%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE079+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Thu Sep 24 12:58:18 PM UTC 2026
% Result : Theorem 35.77s 5.26s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE079+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.65 % Computer : n014.cluster.edu
% 0.14/0.65 % Model : x86_64 x86_64
% 0.14/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.65 % Memory : 8046.5625MB
% 0.14/0.65 % OS : Linux 6.8.0-71-generic
% 0.14/0.65 % CPULimit : 300
% 0.14/0.65 % WCLimit : 300
% 0.14/0.65 % DateTime : Sun Sep 20 22:42:22 UTC 2026
% 0.14/0.65 % CPUTime :
% 0.19/0.67 % Drodi V4.1.1
% 35.77/5.26 % Refutation found
% 35.77/5.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 35.77/5.26 % SZS output start CNFRefutation for theBenchmark
% 35.77/5.26 fof(f1,axiom,(
% 35.77/5.26 (! [A,B] : addition(A,B) = addition(B,A) )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f2,axiom,(
% 35.77/5.26 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f4,axiom,(
% 35.77/5.26 (! [A] : addition(A,A) = A )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f5,axiom,(
% 35.77/5.26 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f7,axiom,(
% 35.77/5.26 (! [A] : multiplication(one,A) = A )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f9,axiom,(
% 35.77/5.26 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f11,axiom,(
% 35.77/5.26 (! [A] : multiplication(zero,A) = zero )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f13,axiom,(
% 35.77/5.26 (! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f14,axiom,(
% 35.77/5.26 (! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f15,axiom,(
% 35.77/5.26 (! [X0] : addition(domain(X0),one) = one )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f16,axiom,(
% 35.77/5.26 domain(zero) = zero ),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f17,axiom,(
% 35.77/5.26 (! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f18,conjecture,(
% 35.77/5.26 (! [X0] :( (! [X1] :( addition(domain(X1),antidomain(X1)) = one& multiplication(domain(X1),antidomain(X1)) = zero ))=> multiplication(antidomain(X0),domain(X0)) = zero ) )),
% 35.77/5.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.77/5.26 fof(f19,negated_conjecture,(
% 35.77/5.26 ~((! [X0] :( (! [X1] :( addition(domain(X1),antidomain(X1)) = one& multiplication(domain(X1),antidomain(X1)) = zero ))=> multiplication(antidomain(X0),domain(X0)) = zero ) ))),
% 35.77/5.26 inference(negated_conjecture,[status(cth)],[f18])).
% 35.77/5.26 fof(f20,plain,(
% 35.77/5.26 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f1])).
% 35.77/5.26 fof(f21,plain,(
% 35.77/5.26 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f2])).
% 35.77/5.26 fof(f23,plain,(
% 35.77/5.26 ![X0]: (addition(X0,X0)=X0)),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f4])).
% 35.77/5.26 fof(f24,plain,(
% 35.77/5.26 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f5])).
% 35.77/5.26 fof(f26,plain,(
% 35.77/5.26 ![X0]: (multiplication(one,X0)=X0)),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f7])).
% 35.77/5.26 fof(f28,plain,(
% 35.77/5.26 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f9])).
% 35.77/5.26 fof(f30,plain,(
% 35.77/5.26 ![X0]: (multiplication(zero,X0)=zero)),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f11])).
% 35.77/5.26 fof(f35,plain,(
% 35.77/5.26 ![X0]: (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0))),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f13])).
% 35.77/5.26 fof(f36,plain,(
% 35.77/5.26 ![X0,X1]: (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))))),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f14])).
% 35.77/5.26 fof(f37,plain,(
% 35.77/5.26 ![X0]: (addition(domain(X0),one)=one)),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f15])).
% 35.77/5.26 fof(f38,plain,(
% 35.77/5.26 domain(zero)=zero),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f16])).
% 35.77/5.26 fof(f39,plain,(
% 35.77/5.26 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X0),domain(X1)))),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f17])).
% 35.77/5.26 fof(f40,plain,(
% 35.77/5.26 (?[X0]: ((![X1]: (addition(domain(X1),antidomain(X1))=one&multiplication(domain(X1),antidomain(X1))=zero))&~multiplication(antidomain(X0),domain(X0))=zero))),
% 35.77/5.26 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 35.77/5.26 fof(f41,plain,(
% 35.77/5.26 ((![X1]: addition(domain(X1),antidomain(X1))=one)&(![X1]: multiplication(domain(X1),antidomain(X1))=zero))&(?[X0]: ~multiplication(antidomain(X0),domain(X0))=zero)),
% 35.77/5.26 inference(miniscoping,[status(thm)],[f40])).
% 35.77/5.26 fof(f42,plain,(
% 35.77/5.26 ((![X1]: addition(domain(X1),antidomain(X1))=one)&(![X1]: multiplication(domain(X1),antidomain(X1))=zero))&~multiplication(antidomain(sK0_skl),domain(sK0_skl))=zero),
% 35.77/5.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f41])).
% 35.77/5.26 fof(f43,plain,(
% 35.77/5.26 ![X0]: (addition(domain(X0),antidomain(X0))=one)),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f42])).
% 35.77/5.26 fof(f44,plain,(
% 35.77/5.26 ![X0]: (multiplication(domain(X0),antidomain(X0))=zero)),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f42])).
% 35.77/5.26 fof(f45,plain,(
% 35.77/5.26 ~multiplication(antidomain(sK0_skl),domain(sK0_skl))=zero),
% 35.77/5.26 inference(cnf_transformation,[status(thm)],[f42])).
% 35.77/5.26 fof(f79,plain,(
% 35.77/5.26 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f20,f21])).
% 35.77/5.26 fof(f100,plain,(
% 35.77/5.26 ![X0,X1]: (multiplication(domain(X0),multiplication(antidomain(X0),X1))=multiplication(zero,X1))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f44,f24])).
% 35.77/5.26 fof(f109,plain,(
% 35.77/5.26 ![X0,X1]: (multiplication(domain(X0),multiplication(antidomain(X0),X1))=zero)),
% 35.77/5.26 inference(forward_demodulation,[status(thm)],[f30,f100])).
% 35.77/5.26 fof(f113,plain,(
% 35.77/5.26 ![X0]: (addition(one,domain(X0))=one)),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f20,f37])).
% 35.77/5.26 fof(f217,plain,(
% 35.77/5.26 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X1),domain(X0)))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f20,f39])).
% 35.77/5.26 fof(f264,plain,(
% 35.77/5.26 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(X0,X1)))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f23,f79])).
% 35.77/5.26 fof(f362,plain,(
% 35.77/5.26 ![X0]: (addition(domain(X0),antidomain(X0))=addition(antidomain(X0),one))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f43,f264])).
% 35.77/5.26 fof(f392,plain,(
% 35.77/5.26 ![X0]: (one=addition(antidomain(X0),one))),
% 35.77/5.26 inference(forward_demodulation,[status(thm)],[f43,f362])).
% 35.77/5.26 fof(f420,plain,(
% 35.77/5.26 ![X0]: (one=addition(one,antidomain(X0)))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f20,f392])).
% 35.77/5.26 fof(f498,plain,(
% 35.77/5.26 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(X1,multiplication(X0,X1)))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f26,f28])).
% 35.77/5.26 fof(f503,plain,(
% 35.77/5.26 ![X0,X1,X2,X3]: (multiplication(addition(X0,multiplication(X1,X2)),X3)=addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f24,f28])).
% 35.77/5.26 fof(f1384,plain,(
% 35.77/5.26 ![X0,X1]: (addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))))=multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f36,f35])).
% 35.77/5.26 fof(f1450,plain,(
% 35.77/5.26 ![X0,X1]: (multiplication(addition(X0,multiplication(domain(multiplication(X0,X1)),X0)),domain(X1))=multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))))),
% 35.77/5.26 inference(forward_demodulation,[status(thm)],[f503,f1384])).
% 35.77/5.26 fof(f1451,plain,(
% 35.77/5.26 ![X0,X1]: (multiplication(addition(X0,multiplication(domain(multiplication(X0,X1)),X0)),domain(X1))=multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))))),
% 35.77/5.26 inference(forward_demodulation,[status(thm)],[f36,f1450])).
% 35.77/5.26 fof(f5852,plain,(
% 35.77/5.26 ![X0,X1]: (multiplication(one,X0)=addition(X0,multiplication(antidomain(X1),X0)))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f420,f498])).
% 35.77/5.26 fof(f5853,plain,(
% 35.77/5.26 ![X0,X1]: (multiplication(one,X0)=addition(X0,multiplication(domain(X1),X0)))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f113,f498])).
% 35.77/5.26 fof(f5878,plain,(
% 35.77/5.26 ![X0]: (multiplication(addition(one,domain(X0)),X0)=multiplication(domain(X0),X0))),
% 35.77/5.26 inference(paramodulation,[status(thm)],[f35,f498])).
% 35.77/5.26 fof(f5947,plain,(
% 35.77/5.26 ![X0,X1]: (X0=addition(X0,multiplication(antidomain(X1),X0)))),
% 35.77/5.26 inference(forward_demodulation,[status(thm)],[f26,f5852])).
% 35.77/5.26 fof(f5950,plain,(
% 35.77/5.26 ![X0,X1]: (multiplication(X0,domain(X1))=multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))))),
% 35.77/5.29 inference(backward_demodulation,[status(thm)],[f5951,f1451])).
% 35.77/5.29 fof(f5951,plain,(
% 35.77/5.29 ![X0,X1]: (X0=addition(X0,multiplication(domain(X1),X0)))),
% 35.77/5.29 inference(forward_demodulation,[status(thm)],[f26,f5853])).
% 35.77/5.29 fof(f5983,plain,(
% 35.77/5.29 ![X0]: (multiplication(one,X0)=multiplication(domain(X0),X0))),
% 35.77/5.29 inference(forward_demodulation,[status(thm)],[f113,f5878])).
% 35.77/5.29 fof(f6008,plain,(
% 35.77/5.29 ![X0]: (X0=multiplication(domain(X0),X0))),
% 35.77/5.29 inference(forward_demodulation,[status(thm)],[f26,f5983])).
% 35.77/5.29 fof(f6145,plain,(
% 35.77/5.29 ![X0,X1]: (multiplication(addition(domain(X0),X1),X0)=addition(X0,multiplication(X1,X0)))),
% 35.77/5.29 inference(paramodulation,[status(thm)],[f6008,f28])).
% 35.77/5.29 fof(f18371,plain,(
% 35.77/5.29 ![X0,X1]: (multiplication(domain(addition(X0,X1)),X1)=addition(X1,multiplication(domain(X0),X1)))),
% 35.77/5.29 inference(paramodulation,[status(thm)],[f217,f6145])).
% 35.77/5.29 fof(f18502,plain,(
% 35.77/5.29 ![X0,X1]: (multiplication(domain(addition(X0,X1)),X1)=X1)),
% 35.77/5.29 inference(forward_demodulation,[status(thm)],[f5951,f18371])).
% 35.77/5.29 fof(f18885,plain,(
% 35.77/5.29 ![X0,X1]: (multiplication(domain(X0),multiplication(antidomain(X1),X0))=multiplication(antidomain(X1),X0))),
% 35.77/5.29 inference(paramodulation,[status(thm)],[f5947,f18502])).
% 35.77/5.29 fof(f23287,plain,(
% 35.77/5.29 ![X0]: (zero=multiplication(antidomain(X0),X0))),
% 35.77/5.29 inference(paramodulation,[status(thm)],[f109,f18885])).
% 35.77/5.29 fof(f23650,plain,(
% 35.77/5.29 ![X0]: (multiplication(antidomain(X0),domain(X0))=multiplication(domain(zero),multiplication(antidomain(X0),domain(X0))))),
% 35.77/5.29 inference(paramodulation,[status(thm)],[f23287,f5950])).
% 35.77/5.29 fof(f23711,plain,(
% 35.77/5.29 ![X0]: (multiplication(antidomain(X0),domain(X0))=multiplication(zero,multiplication(antidomain(X0),domain(X0))))),
% 35.77/5.29 inference(forward_demodulation,[status(thm)],[f38,f23650])).
% 35.77/5.29 fof(f23712,plain,(
% 35.77/5.29 ~zero=zero),
% 35.77/5.29 inference(backward_demodulation,[status(thm)],[f23713,f45])).
% 35.77/5.29 fof(f23713,plain,(
% 35.77/5.29 ![X0]: (multiplication(antidomain(X0),domain(X0))=zero)),
% 35.77/5.29 inference(forward_demodulation,[status(thm)],[f30,f23711])).
% 35.77/5.29 fof(f23755,plain,(
% 35.77/5.29 $false),
% 35.77/5.29 inference(trivial_equality_resolution,[status(thm)],[f23712])).
% 35.77/5.29 % SZS output end CNFRefutation for theBenchmark.p
% 2.96/5.31 % Elapsed time: 4.641765 seconds
% 2.96/5.31 % CPU time: 36.438500 seconds
% 2.96/5.31 % Total memory used: 311.642 MB
% 2.96/5.31 % Net memory used: 303.112 MB
%------------------------------------------------------------------------------