%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:58:21 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:46:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.41 fof(f1,axiom,(
% 0.09/0.41 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f3,axiom,(
% 0.09/0.41 (! [A] : addition(A,zero) = A )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f7,axiom,(
% 0.09/0.41 (! [A] : multiplication(one,A) = A )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f10,axiom,(
% 0.09/0.41 (! [A] : multiplication(A,zero) = zero )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f17,axiom,(
% 0.09/0.41 (! [X0] : multiplication(X0,coantidomain(X0)) = zero )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f19,axiom,(
% 0.09/0.41 (! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f20,axiom,(
% 0.09/0.41 (! [X0] : codomain(X0) = coantidomain(coantidomain(X0)) )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f24,axiom,(
% 0.09/0.41 (! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)) )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f27,conjecture,(
% 0.09/0.41 (! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1) )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f28,negated_conjecture,(
% 0.09/0.41 ~((! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1) ))),
% 0.09/0.41 inference(negated_conjecture,[status(cth)],[f27])).
% 0.09/0.41 fof(f29,plain,(
% 0.09/0.41 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.41 fof(f31,plain,(
% 0.09/0.41 ![X0]: (addition(X0,zero)=X0)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.41 fof(f35,plain,(
% 0.09/0.41 ![X0]: (multiplication(one,X0)=X0)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.41 fof(f38,plain,(
% 0.09/0.41 ![X0]: (multiplication(X0,zero)=zero)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/0.41 fof(f48,plain,(
% 0.09/0.41 ![X0]: (multiplication(X0,coantidomain(X0))=zero)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.41 fof(f50,plain,(
% 0.09/0.41 ![X0]: (addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.09/0.41 fof(f51,plain,(
% 0.09/0.41 ![X0]: (codomain(X0)=coantidomain(coantidomain(X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f20])).
% 0.09/0.41 fof(f55,plain,(
% 0.09/0.41 ![X0,X1]: (backward_diamond(X0,X1)=codomain(multiplication(codomain(X1),X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f24])).
% 0.09/0.41 fof(f58,plain,(
% 0.09/0.41 (?[X0,X1]: ~addition(backward_diamond(zero,domain(X0)),domain(X1))=domain(X1))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.09/0.41 fof(f59,plain,(
% 0.09/0.41 ~addition(backward_diamond(zero,domain(sK0_skl)),domain(sK1_skl))=domain(sK1_skl)),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f58])).
% 0.09/0.41 fof(f60,plain,(
% 0.09/0.41 ~addition(backward_diamond(zero,domain(sK0_skl)),domain(sK1_skl))=domain(sK1_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f59])).
% 0.09/0.41 fof(f63,plain,(
% 0.09/0.41 ![X0]: (addition(codomain(X0),coantidomain(X0))=one)),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f51,f50])).
% 0.09/0.41 fof(f71,plain,(
% 0.09/0.41 ![X0]: (X0=addition(zero,X0))),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f31,f29])).
% 0.09/0.41 fof(f111,plain,(
% 0.09/0.41 ![X0]: (backward_diamond(zero,X0)=codomain(zero))),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f38,f55])).
% 0.09/0.41 fof(f114,plain,(
% 0.09/0.41 ~addition(codomain(zero),domain(sK1_skl))=domain(sK1_skl)),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f111,f60])).
% 0.09/0.41 fof(f245,plain,(
% 0.09/0.41 ![X0]: (codomain(coantidomain(X0))=coantidomain(codomain(X0)))),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f51,f51])).
% 0.09/0.41 fof(f403,plain,(
% 0.09/0.41 coantidomain(one)=zero),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f35,f48])).
% 0.09/0.41 fof(f443,plain,(
% 0.09/0.41 addition(codomain(one),zero)=one),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f403,f63])).
% 0.09/0.41 fof(f445,plain,(
% 0.09/0.41 codomain(one)=one),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f31,f443])).
% 0.09/0.41 fof(f448,plain,(
% 0.09/0.41 codomain(coantidomain(one))=coantidomain(one)),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f445,f245])).
% 0.09/0.41 fof(f452,plain,(
% 0.09/0.41 codomain(zero)=coantidomain(one)),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f403,f448])).
% 0.09/0.41 fof(f453,plain,(
% 0.09/0.41 ~addition(zero,domain(sK1_skl))=domain(sK1_skl)),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f457,f114])).
% 0.09/0.41 fof(f457,plain,(
% 0.09/0.41 codomain(zero)=zero),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f403,f452])).
% 0.09/0.41 fof(f462,plain,(
% 0.09/0.41 ~domain(sK1_skl)=domain(sK1_skl)),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f71,f453])).
% 0.09/0.41 fof(f463,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(trivial_equality_resolution,[status(thm)],[f462])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.44 % Elapsed time: 0.074076 seconds
% 0.09/0.44 % CPU time: 0.256895 seconds
% 0.09/0.44 % Total memory used: 69.272 MB
% 0.09/0.44 % Net memory used: 69.033 MB
%------------------------------------------------------------------------------