TSTP Solution File: KLE120+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE120+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:32:11 EDT 2023
% Result : Theorem 17.14s 3.19s
% Output : CNFRefutation 17.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 21
% Syntax : Number of formulae : 193 ( 192 unt; 0 def)
% Number of atoms : 194 ( 193 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 258 ( 22 sgn; 82 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X3] : zero = multiplication(antidomain(X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X3,X4] : antidomain(multiplication(X3,antidomain(antidomain(X4)))) = addition(antidomain(multiplication(X3,X4)),antidomain(multiplication(X3,antidomain(antidomain(X4))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f15,axiom,
! [X3] : one = addition(antidomain(antidomain(X3)),antidomain(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X3] : antidomain(antidomain(X3)) = domain(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f17,axiom,
! [X3] : zero = multiplication(X3,coantidomain(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
fof(f18,axiom,
! [X3,X4] : coantidomain(multiplication(coantidomain(coantidomain(X3)),X4)) = addition(coantidomain(multiplication(X3,X4)),coantidomain(multiplication(coantidomain(coantidomain(X3)),X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).
fof(f19,axiom,
! [X3] : one = addition(coantidomain(coantidomain(X3)),coantidomain(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
fof(f20,axiom,
! [X3] : coantidomain(coantidomain(X3)) = codomain(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
fof(f24,axiom,
! [X3,X4] : backward_diamond(X3,X4) = codomain(multiplication(codomain(X4),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_diamond) ).
fof(f27,conjecture,
! [X3] : domain(X3) = addition(backward_diamond(one,domain(X3)),domain(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X3] : domain(X3) = addition(backward_diamond(one,domain(X3)),domain(X3)),
inference(negated_conjecture,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f30,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(rectify,[],[f13]) ).
fof(f31,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(rectify,[],[f14]) ).
fof(f32,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(rectify,[],[f15]) ).
fof(f33,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(rectify,[],[f16]) ).
fof(f34,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(rectify,[],[f17]) ).
fof(f35,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(rectify,[],[f18]) ).
fof(f36,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(rectify,[],[f19]) ).
fof(f37,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(rectify,[],[f20]) ).
fof(f41,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(rectify,[],[f24]) ).
fof(f44,plain,
~ ! [X0] : domain(X0) = addition(backward_diamond(one,domain(X0)),domain(X0)),
inference(rectify,[],[f28]) ).
fof(f45,plain,
? [X0] : domain(X0) != addition(backward_diamond(one,domain(X0)),domain(X0)),
inference(ennf_transformation,[],[f44]) ).
fof(f46,plain,
( ? [X0] : domain(X0) != addition(backward_diamond(one,domain(X0)),domain(X0))
=> domain(sK0) != addition(backward_diamond(one,domain(sK0)),domain(sK0)) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
domain(sK0) != addition(backward_diamond(one,domain(sK0)),domain(sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f45,f46]) ).
fof(f48,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f49,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f51,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f52,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f54,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f55,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f56,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f58,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f59,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f30]) ).
fof(f60,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f31]) ).
fof(f61,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f32]) ).
fof(f62,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f33]) ).
fof(f63,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f34]) ).
fof(f64,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f37]) ).
fof(f70,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f41]) ).
fof(f73,plain,
domain(sK0) != addition(backward_diamond(one,domain(sK0)),domain(sK0)),
inference(cnf_transformation,[],[f47]) ).
fof(f75,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f70,f66,f66]) ).
fof(f80,plain,
antidomain(antidomain(sK0)) != addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),one))),antidomain(antidomain(sK0))),
inference(definition_unfolding,[],[f73,f62,f75,f62,f62]) ).
cnf(c_49,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f48]) ).
cnf(c_50,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f49]) ).
cnf(c_51,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[],[f50]) ).
cnf(c_52,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[],[f51]) ).
cnf(c_53,plain,
multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f52]) ).
cnf(c_54,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f53]) ).
cnf(c_55,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f54]) ).
cnf(c_56,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f55]) ).
cnf(c_57,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f56]) ).
cnf(c_59,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f58]) ).
cnf(c_60,plain,
multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f59]) ).
cnf(c_61,plain,
addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[],[f60]) ).
cnf(c_62,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f61]) ).
cnf(c_63,plain,
multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f63]) ).
cnf(c_64,plain,
addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(cnf_transformation,[],[f64]) ).
cnf(c_65,plain,
addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f65]) ).
cnf(c_66,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),one))),antidomain(antidomain(sK0))) != antidomain(antidomain(sK0)),
inference(cnf_transformation,[],[f80]) ).
cnf(c_82,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
cnf(c_83,plain,
addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_65,c_50,c_49]) ).
cnf(c_84,negated_conjecture,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),one)))) != antidomain(antidomain(sK0)),
inference(theory_normalisation,[status(thm)],[c_66,c_50,c_49]) ).
cnf(c_123,plain,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(sK0))))))) != antidomain(antidomain(sK0)),
inference(demodulation,[status(thm)],[c_84,c_54]) ).
cnf(c_204,plain,
addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_205,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_54,c_60]) ).
cnf(c_207,plain,
coantidomain(one) = zero,
inference(superposition,[status(thm)],[c_55,c_63]) ).
cnf(c_209,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
cnf(c_216,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
cnf(c_221,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_205,c_82]) ).
cnf(c_223,plain,
addition(zero,coantidomain(zero)) = one,
inference(superposition,[status(thm)],[c_207,c_83]) ).
cnf(c_230,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_221,c_209]) ).
cnf(c_234,plain,
coantidomain(zero) = one,
inference(demodulation,[status(thm)],[c_223,c_209]) ).
cnf(c_244,plain,
addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_82,c_216]) ).
cnf(c_245,plain,
addition(coantidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_83,c_216]) ).
cnf(c_248,plain,
addition(one,coantidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_245,c_50,c_49]) ).
cnf(c_249,plain,
addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_244,c_50,c_49]) ).
cnf(c_300,plain,
addition(one,addition(X0,antidomain(X1))) = addition(X0,one),
inference(superposition,[status(thm)],[c_249,c_204]) ).
cnf(c_321,plain,
multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c_60,c_53]) ).
cnf(c_325,plain,
multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(superposition,[status(thm)],[c_53,c_63]) ).
cnf(c_336,plain,
addition(multiplication(X0,antidomain(X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_82,c_56]) ).
cnf(c_337,plain,
addition(multiplication(X0,coantidomain(X1)),multiplication(X0,coantidomain(coantidomain(X1)))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_83,c_56]) ).
cnf(c_348,plain,
addition(multiplication(antidomain(addition(X0,X1)),X0),multiplication(antidomain(addition(X0,X1)),X1)) = zero,
inference(superposition,[status(thm)],[c_56,c_60]) ).
cnf(c_359,plain,
addition(multiplication(X0,coantidomain(X1)),multiplication(X0,coantidomain(coantidomain(X1)))) = X0,
inference(light_normalisation,[status(thm)],[c_337,c_54]) ).
cnf(c_360,plain,
addition(multiplication(X0,antidomain(X1)),multiplication(X0,antidomain(antidomain(X1)))) = X0,
inference(light_normalisation,[status(thm)],[c_336,c_54]) ).
cnf(c_375,plain,
addition(multiplication(antidomain(X0),X1),multiplication(antidomain(antidomain(X0)),X1)) = multiplication(one,X1),
inference(superposition,[status(thm)],[c_82,c_57]) ).
cnf(c_376,plain,
addition(multiplication(coantidomain(X0),X1),multiplication(coantidomain(coantidomain(X0)),X1)) = multiplication(one,X1),
inference(superposition,[status(thm)],[c_83,c_57]) ).
cnf(c_380,plain,
addition(multiplication(one,X0),multiplication(coantidomain(X1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_248,c_57]) ).
cnf(c_381,plain,
addition(multiplication(one,X0),multiplication(antidomain(X1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_249,c_57]) ).
cnf(c_387,plain,
addition(multiplication(X0,coantidomain(addition(X0,X1))),multiplication(X1,coantidomain(addition(X0,X1)))) = zero,
inference(superposition,[status(thm)],[c_57,c_63]) ).
cnf(c_395,plain,
addition(X0,multiplication(antidomain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_381,c_55]) ).
cnf(c_396,plain,
addition(X0,multiplication(coantidomain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_380,c_55]) ).
cnf(c_407,plain,
addition(antidomain(zero),antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0)))))) = antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(superposition,[status(thm)],[c_63,c_61]) ).
cnf(c_409,plain,
addition(antidomain(multiplication(one,X0)),antidomain(antidomain(antidomain(X0)))) = antidomain(antidomain(antidomain(X0))),
inference(superposition,[status(thm)],[c_55,c_61]) ).
cnf(c_424,plain,
addition(antidomain(X0),antidomain(antidomain(antidomain(X0)))) = antidomain(antidomain(antidomain(X0))),
inference(light_normalisation,[status(thm)],[c_409,c_55]) ).
cnf(c_430,plain,
addition(one,antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0)))))) = antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(light_normalisation,[status(thm)],[c_407,c_230]) ).
cnf(c_836,plain,
multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(demodulation,[status(thm)],[c_321,c_59]) ).
cnf(c_967,plain,
addition(one,antidomain(multiplication(X0,antidomain(antidomain(X1))))) = addition(antidomain(multiplication(X0,X1)),one),
inference(superposition,[status(thm)],[c_61,c_300]) ).
cnf(c_999,plain,
addition(one,antidomain(multiplication(X0,antidomain(antidomain(X1))))) = addition(one,antidomain(multiplication(X0,X1))),
inference(theory_normalisation,[status(thm)],[c_967,c_50,c_49]) ).
cnf(c_1634,plain,
addition(zero,multiplication(antidomain(coantidomain(X0)),coantidomain(coantidomain(X0)))) = antidomain(coantidomain(X0)),
inference(superposition,[status(thm)],[c_60,c_359]) ).
cnf(c_1635,plain,
addition(zero,multiplication(X0,coantidomain(coantidomain(X0)))) = X0,
inference(superposition,[status(thm)],[c_63,c_359]) ).
cnf(c_1642,plain,
addition(multiplication(antidomain(coantidomain(coantidomain(X0))),coantidomain(X0)),zero) = antidomain(coantidomain(coantidomain(X0))),
inference(superposition,[status(thm)],[c_60,c_359]) ).
cnf(c_1659,plain,
addition(zero,multiplication(antidomain(coantidomain(coantidomain(X0))),coantidomain(X0))) = antidomain(coantidomain(coantidomain(X0))),
inference(theory_normalisation,[status(thm)],[c_1642,c_50,c_49]) ).
cnf(c_1662,plain,
multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(demodulation,[status(thm)],[c_1635,c_209]) ).
cnf(c_1672,plain,
multiplication(X0,multiplication(coantidomain(coantidomain(X0)),X1)) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c_1662,c_53]) ).
cnf(c_1745,plain,
multiplication(X0,coantidomain(coantidomain(coantidomain(coantidomain(X0))))) = multiplication(X0,coantidomain(coantidomain(X0))),
inference(superposition,[status(thm)],[c_1662,c_1672]) ).
cnf(c_1781,plain,
multiplication(X0,coantidomain(coantidomain(coantidomain(coantidomain(X0))))) = X0,
inference(light_normalisation,[status(thm)],[c_1745,c_1662]) ).
cnf(c_1874,plain,
addition(coantidomain(coantidomain(coantidomain(coantidomain(antidomain(X0))))),antidomain(X0)) = coantidomain(coantidomain(coantidomain(coantidomain(antidomain(X0))))),
inference(superposition,[status(thm)],[c_1781,c_395]) ).
cnf(c_1891,plain,
addition(antidomain(X0),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(X0)))))) = coantidomain(coantidomain(coantidomain(coantidomain(antidomain(X0))))),
inference(theory_normalisation,[status(thm)],[c_1874,c_50,c_49]) ).
cnf(c_1894,plain,
coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(sK0)))))) != antidomain(antidomain(sK0)),
inference(demodulation,[status(thm)],[c_123,c_1891]) ).
cnf(c_5127,plain,
addition(multiplication(antidomain(addition(X0,X1)),X0),zero) = zero,
inference(superposition,[status(thm)],[c_348,c_216]) ).
cnf(c_5150,plain,
addition(zero,multiplication(antidomain(addition(X0,X1)),X0)) = zero,
inference(theory_normalisation,[status(thm)],[c_5127,c_50,c_49]) ).
cnf(c_5470,plain,
multiplication(antidomain(addition(X0,X1)),X0) = zero,
inference(demodulation,[status(thm)],[c_5150,c_209]) ).
cnf(c_5474,plain,
multiplication(antidomain(addition(X0,X1)),X1) = zero,
inference(superposition,[status(thm)],[c_49,c_5470]) ).
cnf(c_5481,plain,
multiplication(antidomain(coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),coantidomain(multiplication(X0,X1))) = zero,
inference(superposition,[status(thm)],[c_64,c_5470]) ).
cnf(c_5517,plain,
multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(X0)) = zero,
inference(superposition,[status(thm)],[c_424,c_5470]) ).
cnf(c_5964,plain,
multiplication(antidomain(X0),multiplication(coantidomain(X1),X0)) = zero,
inference(superposition,[status(thm)],[c_396,c_5474]) ).
cnf(c_9928,plain,
addition(multiplication(antidomain(X0),X1),multiplication(antidomain(antidomain(X0)),X1)) = X1,
inference(demodulation,[status(thm)],[c_375,c_55]) ).
cnf(c_9932,plain,
addition(zero,multiplication(antidomain(antidomain(X0)),X0)) = X0,
inference(superposition,[status(thm)],[c_60,c_9928]) ).
cnf(c_9956,plain,
addition(zero,multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(X0))))),antidomain(X0))) = antidomain(X0),
inference(superposition,[status(thm)],[c_5517,c_9928]) ).
cnf(c_10081,plain,
multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(demodulation,[status(thm)],[c_9932,c_209]) ).
cnf(c_10101,plain,
multiplication(antidomain(antidomain(antidomain(X0))),X0) = zero,
inference(superposition,[status(thm)],[c_10081,c_836]) ).
cnf(c_10104,plain,
multiplication(antidomain(antidomain(X0)),multiplication(X0,X1)) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c_10081,c_53]) ).
cnf(c_10108,plain,
addition(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(X0)),antidomain(antidomain(X0))) = antidomain(antidomain(antidomain(antidomain(X0)))),
inference(superposition,[status(thm)],[c_10081,c_360]) ).
cnf(c_10174,plain,
addition(antidomain(antidomain(X0)),multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(X0))) = antidomain(antidomain(antidomain(antidomain(X0)))),
inference(theory_normalisation,[status(thm)],[c_10108,c_50,c_49]) ).
cnf(c_10175,plain,
addition(antidomain(antidomain(X0)),zero) = antidomain(antidomain(antidomain(antidomain(X0)))),
inference(light_normalisation,[status(thm)],[c_10174,c_5517]) ).
cnf(c_10176,plain,
addition(zero,antidomain(antidomain(X0))) = antidomain(antidomain(antidomain(antidomain(X0)))),
inference(theory_normalisation,[status(thm)],[c_10175,c_50,c_49]) ).
cnf(c_10301,plain,
addition(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(X0))))),antidomain(X0)),zero) = antidomain(antidomain(antidomain(antidomain(antidomain(X0))))),
inference(superposition,[status(thm)],[c_10101,c_360]) ).
cnf(c_10381,plain,
addition(zero,multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(X0))))),antidomain(X0))) = antidomain(antidomain(antidomain(antidomain(antidomain(X0))))),
inference(theory_normalisation,[status(thm)],[c_10301,c_50,c_49]) ).
cnf(c_10382,plain,
antidomain(addition(zero,antidomain(antidomain(X0)))) = antidomain(X0),
inference(light_normalisation,[status(thm)],[c_10381,c_9956,c_10176]) ).
cnf(c_10393,plain,
antidomain(antidomain(antidomain(X0))) = antidomain(X0),
inference(demodulation,[status(thm)],[c_10382,c_209]) ).
cnf(c_11094,plain,
addition(multiplication(coantidomain(X0),X1),multiplication(coantidomain(coantidomain(X0)),X1)) = X1,
inference(demodulation,[status(thm)],[c_376,c_55]) ).
cnf(c_13411,plain,
multiplication(antidomain(coantidomain(X0)),coantidomain(coantidomain(X0))) = antidomain(coantidomain(X0)),
inference(demodulation,[status(thm)],[c_1634,c_209]) ).
cnf(c_13428,plain,
multiplication(antidomain(coantidomain(X0)),multiplication(coantidomain(coantidomain(X0)),X1)) = multiplication(antidomain(coantidomain(X0)),X1),
inference(superposition,[status(thm)],[c_13411,c_53]) ).
cnf(c_14654,plain,
addition(multiplication(X0,coantidomain(addition(X0,X1))),zero) = zero,
inference(superposition,[status(thm)],[c_387,c_216]) ).
cnf(c_14685,plain,
addition(zero,multiplication(X0,coantidomain(addition(X0,X1)))) = zero,
inference(theory_normalisation,[status(thm)],[c_14654,c_50,c_49]) ).
cnf(c_15119,plain,
multiplication(X0,coantidomain(addition(X0,X1))) = zero,
inference(demodulation,[status(thm)],[c_14685,c_209]) ).
cnf(c_15161,plain,
multiplication(multiplication(X0,antidomain(X1)),coantidomain(X0)) = zero,
inference(superposition,[status(thm)],[c_360,c_15119]) ).
cnf(c_16388,plain,
multiplication(X0,multiplication(antidomain(X1),coantidomain(X0))) = zero,
inference(demodulation,[status(thm)],[c_15161,c_53]) ).
cnf(c_16401,plain,
multiplication(coantidomain(antidomain(X0)),antidomain(X0)) = zero,
inference(superposition,[status(thm)],[c_1662,c_16388]) ).
cnf(c_16572,plain,
multiplication(coantidomain(antidomain(X0)),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c_16401,c_53]) ).
cnf(c_21958,plain,
multiplication(coantidomain(antidomain(X0)),multiplication(antidomain(X0),X1)) = zero,
inference(demodulation,[status(thm)],[c_16572,c_59]) ).
cnf(c_22018,plain,
multiplication(coantidomain(antidomain(antidomain(X0))),X0) = zero,
inference(superposition,[status(thm)],[c_10081,c_21958]) ).
cnf(c_22765,plain,
addition(zero,multiplication(coantidomain(coantidomain(antidomain(antidomain(X0)))),X0)) = X0,
inference(superposition,[status(thm)],[c_22018,c_11094]) ).
cnf(c_33731,plain,
antidomain(multiplication(X0,antidomain(antidomain(coantidomain(X0))))) = one,
inference(demodulation,[status(thm)],[c_430,c_249,c_999]) ).
cnf(c_33793,plain,
multiplication(one,multiplication(X0,antidomain(antidomain(coantidomain(X0))))) = zero,
inference(superposition,[status(thm)],[c_33731,c_60]) ).
cnf(c_33935,plain,
multiplication(X0,antidomain(antidomain(coantidomain(X0)))) = zero,
inference(demodulation,[status(thm)],[c_33793,c_55]) ).
cnf(c_33987,plain,
addition(multiplication(X0,antidomain(coantidomain(X0))),zero) = X0,
inference(superposition,[status(thm)],[c_33935,c_360]) ).
cnf(c_34066,plain,
addition(zero,multiplication(X0,antidomain(coantidomain(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_33987,c_50,c_49]) ).
cnf(c_34975,plain,
multiplication(X0,antidomain(coantidomain(X0))) = X0,
inference(demodulation,[status(thm)],[c_34066,c_209]) ).
cnf(c_35041,plain,
multiplication(antidomain(antidomain(coantidomain(coantidomain(X0)))),coantidomain(X0)) = zero,
inference(superposition,[status(thm)],[c_34975,c_5964]) ).
cnf(c_36854,plain,
addition(multiplication(antidomain(coantidomain(coantidomain(X0))),coantidomain(X0)),zero) = coantidomain(X0),
inference(superposition,[status(thm)],[c_35041,c_9928]) ).
cnf(c_36888,plain,
addition(zero,multiplication(antidomain(coantidomain(coantidomain(X0))),coantidomain(X0))) = coantidomain(X0),
inference(theory_normalisation,[status(thm)],[c_36854,c_50,c_49]) ).
cnf(c_36889,plain,
antidomain(coantidomain(coantidomain(X0))) = coantidomain(X0),
inference(light_normalisation,[status(thm)],[c_36888,c_1659]) ).
cnf(c_36960,plain,
multiplication(antidomain(coantidomain(X0)),multiplication(coantidomain(coantidomain(X0)),X1)) = multiplication(coantidomain(coantidomain(X0)),X1),
inference(superposition,[status(thm)],[c_36889,c_10104]) ).
cnf(c_36964,plain,
antidomain(antidomain(coantidomain(X0))) = coantidomain(X0),
inference(superposition,[status(thm)],[c_36889,c_10393]) ).
cnf(c_36966,plain,
multiplication(antidomain(coantidomain(X0)),coantidomain(coantidomain(X0))) = coantidomain(coantidomain(X0)),
inference(superposition,[status(thm)],[c_36889,c_10081]) ).
cnf(c_37058,plain,
antidomain(coantidomain(X0)) = coantidomain(coantidomain(X0)),
inference(light_normalisation,[status(thm)],[c_36966,c_13411]) ).
cnf(c_37060,plain,
multiplication(antidomain(coantidomain(X0)),X1) = multiplication(coantidomain(coantidomain(X0)),X1),
inference(light_normalisation,[status(thm)],[c_36960,c_13428]) ).
cnf(c_37111,plain,
coantidomain(coantidomain(antidomain(coantidomain(antidomain(antidomain(sK0)))))) != antidomain(antidomain(sK0)),
inference(demodulation,[status(thm)],[c_1894,c_37058]) ).
cnf(c_37114,plain,
antidomain(coantidomain(antidomain(coantidomain(antidomain(antidomain(sK0)))))) != antidomain(antidomain(sK0)),
inference(demodulation,[status(thm)],[c_37111,c_37058]) ).
cnf(c_37268,plain,
antidomain(antidomain(coantidomain(X0))) = coantidomain(antidomain(coantidomain(X0))),
inference(superposition,[status(thm)],[c_37058,c_37058]) ).
cnf(c_37347,plain,
coantidomain(antidomain(coantidomain(X0))) = coantidomain(X0),
inference(light_normalisation,[status(thm)],[c_37268,c_36964]) ).
cnf(c_37357,plain,
antidomain(coantidomain(antidomain(antidomain(sK0)))) != antidomain(antidomain(sK0)),
inference(demodulation,[status(thm)],[c_37114,c_37347]) ).
cnf(c_40083,plain,
multiplication(antidomain(coantidomain(antidomain(antidomain(X0)))),X0) = X0,
inference(demodulation,[status(thm)],[c_22765,c_209,c_37060]) ).
cnf(c_40087,plain,
multiplication(antidomain(coantidomain(antidomain(X0))),antidomain(X0)) = antidomain(X0),
inference(superposition,[status(thm)],[c_10393,c_40083]) ).
cnf(c_64854,plain,
multiplication(antidomain(coantidomain(multiplication(antidomain(coantidomain(X0)),X1))),coantidomain(multiplication(X0,X1))) = zero,
inference(light_normalisation,[status(thm)],[c_5481,c_37060]) ).
cnf(c_64943,plain,
multiplication(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(X0))),X0))),coantidomain(zero)) = zero,
inference(superposition,[status(thm)],[c_60,c_64854]) ).
cnf(c_65181,plain,
multiplication(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(X0))),X0))),one) = zero,
inference(light_normalisation,[status(thm)],[c_64943,c_234]) ).
cnf(c_66683,plain,
antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(X0))),X0))) = zero,
inference(demodulation,[status(thm)],[c_65181,c_54]) ).
cnf(c_66861,plain,
coantidomain(multiplication(antidomain(coantidomain(antidomain(X0))),X0)) = antidomain(zero),
inference(superposition,[status(thm)],[c_66683,c_36964]) ).
cnf(c_66907,plain,
coantidomain(multiplication(antidomain(coantidomain(antidomain(X0))),X0)) = one,
inference(light_normalisation,[status(thm)],[c_66861,c_230]) ).
cnf(c_67087,plain,
multiplication(antidomain(coantidomain(antidomain(X0))),multiplication(X0,one)) = zero,
inference(superposition,[status(thm)],[c_66907,c_325]) ).
cnf(c_67193,plain,
multiplication(antidomain(coantidomain(antidomain(X0))),X0) = zero,
inference(light_normalisation,[status(thm)],[c_67087,c_54]) ).
cnf(c_67319,plain,
addition(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(X0))))),antidomain(X0)),zero) = antidomain(coantidomain(antidomain(antidomain(antidomain(X0))))),
inference(superposition,[status(thm)],[c_67193,c_360]) ).
cnf(c_67487,plain,
addition(zero,multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(X0))))),antidomain(X0))) = antidomain(coantidomain(antidomain(antidomain(antidomain(X0))))),
inference(theory_normalisation,[status(thm)],[c_67319,c_50,c_49]) ).
cnf(c_67488,plain,
addition(zero,antidomain(X0)) = antidomain(coantidomain(antidomain(X0))),
inference(light_normalisation,[status(thm)],[c_67487,c_10393,c_40087]) ).
cnf(c_67550,plain,
addition(zero,antidomain(antidomain(sK0))) != antidomain(antidomain(sK0)),
inference(demodulation,[status(thm)],[c_37357,c_67488]) ).
cnf(c_67551,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_67550,c_209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE120+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 12:16:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.14/3.19 % SZS status Started for theBenchmark.p
% 17.14/3.19 % SZS status Theorem for theBenchmark.p
% 17.14/3.19
% 17.14/3.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.14/3.19
% 17.14/3.19 ------ iProver source info
% 17.14/3.19
% 17.14/3.19 git: date: 2023-05-31 18:12:56 +0000
% 17.14/3.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.14/3.19 git: non_committed_changes: false
% 17.14/3.19 git: last_make_outside_of_git: false
% 17.14/3.19
% 17.14/3.19 ------ Parsing...
% 17.14/3.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.14/3.19
% 17.14/3.19 ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e
% 17.14/3.19
% 17.14/3.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.14/3.19
% 17.14/3.19 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 17.14/3.19 ------ Proving...
% 17.14/3.19 ------ Problem Properties
% 17.14/3.19
% 17.14/3.19
% 17.14/3.19 clauses 18
% 17.14/3.19 conjectures 0
% 17.14/3.19 EPR 0
% 17.14/3.19 Horn 18
% 17.14/3.19 unary 18
% 17.14/3.19 binary 0
% 17.14/3.19 lits 18
% 17.14/3.19 lits eq 18
% 17.14/3.19 fd_pure 0
% 17.14/3.19 fd_pseudo 0
% 17.14/3.19 fd_cond 0
% 17.14/3.19 fd_pseudo_cond 0
% 17.14/3.19 AC symbols 1
% 17.14/3.19
% 17.14/3.19 ------ Schedule UEQ
% 17.14/3.19
% 17.14/3.19 ------ Option_UEQ Time Limit: 10.
% 17.14/3.19
% 17.14/3.19
% 17.14/3.19 ------
% 17.14/3.19 Current options:
% 17.14/3.19 ------
% 17.14/3.19
% 17.14/3.19
% 17.14/3.19
% 17.14/3.19
% 17.14/3.19 ------ Proving...
% 17.14/3.19
% 17.14/3.19
% 17.14/3.19 % SZS status Theorem for theBenchmark.p
% 17.14/3.19
% 17.14/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.14/3.20
% 17.14/3.20
%------------------------------------------------------------------------------