%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE131+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 : n009.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 12:58:22 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE131+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 22:45:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.40 fof(f1,axiom,(
% 0.13/0.40 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f3,axiom,(
% 0.13/0.40 (! [A] : addition(A,zero) = A )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f6,axiom,(
% 0.13/0.40 (! [A] : multiplication(A,one) = A )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f10,axiom,(
% 0.13/0.40 (! [A] : multiplication(A,zero) = zero )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f13,axiom,(
% 0.13/0.40 (! [X0] : multiplication(antidomain(X0),X0) = zero )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f15,axiom,(
% 0.13/0.40 (! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f16,axiom,(
% 0.13/0.40 (! [X0] : domain(X0) = antidomain(antidomain(X0)) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f22,axiom,(
% 0.13/0.40 (! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f23,axiom,(
% 0.13/0.40 (! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f27,axiom,(
% 0.13/0.40 (! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f29,conjecture,(
% 0.13/0.40 (! [X0] :( divergence(X0) = zero<= (! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) )) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f30,negated_conjecture,(
% 0.13/0.40 ~((! [X0] :( divergence(X0) = zero<= (! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) )) ))),
% 0.13/0.40 inference(negated_conjecture,[status(cth)],[f29])).
% 0.13/0.40 fof(f31,plain,(
% 0.13/0.40 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.40 fof(f33,plain,(
% 0.13/0.40 ![X0]: (addition(X0,zero)=X0)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.40 fof(f36,plain,(
% 0.13/0.40 ![X0]: (multiplication(X0,one)=X0)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.40 fof(f40,plain,(
% 0.13/0.40 ![X0]: (multiplication(X0,zero)=zero)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/0.40 fof(f46,plain,(
% 0.13/0.40 ![X0]: (multiplication(antidomain(X0),X0)=zero)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.40 fof(f48,plain,(
% 0.13/0.40 ![X0]: (addition(antidomain(antidomain(X0)),antidomain(X0))=one)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f15])).
% 0.13/0.40 fof(f49,plain,(
% 0.13/0.40 ![X0]: (domain(X0)=antidomain(antidomain(X0)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f16])).
% 0.13/0.40 fof(f55,plain,(
% 0.13/0.40 ![X0,X1]: (domain_difference(X0,X1)=multiplication(domain(X0),antidomain(X1)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f22])).
% 0.13/0.40 fof(f56,plain,(
% 0.13/0.40 ![X0,X1]: (forward_diamond(X0,X1)=domain(multiplication(X0,domain(X1))))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f23])).
% 0.13/0.40 fof(f60,plain,(
% 0.13/0.40 ![X0]: (forward_diamond(X0,divergence(X0))=divergence(X0))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.40 fof(f63,plain,(
% 0.13/0.40 (?[X0]: (~divergence(X0)=zero&(![X1]: addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))=forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))))),
% 0.13/0.40 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.13/0.40 fof(f64,plain,(
% 0.13/0.40 (~divergence(sK0_skl)=zero&(![X1]: addition(domain(X1),forward_diamond(star(sK0_skl),domain_difference(domain(X1),forward_diamond(sK0_skl,domain(X1)))))=forward_diamond(star(sK0_skl),domain_difference(domain(X1),forward_diamond(sK0_skl,domain(X1))))))),
% 0.13/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f63])).
% 0.13/0.40 fof(f65,plain,(
% 0.13/0.40 ~divergence(sK0_skl)=zero),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f64])).
% 0.13/0.40 fof(f66,plain,(
% 0.13/0.40 ![X0]: (addition(domain(X0),forward_diamond(star(sK0_skl),domain_difference(domain(X0),forward_diamond(sK0_skl,domain(X0)))))=forward_diamond(star(sK0_skl),domain_difference(domain(X0),forward_diamond(sK0_skl,domain(X0)))))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f64])).
% 0.13/0.40 fof(f69,plain,(
% 0.13/0.40 ![X0]: (X0=addition(zero,X0))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f33,f31])).
% 0.13/0.40 fof(f211,plain,(
% 0.13/0.40 antidomain(one)=zero),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f36,f46])).
% 0.13/0.40 fof(f335,plain,(
% 0.13/0.40 ![X0,X1]: (addition(domain(multiplication(X0,domain(X1))),forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))))))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f56,f66])).
% 0.13/0.40 fof(f374,plain,(
% 0.13/0.40 ![X0,X1]: (addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f56,f335])).
% 0.13/0.40 fof(f375,plain,(
% 0.13/0.40 ![X0,X1]: (addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f56,f374])).
% 0.13/0.40 fof(f376,plain,(
% 0.13/0.40 ![X0,X1]: (addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f56,f375])).
% 0.13/0.40 fof(f377,plain,(
% 0.13/0.40 ![X0,X1]: (addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1)))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f56,f376])).
% 0.13/0.40 fof(f387,plain,(
% 0.13/0.40 ![X0]: (addition(antidomain(X0),antidomain(antidomain(X0)))=one)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f31,f48])).
% 0.13/0.40 fof(f388,plain,(
% 0.13/0.40 addition(zero,antidomain(antidomain(one)))=one),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f211,f387])).
% 0.13/0.40 fof(f391,plain,(
% 0.13/0.40 antidomain(antidomain(one))=one),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f69,f388])).
% 0.13/0.40 fof(f392,plain,(
% 0.13/0.40 antidomain(zero)=one),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f211,f391])).
% 0.13/0.40 fof(f400,plain,(
% 0.13/0.40 ![X0]: (multiplication(domain(X0),antidomain(X0))=zero)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f49,f46])).
% 0.13/0.40 fof(f403,plain,(
% 0.13/0.40 ![X0]: (domain_difference(X0,X0)=zero)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f55,f400])).
% 0.13/0.40 fof(f437,plain,(
% 0.13/0.40 domain(zero)=antidomain(one)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f392,f49])).
% 0.13/0.40 fof(f440,plain,(
% 0.13/0.40 domain(zero)=zero),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f211,f437])).
% 0.13/0.40 fof(f442,plain,(
% 0.13/0.40 ![X0]: (addition(forward_diamond(X0,divergence(X0)),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sK0_skl,divergence(X0)))))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0))))))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f60,f377])).
% 0.13/0.40 fof(f445,plain,(
% 0.13/0.40 ![X0]: (addition(divergence(X0),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sK0_skl,divergence(X0)))))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0))))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f60,f442])).
% 0.13/0.40 fof(f446,plain,(
% 0.13/0.40 ![X0]: (addition(divergence(X0),forward_diamond(star(sK0_skl),domain_difference(divergence(X0),forward_diamond(sK0_skl,divergence(X0)))))=forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0))))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f60,f445])).
% 0.13/0.40 fof(f447,plain,(
% 0.13/0.40 ![X0]: (addition(divergence(X0),forward_diamond(star(sK0_skl),domain_difference(divergence(X0),forward_diamond(sK0_skl,divergence(X0)))))=forward_diamond(star(sK0_skl),domain_difference(divergence(X0),forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0))))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f60,f446])).
% 0.13/0.40 fof(f448,plain,(
% 0.13/0.40 ![X0]: (addition(divergence(X0),forward_diamond(star(sK0_skl),domain_difference(divergence(X0),forward_diamond(sK0_skl,divergence(X0)))))=forward_diamond(star(sK0_skl),domain_difference(divergence(X0),forward_diamond(sK0_skl,divergence(X0)))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f60,f447])).
% 0.13/0.40 fof(f473,plain,(
% 0.13/0.40 ![X0]: (forward_diamond(X0,zero)=domain(multiplication(X0,zero)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f440,f56])).
% 0.13/0.40 fof(f498,plain,(
% 0.13/0.40 ![X0]: (forward_diamond(X0,zero)=domain(zero))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f40,f473])).
% 0.13/0.40 fof(f499,plain,(
% 0.13/0.40 ![X0]: (forward_diamond(X0,zero)=zero)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f440,f498])).
% 0.13/0.40 fof(f591,plain,(
% 0.13/0.40 addition(divergence(sK0_skl),forward_diamond(star(sK0_skl),domain_difference(divergence(sK0_skl),divergence(sK0_skl))))=forward_diamond(star(sK0_skl),domain_difference(divergence(sK0_skl),forward_diamond(sK0_skl,divergence(sK0_skl))))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f60,f448])).
% 0.13/0.40 fof(f593,plain,(
% 0.13/0.40 addition(divergence(sK0_skl),forward_diamond(star(sK0_skl),zero))=forward_diamond(star(sK0_skl),domain_difference(divergence(sK0_skl),forward_diamond(sK0_skl,divergence(sK0_skl))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f403,f591])).
% 0.13/0.40 fof(f594,plain,(
% 0.13/0.40 addition(divergence(sK0_skl),zero)=forward_diamond(star(sK0_skl),domain_difference(divergence(sK0_skl),forward_diamond(sK0_skl,divergence(sK0_skl))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f499,f593])).
% 0.13/0.40 fof(f595,plain,(
% 0.13/0.40 divergence(sK0_skl)=forward_diamond(star(sK0_skl),domain_difference(divergence(sK0_skl),forward_diamond(sK0_skl,divergence(sK0_skl))))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f33,f594])).
% 0.13/0.40 fof(f596,plain,(
% 0.13/0.40 divergence(sK0_skl)=forward_diamond(star(sK0_skl),domain_difference(divergence(sK0_skl),divergence(sK0_skl)))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f60,f595])).
% 0.13/0.40 fof(f597,plain,(
% 0.13/0.40 divergence(sK0_skl)=forward_diamond(star(sK0_skl),zero)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f403,f596])).
% 0.13/0.40 fof(f598,plain,(
% 0.13/0.40 divergence(sK0_skl)=zero),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f499,f597])).
% 0.13/0.40 fof(f599,plain,(
% 0.13/0.40 $false),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f598,f65])).
% 0.13/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.055151 seconds
% 0.13/0.42 % CPU time: 0.202575 seconds
% 0.13/0.42 % Total memory used: 67.016 MB
% 0.13/0.42 % Net memory used: 66.815 MB
%------------------------------------------------------------------------------