coantidomain(X1)),
inference(forward_demodulation,[],[f132,f90]) ).
fof(f188,plain,
! [X0,X1] : multiplication(coantidomain(multiplication(X0,X1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))) = multiplication(coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))),
inference(superposition,[],[f138,f48]) ).
fof(f189,plain,
! [X0,X1] : zero = multiplication(coantidomain(multiplication(X0,X1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))),
inference(forward_demodulation,[],[f188,f33]) ).
fof(f200,plain,
! [X2,X0,X1] : addition(zero,multiplication(antidomain(multiplication(X0,X2)),multiplication(X0,X1))) = multiplication(antidomain(multiplication(X0,X2)),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f84,f52]) ).
fof(f201,plain,
! [X2,X0,X1] : addition(zero,multiplication(antidomain(multiplication(X1,X2)),multiplication(X0,X2))) = multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f84,f51]) ).
fof(f202,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),one),
inference(superposition,[],[f84,f66]) ).
fof(f203,plain,
! [X0] : addition(zero,multiplication(antidomain(coantidomain(coantidomain(X0))),coantidomain(X0))) = multiplication(antidomain(coantidomain(coantidomain(X0))),one),
inference(superposition,[],[f84,f67]) ).
fof(f205,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)),
inference(superposition,[],[f90,f84]) ).
fof(f221,plain,
! [X0] : antidomain(coantidomain(coantidomain(X0))) = addition(zero,multiplication(antidomain(coantidomain(coantidomain(X0))),coantidomain(X0))),
inference(forward_demodulation,[],[f203,f57]) ).
fof(f222,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = addition(zero,multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0))),
inference(forward_demodulation,[],[f202,f57]) ).
fof(f223,plain,
! [X2,X0,X1] : multiplication(antidomain(multiplication(X1,X2)),multiplication(X0,X2)) = multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[],[f201,f90]) ).
fof(f224,plain,
! [X2,X0,X1] : multiplication(antidomain(multiplication(X0,X2)),multiplication(X0,X1)) = multiplication(antidomain(multiplication(X0,X2)),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[],[f200,f90]) ).
fof(f237,plain,
! [X0] : antidomain(coantidomain(coantidomain(X0))) = multiplication(antidomain(coantidomain(coantidomain(X0))),coantidomain(X0)),
inference(forward_demodulation,[],[f221,f90]) ).
fof(f238,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)),
inference(forward_demodulation,[],[f222,f90]) ).
fof(f264,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),multiplication(antidomain(X0),X1)) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),multiplication(one,X1)),
inference(superposition,[],[f223,f66]) ).
fof(f280,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),multiplication(antidomain(X0),X1)) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),X1),
inference(forward_demodulation,[],[f264,f56]) ).
fof(f314,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,antidomain(X1))) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,one)),
inference(superposition,[],[f224,f66]) ).
fof(f338,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,antidomain(X1))) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),X0),
inference(forward_demodulation,[],[f314,f57]) ).
fof(f399,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f52,f57]) ).
fof(f405,plain,
zero = antidomain(one),
inference(superposition,[],[f34,f57]) ).
fof(f418,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(superposition,[],[f133,f66]) ).
fof(f446,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f418,f56]) ).
fof(f461,plain,
one = antidomain(antidomain(one)),
inference(superposition,[],[f57,f446]) ).
fof(f462,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f461,f405]) ).
fof(f482,plain,
! [X0] : multiplication(antidomain(X0),antidomain(X0)) = multiplication(one,antidomain(X0)),
inference(superposition,[],[f136,f66]) ).
fof(f504,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(X0),antidomain(X0)),
inference(forward_demodulation,[],[f482,f56]) ).
fof(f517,plain,
! [X0] : antidomain(X0) = antidomain(antidomain(antidomain(X0))),
inference(superposition,[],[f446,f238]) ).
fof(f522,plain,
! [X0,X1] : multiplication(antidomain(antidomain(antidomain(X0))),addition(antidomain(X0),X1)) = addition(antidomain(antidomain(antidomain(X0))),multiplication(antidomain(antidomain(antidomain(X0))),X1)),
inference(superposition,[],[f52,f238]) ).
fof(f528,plain,
! [X0,X1] : multiplication(antidomain(antidomain(antidomain(X0))),addition(antidomain(X0),X1)) = multiplication(antidomain(antidomain(antidomain(X0))),addition(one,X1)),
inference(forward_demodulation,[],[f522,f399]) ).
fof(f533,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(antidomain(X0),X1)) = multiplication(antidomain(X0),addition(one,X1)),
inference(forward_demodulation,[],[f528,f517]) ).
fof(f541,plain,
zero != multiplication(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(sK1))))),antidomain(antidomain(sK2))),
inference(superposition,[],[f64,f517]) ).
fof(f556,plain,
! [X0] : multiplication(X0,one) = addition(zero,multiplication(X0,coantidomain(coantidomain(X0)))),
inference(superposition,[],[f72,f67]) ).
fof(f603,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,coantidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f556,f90]) ).
fof(f619,plain,
! [X0] : multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(forward_demodulation,[],[f603,f57]) ).
fof(f642,plain,
one = coantidomain(coantidomain(one)),
inference(superposition,[],[f56,f619]) ).
fof(f647,plain,
one = coantidomain(zero),
inference(forward_demodulation,[],[f642,f69]) ).
fof(f672,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f54,f53]) ).
fof(f676,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f54,f52]) ).
fof(f756,plain,
! [X0] : addition(zero,multiplication(antidomain(coantidomain(X0)),coantidomain(coantidomain(X0)))) = multiplication(antidomain(coantidomain(X0)),one),
inference(superposition,[],[f71,f67]) ).
fof(f818,plain,
! [X0] : antidomain(coantidomain(X0)) = addition(zero,multiplication(antidomain(coantidomain(X0)),coantidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f756,f57]) ).
fof(f844,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(antidomain(coantidomain(X0)),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f818,f90]) ).
fof(f1070,plain,
! [X0] : one = addition(antidomain(X0),one),
inference(superposition,[],[f672,f66]) ).
fof(f1071,plain,
! [X0] : one = addition(coantidomain(X0),one),
inference(superposition,[],[f672,f67]) ).
fof(f1076,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),addition(X0,X1)) = addition(zero,multiplication(antidomain(addition(X0,X1)),X0)),
inference(superposition,[],[f84,f672]) ).
fof(f1086,plain,
! [X0,X1] : multiplication(antidomain(addition(X0,X1)),X0) = multiplication(antidomain(addition(X0,X1)),addition(X0,X1)),
inference(forward_demodulation,[],[f1076,f90]) ).
fof(f1089,plain,
! [X0] : one = addition(one,coantidomain(X0)),
inference(forward_demodulation,[],[f1071,f55]) ).
fof(f1090,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f1070,f55]) ).
fof(f1095,plain,
! [X0,X1] : zero = multiplication(antidomain(addition(X0,X1)),X0),
inference(forward_demodulation,[],[f1086,f34]) ).
fof(f1233,plain,
! [X0] : antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))) = addition(antidomain(zero),antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0)))))),
inference(superposition,[],[f50,f33]) ).
fof(f1262,plain,
! [X2,X0,X1] : antidomain(multiplication(X0,multiplication(X1,antidomain(antidomain(X2))))) = addition(antidomain(multiplication(multiplication(X0,X1),X2)),antidomain(multiplication(X0,multiplication(X1,antidomain(antidomain(X2)))))),
inference(superposition,[],[f50,f38]) ).
fof(f1269,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,[],[f136,f50]) ).
fof(f1282,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f1269,f34]) ).
fof(f1289,plain,
! [X2,X0,X1] : antidomain(multiplication(X0,multiplication(X1,antidomain(antidomain(X2))))) = addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,antidomain(antidomain(X2)))))),
inference(forward_demodulation,[],[f1262,f38]) ).
fof(f1309,plain,
! [X0] : antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))) = addition(one,antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0)))))),
inference(forward_demodulation,[],[f1233,f462]) ).
fof(f1329,plain,
! [X0] : one = antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(forward_demodulation,[],[f1309,f1090]) ).
fof(f1352,plain,
! [X0] : zero = multiplication(antidomain(zero),multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(superposition,[],[f1282,f33]) ).
fof(f1364,plain,
! [X0,X1] : zero = multiplication(antidomain(zero),multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1))))),
inference(superposition,[],[f1282,f102]) ).
fof(f1422,plain,
! [X0,X1] : zero = multiplication(one,multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1))))),
inference(forward_demodulation,[],[f1364,f462]) ).
fof(f1430,plain,
! [X0] : zero = multiplication(one,multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(forward_demodulation,[],[f1352,f462]) ).
fof(f1448,plain,
! [X0,X1] : zero = multiplication(antidomain(X0),antidomain(antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f1422,f56]) ).
fof(f1449,plain,
! [X0] : zero = multiplication(X0,antidomain(antidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f1430,f56]) ).
fof(f1822,plain,
! [X0] : multiplication(antidomain(zero),X0) = multiplication(antidomain(zero),multiplication(X0,antidomain(coantidomain(X0)))),
inference(superposition,[],[f338,f1449]) ).
fof(f1828,plain,
! [X0,X1] : multiplication(antidomain(zero),multiplication(antidomain(X0),antidomain(multiplication(X0,X1)))) = multiplication(antidomain(zero),antidomain(X0)),
inference(superposition,[],[f338,f1448]) ).
fof(f1883,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = multiplication(one,multiplication(antidomain(X0),antidomain(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f1828,f462]) ).
fof(f1889,plain,
! [X0] : multiplication(one,X0) = multiplication(one,multiplication(X0,antidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f1822,f462]) ).
fof(f1901,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = multiplication(antidomain(X0),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f1883,f56]) ).
fof(f1905,plain,
! [X0] : multiplication(one,X0) = multiplication(X0,antidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f1889,f56]) ).
fof(f1909,plain,
! [X0,X1] : antidomain(X0) = multiplication(antidomain(X0),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f1901,f56]) ).
fof(f1910,plain,
! [X0] : multiplication(X0,antidomain(coantidomain(X0))) = X0,
inference(forward_demodulation,[],[f1905,f56]) ).
fof(f1997,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),antidomain(multiplication(X0,X1))) = addition(antidomain(multiplication(X0,X1)),antidomain(X0)),
inference(superposition,[],[f113,f1909]) ).
fof(f2003,plain,
! [X0,X1] : multiplication(addition(one,antidomain(X0)),antidomain(multiplication(X0,X1))) = addition(antidomain(X0),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f1997,f55]) ).
fof(f2027,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(multiplication(X0,X1))) = multiplication(one,antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f2003,f1090]) ).
fof(f2033,plain,
! [X0,X1] : antidomain(multiplication(X0,X1)) = addition(antidomain(X0),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f2027,f56]) ).
fof(f2110,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),X1)) = addition(antidomain(X0),antidomain(multiplication(antidomain(antidomain(X0)),X1))),
inference(superposition,[],[f2033,f517]) ).
fof(f2125,plain,
! [X2,X0,X1] : antidomain(multiplication(X0,multiplication(X1,X2))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,multiplication(X1,X2)))),
inference(superposition,[],[f2033,f38]) ).
fof(f2346,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,[],[f676,f51]) ).
fof(f2897,plain,
! [X0,X1] : antidomain(multiplication(X1,antidomain(antidomain(X0)))) = addition(antidomain(multiplication(X1,multiplication(antidomain(antidomain(X0)),X0))),antidomain(multiplication(X1,antidomain(antidomain(X0))))),
inference(superposition,[],[f1289,f504]) ).
fof(f2960,plain,
! [X0,X1] : antidomain(multiplication(X1,antidomain(antidomain(X0)))) = addition(antidomain(multiplication(X1,antidomain(antidomain(X0)))),antidomain(multiplication(X1,multiplication(antidomain(antidomain(X0)),X0)))),
inference(forward_demodulation,[],[f2897,f55]) ).
fof(f3021,plain,
! [X0,X1] : antidomain(multiplication(X1,antidomain(antidomain(X0)))) = antidomain(multiplication(X1,multiplication(antidomain(antidomain(X0)),X0))),
inference(forward_demodulation,[],[f2960,f2125]) ).
fof(f3044,plain,
! [X0,X1] : antidomain(multiplication(X1,X0)) = antidomain(multiplication(X1,antidomain(antidomain(X0)))),
inference(forward_demodulation,[],[f3021,f446]) ).
fof(f3073,plain,
zero != multiplication(antidomain(antidomain(multiplication(sK0,sK1))),antidomain(antidomain(sK2))),
inference(superposition,[],[f541,f3044]) ).
fof(f3242,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(X0),X1)),multiplication(antidomain(antidomain(X0)),X1)) = multiplication(antidomain(multiplication(antidomain(X0),X1)),X1),
inference(superposition,[],[f280,f517]) ).
fof(f3306,plain,
! [X0,X1] : multiplication(addition(one,antidomain(multiplication(antidomain(antidomain(X0)),X1))),multiplication(antidomain(X0),X1)) = addition(multiplication(antidomain(X0),X1),multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),X1)),
inference(superposition,[],[f113,f280]) ).
fof(f3321,plain,
! [X0,X1] : multiplication(addition(one,antidomain(multiplication(antidomain(antidomain(X0)),X1))),multiplication(antidomain(X0),X1)) = multiplication(addition(antidomain(X0),antidomain(multiplication(antidomain(antidomain(X0)),X1))),X1),
inference(forward_demodulation,[],[f3306,f51]) ).
fof(f3368,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),X1) = multiplication(addition(one,antidomain(multiplication(antidomain(antidomain(X0)),X1))),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[],[f3321,f2110]) ).
fof(f3397,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),X1) = multiplication(one,multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[],[f3368,f1090]) ).
fof(f3411,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),X1),
inference(forward_demodulation,[],[f3397,f56]) ).
fof(f3419,plain,
! [X0,X1] : multiplication(antidomain(antidomain(X0)),X1) = multiplication(antidomain(multiplication(antidomain(X0),X1)),X1),
inference(superposition,[],[f3411,f517]) ).
fof(f3425,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(antidomain(X0),X1)) = multiplication(antidomain(addition(zero,multiplication(antidomain(antidomain(X0)),X1))),addition(antidomain(X0),X1)),
inference(superposition,[],[f3411,f71]) ).
fof(f3439,plain,
! [X0,X1] : multiplication(antidomain(X0),antidomain(antidomain(X1))) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),antidomain(antidomain(X1))),
inference(superposition,[],[f3411,f3044]) ).
fof(f3506,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(antidomain(X0),X1)) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),addition(antidomain(X0),X1)),
inference(forward_demodulation,[],[f3425,f90]) ).
fof(f3533,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(one,X1)) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),X1)),addition(antidomain(X0),X1)),
inference(forward_demodulation,[],[f3506,f533]) ).
fof(f3562,plain,
! [X2,X0,X1] : addition(multiplication(X0,one),multiplication(addition(X0,X2),antidomain(X1))) = addition(multiplication(X0,one),multiplication(X2,antidomain(X1))),
inference(superposition,[],[f2346,f1090]) ).
fof(f3563,plain,
! [X2,X0,X1] : addition(multiplication(X0,one),multiplication(addition(X0,X2),coantidomain(X1))) = addition(multiplication(X0,one),multiplication(X2,coantidomain(X1))),
inference(superposition,[],[f2346,f1089]) ).
fof(f3672,plain,
! [X2,X0,X1] : addition(multiplication(antidomain(X0),addition(X1,X2)),multiplication(antidomain(antidomain(X0)),X2)) = addition(multiplication(antidomain(X0),X1),multiplication(one,X2)),
inference(superposition,[],[f2346,f66]) ).
fof(f3676,plain,
! [X2,X0,X1] : addition(multiplication(coantidomain(X0),addition(X1,X2)),multiplication(coantidomain(coantidomain(X0)),X2)) = addition(multiplication(coantidomain(X0),X1),multiplication(one,X2)),
inference(superposition,[],[f2346,f67]) ).
fof(f3745,plain,
! [X2,X0,X1] : addition(multiplication(coantidomain(X0),X1),X2) = addition(multiplication(coantidomain(X0),addition(X1,X2)),multiplication(coantidomain(coantidomain(X0)),X2)),
inference(forward_demodulation,[],[f3676,f56]) ).
fof(f3748,plain,
! [X2,X0,X1] : addition(multiplication(antidomain(X0),X1),X2) = addition(multiplication(antidomain(X0),addition(X1,X2)),multiplication(antidomain(antidomain(X0)),X2)),
inference(forward_demodulation,[],[f3672,f56]) ).
fof(f3845,plain,
! [X2,X0,X1] : addition(X0,multiplication(addition(X0,X2),coantidomain(X1))) = addition(X0,multiplication(X2,coantidomain(X1))),
inference(forward_demodulation,[],[f3563,f57]) ).
fof(f3846,plain,
! [X2,X0,X1] : addition(X0,multiplication(addition(X0,X2),antidomain(X1))) = addition(X0,multiplication(X2,antidomain(X1))),
inference(forward_demodulation,[],[f3562,f57]) ).
fof(f3868,plain,
! [X2,X0,X1] : addition(multiplication(coantidomain(X0),X1),X2) = addition(multiplication(coantidomain(coantidomain(X0)),X2),multiplication(coantidomain(X0),addition(X1,X2))),
inference(forward_demodulation,[],[f3745,f55]) ).
fof(f3871,plain,
! [X2,X0,X1] : addition(multiplication(antidomain(X0),X1),X2) = addition(multiplication(antidomain(antidomain(X0)),X2),multiplication(antidomain(X0),addition(X1,X2))),
inference(forward_demodulation,[],[f3748,f55]) ).
fof(f4027,plain,
! [X0,X1] : addition(antidomain(X0),multiplication(antidomain(antidomain(X0)),antidomain(X1))) = addition(antidomain(X0),multiplication(one,antidomain(X1))),
inference(superposition,[],[f3846,f66]) ).
fof(f4028,plain,
! [X0,X1] : addition(coantidomain(X0),multiplication(coantidomain(coantidomain(X0)),antidomain(X1))) = addition(coantidomain(X0),multiplication(one,antidomain(X1))),
inference(superposition,[],[f3846,f67]) ).
fof(f4087,plain,
! [X0,X1] : addition(coantidomain(X0),multiplication(coantidomain(coantidomain(X0)),antidomain(X1))) = addition(coantidomain(X0),antidomain(X1)),
inference(forward_demodulation,[],[f4028,f56]) ).
fof(f4088,plain,
! [X0,X1] : addition(antidomain(X0),multiplication(antidomain(antidomain(X0)),antidomain(X1))) = addition(antidomain(X0),antidomain(X1)),
inference(forward_demodulation,[],[f4027,f56]) ).
fof(f4158,plain,
! [X0,X1] : multiplication(multiplication(antidomain(antidomain(X0)),antidomain(X1)),X0) = multiplication(addition(antidomain(X0),antidomain(X1)),X0),
inference(superposition,[],[f133,f4088]) ).
fof(f4162,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))),antidomain(X0))) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))),addition(antidomain(X0),antidomain(X1))),
inference(superposition,[],[f84,f4088]) ).
fof(f4180,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))),antidomain(X0))) = multiplication(antidomain(X0),addition(one,antidomain(X1))),
inference(forward_demodulation,[],[f4162,f3533]) ).
fof(f4184,plain,
! [X0,X1] : multiplication(antidomain(X1),X0) = multiplication(multiplication(antidomain(antidomain(X0)),antidomain(X1)),X0),
inference(forward_demodulation,[],[f4158,f133]) ).
fof(f4199,plain,
! [X0,X1] : multiplication(antidomain(X0),one) = addition(zero,multiplication(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))),antidomain(X0))),
inference(forward_demodulation,[],[f4180,f1090]) ).
fof(f4202,plain,
! [X0,X1] : multiplication(antidomain(X1),X0) = multiplication(antidomain(antidomain(X0)),multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[],[f4184,f38]) ).
fof(f4210,plain,
! [X0,X1] : multiplication(antidomain(X0),one) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))),antidomain(X0)),
inference(forward_demodulation,[],[f4199,f90]) ).
fof(f4215,plain,
! [X0,X1] : antidomain(X0) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))),antidomain(X0)),
inference(forward_demodulation,[],[f4210,f57]) ).
fof(f4286,plain,
! [X0,X1] : addition(antidomain(X0),multiplication(antidomain(antidomain(X0)),coantidomain(X1))) = addition(antidomain(X0),multiplication(one,coantidomain(X1))),
inference(superposition,[],[f3845,f66]) ).
fof(f4288,plain,
! [X0,X1] : addition(coantidomain(X0),multiplication(coantidomain(coantidomain(X0)),coantidomain(X1))) = addition(coantidomain(X0),multiplication(one,coantidomain(X1))),
inference(superposition,[],[f3845,f67]) ).
fof(f4349,plain,
! [X0,X1] : addition(coantidomain(X0),multiplication(coantidomain(coantidomain(X0)),coantidomain(X1))) = addition(coantidomain(X0),coantidomain(X1)),
inference(forward_demodulation,[],[f4288,f56]) ).
fof(f4351,plain,
! [X0,X1] : addition(antidomain(X0),multiplication(antidomain(antidomain(X0)),coantidomain(X1))) = addition(antidomain(X0),coantidomain(X1)),
inference(forward_demodulation,[],[f4286,f56]) ).
fof(f4423,plain,
! [X0,X1] : multiplication(multiplication(antidomain(antidomain(X0)),coantidomain(X1)),X0) = multiplication(addition(antidomain(X0),coantidomain(X1)),X0),
inference(superposition,[],[f133,f4351]) ).
fof(f4449,plain,
! [X0,X1] : multiplication(multiplication(antidomain(antidomain(X0)),coantidomain(X1)),X0) = multiplication(coantidomain(X1),X0),
inference(forward_demodulation,[],[f4423,f133]) ).
fof(f4462,plain,
! [X0,X1] : multiplication(coantidomain(X1),X0) = multiplication(antidomain(antidomain(X0)),multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[],[f4449,f38]) ).
fof(f4704,plain,
! [X0,X1] : addition(multiplication(coantidomain(X0),antidomain(X1)),antidomain(antidomain(X1))) = addition(multiplication(coantidomain(coantidomain(X0)),antidomain(antidomain(X1))),multiplication(coantidomain(X0),one)),
inference(superposition,[],[f3868,f66]) ).
fof(f4710,plain,
! [X0,X1] : addition(multiplication(coantidomain(X0),coantidomain(X1)),coantidomain(coantidomain(X1))) = addition(multiplication(coantidomain(coantidomain(X0)),coantidomain(coantidomain(X1))),multiplication(coantidomain(X0),one)),
inference(superposition,[],[f3868,f67]) ).
fof(f4748,plain,
! [X0,X1] : addition(multiplication(coantidomain(X0),coantidomain(X1)),coantidomain(coantidomain(X1))) = addition(multiplication(coantidomain(X0),one),multiplication(coantidomain(coantidomain(X0)),coantidomain(coantidomain(X1)))),
inference(forward_demodulation,[],[f4710,f55]) ).
fof(f4754,plain,
! [X0,X1] : addition(multiplication(coantidomain(X0),antidomain(X1)),antidomain(antidomain(X1))) = addition(multiplication(coantidomain(X0),one),multiplication(coantidomain(coantidomain(X0)),antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f4704,f55]) ).
fof(f4786,plain,
! [X0,X1] : addition(multiplication(coantidomain(X0),coantidomain(X1)),coantidomain(coantidomain(X1))) = addition(coantidomain(X0),multiplication(coantidomain(coantidomain(X0)),coantidomain(coantidomain(X1)))),
inference(forward_demodulation,[],[f4748,f57]) ).
fof(f4792,plain,
! [X0,X1] : addition(multiplication(coantidomain(X0),antidomain(X1)),antidomain(antidomain(X1))) = addition(coantidomain(X0),multiplication(coantidomain(coantidomain(X0)),antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f4754,f57]) ).
fof(f4810,plain,
! [X0,X1] : addition(multiplication(coantidomain(X0),coantidomain(X1)),coantidomain(coantidomain(X1))) = addition(coantidomain(X0),coantidomain(coantidomain(X1))),
inference(forward_demodulation,[],[f4786,f4349]) ).
fof(f4816,plain,
! [X0,X1] : addition(multiplication(coantidomain(X0),antidomain(X1)),antidomain(antidomain(X1))) = addition(coantidomain(X0),antidomain(antidomain(X1))),
inference(forward_demodulation,[],[f4792,f4087]) ).
fof(f4826,plain,
! [X0,X1] : addition(coantidomain(X0),coantidomain(coantidomain(X1))) = addition(coantidomain(coantidomain(X1)),multiplication(coantidomain(X0),coantidomain(X1))),
inference(forward_demodulation,[],[f4810,f55]) ).
fof(f4830,plain,
! [X0,X1] : addition(coantidomain(X0),antidomain(antidomain(X1))) = addition(antidomain(antidomain(X1)),multiplication(coantidomain(X0),antidomain(X1))),
inference(forward_demodulation,[],[f4816,f55]) ).
fof(f4869,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(antidomain(antidomain(X1))),multiplication(coantidomain(X0),antidomain(X1)))) = multiplication(antidomain(antidomain(antidomain(X1))),addition(coantidomain(X0),antidomain(antidomain(X1)))),
inference(superposition,[],[f71,f4830]) ).
fof(f4892,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(antidomain(antidomain(X1))),multiplication(coantidomain(X0),antidomain(X1)))) = addition(zero,multiplication(antidomain(antidomain(antidomain(X1))),coantidomain(X0))),
inference(forward_demodulation,[],[f4869,f84]) ).
fof(f4904,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(antidomain(antidomain(X1))),multiplication(coantidomain(X0),antidomain(X1)))) = multiplication(antidomain(antidomain(antidomain(X1))),coantidomain(X0)),
inference(forward_demodulation,[],[f4892,f90]) ).
fof(f4909,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(X1),multiplication(coantidomain(X0),antidomain(X1)))) = multiplication(antidomain(X1),coantidomain(X0)),
inference(forward_demodulation,[],[f4904,f517]) ).
fof(f4913,plain,
! [X0,X1] : multiplication(antidomain(X1),multiplication(coantidomain(X0),antidomain(X1))) = multiplication(antidomain(X1),coantidomain(X0)),
inference(forward_demodulation,[],[f4909,f90]) ).
fof(f4931,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),coantidomain(X1))) = addition(antidomain(multiplication(antidomain(antidomain(X0)),multiplication(coantidomain(X1),X0))),antidomain(multiplication(antidomain(antidomain(X0)),coantidomain(X1)))),
inference(superposition,[],[f1289,f4913]) ).
fof(f4965,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),coantidomain(X1))) = addition(antidomain(multiplication(antidomain(antidomain(X0)),coantidomain(X1))),antidomain(multiplication(antidomain(antidomain(X0)),multiplication(coantidomain(X1),X0)))),
inference(forward_demodulation,[],[f4931,f55]) ).
fof(f4978,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),coantidomain(X1))) = antidomain(multiplication(antidomain(antidomain(X0)),multiplication(coantidomain(X1),X0))),
inference(forward_demodulation,[],[f4965,f2125]) ).
fof(f4985,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),coantidomain(X1))) = antidomain(multiplication(coantidomain(X1),X0)),
inference(forward_demodulation,[],[f4978,f4462]) ).
fof(f5035,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),antidomain(X1)),antidomain(antidomain(X1))) = addition(multiplication(antidomain(antidomain(X0)),antidomain(antidomain(X1))),multiplication(antidomain(X0),one)),
inference(superposition,[],[f3871,f66]) ).
fof(f5048,plain,
! [X0,X1] : addition(multiplication(antidomain(addition(X0,X1)),X0),X1) = addition(multiplication(antidomain(antidomain(addition(X0,X1))),X1),zero),
inference(superposition,[],[f3871,f34]) ).
fof(f5092,plain,
! [X0,X1] : addition(multiplication(antidomain(addition(X0,X1)),X0),X1) = addition(zero,multiplication(antidomain(antidomain(addition(X0,X1))),X1)),
inference(forward_demodulation,[],[f5048,f55]) ).
fof(f5105,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),antidomain(X1)),antidomain(antidomain(X1))) = addition(multiplication(antidomain(X0),one),multiplication(antidomain(antidomain(X0)),antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f5035,f55]) ).
fof(f5151,plain,
! [X0,X1] : multiplication(antidomain(antidomain(addition(X0,X1))),X1) = addition(multiplication(antidomain(addition(X0,X1)),X0),X1),
inference(forward_demodulation,[],[f5092,f90]) ).
fof(f5163,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),antidomain(X1)),antidomain(antidomain(X1))) = addition(antidomain(X0),multiplication(antidomain(antidomain(X0)),antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f5105,f57]) ).
fof(f5191,plain,
! [X0,X1] : multiplication(antidomain(antidomain(addition(X0,X1))),X1) = addition(X1,multiplication(antidomain(addition(X0,X1)),X0)),
inference(forward_demodulation,[],[f5151,f55]) ).
fof(f5200,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),antidomain(X1)),antidomain(antidomain(X1))) = addition(antidomain(X0),antidomain(antidomain(X1))),
inference(forward_demodulation,[],[f5163,f4088]) ).
fof(f5219,plain,
! [X0,X1] : addition(X1,zero) = multiplication(antidomain(antidomain(addition(X0,X1))),X1),
inference(forward_demodulation,[],[f5191,f1095]) ).
fof(f5226,plain,
! [X0,X1] : addition(antidomain(X0),antidomain(antidomain(X1))) = addition(antidomain(antidomain(X1)),multiplication(antidomain(X0),antidomain(X1))),
inference(forward_demodulation,[],[f5200,f55]) ).
fof(f5243,plain,
! [X0,X1] : multiplication(antidomain(antidomain(addition(X0,X1))),X1) = X1,
inference(forward_demodulation,[],[f5219,f37]) ).
fof(f5274,plain,
! [X0,X1] : multiplication(antidomain(antidomain(addition(X0,X1))),X0) = X0,
inference(superposition,[],[f5243,f55]) ).
fof(f5431,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(antidomain(antidomain(X1))),multiplication(antidomain(X0),antidomain(X1)))) = multiplication(antidomain(antidomain(antidomain(X1))),addition(antidomain(X0),antidomain(antidomain(X1)))),
inference(superposition,[],[f71,f5226]) ).
fof(f5457,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(antidomain(antidomain(X1))),multiplication(antidomain(X0),antidomain(X1)))) = addition(zero,multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X0))),
inference(forward_demodulation,[],[f5431,f84]) ).
fof(f5485,plain,
! [X0,X1] : addition(zero,multiplication(antidomain(antidomain(antidomain(X1))),multiplication(antidomain(X0),antidomain(X1)))) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X0)),
inference(forward_demodulation,[],[f5457,f90]) ).
fof(f5506,plain,
! [X0,X1] : multiplication(antidomain(X1),antidomain(X0)) = addition(zero,multiplication(antidomain(X1),multiplication(antidomain(X0),antidomain(X1)))),
inference(forward_demodulation,[],[f5485,f517]) ).
fof(f5523,plain,
! [X0,X1] : multiplication(antidomain(X1),antidomain(X0)) = multiplication(antidomain(X1),multiplication(antidomain(X0),antidomain(X1))),
inference(forward_demodulation,[],[f5506,f90]) ).
fof(f5558,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))) = addition(antidomain(multiplication(antidomain(antidomain(X0)),multiplication(antidomain(X1),X0))),antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1)))),
inference(superposition,[],[f1289,f5523]) ).
fof(f5592,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))) = addition(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))),antidomain(multiplication(antidomain(antidomain(X0)),multiplication(antidomain(X1),X0)))),
inference(forward_demodulation,[],[f5558,f55]) ).
fof(f5616,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))) = antidomain(multiplication(antidomain(antidomain(X0)),multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[],[f5592,f2125]) ).
fof(f5625,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1))) = antidomain(multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[],[f5616,f4202]) ).
fof(f5870,plain,
! [X0,X1] : zero = multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(X1)))),antidomain(X0)),
inference(superposition,[],[f102,f4215]) ).
fof(f5896,plain,
! [X0,X1] : zero = multiplication(antidomain(antidomain(multiplication(antidomain(X1),X0))),antidomain(X0)),
inference(forward_demodulation,[],[f5870,f5625]) ).
fof(f5999,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(X0),X1)),antidomain(X1)) = multiplication(antidomain(zero),antidomain(X1)),
inference(superposition,[],[f3411,f5896]) ).
fof(f6012,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(multiplication(antidomain(X0),X1))),antidomain(antidomain(antidomain(X1))))) = addition(antidomain(zero),antidomain(multiplication(antidomain(antidomain(multiplication(antidomain(X0),X1))),antidomain(antidomain(antidomain(X1)))))),
inference(superposition,[],[f50,f5896]) ).
fof(f6048,plain,
! [X0,X1] : antidomain(multiplication(antidomain(antidomain(antidomain(X1))),multiplication(antidomain(X0),X1))) = addition(antidomain(zero),antidomain(multiplication(antidomain(antidomain(antidomain(X1))),multiplication(antidomain(X0),X1)))),
inference(forward_demodulation,[],[f6012,f5625]) ).
fof(f6060,plain,
! [X0,X1] : multiplication(one,antidomain(X1)) = multiplication(antidomain(multiplication(antidomain(X0),X1)),antidomain(X1)),
inference(forward_demodulation,[],[f5999,f462]) ).
fof(f6110,plain,
! [X0,X1] : antidomain(multiplication(antidomain(X1),multiplication(antidomain(X0),X1))) = addition(antidomain(zero),antidomain(multiplication(antidomain(X1),multiplication(antidomain(X0),X1)))),
inference(forward_demodulation,[],[f6048,f517]) ).
fof(f6119,plain,
! [X0,X1] : antidomain(X1) = multiplication(antidomain(multiplication(antidomain(X0),X1)),antidomain(X1)),
inference(forward_demodulation,[],[f6060,f56]) ).
fof(f6143,plain,
! [X0,X1] : antidomain(multiplication(antidomain(X1),multiplication(antidomain(X0),X1))) = addition(one,antidomain(multiplication(antidomain(X1),multiplication(antidomain(X0),X1)))),
inference(forward_demodulation,[],[f6110,f462]) ).
fof(f6157,plain,
! [X0,X1] : one = antidomain(multiplication(antidomain(X1),multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[],[f6143,f1090]) ).
fof(f6501,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X0)),antidomain(antidomain(X0)))),antidomain(multiplication(antidomain(X1),X0))) = multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X0)),antidomain(antidomain(X0)))),antidomain(X0)),
inference(superposition,[],[f338,f6119]) ).
fof(f6535,plain,
! [X0,X1] : multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X0)),X0)),antidomain(multiplication(antidomain(X1),X0))) = multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X0)),X0)),antidomain(X0)),
inference(forward_demodulation,[],[f6501,f3044]) ).
fof(f6576,plain,
! [X0,X1] : antidomain(X0) = multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X0)),X0)),antidomain(multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[],[f6535,f6119]) ).
fof(f6591,plain,
! [X0,X1] : antidomain(X0) = multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X0)),antidomain(multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[],[f6576,f3419]) ).
fof(f6639,plain,
! [X0,X1] : antidomain(multiplication(antidomain(X1),antidomain(X0))) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),multiplication(antidomain(X1),antidomain(X0)))),antidomain(multiplication(antidomain(X0),antidomain(X1)))),
inference(superposition,[],[f6591,f5523]) ).
fof(f6655,plain,
! [X0,X1] : antidomain(antidomain(multiplication(antidomain(X1),X0))) = multiplication(antidomain(multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X0))),antidomain(multiplication(antidomain(X1),X0)))),antidomain(antidomain(X0))),
inference(superposition,[],[f6591,f6591]) ).
fof(f6665,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(antidomain(multiplication(antidomain(antidomain(coantidomain(coantidomain(X0)))),coantidomain(X0))),antidomain(antidomain(coantidomain(coantidomain(X0))))),
inference(superposition,[],[f6591,f237]) ).
fof(f6675,plain,
! [X0,X1] : antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(multiplication(antidomain(antidomain(X0)),antidomain(antidomain(X1)))),antidomain(multiplication(antidomain(X0),X1))),
inference(superposition,[],[f6591,f3044]) ).
fof(f6726,plain,
! [X0,X1] : antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X0)),antidomain(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[],[f6675,f5625]) ).
fof(f6734,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(antidomain(multiplication(coantidomain(X0),coantidomain(coantidomain(X0)))),antidomain(antidomain(coantidomain(coantidomain(X0))))),
inference(forward_demodulation,[],[f6665,f4985]) ).
fof(f6738,plain,
! [X0,X1] : antidomain(antidomain(multiplication(antidomain(X1),X0))) = multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X0)),multiplication(antidomain(antidomain(X1)),X0))),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f6655,f5625]) ).
fof(f6749,plain,
! [X0,X1] : antidomain(multiplication(antidomain(X1),antidomain(X0))) = multiplication(one,antidomain(multiplication(antidomain(X0),antidomain(X1)))),
inference(forward_demodulation,[],[f6639,f6157]) ).
fof(f6789,plain,
! [X0,X1] : antidomain(X1) = multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X0)),antidomain(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[],[f6726,f517]) ).
fof(f6793,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(antidomain(zero),antidomain(antidomain(coantidomain(coantidomain(X0))))),
inference(forward_demodulation,[],[f6734,f33]) ).
fof(f6796,plain,
! [X0,X1] : antidomain(antidomain(multiplication(antidomain(X1),X0))) = multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X0)),X0)),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f6738,f3242]) ).
fof(f6804,plain,
! [X0,X1] : antidomain(multiplication(antidomain(X0),antidomain(X1))) = antidomain(multiplication(antidomain(X1),antidomain(X0))),
inference(forward_demodulation,[],[f6749,f56]) ).
fof(f6832,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(one,antidomain(antidomain(coantidomain(coantidomain(X0))))),
inference(forward_demodulation,[],[f6793,f462]) ).
fof(f6835,plain,
! [X0,X1] : antidomain(antidomain(multiplication(antidomain(X1),X0))) = multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X0)),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f6796,f3419]) ).
fof(f6850,plain,
! [X0] : antidomain(coantidomain(X0)) = antidomain(antidomain(coantidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f6832,f56]) ).
fof(f6851,plain,
! [X0,X1] : multiplication(antidomain(X1),antidomain(antidomain(X0))) = antidomain(antidomain(multiplication(antidomain(X1),X0))),
inference(forward_demodulation,[],[f6835,f3439]) ).
fof(f7189,plain,
! [X0,X1] : antidomain(addition(X1,X0)) = multiplication(antidomain(multiplication(antidomain(antidomain(addition(X1,X0))),X0)),antidomain(multiplication(antidomain(X0),X1))),
inference(superposition,[],[f6789,f205]) ).
fof(f7191,plain,
! [X0,X1] : antidomain(addition(X0,X1)) = multiplication(antidomain(multiplication(antidomain(antidomain(addition(X0,X1))),X0)),antidomain(addition(zero,multiplication(antidomain(X0),X1)))),
inference(superposition,[],[f6789,f71]) ).
fof(f7319,plain,
! [X0,X1] : antidomain(addition(X0,X1)) = multiplication(antidomain(multiplication(antidomain(antidomain(addition(X0,X1))),X0)),antidomain(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[],[f7191,f90]) ).
fof(f7321,plain,
! [X0,X1] : antidomain(addition(X1,X0)) = multiplication(antidomain(X0),antidomain(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[],[f7189,f5243]) ).
fof(f7396,plain,
! [X0,X1] : antidomain(addition(X0,X1)) = multiplication(antidomain(X0),antidomain(multiplication(antidomain(X0),X1))),
inference(forward_demodulation,[],[f7319,f5274]) ).
fof(f7527,plain,
! [X0,X1] : multiplication(antidomain(X1),antidomain(antidomain(antidomain(X0)))) = antidomain(antidomain(multiplication(antidomain(X0),antidomain(X1)))),
inference(superposition,[],[f6851,f6804]) ).
fof(f7668,plain,
! [X0,X1] : multiplication(antidomain(X1),antidomain(antidomain(antidomain(X0)))) = multiplication(antidomain(X0),antidomain(antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f7527,f6851]) ).
fof(f7738,plain,
! [X0,X1] : multiplication(antidomain(X0),antidomain(X1)) = multiplication(antidomain(X1),antidomain(antidomain(antidomain(X0)))),
inference(forward_demodulation,[],[f7668,f517]) ).
fof(f7777,plain,
! [X0,X1] : multiplication(antidomain(X0),antidomain(X1)) = multiplication(antidomain(X1),antidomain(X0)),
inference(forward_demodulation,[],[f7738,f517]) ).
fof(f7931,plain,
! [X0,X1] : multiplication(antidomain(X1),antidomain(X0)) = multiplication(antidomain(X0),antidomain(multiplication(antidomain(antidomain(X1)),antidomain(X0)))),
inference(superposition,[],[f3411,f7777]) ).
fof(f7995,plain,
! [X0,X1] : multiplication(antidomain(X0),antidomain(multiplication(antidomain(X0),X1))) = multiplication(antidomain(X1),antidomain(X0)),
inference(forward_demodulation,[],[f7931,f5625]) ).
fof(f8059,plain,
! [X0,X1] : antidomain(addition(X1,X0)) = multiplication(antidomain(X1),antidomain(X0)),
inference(forward_demodulation,[],[f7995,f7321]) ).
fof(f8558,plain,
zero != antidomain(addition(antidomain(multiplication(sK0,sK1)),antidomain(sK2))),
inference(superposition,[],[f3073,f8059]) ).
fof(f8623,plain,
zero != antidomain(addition(antidomain(sK2),antidomain(multiplication(sK0,sK1)))),
inference(forward_demodulation,[],[f8558,f55]) ).
fof(f9606,plain,
! [X0] : coantidomain(coantidomain(X0)) = multiplication(antidomain(coantidomain(X0)),coantidomain(coantidomain(X0))),
inference(superposition,[],[f446,f6850]) ).
fof(f9718,plain,
! [X0] : coantidomain(coantidomain(X0)) = antidomain(coantidomain(X0)),
inference(forward_demodulation,[],[f9606,f844]) ).
fof(f9805,plain,
! [X0] : antidomain(antidomain(coantidomain(X0))) = multiplication(antidomain(antidomain(coantidomain(X0))),coantidomain(X0)),
inference(superposition,[],[f237,f9718]) ).
fof(f9808,plain,
! [X0,X1] : addition(coantidomain(X0),antidomain(X1)) = addition(coantidomain(X0),multiplication(antidomain(coantidomain(X0)),antidomain(X1))),
inference(superposition,[],[f4087,f9718]) ).
fof(f9842,plain,
! [X0,X1] : addition(coantidomain(X0),antidomain(X1)) = addition(coantidomain(X0),antidomain(addition(coantidomain(X0),X1))),
inference(forward_demodulation,[],[f9808,f8059]) ).
fof(f9843,plain,
! [X0] : coantidomain(X0) = antidomain(antidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f9805,f446]) ).
fof(f9908,plain,
! [X0,X1] : antidomain(multiplication(antidomain(coantidomain(X0)),X1)) = addition(coantidomain(X0),antidomain(multiplication(antidomain(coantidomain(X0)),X1))),
inference(superposition,[],[f2033,f9843]) ).
fof(f9939,plain,
! [X0,X1] : antidomain(addition(antidomain(coantidomain(X0)),X1)) = multiplication(coantidomain(X0),antidomain(multiplication(coantidomain(X0),X1))),
inference(superposition,[],[f7396,f9843]) ).
fof(f9944,plain,
! [X0,X1] : multiplication(coantidomain(X0),antidomain(X1)) = antidomain(addition(antidomain(coantidomain(X0)),X1)),
inference(superposition,[],[f8059,f9843]) ).
fof(f9946,plain,
! [X0,X1] : multiplication(coantidomain(X0),antidomain(X1)) = multiplication(coantidomain(X0),antidomain(multiplication(coantidomain(X0),X1))),
inference(forward_demodulation,[],[f9939,f9944]) ).
fof(f14239,plain,
! [X0,X1] : addition(coantidomain(X0),multiplication(coantidomain(coantidomain(X0)),antidomain(X1))) = addition(coantidomain(X0),antidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(superposition,[],[f4087,f9946]) ).
fof(f14292,plain,
! [X0,X1] : addition(coantidomain(X0),multiplication(antidomain(coantidomain(X0)),antidomain(X1))) = addition(coantidomain(X0),antidomain(multiplication(antidomain(coantidomain(X0)),X1))),
inference(forward_demodulation,[],[f14239,f9718]) ).
fof(f14323,plain,
! [X0,X1] : antidomain(multiplication(antidomain(coantidomain(X0)),X1)) = addition(coantidomain(X0),multiplication(antidomain(coantidomain(X0)),antidomain(X1))),
inference(forward_demodulation,[],[f14292,f9908]) ).
fof(f14345,plain,
! [X0,X1] : antidomain(multiplication(antidomain(coantidomain(X0)),X1)) = addition(coantidomain(X0),antidomain(addition(coantidomain(X0),X1))),
inference(forward_demodulation,[],[f14323,f8059]) ).
fof(f14360,plain,
! [X0,X1] : addition(coantidomain(X0),antidomain(X1)) = antidomain(multiplication(antidomain(coantidomain(X0)),X1)),
inference(forward_demodulation,[],[f14345,f9842]) ).
fof(f16309,plain,
! [X0] : zero = multiplication(coantidomain(zero),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(X0))),X0)))),
inference(superposition,[],[f189,f34]) ).
fof(f16510,plain,
! [X0] : zero = multiplication(coantidomain(zero),antidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(X0))),X0)))),
inference(forward_demodulation,[],[f16309,f9718]) ).
fof(f16625,plain,
! [X0] : zero = multiplication(coantidomain(zero),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(X0))),X0)))),
inference(forward_demodulation,[],[f16510,f9718]) ).
fof(f16722,plain,
! [X0] : zero = multiplication(one,antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(X0))),X0)))),
inference(forward_demodulation,[],[f16625,f647]) ).
fof(f16793,plain,
! [X0] : zero = antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(X0))),X0))),
inference(forward_demodulation,[],[f16722,f56]) ).
fof(f16917,plain,
! [X0] : one = antidomain(multiplication(multiplication(antidomain(coantidomain(antidomain(X0))),X0),antidomain(zero))),
inference(superposition,[],[f1329,f16793]) ).
fof(f17073,plain,
! [X0] : one = antidomain(multiplication(antidomain(coantidomain(antidomain(X0))),multiplication(X0,antidomain(zero)))),
inference(forward_demodulation,[],[f16917,f38]) ).
fof(f17134,plain,
! [X0] : one = addition(coantidomain(antidomain(X0)),antidomain(multiplication(X0,antidomain(zero)))),
inference(forward_demodulation,[],[f17073,f14360]) ).
fof(f17178,plain,
! [X0] : one = addition(coantidomain(antidomain(X0)),antidomain(multiplication(X0,one))),
inference(forward_demodulation,[],[f17134,f462]) ).
fof(f17206,plain,
! [X0] : one = addition(coantidomain(antidomain(X0)),antidomain(X0)),
inference(forward_demodulation,[],[f17178,f57]) ).
fof(f17226,plain,
! [X0] : one = addition(antidomain(X0),coantidomain(antidomain(X0))),
inference(forward_demodulation,[],[f17206,f55]) ).
fof(f17273,plain,
! [X0] : multiplication(antidomain(coantidomain(antidomain(X0))),antidomain(X0)) = multiplication(antidomain(coantidomain(antidomain(X0))),one),
inference(superposition,[],[f205,f17226]) ).
fof(f17306,plain,
! [X0] : antidomain(coantidomain(antidomain(X0))) = multiplication(antidomain(coantidomain(antidomain(X0))),antidomain(X0)),
inference(forward_demodulation,[],[f17273,f57]) ).
fof(f17329,plain,
! [X0] : antidomain(coantidomain(antidomain(X0))) = multiplication(antidomain(X0),antidomain(coantidomain(antidomain(X0)))),
inference(forward_demodulation,[],[f17306,f7777]) ).
fof(f17340,plain,
! [X0] : antidomain(X0) = antidomain(coantidomain(antidomain(X0))),
inference(forward_demodulation,[],[f17329,f1910]) ).
fof(f23695,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(sK1)),multiplication(coantidomain(X0),coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0))))) = multiplication(antidomain(antidomain(sK1)),addition(coantidomain(X0),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0))))),
inference(superposition,[],[f70,f4826]) ).
fof(f23749,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(sK1)),coantidomain(X0))) = addition(zero,multiplication(antidomain(antidomain(sK1)),multiplication(coantidomain(X0),coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0))))),
inference(forward_demodulation,[],[f23695,f85]) ).
fof(f23782,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(sK1)),coantidomain(X0))) = multiplication(antidomain(antidomain(sK1)),multiplication(coantidomain(X0),coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0)))),
inference(forward_demodulation,[],[f23749,f90]) ).
fof(f23807,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(sK1)),coantidomain(X0))) = multiplication(antidomain(antidomain(sK1)),multiplication(coantidomain(X0),coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(sK2)))),sK0)))),
inference(forward_demodulation,[],[f23782,f9718]) ).
fof(f23824,plain,
! [X0] : addition(zero,multiplication(antidomain(antidomain(sK1)),coantidomain(X0))) = multiplication(antidomain(antidomain(sK1)),multiplication(coantidomain(X0),coantidomain(multiplication(antidomain(antidomain(sK2)),sK0)))),
inference(forward_demodulation,[],[f23807,f17340]) ).
fof(f23836,plain,
! [X0] : multiplication(antidomain(antidomain(sK1)),coantidomain(X0)) = multiplication(antidomain(antidomain(sK1)),multiplication(coantidomain(X0),coantidomain(multiplication(antidomain(antidomain(sK2)),sK0)))),
inference(forward_demodulation,[],[f23824,f90]) ).
fof(f29149,plain,
multiplication(antidomain(antidomain(sK1)),one) = multiplication(antidomain(antidomain(sK1)),multiplication(one,coantidomain(multiplication(antidomain(antidomain(sK2)),sK0)))),
inference(superposition,[],[f23836,f647]) ).
fof(f29240,plain,
multiplication(antidomain(antidomain(sK1)),one) = multiplication(antidomain(antidomain(sK1)),coantidomain(multiplication(antidomain(antidomain(sK2)),sK0))),
inference(forward_demodulation,[],[f29149,f56]) ).
fof(f29266,plain,
antidomain(antidomain(sK1)) = multiplication(antidomain(antidomain(sK1)),coantidomain(multiplication(antidomain(antidomain(sK2)),sK0))),
inference(forward_demodulation,[],[f29240,f57]) ).
fof(f29326,plain,
addition(antidomain(sK1),coantidomain(multiplication(antidomain(antidomain(sK2)),sK0))) = addition(antidomain(sK1),antidomain(antidomain(sK1))),
inference(superposition,[],[f4351,f29266]) ).
fof(f29406,plain,
one = addition(antidomain(sK1),coantidomain(multiplication(antidomain(antidomain(sK2)),sK0))),
inference(forward_demodulation,[],[f29326,f66]) ).
fof(f29465,plain,
multiplication(coantidomain(multiplication(antidomain(antidomain(sK2)),sK0)),sK1) = multiplication(one,sK1),
inference(superposition,[],[f133,f29406]) ).
fof(f29528,plain,
sK1 = multiplication(coantidomain(multiplication(antidomain(antidomain(sK2)),sK0)),sK1),
inference(forward_demodulation,[],[f29465,f56]) ).
fof(f33753,plain,
zero = multiplication(multiplication(antidomain(antidomain(sK2)),sK0),sK1),
inference(superposition,[],[f105,f29528]) ).
fof(f33802,plain,
zero = multiplication(antidomain(antidomain(sK2)),multiplication(sK0,sK1)),
inference(forward_demodulation,[],[f33753,f38]) ).
fof(f33838,plain,
antidomain(antidomain(zero)) = multiplication(antidomain(antidomain(sK2)),antidomain(antidomain(multiplication(sK0,sK1)))),
inference(superposition,[],[f6851,f33802]) ).
fof(f33904,plain,
antidomain(antidomain(zero)) = antidomain(addition(antidomain(sK2),antidomain(multiplication(sK0,sK1)))),
inference(forward_demodulation,[],[f33838,f8059]) ).
fof(f33943,plain,
antidomain(one) = antidomain(addition(antidomain(sK2),antidomain(multiplication(sK0,sK1)))),
inference(forward_demodulation,[],[f33904,f462]) ).
fof(f33971,plain,
zero = antidomain(addition(antidomain(sK2),antidomain(multiplication(sK0,sK1)))),
inference(forward_demodulation,[],[f33943,f405]) ).
fof(f33988,plain,
$false,
inference(forward_subsumption_resolution,[],[f33971,f8623]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE102+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n005.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 13:09:47 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 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
% 17.47/3.38 % (3980059)Detected formulas, will run a generic FOF schedule.
% 17.47/3.38 % (3980068)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2471585513:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 17.47/3.38 % (3980065)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=320807064:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 17.47/3.38 % (3980068)Instruction limit reached!
% 17.47/3.38 % (3980068)------------------------------
% 17.47/3.38 % (3980068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.47/3.38 % (3980068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.47/3.38 % (3980068)CaDiCaL version: 2.1.3
% 17.47/3.38 % (3980068)Termination reason: Instruction limit
% 17.47/3.38 % (3980068)Termination phase: Saturation
% 17.47/3.38 % (3980068)Time elapsed: 0.059 s
% 17.47/3.38 % (3980068)Peak memory usage: 89 MB
% 17.47/3.38 % (3980068)Instructions burned: 121 (million)
% 17.47/3.38 % (3980070)dis-21_1_sil=8000:lcm=predicate:random_seed=981013210: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)
% 17.47/3.38 % (3980064)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=3019599562:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 17.47/3.38 % (3980069)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1779458128:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 17.47/3.38 % (3980067)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3379610577:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 17.47/3.38 % (3980070)Refutation not found, incomplete strategy
% 17.47/3.38 % (3980070)------------------------------
% 17.47/3.38 % (3980070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.47/3.38 % (3980070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.47/3.38 % (3980067)Refutation not found, incomplete strategy
% 17.47/3.38 % (3980067)------------------------------
% 17.47/3.38 % (3980067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.47/3.38 % (3980070)CaDiCaL version: 2.1.3
% 17.47/3.38 % (3980070)Termination reason: Refutation not found, incomplete strategy
% 17.47/3.38 % (3980070)Time elapsed: 0.003 s
% 17.47/3.38 % (3980070)Peak memory usage: 88 MB
% 17.47/3.38 % (3980067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.47/3.38 % (3980070)Instructions burned: 1 (million)
% 17.47/3.38 % (3980067)CaDiCaL version: 2.1.3
% 17.47/3.38 % (3980067)Termination reason: Refutation not found, incomplete strategy
% 17.47/3.38 % (3980067)Time elapsed: 0.003 s
% 17.47/3.38 % (3980067)Peak memory usage: 88 MB
% 17.47/3.38 % (3980067)Instructions burned: 1 (million)
% 17.47/3.38 % (3980066)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=3090773631:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 17.47/3.38 % (3980069)Instruction limit reached!
% 17.47/3.38 % (3980069)------------------------------
% 17.47/3.38 % (3980069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.47/3.38 % (3980069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.47/3.38 % (3980069)CaDiCaL version: 2.1.3
% 17.47/3.38 % (3980069)Termination reason: Instruction limit
% 17.47/3.38 % (3980069)Termination phase: Saturation
% 17.47/3.38 % (3980069)Time elapsed: 0.134 s
% 17.47/3.38 % (3980069)Peak memory usage: 89 MB
% 17.47/3.38 % (3980069)Instructions burned: 140 (million)
% 17.47/3.38 % (3980073)lrs+10_1_sil=8000:sp=occurrence:random_seed=652937729:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 17.47/3.38 % (3980073)Instruction limit reached!
% 17.47/3.38 % (3980073)------------------------------
% 17.47/3.38 % (3980073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.47/3.38 % (3980073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.47/3.38 % (3980073)CaDiCaL version: 2.1.3
% 17.47/3.38 % (3980073)Termination reason: Instruction limit
% 17.47/3.38 % (3980073)Termination phase: Saturation
% 17.47/3.38 % (3980073)Time elapsed: 0.150 s
% 17.47/3.38 % (3980073)Peak memory usage: 91 MB
% 17.47/3.38 % (3980073)Instructions burned: 286 (million)
% 17.47/3.38 % (3980079)lrs+10_1_sil=32000:urr=on:br=off:random_seed=420497982:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 23.24/4.16 % (3980070)------------------------------
% 23.24/4.16 % (3980070)------------------------------
% 23.24/4.16 % (3980067)------------------------------
% 23.24/4.16 % (3980067)------------------------------
% 23.24/4.16 % (3980079)Instruction limit reached!
% 23.24/4.16 % (3980079)------------------------------
% 23.24/4.16 % (3980079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.24/4.16 % (3980079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.24/4.16 % (3980079)CaDiCaL version: 2.1.3
% 23.24/4.16 % (3980079)Termination reason: Instruction limit
% 23.24/4.16 % (3980079)Termination phase: Saturation
% 23.24/4.16 % (3980079)Time elapsed: 0.120 s
% 23.24/4.16 % (3980079)Peak memory usage: 89 MB
% 23.24/4.16 % (3980079)Instructions burned: 157 (million)
% 23.24/4.16 % (3980084)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=1453280107:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 23.24/4.16 % (3980081)lrs+1011_1_sil=32000:sp=occurrence:random_seed=874254567:i=325:sd=1:ss=axioms:sgt=32_2994 on theBenchmark for (2994ds/325Mi)
% 23.24/4.16 % (3980085)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2698065444:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 23.24/4.16 % (3980086)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=900546189:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 23.24/4.16 % (3980084)Instruction limit reached!
% 23.24/4.16 % (3980084)------------------------------
% 23.24/4.16 % (3980084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.24/4.16 % (3980084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.24/4.16 % (3980084)CaDiCaL version: 2.1.3
% 23.24/4.16 % (3980084)Termination reason: Instruction limit
% 23.24/4.16 % (3980084)Termination phase: Saturation
% 23.24/4.16 % (3980084)Time elapsed: 0.238 s
% 23.24/4.16 % (3980084)Peak memory usage: 91 MB
% 23.24/4.16 % (3980084)Instructions burned: 249 (million)
% 23.24/4.16 % (3980081)Instruction limit reached!
% 23.24/4.16 % (3980081)------------------------------
% 23.24/4.16 % (3980081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.24/4.16 % (3980081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.24/4.16 % (3980081)CaDiCaL version: 2.1.3
% 23.24/4.16 % (3980081)Termination reason: Instruction limit
% 23.24/4.16 % (3980081)Termination phase: Saturation
% 23.24/4.16 % (3980081)Time elapsed: 0.314 s
% 23.24/4.16 % (3980081)Peak memory usage: 91 MB
% 23.24/4.16 % (3980081)Instructions burned: 325 (million)
% 23.24/4.16 % (3980085)Instruction limit reached!
% 23.24/4.16 % (3980085)------------------------------
% 23.24/4.16 % (3980085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.24/4.16 % (3980085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.24/4.16 % (3980085)CaDiCaL version: 2.1.3
% 23.24/4.16 % (3980085)Termination reason: Instruction limit
% 23.24/4.16 % (3980085)Termination phase: Saturation
% 23.24/4.16 % (3980085)Time elapsed: 0.268 s
% 23.24/4.16 % (3980085)Peak memory usage: 89 MB
% 23.24/4.16 % (3980085)Instructions burned: 295 (million)
% 23.24/4.16 % (3980066)Refutation not found, incomplete strategy
% 23.24/4.16 % (3980066)------------------------------
% 23.24/4.16 % (3980066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.24/4.16 % (3980066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.24/4.16 % (3980066)CaDiCaL version: 2.1.3
% 23.24/4.16 % (3980066)Termination reason: Refutation not found, incomplete strategy
% 23.24/4.16 % (3980066)Time elapsed: 0.984 s
% 23.24/4.16 % (3980066)Peak memory usage: 128 MB
% 23.24/4.16 % (3980066)Instructions burned: 898 (million)
% 23.24/4.16 % (3980094)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1904162675:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 23.24/4.16 % (3980096)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2591733925:i=127:av=off:fsr=off:sup=off_2988 on theBenchmark for (2988ds/127Mi)
% 23.24/4.16 % (3980096)Refutation not found, incomplete strategy
% 23.24/4.16 % (3980096)------------------------------
% 23.24/4.16 % (3980096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.24/4.16 % (3980096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980096)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980096)Termination reason: Refutation not found, incomplete strategy
% 29.35/5.72 % (3980096)Time elapsed: 0.002 s
% 29.35/5.72 % (3980096)Peak memory usage: 88 MB
% 29.35/5.72 % (3980096)Instructions burned: 1 (million)
% 29.35/5.72 % (3980094)Instruction limit reached!
% 29.35/5.72 % (3980094)------------------------------
% 29.35/5.72 % (3980094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980094)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980094)Termination reason: Instruction limit
% 29.35/5.72 % (3980094)Termination phase: Saturation
% 29.35/5.72 % (3980094)Time elapsed: 0.107 s
% 29.35/5.72 % (3980094)Peak memory usage: 90 MB
% 29.35/5.72 % (3980094)Instructions burned: 114 (million)
% 29.35/5.72 % (3980098)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3802558539:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2987 on theBenchmark for (2987ds/114Mi)
% 29.35/5.72 % (3980098)Refutation not found, incomplete strategy
% 29.35/5.72 % (3980098)------------------------------
% 29.35/5.72 % (3980098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980098)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980098)Termination reason: Refutation not found, incomplete strategy
% 29.35/5.72 % (3980098)Time elapsed: 0.004 s
% 29.35/5.72 % (3980098)Peak memory usage: 88 MB
% 29.35/5.72 % (3980098)Instructions burned: 2 (million)
% 29.35/5.72 % (3980066)------------------------------
% 29.35/5.72 % (3980066)------------------------------
% 29.35/5.72 % (3980104)lrs+10_1_sil=8000:sp=occurrence:random_seed=1346388003:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2985 on theBenchmark for (2985ds/907Mi)
% 29.35/5.72 % (3980096)------------------------------
% 29.35/5.72 % (3980096)------------------------------
% 29.35/5.72 % (3980107)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2253869969:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 29.35/5.72 % (3980107)Refutation not found, incomplete strategy
% 29.35/5.72 % (3980107)------------------------------
% 29.35/5.72 % (3980107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980107)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980107)Termination reason: Refutation not found, incomplete strategy
% 29.35/5.72 % (3980107)Time elapsed: 0.003 s
% 29.35/5.72 % (3980107)Peak memory usage: 88 MB
% 29.35/5.72 % (3980107)Instructions burned: 1 (million)
% 29.35/5.72 % (3980098)------------------------------
% 29.35/5.72 % (3980098)------------------------------
% 29.35/5.72 % (3980110)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4113757022:i=5202:ss=axioms:sgt=16_2981 on theBenchmark for (2981ds/5202Mi)
% 29.35/5.72 % (3980112)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=56228152:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2980 on theBenchmark for (2980ds/134Mi)
% 29.35/5.72 % (3980112)Refutation not found, incomplete strategy
% 29.35/5.72 % (3980112)------------------------------
% 29.35/5.72 % (3980112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980112)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980112)Termination reason: Refutation not found, incomplete strategy
% 29.35/5.72 % (3980112)Time elapsed: 0.003 s
% 29.35/5.72 % (3980112)Peak memory usage: 89 MB
% 29.35/5.72 % (3980112)Instructions burned: 1 (million)
% 29.35/5.72 % (3980107)------------------------------
% 29.35/5.72 % (3980107)------------------------------
% 29.35/5.72 % (3980086)Instruction limit reached!
% 29.35/5.72 % (3980086)------------------------------
% 29.35/5.72 % (3980086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980086)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980086)Termination reason: Instruction limit
% 29.35/5.72 % (3980086)Termination phase: Saturation
% 29.35/5.72 % (3980086)Time elapsed: 1.348 s
% 29.35/5.72 % (3980086)Peak memory usage: 143 MB
% 29.35/5.72 % (3980086)Instructions burned: 2351 (million)
% 29.35/5.72 % (3980116)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4056392044:st=8:i=592:sd=3:ep=RST:ss=axioms_2977 on theBenchmark for (2977ds/592Mi)
% 29.35/5.72 % (3980112)------------------------------
% 29.35/5.72 % (3980112)------------------------------
% 29.35/5.72 % (3980117)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2335196562:st=3:i=13193:sd=3:ss=axioms_2976 on theBenchmark for (2976ds/13193Mi)
% 29.35/5.72 % (3980104)Instruction limit reached!
% 29.35/5.72 % (3980104)------------------------------
% 29.35/5.72 % (3980104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980104)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980104)Termination reason: Instruction limit
% 29.35/5.72 % (3980104)Termination phase: Saturation
% 29.35/5.72 % (3980104)Time elapsed: 0.881 s
% 29.35/5.72 % (3980104)Peak memory usage: 97 MB
% 29.35/5.72 % (3980104)Instructions burned: 908 (million)
% 29.35/5.72 % (3980116)Instruction limit reached!
% 29.35/5.72 % (3980116)------------------------------
% 29.35/5.72 % (3980116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980116)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980116)Termination reason: Instruction limit
% 29.35/5.72 % (3980116)Termination phase: Saturation
% 29.35/5.72 % (3980116)Time elapsed: 0.331 s
% 29.35/5.72 % (3980116)Peak memory usage: 95 MB
% 29.35/5.72 % (3980116)Instructions burned: 593 (million)
% 29.35/5.72 % (3980121)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=2803247999:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2973 on theBenchmark for (2973ds/125Mi)
% 29.35/5.72 % (3980123)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=4157428608:i=134:gtgl=5:slsql=off:gtg=exists_sym_2973 on theBenchmark for (2973ds/134Mi)
% 29.35/5.72 % (3980121)Instruction limit reached!
% 29.35/5.72 % (3980121)------------------------------
% 29.35/5.72 % (3980121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980121)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980121)Termination reason: Instruction limit
% 29.35/5.72 % (3980121)Termination phase: Saturation
% 29.35/5.72 % (3980121)Time elapsed: 0.139 s
% 29.35/5.72 % (3980121)Peak memory usage: 90 MB
% 29.35/5.72 % (3980121)Instructions burned: 125 (million)
% 29.35/5.72 % (3980123)Instruction limit reached!
% 29.35/5.72 % (3980123)------------------------------
% 29.35/5.72 % (3980123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980123)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980123)Termination reason: Instruction limit
% 29.35/5.72 % (3980123)Termination phase: Saturation
% 29.35/5.72 % (3980123)Time elapsed: 0.125 s
% 29.35/5.72 % (3980123)Peak memory usage: 89 MB
% 29.35/5.72 % (3980123)Instructions burned: 134 (million)
% 29.35/5.72 % (3980126)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3659730286:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2971 on theBenchmark for (2971ds/141Mi)
% 29.35/5.72 % (3980126)Refutation not found, incomplete strategy
% 29.35/5.72 % (3980126)------------------------------
% 29.35/5.72 % (3980126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980126)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980126)Termination reason: Refutation not found, incomplete strategy
% 29.35/5.72 % (3980126)Time elapsed: 0.001 s
% 29.35/5.72 % (3980126)Peak memory usage: 88 MB
% 29.35/5.72 % (3980126)------------------------------
% 29.35/5.72 % (3980126)------------------------------
% 29.35/5.72 % (3980129)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=2051472098:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2969 on theBenchmark for (2969ds/431Mi)
% 29.35/5.72 % (3980129)Refutation not found, incomplete strategy
% 29.35/5.72 % (3980129)------------------------------
% 29.35/5.72 % (3980129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980129)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980129)Termination reason: Refutation not found, incomplete strategy
% 29.35/5.72 % (3980129)Time elapsed: 0.003 s
% 29.35/5.72 % (3980129)Peak memory usage: 88 MB
% 29.35/5.72 % (3980129)Instructions burned: 1 (million)
% 29.35/5.72 % (3980130)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=2587805684:i=6060:aac=none:ins=25_2969 on theBenchmark for (2969ds/6060Mi)
% 29.35/5.72 % (3980133)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1233378537:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2966 on theBenchmark for (2966ds/150Mi)
% 29.35/5.72 % (3980133)Instruction limit reached!
% 29.35/5.72 % (3980133)------------------------------
% 29.35/5.72 % (3980133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980133)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980133)Termination reason: Instruction limit
% 29.35/5.72 % (3980133)Termination phase: Saturation
% 29.35/5.72 % (3980133)Time elapsed: 0.082 s
% 29.35/5.72 % (3980133)Peak memory usage: 91 MB
% 29.35/5.72 % (3980133)Instructions burned: 152 (million)
% 29.35/5.72 % (3980129)------------------------------
% 29.35/5.72 % (3980129)------------------------------
% 29.35/5.72 % (3980136)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=4236615966:i=14155:bd=all_2963 on theBenchmark for (2963ds/14155Mi)
% 29.35/5.72 % (3980137)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=3120849743:i=667:av=off:fsr=off_2962 on theBenchmark for (2962ds/667Mi)
% 29.35/5.72 % (3980065)First to succeed.
% 29.35/5.72 % (3980065)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3980059"
% 29.35/5.72 % (3980137)Instruction limit reached!
% 29.35/5.72 % (3980137)------------------------------
% 29.35/5.72 % (3980137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.35/5.72 % (3980137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.35/5.72 % (3980137)CaDiCaL version: 2.1.3
% 29.35/5.72 % (3980137)Termination reason: Instruction limit
% 29.35/5.72 % (3980137)Termination phase: Saturation
% 29.35/5.72 % (3980137)Time elapsed: 0.452 s
% 29.35/5.72 % (3980137)Peak memory usage: 89 MB
% 29.35/5.72 % (3980137)Instructions burned: 668 (million)
% 29.35/5.72 % (3980142)ott-1011_3:1_anc=all_dependent:to=lpo:sil=8000:drc=ordering:sas=cadical:fdtod=off:sp=reverse_frequency:spb=goal_then_units:urr=full:lftc=20:newcnf=on:random_seed=3459200711:s2a=on:i=185:s2at=1.8:fdi=4_2955 on theBenchmark for (2955ds/185Mi)
% 29.35/5.72 % (3980065)Refutation found. Thanks to Tanya!
% 29.35/5.72 % SZS status Theorem for theBenchmark
% 29.35/5.72 % SZS output start Proof for theBenchmark
% See solution above
% 34.99/5.99 % (3980065)------------------------------
% 34.99/5.99 % (3980065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.99/5.99 % (3980065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.99/5.99 % (3980065)CaDiCaL version: 2.1.3
% 34.99/5.99 % (3980065)Termination reason: Refutation
% 34.99/5.99 % (3980065)Time elapsed: 4.238 s
% 34.99/5.99 % (3980065)Peak memory usage: 160 MB
% 34.99/5.99 % (3980065)Instructions burned: 3984 (million)
% 34.99/5.99 % (3980065)------------------------------
% 34.99/5.99 % (3980065)------------------------------
% 34.99/5.99 % (3980059)Success in time 4.876 s
% 34.99/5.99 % Vampire exiting
%------------------------------------------------------------------------------