%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE113+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 : n011.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 0.57s 15.74s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.15/15.68 % CPULimit : 300
% 0.15/15.68 % WCLimit : 300
% 0.15/15.68 % DateTime : Sun Sep 20 22:43:44 UTC 2026
% 0.15/15.68 % CPUTime :
% 0.57/15.70 % Drodi V4.1.1
% 0.57/15.74 % Refutation found
% 0.57/15.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.57/15.74 % SZS output start CNFRefutation for theBenchmark
% 0.57/15.74 fof(f1,axiom,(
% 0.57/15.74 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f3,axiom,(
% 0.57/15.74 (! [A] : addition(A,zero) = A )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f6,axiom,(
% 0.57/15.74 (! [A] : multiplication(A,one) = A )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f10,axiom,(
% 0.57/15.74 (! [A] : multiplication(A,zero) = zero )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f13,axiom,(
% 0.57/15.74 (! [X0] : multiplication(antidomain(X0),X0) = zero )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f15,axiom,(
% 0.57/15.74 (! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f16,axiom,(
% 0.57/15.74 (! [X0] : domain(X0) = antidomain(antidomain(X0)) )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f23,axiom,(
% 0.57/15.74 (! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))) )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f27,conjecture,(
% 0.57/15.74 (! [X0] : forward_diamond(X0,zero) = zero )),
% 0.57/15.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.57/15.74 fof(f28,negated_conjecture,(
% 0.57/15.74 ~((! [X0] : forward_diamond(X0,zero) = zero ))),
% 0.57/15.74 inference(negated_conjecture,[status(cth)],[f27])).
% 0.57/15.74 fof(f29,plain,(
% 0.57/15.74 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f1])).
% 0.57/15.74 fof(f31,plain,(
% 0.57/15.74 ![X0]: (addition(X0,zero)=X0)),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f3])).
% 0.57/15.74 fof(f34,plain,(
% 0.57/15.74 ![X0]: (multiplication(X0,one)=X0)),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f6])).
% 0.57/15.74 fof(f38,plain,(
% 0.57/15.74 ![X0]: (multiplication(X0,zero)=zero)),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f10])).
% 0.57/15.74 fof(f44,plain,(
% 0.57/15.74 ![X0]: (multiplication(antidomain(X0),X0)=zero)),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f13])).
% 0.57/15.74 fof(f46,plain,(
% 0.57/15.74 ![X0]: (addition(antidomain(antidomain(X0)),antidomain(X0))=one)),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f15])).
% 0.57/15.74 fof(f47,plain,(
% 0.57/15.74 ![X0]: (domain(X0)=antidomain(antidomain(X0)))),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f16])).
% 0.57/15.74 fof(f54,plain,(
% 0.57/15.74 ![X0,X1]: (forward_diamond(X0,X1)=domain(multiplication(X0,domain(X1))))),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f23])).
% 0.57/15.74 fof(f58,plain,(
% 0.57/15.74 (?[X0]: ~forward_diamond(X0,zero)=zero)),
% 0.57/15.74 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.57/15.74 fof(f59,plain,(
% 0.57/15.74 ~forward_diamond(sK0_skl,zero)=zero),
% 0.57/15.74 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f58])).
% 0.57/15.74 fof(f60,plain,(
% 0.57/15.74 ~forward_diamond(sK0_skl,zero)=zero),
% 0.57/15.74 inference(cnf_transformation,[status(thm)],[f59])).
% 0.57/15.74 fof(f69,plain,(
% 0.57/15.74 zero=antidomain(one)),
% 0.57/15.74 inference(paramodulation,[status(thm)],[f44,f34])).
% 0.57/15.74 fof(f317,plain,(
% 0.57/15.74 domain(one)=antidomain(zero)),
% 0.57/15.74 inference(paramodulation,[status(thm)],[f69,f47])).
% 0.57/15.74 fof(f375,plain,(
% 0.57/15.74 ![X0]: (addition(antidomain(X0),antidomain(antidomain(X0)))=one)),
% 0.57/15.74 inference(forward_demodulation,[status(thm)],[f29,f46])).
% 0.57/15.74 fof(f376,plain,(
% 0.57/15.74 ![X0]: (addition(antidomain(X0),domain(X0))=one)),
% 0.57/15.74 inference(forward_demodulation,[status(thm)],[f47,f375])).
% 0.57/15.74 fof(f377,plain,(
% 0.57/15.74 ![X0]: (addition(domain(X0),antidomain(X0))=one)),
% 0.57/15.74 inference(forward_demodulation,[status(thm)],[f29,f376])).
% 0.57/15.74 fof(f382,plain,(
% 0.57/15.74 addition(domain(one),zero)=one),
% 0.57/15.74 inference(paramodulation,[status(thm)],[f69,f377])).
% 0.57/15.74 fof(f389,plain,(
% 0.57/15.74 domain(one)=one),
% 0.57/15.74 inference(forward_demodulation,[status(thm)],[f31,f382])).
% 0.57/15.74 fof(f402,plain,(
% 0.57/15.74 one=antidomain(zero)),
% 0.57/15.74 inference(forward_demodulation,[status(thm)],[f389,f317])).
% 0.57/15.74 fof(f404,plain,(
% 0.57/15.74 domain(zero)=antidomain(one)),
% 0.57/15.74 inference(paramodulation,[status(thm)],[f402,f47])).
% 0.57/15.74 fof(f408,plain,(
% 0.57/15.74 domain(zero)=zero),
% 0.57/15.74 inference(forward_demodulation,[status(thm)],[f69,f404])).
% 0.57/15.74 fof(f451,plain,(
% 0.57/15.74 ![X0]: (forward_diamond(X0,zero)=domain(multiplication(X0,zero)))),
% 0.57/15.74 inference(paramodulation,[status(thm)],[f408,f54])).
% 0.57/15.74 fof(f463,plain,(
% 0.57/15.74 ![X0]: (forward_diamond(X0,zero)=domain(zero))),
% 0.57/15.75 inference(forward_demodulation,[status(thm)],[f38,f451])).
% 0.57/15.75 fof(f464,plain,(
% 0.57/15.75 ![X0]: (forward_diamond(X0,zero)=zero)),
% 0.57/15.75 inference(forward_demodulation,[status(thm)],[f408,f463])).
% 0.57/15.75 fof(f556,plain,(
% 0.57/15.75 ~zero=zero),
% 0.57/15.75 inference(backward_demodulation,[status(thm)],[f464,f60])).
% 0.57/15.75 fof(f560,plain,(
% 0.57/15.75 $false),
% 0.57/15.75 inference(trivial_equality_resolution,[status(thm)],[f556])).
% 0.57/15.75 % SZS output end CNFRefutation for theBenchmark.p
% 0.57/15.75 % Elapsed time: 0.060970 seconds
% 0.57/15.75 % CPU time: 0.259234 seconds
% 0.57/15.75 % Total memory used: 44.818 MB
% 0.57/15.75 % Net memory used: 44.728 MB
%------------------------------------------------------------------------------