%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE114+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 : n002.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 0.17s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE114+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
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 22:46:31 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.49 % Refutation found
% 0.17/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.49 fof(f1,axiom,(
% 0.17/0.49 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f3,axiom,(
% 0.17/0.49 (! [A] : addition(A,zero) = A )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f6,axiom,(
% 0.17/0.49 (! [A] : multiplication(A,one) = A )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f10,axiom,(
% 0.17/0.49 (! [A] : multiplication(A,zero) = zero )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f13,axiom,(
% 0.17/0.49 (! [X0] : multiplication(antidomain(X0),X0) = zero )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f15,axiom,(
% 0.17/0.49 (! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f16,axiom,(
% 0.17/0.49 (! [X0] : domain(X0) = antidomain(antidomain(X0)) )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f21,axiom,(
% 0.17/0.49 (! [X0] : c(X0) = antidomain(domain(X0)) )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f23,axiom,(
% 0.17/0.49 (! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))) )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f25,axiom,(
% 0.17/0.49 (! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))) )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f27,conjecture,(
% 0.17/0.49 (! [X0] : forward_box(X0,one) = one )),
% 0.17/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f28,negated_conjecture,(
% 0.17/0.49 ~((! [X0] : forward_box(X0,one) = one ))),
% 0.17/0.49 inference(negated_conjecture,[status(cth)],[f27])).
% 0.17/0.49 fof(f29,plain,(
% 0.17/0.49 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f1])).
% 0.17/0.49 fof(f31,plain,(
% 0.17/0.49 ![X0]: (addition(X0,zero)=X0)),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f3])).
% 0.17/0.49 fof(f34,plain,(
% 0.17/0.49 ![X0]: (multiplication(X0,one)=X0)),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f6])).
% 0.17/0.49 fof(f38,plain,(
% 0.17/0.49 ![X0]: (multiplication(X0,zero)=zero)),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f10])).
% 0.17/0.49 fof(f44,plain,(
% 0.17/0.49 ![X0]: (multiplication(antidomain(X0),X0)=zero)),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f13])).
% 0.17/0.49 fof(f46,plain,(
% 0.17/0.49 ![X0]: (addition(antidomain(antidomain(X0)),antidomain(X0))=one)),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f15])).
% 0.17/0.49 fof(f47,plain,(
% 0.17/0.49 ![X0]: (domain(X0)=antidomain(antidomain(X0)))),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f16])).
% 0.17/0.49 fof(f52,plain,(
% 0.17/0.49 ![X0]: (c(X0)=antidomain(domain(X0)))),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f21])).
% 0.17/0.49 fof(f54,plain,(
% 0.17/0.49 ![X0,X1]: (forward_diamond(X0,X1)=domain(multiplication(X0,domain(X1))))),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f23])).
% 0.17/0.49 fof(f56,plain,(
% 0.17/0.49 ![X0,X1]: (forward_box(X0,X1)=c(forward_diamond(X0,c(X1))))),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f25])).
% 0.17/0.49 fof(f58,plain,(
% 0.17/0.49 (?[X0]: ~forward_box(X0,one)=one)),
% 0.17/0.49 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.17/0.49 fof(f59,plain,(
% 0.17/0.49 ~forward_box(sK0_skl,one)=one),
% 0.17/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f58])).
% 0.17/0.49 fof(f60,plain,(
% 0.17/0.49 ~forward_box(sK0_skl,one)=one),
% 0.17/0.49 inference(cnf_transformation,[status(thm)],[f59])).
% 0.17/0.49 fof(f61,plain,(
% 0.17/0.49 ![X0]: (addition(antidomain(X0),antidomain(antidomain(X0)))=one)),
% 0.17/0.49 inference(forward_demodulation,[status(thm)],[f29,f46])).
% 0.17/0.49 fof(f62,plain,(
% 0.17/0.49 ![X0]: (addition(antidomain(X0),domain(X0))=one)),
% 0.17/0.49 inference(backward_demodulation,[status(thm)],[f47,f61])).
% 0.17/0.49 fof(f73,plain,(
% 0.17/0.49 ![X0]: (addition(zero,X0)=X0)),
% 0.17/0.49 inference(paramodulation,[status(thm)],[f29,f31])).
% 0.17/0.49 fof(f190,plain,(
% 0.17/0.49 antidomain(one)=zero),
% 0.17/0.49 inference(paramodulation,[status(thm)],[f34,f44])).
% 0.17/0.49 fof(f218,plain,(
% 0.17/0.49 ![X0]: (domain(antidomain(X0))=antidomain(domain(X0)))),
% 0.17/0.49 inference(paramodulation,[status(thm)],[f47,f47])).
% 0.17/0.49 fof(f219,plain,(
% 0.17/0.49 domain(one)=antidomain(zero)),
% 0.17/0.49 inference(paramodulation,[status(thm)],[f190,f47])).
% 0.17/0.49 fof(f221,plain,(
% 0.17/0.49 ![X0]: (domain(antidomain(X0))=c(X0))),
% 0.17/0.49 inference(forward_demodulation,[status(thm)],[f52,f218])).
% 0.17/0.51 fof(f299,plain,(
% 0.17/0.51 domain(zero)=c(one)),
% 0.17/0.51 inference(paramodulation,[status(thm)],[f190,f221])).
% 0.17/0.51 fof(f315,plain,(
% 0.17/0.51 addition(zero,domain(one))=one),
% 0.17/0.51 inference(paramodulation,[status(thm)],[f190,f62])).
% 0.17/0.51 fof(f316,plain,(
% 0.17/0.51 addition(antidomain(one),antidomain(zero))=one),
% 0.17/0.51 inference(paramodulation,[status(thm)],[f219,f62])).
% 0.17/0.51 fof(f324,plain,(
% 0.17/0.51 domain(one)=one),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f73,f315])).
% 0.17/0.51 fof(f325,plain,(
% 0.17/0.51 addition(antidomain(zero),antidomain(one))=one),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f29,f316])).
% 0.17/0.51 fof(f326,plain,(
% 0.17/0.51 addition(antidomain(zero),zero)=one),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f190,f325])).
% 0.17/0.51 fof(f329,plain,(
% 0.17/0.51 antidomain(zero)=one),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f31,f326])).
% 0.17/0.51 fof(f339,plain,(
% 0.17/0.51 c(one)=antidomain(one)),
% 0.17/0.51 inference(paramodulation,[status(thm)],[f324,f52])).
% 0.17/0.51 fof(f344,plain,(
% 0.17/0.51 domain(zero)=zero),
% 0.17/0.51 inference(backward_demodulation,[status(thm)],[f345,f299])).
% 0.17/0.51 fof(f345,plain,(
% 0.17/0.51 c(one)=zero),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f190,f339])).
% 0.17/0.51 fof(f421,plain,(
% 0.17/0.51 domain(one)=c(zero)),
% 0.17/0.51 inference(paramodulation,[status(thm)],[f329,f221])).
% 0.17/0.51 fof(f426,plain,(
% 0.17/0.51 one=c(zero)),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f324,f421])).
% 0.17/0.51 fof(f446,plain,(
% 0.17/0.51 ![X0]: (forward_box(X0,one)=c(forward_diamond(X0,zero)))),
% 0.17/0.51 inference(paramodulation,[status(thm)],[f345,f56])).
% 0.17/0.51 fof(f498,plain,(
% 0.17/0.51 ![X0]: (forward_diamond(X0,zero)=domain(multiplication(X0,zero)))),
% 0.17/0.51 inference(paramodulation,[status(thm)],[f344,f54])).
% 0.17/0.51 fof(f508,plain,(
% 0.17/0.51 ![X0]: (forward_diamond(X0,zero)=domain(zero))),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f38,f498])).
% 0.17/0.51 fof(f509,plain,(
% 0.17/0.51 ![X0]: (forward_box(X0,one)=c(zero))),
% 0.17/0.51 inference(backward_demodulation,[status(thm)],[f510,f446])).
% 0.17/0.51 fof(f510,plain,(
% 0.17/0.51 ![X0]: (forward_diamond(X0,zero)=zero)),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f344,f508])).
% 0.17/0.51 fof(f513,plain,(
% 0.17/0.51 ~one=one),
% 0.17/0.51 inference(backward_demodulation,[status(thm)],[f514,f60])).
% 0.17/0.51 fof(f514,plain,(
% 0.17/0.51 ![X0]: (forward_box(X0,one)=one)),
% 0.17/0.51 inference(forward_demodulation,[status(thm)],[f426,f509])).
% 0.17/0.51 fof(f515,plain,(
% 0.17/0.51 $false),
% 0.17/0.51 inference(trivial_equality_resolution,[status(thm)],[f513])).
% 0.17/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.52 % Elapsed time: 0.070647 seconds
% 0.17/0.52 % CPU time: 0.271774 seconds
% 0.17/0.52 % Total memory used: 40.089 MB
% 0.17/0.52 % Net memory used: 40.025 MB
%------------------------------------------------------------------------------