%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE088+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 : n006.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 12:58:19 PM UTC 2026
% Result : Theorem 9.02s 11.66s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.43 % Computer : n006.cluster.edu
% 0.17/10.43 % Model : x86_64 x86_64
% 0.17/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.43 % Memory : 8046.5625MB
% 0.17/10.43 % OS : Linux 6.8.0-71-generic
% 0.17/10.43 % CPULimit : 300
% 0.17/10.43 % WCLimit : 300
% 0.17/10.43 % DateTime : Sun Sep 20 22:42:23 UTC 2026
% 0.17/10.43 % CPUTime :
% 0.17/10.44 % Drodi V4.1.1
% 9.02/11.66 % Refutation found
% 9.02/11.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.02/11.66 % SZS output start CNFRefutation for theBenchmark
% 9.02/11.66 fof(f1,axiom,(
% 9.02/11.66 (! [A,B] : addition(A,B) = addition(B,A) )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f2,axiom,(
% 9.02/11.66 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f3,axiom,(
% 9.02/11.66 (! [A] : addition(A,zero) = A )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f4,axiom,(
% 9.02/11.66 (! [A] : addition(A,A) = A )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f6,axiom,(
% 9.02/11.66 (! [A] : multiplication(A,one) = A )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f7,axiom,(
% 9.02/11.66 (! [A] : multiplication(one,A) = A )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f8,axiom,(
% 9.02/11.66 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f9,axiom,(
% 9.02/11.66 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f13,axiom,(
% 9.02/11.66 (! [X0] : multiplication(antidomain(X0),X0) = zero )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f14,axiom,(
% 9.02/11.66 (! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))) )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f15,axiom,(
% 9.02/11.66 (! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f16,axiom,(
% 9.02/11.66 (! [X0] : domain(X0) = antidomain(antidomain(X0)) )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f21,conjecture,(
% 9.02/11.66 (! [X0,X1] :( multiplication(domain(X0),X1) = zero=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ) )),
% 9.02/11.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.02/11.66 fof(f22,negated_conjecture,(
% 9.02/11.66 ~((! [X0,X1] :( multiplication(domain(X0),X1) = zero=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ) ))),
% 9.02/11.66 inference(negated_conjecture,[status(cth)],[f21])).
% 9.02/11.66 fof(f23,plain,(
% 9.02/11.66 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f1])).
% 9.02/11.66 fof(f24,plain,(
% 9.02/11.66 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f2])).
% 9.02/11.66 fof(f25,plain,(
% 9.02/11.66 ![X0]: (addition(X0,zero)=X0)),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f3])).
% 9.02/11.66 fof(f26,plain,(
% 9.02/11.66 ![X0]: (addition(X0,X0)=X0)),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f4])).
% 9.02/11.66 fof(f28,plain,(
% 9.02/11.66 ![X0]: (multiplication(X0,one)=X0)),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f6])).
% 9.02/11.66 fof(f29,plain,(
% 9.02/11.66 ![X0]: (multiplication(one,X0)=X0)),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f7])).
% 9.02/11.66 fof(f30,plain,(
% 9.02/11.66 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f8])).
% 9.02/11.66 fof(f31,plain,(
% 9.02/11.66 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f9])).
% 9.02/11.66 fof(f38,plain,(
% 9.02/11.66 ![X0]: (multiplication(antidomain(X0),X0)=zero)),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f13])).
% 9.02/11.66 fof(f39,plain,(
% 9.02/11.66 ![X0,X1]: (addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1)))))),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f14])).
% 9.02/11.66 fof(f40,plain,(
% 9.02/11.66 ![X0]: (addition(antidomain(antidomain(X0)),antidomain(X0))=one)),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f15])).
% 9.02/11.66 fof(f41,plain,(
% 9.02/11.66 ![X0]: (domain(X0)=antidomain(antidomain(X0)))),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f16])).
% 9.02/11.66 fof(f46,plain,(
% 9.02/11.66 (?[X0,X1]: (multiplication(domain(X0),X1)=zero&~addition(domain(X0),antidomain(X1))=antidomain(X1)))),
% 9.02/11.66 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 9.02/11.66 fof(f47,plain,(
% 9.02/11.66 (multiplication(domain(sK0_skl),sK1_skl)=zero&~addition(domain(sK0_skl),antidomain(sK1_skl))=antidomain(sK1_skl))),
% 9.02/11.66 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f46])).
% 9.02/11.66 fof(f48,plain,(
% 9.02/11.66 multiplication(domain(sK0_skl),sK1_skl)=zero),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f47])).
% 9.02/11.66 fof(f49,plain,(
% 9.02/11.66 ~addition(domain(sK0_skl),antidomain(sK1_skl))=antidomain(sK1_skl)),
% 9.02/11.66 inference(cnf_transformation,[status(thm)],[f47])).
% 9.02/11.66 fof(f60,plain,(
% 9.02/11.66 ~addition(antidomain(sK1_skl),domain(sK0_skl))=antidomain(sK1_skl)),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f23,f49])).
% 9.02/11.66 fof(f91,plain,(
% 9.02/11.66 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f26,f24])).
% 9.02/11.66 fof(f213,plain,(
% 9.02/11.66 zero=antidomain(one)),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f38,f28])).
% 9.02/11.66 fof(f232,plain,(
% 9.02/11.66 domain(one)=antidomain(zero)),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f213,f41])).
% 9.02/11.66 fof(f334,plain,(
% 9.02/11.66 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(X1,multiplication(X0,X1)))),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f29,f31])).
% 9.02/11.66 fof(f383,plain,(
% 9.02/11.66 ![X0,X1]: (addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1))))=antidomain(multiplication(X0,antidomain(antidomain(X1)))))),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f41,f39])).
% 9.02/11.66 fof(f384,plain,(
% 9.02/11.66 ![X0,X1]: (addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1))))=antidomain(multiplication(X0,domain(X1))))),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f41,f383])).
% 9.02/11.66 fof(f391,plain,(
% 9.02/11.66 addition(antidomain(zero),antidomain(multiplication(domain(sK0_skl),domain(sK1_skl))))=antidomain(multiplication(domain(sK0_skl),domain(sK1_skl)))),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f48,f384])).
% 9.02/11.66 fof(f428,plain,(
% 9.02/11.66 ![X0]: (addition(domain(X0),antidomain(X0))=one)),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f41,f40])).
% 9.02/11.66 fof(f429,plain,(
% 9.02/11.66 ![X0]: (addition(antidomain(X0),domain(X0))=one)),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f23,f428])).
% 9.02/11.66 fof(f431,plain,(
% 9.02/11.66 addition(antidomain(zero),antidomain(one))=one),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f232,f428])).
% 9.02/11.66 fof(f438,plain,(
% 9.02/11.66 ![X0]: (addition(domain(X0),one)=addition(domain(X0),antidomain(X0)))),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f428,f91])).
% 9.02/11.66 fof(f442,plain,(
% 9.02/11.66 addition(antidomain(zero),zero)=one),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f213,f431])).
% 9.02/11.66 fof(f443,plain,(
% 9.02/11.66 antidomain(zero)=one),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f25,f442])).
% 9.02/11.66 fof(f447,plain,(
% 9.02/11.66 ![X0]: (addition(domain(X0),one)=one)),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f428,f438])).
% 9.02/11.66 fof(f558,plain,(
% 9.02/11.66 ![X0]: (addition(one,domain(X0))=one)),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f23,f447])).
% 9.02/11.66 fof(f752,plain,(
% 9.02/11.66 ![X0]: (addition(antidomain(X0),one)=addition(antidomain(X0),domain(X0)))),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f429,f91])).
% 9.02/11.66 fof(f760,plain,(
% 9.02/11.66 ![X0]: (addition(antidomain(X0),one)=one)),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f429,f752])).
% 9.02/11.66 fof(f762,plain,(
% 9.02/11.66 ![X0]: (addition(one,antidomain(X0))=one)),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f23,f760])).
% 9.02/11.66 fof(f1068,plain,(
% 9.02/11.66 addition(one,antidomain(multiplication(domain(sK0_skl),domain(sK1_skl))))=antidomain(multiplication(domain(sK0_skl),domain(sK1_skl)))),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f443,f391])).
% 9.02/11.66 fof(f1069,plain,(
% 9.02/11.66 one=antidomain(multiplication(domain(sK0_skl),domain(sK1_skl)))),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f762,f1068])).
% 9.02/11.66 fof(f1080,plain,(
% 9.02/11.66 multiplication(one,multiplication(domain(sK0_skl),domain(sK1_skl)))=zero),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f1069,f38])).
% 9.02/11.66 fof(f1088,plain,(
% 9.02/11.66 multiplication(domain(sK0_skl),domain(sK1_skl))=zero),
% 9.02/11.66 inference(forward_demodulation,[status(thm)],[f29,f1080])).
% 9.02/11.66 fof(f1096,plain,(
% 9.02/11.66 ![X0]: (multiplication(domain(sK0_skl),addition(X0,domain(sK1_skl)))=addition(multiplication(domain(sK0_skl),X0),zero))),
% 9.02/11.66 inference(paramodulation,[status(thm)],[f1088,f30])).
% 9.02/11.67 fof(f1107,plain,(
% 9.02/11.67 ![X0]: (multiplication(domain(sK0_skl),addition(X0,domain(sK1_skl)))=multiplication(domain(sK0_skl),X0))),
% 9.02/11.67 inference(forward_demodulation,[status(thm)],[f25,f1096])).
% 9.02/11.67 fof(f4278,plain,(
% 9.02/11.67 multiplication(domain(sK0_skl),one)=multiplication(domain(sK0_skl),antidomain(sK1_skl))),
% 9.02/11.67 inference(paramodulation,[status(thm)],[f429,f1107])).
% 9.02/11.67 fof(f4305,plain,(
% 9.02/11.67 domain(sK0_skl)=multiplication(domain(sK0_skl),antidomain(sK1_skl))),
% 9.02/11.67 inference(forward_demodulation,[status(thm)],[f28,f4278])).
% 9.02/11.67 fof(f6537,plain,(
% 9.02/11.67 multiplication(addition(one,domain(sK0_skl)),antidomain(sK1_skl))=addition(antidomain(sK1_skl),domain(sK0_skl))),
% 9.02/11.67 inference(paramodulation,[status(thm)],[f4305,f334])).
% 9.02/11.67 fof(f6659,plain,(
% 9.02/11.67 multiplication(one,antidomain(sK1_skl))=addition(antidomain(sK1_skl),domain(sK0_skl))),
% 9.02/11.67 inference(forward_demodulation,[status(thm)],[f558,f6537])).
% 9.02/11.67 fof(f6660,plain,(
% 9.02/11.67 antidomain(sK1_skl)=addition(antidomain(sK1_skl),domain(sK0_skl))),
% 9.02/11.67 inference(forward_demodulation,[status(thm)],[f29,f6659])).
% 9.02/11.67 fof(f6661,plain,(
% 9.02/11.67 $false),
% 9.02/11.67 inference(forward_subsumption_resolution,[status(thm)],[f6660,f60])).
% 9.02/11.67 % SZS output end CNFRefutation for theBenchmark.p
% 9.02/11.69 % Elapsed time: 1.240068 seconds
% 9.02/11.69 % CPU time: 9.587558 seconds
% 9.02/11.69 % Total memory used: 177.460 MB
% 9.02/11.69 % Net memory used: 173.563 MB
%------------------------------------------------------------------------------