TSTP Solution File: KLE120+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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  
%------------------------------------------------------------------------------