%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE055+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 : 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 12:58:16 PM UTC 2026
% Result : Theorem 0.28s 0.92s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n006.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 20 22:41:13 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.28/0.92 % Refutation found
% 0.28/0.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.28/0.92 % SZS output start CNFRefutation for theBenchmark
% 0.28/0.92 fof(f1,axiom,(
% 0.28/0.92 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.28/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.92 fof(f2,axiom,(
% 0.28/0.92 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.28/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.92 fof(f4,axiom,(
% 0.28/0.92 (! [A] : addition(A,A) = A )),
% 0.28/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.92 fof(f6,axiom,(
% 0.28/0.92 (! [A] : multiplication(A,one) = A )),
% 0.28/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.92 fof(f8,axiom,(
% 0.28/0.92 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.28/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.92 fof(f12,axiom,(
% 0.28/0.92 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.28/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.92 fof(f13,axiom,(
% 0.28/0.92 (! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) )),
% 0.28/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.92 fof(f18,conjecture,(
% 0.28/0.92 (! [X0] :( addition(X0,one) = one=> addition(X0,domain(X0)) = domain(X0) ) )),
% 0.28/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.92 fof(f19,negated_conjecture,(
% 0.28/0.92 ~((! [X0] :( addition(X0,one) = one=> addition(X0,domain(X0)) = domain(X0) ) ))),
% 0.28/0.92 inference(negated_conjecture,[status(cth)],[f18])).
% 0.28/0.92 fof(f20,plain,(
% 0.28/0.92 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f1])).
% 0.28/0.92 fof(f21,plain,(
% 0.28/0.92 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f2])).
% 0.28/0.92 fof(f23,plain,(
% 0.28/0.92 ![X0]: (addition(X0,X0)=X0)),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f4])).
% 0.28/0.92 fof(f25,plain,(
% 0.28/0.92 ![X0]: (multiplication(X0,one)=X0)),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f6])).
% 0.28/0.92 fof(f27,plain,(
% 0.28/0.92 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f8])).
% 0.28/0.92 fof(f31,plain,(
% 0.28/0.92 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.28/0.92 inference(NNF_transformation,[status(thm)],[f12])).
% 0.28/0.92 fof(f32,plain,(
% 0.28/0.92 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.28/0.92 inference(miniscoping,[status(thm)],[f31])).
% 0.28/0.92 fof(f33,plain,(
% 0.28/0.92 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f32])).
% 0.28/0.92 fof(f34,plain,(
% 0.28/0.92 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f32])).
% 0.28/0.92 fof(f35,plain,(
% 0.28/0.92 ![X0]: (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0))),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f13])).
% 0.28/0.92 fof(f40,plain,(
% 0.28/0.92 (?[X0]: (addition(X0,one)=one&~addition(X0,domain(X0))=domain(X0)))),
% 0.28/0.92 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.28/0.92 fof(f41,plain,(
% 0.28/0.92 (addition(sK0_skl,one)=one&~addition(sK0_skl,domain(sK0_skl))=domain(sK0_skl))),
% 0.28/0.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40])).
% 0.28/0.92 fof(f42,plain,(
% 0.28/0.92 addition(sK0_skl,one)=one),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f41])).
% 0.28/0.92 fof(f43,plain,(
% 0.28/0.92 ~addition(sK0_skl,domain(sK0_skl))=domain(sK0_skl)),
% 0.28/0.92 inference(cnf_transformation,[status(thm)],[f41])).
% 0.28/0.92 fof(f75,plain,(
% 0.28/0.92 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.28/0.92 inference(paramodulation,[status(thm)],[f23,f21])).
% 0.28/0.92 fof(f86,plain,(
% 0.28/0.92 addition(one,sK0_skl)=one),
% 0.28/0.92 inference(forward_demodulation,[status(thm)],[f20,f42])).
% 0.28/0.92 fof(f239,plain,(
% 0.28/0.92 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 0.28/0.92 inference(resolution,[status(thm)],[f75,f34])).
% 0.28/0.92 fof(f280,plain,(
% 0.28/0.92 ![X0,X1]: (leq(X0,addition(X1,X0)))),
% 0.28/0.92 inference(paramodulation,[status(thm)],[f20,f239])).
% 0.28/0.92 fof(f312,plain,(
% 0.28/0.92 ![X0,X1,X2]: (leq(X0,addition(X1,addition(X2,X0))))),
% 0.28/0.92 inference(paramodulation,[status(thm)],[f21,f280])).
% 0.28/0.92 fof(f357,plain,(
% 0.28/0.92 ![X0,X1,X2]: (leq(X0,addition(addition(X1,X0),X2)))),
% 0.28/0.92 inference(paramodulation,[status(thm)],[f20,f312])).
% 0.28/0.92 fof(f371,plain,(
% 0.28/0.92 ![X0,X1,X2]: (leq(X0,addition(X1,addition(X0,X2))))),
% 0.28/0.95 inference(forward_demodulation,[status(thm)],[f21,f357])).
% 0.28/0.95 fof(f385,plain,(
% 0.28/0.95 ![X0,X1]: (leq(X0,addition(X1,multiplication(domain(X0),X0))))),
% 0.28/0.95 inference(paramodulation,[status(thm)],[f35,f371])).
% 0.28/0.95 fof(f1561,plain,(
% 0.28/0.95 ![X0,X1]: (leq(X0,multiplication(domain(X0),addition(X1,X0))))),
% 0.28/0.95 inference(paramodulation,[status(thm)],[f27,f385])).
% 0.28/0.95 fof(f2525,plain,(
% 0.28/0.95 leq(sK0_skl,multiplication(domain(sK0_skl),one))),
% 0.28/0.95 inference(paramodulation,[status(thm)],[f86,f1561])).
% 0.28/0.95 fof(f2552,plain,(
% 0.28/0.95 leq(sK0_skl,domain(sK0_skl))),
% 0.28/0.95 inference(forward_demodulation,[status(thm)],[f25,f2525])).
% 0.28/0.95 fof(f2557,plain,(
% 0.28/0.95 addition(sK0_skl,domain(sK0_skl))=domain(sK0_skl)),
% 0.28/0.95 inference(resolution,[status(thm)],[f2552,f33])).
% 0.28/0.95 fof(f2558,plain,(
% 0.28/0.95 $false),
% 0.28/0.95 inference(forward_subsumption_resolution,[status(thm)],[f2557,f43])).
% 0.28/0.95 % SZS output end CNFRefutation for theBenchmark.p
% 0.28/0.98 % Elapsed time: 0.511839 seconds
% 0.28/0.98 % CPU time: 3.587267 seconds
% 0.28/0.98 % Total memory used: 90.613 MB
% 0.28/0.98 % Net memory used: 89.406 MB
%------------------------------------------------------------------------------