%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COM021+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 : n020.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 12:10:43 PM UTC 2026
% Result : Theorem 0.15s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM021+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n020.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 14:15:47 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 0.15/0.56 % Refutation found
% 0.15/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.56 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.56 fof(f6,definition,(
% 0.15/0.56 (! [W0,W1,W2] :( ( aElement0(W0)& aRewritingSystem0(W1)& aElement0(W2) )=> ( sdtmndtplgtdt0(W0,W1,W2)<=> ( aReductOfIn0(W2,W0,W1)| (? [W3] :( aElement0(W3)& aReductOfIn0(W3,W0,W1)& sdtmndtplgtdt0(W3,W1,W2) ) )) ) ) )),
% 0.15/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.56 fof(f8,definition,(
% 0.15/0.56 (! [W0,W1,W2] :( ( aElement0(W0)& aRewritingSystem0(W1)& aElement0(W2) )=> ( sdtmndtasgtdt0(W0,W1,W2)<=> ( W0 = W2| sdtmndtplgtdt0(W0,W1,W2) ) ) ) )),
% 0.15/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.56 fof(f13,definition,(
% 0.15/0.56 (! [W0,W1] :( ( aElement0(W0)& aRewritingSystem0(W1) )=> (! [W2] :( aNormalFormOfIn0(W2,W0,W1)<=> ( aElement0(W2)& sdtmndtasgtdt0(W0,W1,W2)& ~ (? [W3] : aReductOfIn0(W3,W2,W1) )) ) )) )),
% 0.15/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.56 fof(f15,hypothesis,(
% 0.15/0.56 aRewritingSystem0(xR) ),
% 0.15/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.56 fof(f22,hypothesis,(
% 0.15/0.56 ( aElement0(xw)& sdtmndtasgtdt0(xu,xR,xw)& sdtmndtasgtdt0(xv,xR,xw) ) ),
% 0.15/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.56 fof(f23,hypothesis,(
% 0.15/0.56 aNormalFormOfIn0(xd,xw,xR) ),
% 0.15/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.56 fof(f24,hypothesis,(
% 0.15/0.56 ( aElement0(xx)& sdtmndtasgtdt0(xb,xR,xx)& sdtmndtasgtdt0(xd,xR,xx) ) ),
% 0.15/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.56 fof(f25,conjecture,(
% 0.15/0.56 sdtmndtasgtdt0(xb,xR,xd) ),
% 0.15/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.56 fof(f26,negated_conjecture,(
% 0.15/0.56 ~(sdtmndtasgtdt0(xb,xR,xd) )),
% 0.15/0.56 inference(negated_conjecture,[status(cth)],[f25])).
% 0.15/0.56 fof(f39,plain,(
% 0.15/0.56 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|(sdtmndtplgtdt0(W0,W1,W2)<=>(aReductOfIn0(W2,W0,W1)|(?[W3]: ((aElement0(W3)&aReductOfIn0(W3,W0,W1))&sdtmndtplgtdt0(W3,W1,W2))))))),
% 0.15/0.56 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.15/0.56 fof(f40,plain,(
% 0.15/0.56 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|((~sdtmndtplgtdt0(W0,W1,W2)|(aReductOfIn0(W2,W0,W1)|(?[W3]: ((aElement0(W3)&aReductOfIn0(W3,W0,W1))&sdtmndtplgtdt0(W3,W1,W2)))))&(sdtmndtplgtdt0(W0,W1,W2)|(~aReductOfIn0(W2,W0,W1)&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,W1))|~sdtmndtplgtdt0(W3,W1,W2)))))))),
% 0.15/0.56 inference(NNF_transformation,[status(thm)],[f39])).
% 0.15/0.56 fof(f41,plain,(
% 0.15/0.56 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|((~sdtmndtplgtdt0(W0,W1,W2)|(aReductOfIn0(W2,W0,W1)|((aElement0(sK0_skl(W2,W1,W0))&aReductOfIn0(sK0_skl(W2,W1,W0),W0,W1))&sdtmndtplgtdt0(sK0_skl(W2,W1,W0),W1,W2))))&(sdtmndtplgtdt0(W0,W1,W2)|(~aReductOfIn0(W2,W0,W1)&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,W1))|~sdtmndtplgtdt0(W3,W1,W2)))))))),
% 0.15/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W3,sK0_skl(W2,W1,W0))],[f40])).
% 0.15/0.56 fof(f43,plain,(
% 0.15/0.56 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|~sdtmndtplgtdt0(X0,X1,X2)|aReductOfIn0(X2,X0,X1)|aReductOfIn0(sK0_skl(X2,X1,X0),X0,X1))),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f41])).
% 0.15/0.56 fof(f49,plain,(
% 0.15/0.56 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|(sdtmndtasgtdt0(W0,W1,W2)<=>(W0=W2|sdtmndtplgtdt0(W0,W1,W2))))),
% 0.15/0.56 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.15/0.56 fof(f50,plain,(
% 0.15/0.56 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|((~sdtmndtasgtdt0(W0,W1,W2)|(W0=W2|sdtmndtplgtdt0(W0,W1,W2)))&(sdtmndtasgtdt0(W0,W1,W2)|(~W0=W2&~sdtmndtplgtdt0(W0,W1,W2)))))),
% 0.15/0.56 inference(NNF_transformation,[status(thm)],[f49])).
% 0.15/0.56 fof(f51,plain,(
% 0.15/0.56 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|~sdtmndtasgtdt0(X0,X1,X2)|X0=X2|sdtmndtplgtdt0(X0,X1,X2))),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f50])).
% 0.15/0.56 fof(f90,plain,(
% 0.15/0.56 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|(![W2]: (aNormalFormOfIn0(W2,W0,W1)<=>((aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2))&(![W3]: ~aReductOfIn0(W3,W2,W1))))))),
% 0.15/0.56 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.15/0.56 fof(f91,plain,(
% 0.15/0.56 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|(![W2]: ((~aNormalFormOfIn0(W2,W0,W1)|((aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2))&(![W3]: ~aReductOfIn0(W3,W2,W1))))&(aNormalFormOfIn0(W2,W0,W1)|((~aElement0(W2)|~sdtmndtasgtdt0(W0,W1,W2))|(?[W3]: aReductOfIn0(W3,W2,W1)))))))),
% 0.15/0.56 inference(NNF_transformation,[status(thm)],[f90])).
% 0.15/0.56 fof(f92,plain,(
% 0.15/0.56 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|((![W2]: (~aNormalFormOfIn0(W2,W0,W1)|((aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2))&(![W3]: ~aReductOfIn0(W3,W2,W1)))))&(![W2]: (aNormalFormOfIn0(W2,W0,W1)|((~aElement0(W2)|~sdtmndtasgtdt0(W0,W1,W2))|(?[W3]: aReductOfIn0(W3,W2,W1)))))))),
% 0.15/0.56 inference(miniscoping,[status(thm)],[f91])).
% 0.15/0.56 fof(f93,plain,(
% 0.15/0.56 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|((![W2]: (~aNormalFormOfIn0(W2,W0,W1)|((aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2))&(![W3]: ~aReductOfIn0(W3,W2,W1)))))&(![W2]: (aNormalFormOfIn0(W2,W0,W1)|((~aElement0(W2)|~sdtmndtasgtdt0(W0,W1,W2))|aReductOfIn0(sK11_skl(W2,W1,W0),W2,W1))))))),
% 0.15/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(W3,sK11_skl(W2,W1,W0))],[f92])).
% 0.15/0.56 fof(f94,plain,(
% 0.15/0.56 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aNormalFormOfIn0(X2,X0,X1)|aElement0(X2))),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f93])).
% 0.15/0.56 fof(f96,plain,(
% 0.15/0.56 ![X0,X1,X2,X3]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aNormalFormOfIn0(X2,X0,X1)|~aReductOfIn0(X3,X2,X1))),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f93])).
% 0.15/0.56 fof(f101,plain,(
% 0.15/0.56 aRewritingSystem0(xR)),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f15])).
% 0.15/0.56 fof(f120,plain,(
% 0.15/0.56 aElement0(xw)),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f22])).
% 0.15/0.56 fof(f123,plain,(
% 0.15/0.56 aNormalFormOfIn0(xd,xw,xR)),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f23])).
% 0.15/0.56 fof(f124,plain,(
% 0.15/0.56 aElement0(xx)),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f24])).
% 0.15/0.56 fof(f125,plain,(
% 0.15/0.56 sdtmndtasgtdt0(xb,xR,xx)),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f24])).
% 0.15/0.56 fof(f126,plain,(
% 0.15/0.56 sdtmndtasgtdt0(xd,xR,xx)),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f24])).
% 0.15/0.56 fof(f127,plain,(
% 0.15/0.56 ~sdtmndtasgtdt0(xb,xR,xd)),
% 0.15/0.56 inference(cnf_transformation,[status(thm)],[f26])).
% 0.15/0.56 fof(f173,plain,(
% 0.15/0.56 ![X0,X1]: (~aElement0(X0)|~aNormalFormOfIn0(X1,X0,xR)|aElement0(X1))),
% 0.15/0.56 inference(resolution,[status(thm)],[f94,f101])).
% 0.15/0.56 fof(f174,plain,(
% 0.15/0.56 ~aElement0(xw)|aElement0(xd)),
% 0.15/0.56 inference(resolution,[status(thm)],[f173,f123])).
% 0.15/0.56 fof(f175,plain,(
% 0.15/0.56 aElement0(xd)),
% 0.15/0.56 inference(forward_subsumption_resolution,[status(thm)],[f174,f120])).
% 0.15/0.56 fof(f184,plain,(
% 0.15/0.56 ![X0,X1,X2]: (~aElement0(X0)|~aNormalFormOfIn0(X1,X0,xR)|~aReductOfIn0(X2,X1,xR))),
% 0.15/0.56 inference(resolution,[status(thm)],[f96,f101])).
% 0.15/0.56 fof(f186,plain,(
% 0.15/0.56 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|~sdtmndtplgtdt0(X0,xR,X1)|aReductOfIn0(X1,X0,xR)|aReductOfIn0(sK0_skl(X1,xR,X0),X0,xR))),
% 0.15/0.56 inference(resolution,[status(thm)],[f43,f101])).
% 0.15/0.56 fof(f187,plain,(
% 0.15/0.56 ![X0]: (~aElement0(xw)|~aReductOfIn0(X0,xd,xR))),
% 0.15/0.56 inference(resolution,[status(thm)],[f184,f123])).
% 0.15/0.56 fof(f188,plain,(
% 0.15/0.56 ![X0]: (~aReductOfIn0(X0,xd,xR))),
% 0.15/0.56 inference(forward_subsumption_resolution,[status(thm)],[f187,f120])).
% 0.15/0.56 fof(f191,plain,(
% 0.15/0.56 ![X0]: (~aElement0(xd)|~aElement0(X0)|~sdtmndtplgtdt0(xd,xR,X0)|aReductOfIn0(X0,xd,xR))),
% 0.15/0.56 inference(resolution,[status(thm)],[f186,f188])).
% 0.15/0.56 fof(f193,plain,(
% 0.15/0.56 ![X0]: (~aElement0(X0)|~sdtmndtplgtdt0(xd,xR,X0)|aReductOfIn0(X0,xd,xR))),
% 0.15/0.56 inference(forward_subsumption_resolution,[status(thm)],[f191,f175])).
% 0.15/0.56 fof(f195,plain,(
% 0.15/0.56 ![X0]: (~aElement0(X0)|~sdtmndtplgtdt0(xd,xR,X0))),
% 0.15/0.56 inference(forward_subsumption_resolution,[status(thm)],[f193,f188])).
% 0.15/0.56 fof(f243,plain,(
% 0.15/0.56 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|~sdtmndtasgtdt0(X0,xR,X1)|X0=X1|sdtmndtplgtdt0(X0,xR,X1))),
% 0.15/0.56 inference(resolution,[status(thm)],[f51,f101])).
% 0.15/0.56 fof(f245,plain,(
% 0.15/0.56 ![X0]: (~aElement0(X0)|~sdtmndtasgtdt0(X0,xR,xx)|X0=xx|sdtmndtplgtdt0(X0,xR,xx))),
% 0.15/0.56 inference(resolution,[status(thm)],[f243,f124])).
% 0.15/0.56 fof(f254,plain,(
% 0.15/0.56 ~aElement0(xd)|xd=xx|sdtmndtplgtdt0(xd,xR,xx)),
% 0.15/0.56 inference(resolution,[status(thm)],[f245,f126])).
% 0.15/0.56 fof(f260,plain,(
% 0.15/0.56 xd=xx|sdtmndtplgtdt0(xd,xR,xx)),
% 0.15/0.56 inference(forward_subsumption_resolution,[status(thm)],[f254,f175])).
% 0.15/0.56 fof(f269,plain,(
% 0.15/0.56 xd=xx|~aElement0(xx)),
% 0.15/0.56 inference(resolution,[status(thm)],[f260,f195])).
% 0.15/0.56 fof(f272,plain,(
% 0.15/0.56 xd=xx),
% 0.15/0.56 inference(forward_subsumption_resolution,[status(thm)],[f269,f124])).
% 0.15/0.56 fof(f284,plain,(
% 0.15/0.56 sdtmndtasgtdt0(xb,xR,xd)),
% 0.15/0.56 inference(backward_demodulation,[status(thm)],[f272,f125])).
% 0.15/0.56 fof(f294,plain,(
% 0.15/0.56 $false),
% 0.15/0.56 inference(forward_subsumption_resolution,[status(thm)],[f284,f127])).
% 0.15/0.56 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.61 % Elapsed time: 0.181003 seconds
% 0.15/0.61 % CPU time: 0.852332 seconds
% 0.15/0.61 % Total memory used: 86.199 MB
% 0.15/0.61 % Net memory used: 85.268 MB
%------------------------------------------------------------------------------