%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COM012+3 : 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 : n018.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 12:10:42 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 14:16:32 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.07/0.37 fof(f7,axiom,(
% 0.07/0.37 (! [W0,W1,W2,W3] :( ( aElement0(W0)& aRewritingSystem0(W1)& aElement0(W2)& aElement0(W3) )=> ( ( sdtmndtplgtdt0(W0,W1,W2)& sdtmndtplgtdt0(W2,W1,W3) )=> sdtmndtplgtdt0(W0,W1,W3) ) ) )),
% 0.07/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.37 fof(f9,hypothesis,(
% 0.07/0.37 ( aElement0(xx)& aRewritingSystem0(xR)& aElement0(xy)& aElement0(xz) ) ),
% 0.07/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.37 fof(f10,conjecture,(
% 0.07/0.37 ( ( ( xx = xy| ( ( aReductOfIn0(xy,xx,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xx,xR)& sdtmndtplgtdt0(W0,xR,xy) ) ))& sdtmndtplgtdt0(xx,xR,xy) ) )& sdtmndtasgtdt0(xx,xR,xy)& ( xy = xz| ( ( aReductOfIn0(xz,xy,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xy,xR)& sdtmndtplgtdt0(W0,xR,xz) ) ))& sdtmndtplgtdt0(xy,xR,xz) ) )& sdtmndtasgtdt0(xy,xR,xz) )=> ( xx = xz| aReductOfIn0(xz,xx,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xx,xR)& sdtmndtplgtdt0(W0,xR,xz) ))| sdtmndtplgtdt0(xx,xR,xz)| sdtmndtasgtdt0(xx,xR,xz) ) ) ),
% 0.07/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.37 fof(f11,negated_conjecture,(
% 0.07/0.37 ~(( ( ( xx = xy| ( ( aReductOfIn0(xy,xx,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xx,xR)& sdtmndtplgtdt0(W0,xR,xy) ) ))& sdtmndtplgtdt0(xx,xR,xy) ) )& sdtmndtasgtdt0(xx,xR,xy)& ( xy = xz| ( ( aReductOfIn0(xz,xy,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xy,xR)& sdtmndtplgtdt0(W0,xR,xz) ) ))& sdtmndtplgtdt0(xy,xR,xz) ) )& sdtmndtasgtdt0(xy,xR,xz) )=> ( xx = xz| aReductOfIn0(xz,xx,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xx,xR)& sdtmndtplgtdt0(W0,xR,xz) ))| sdtmndtplgtdt0(xx,xR,xz)| sdtmndtasgtdt0(xx,xR,xz) ) ) )),
% 0.07/0.37 inference(negated_conjecture,[status(cth)],[f10])).
% 0.07/0.37 fof(f32,plain,(
% 0.07/0.37 ![W0,W1,W2,W3]: ((((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|~aElement0(W3))|((~sdtmndtplgtdt0(W0,W1,W2)|~sdtmndtplgtdt0(W2,W1,W3))|sdtmndtplgtdt0(W0,W1,W3)))),
% 0.07/0.37 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.07/0.37 fof(f33,plain,(
% 0.07/0.37 ![X0,X1,X2,X3]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|~aElement0(X3)|~sdtmndtplgtdt0(X0,X1,X2)|~sdtmndtplgtdt0(X2,X1,X3)|sdtmndtplgtdt0(X0,X1,X3))),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f32])).
% 0.07/0.37 fof(f40,plain,(
% 0.07/0.37 aRewritingSystem0(xR)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.07/0.37 fof(f41,plain,(
% 0.07/0.37 aElement0(xy)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.07/0.37 fof(f42,plain,(
% 0.07/0.37 aElement0(xz)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.07/0.37 fof(f43,plain,(
% 0.07/0.37 (((((xx=xy|((aReductOfIn0(xy,xx,xR)|(?[W0]: ((aElement0(W0)&aReductOfIn0(W0,xx,xR))&sdtmndtplgtdt0(W0,xR,xy))))&sdtmndtplgtdt0(xx,xR,xy)))&sdtmndtasgtdt0(xx,xR,xy))&(xy=xz|((aReductOfIn0(xz,xy,xR)|(?[W0]: ((aElement0(W0)&aReductOfIn0(W0,xy,xR))&sdtmndtplgtdt0(W0,xR,xz))))&sdtmndtplgtdt0(xy,xR,xz))))&sdtmndtasgtdt0(xy,xR,xz))&((((~xx=xz&~aReductOfIn0(xz,xx,xR))&(![W0]: ((~aElement0(W0)|~aReductOfIn0(W0,xx,xR))|~sdtmndtplgtdt0(W0,xR,xz))))&~sdtmndtplgtdt0(xx,xR,xz))&~sdtmndtasgtdt0(xx,xR,xz)))),
% 0.07/0.37 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.07/0.37 fof(f44,plain,(
% 0.07/0.37 ((((xx=xy|((aReductOfIn0(xy,xx,xR)|((aElement0(sK1_skl)&aReductOfIn0(sK1_skl,xx,xR))&sdtmndtplgtdt0(sK1_skl,xR,xy)))&sdtmndtplgtdt0(xx,xR,xy)))&sdtmndtasgtdt0(xx,xR,xy))&(xy=xz|((aReductOfIn0(xz,xy,xR)|((aElement0(sK2_skl)&aReductOfIn0(sK2_skl,xy,xR))&sdtmndtplgtdt0(sK2_skl,xR,xz)))&sdtmndtplgtdt0(xy,xR,xz))))&sdtmndtasgtdt0(xy,xR,xz))&((((~xx=xz&~aReductOfIn0(xz,xx,xR))&(![W0]: ((~aElement0(W0)|~aReductOfIn0(W0,xx,xR))|~sdtmndtplgtdt0(W0,xR,xz))))&~sdtmndtplgtdt0(xx,xR,xz))&~sdtmndtasgtdt0(xx,xR,xz))),
% 0.07/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(W0,sK1_skl),skolemize(W0,sK2_skl)],[f43])).
% 0.07/0.37 fof(f45,plain,(
% 0.07/0.37 xx=xy|aReductOfIn0(xy,xx,xR)|aElement0(sK1_skl)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f46,plain,(
% 0.07/0.37 xx=xy|aReductOfIn0(xy,xx,xR)|aReductOfIn0(sK1_skl,xx,xR)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f47,plain,(
% 0.07/0.37 xx=xy|aReductOfIn0(xy,xx,xR)|sdtmndtplgtdt0(sK1_skl,xR,xy)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f48,plain,(
% 0.07/0.37 xx=xy|sdtmndtplgtdt0(xx,xR,xy)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f53,plain,(
% 0.07/0.37 xy=xz|sdtmndtplgtdt0(xy,xR,xz)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f54,plain,(
% 0.07/0.37 sdtmndtasgtdt0(xy,xR,xz)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f55,plain,(
% 0.07/0.37 ~xx=xz),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f57,plain,(
% 0.07/0.37 ![X0]: (~aElement0(X0)|~aReductOfIn0(X0,xx,xR)|~sdtmndtplgtdt0(X0,xR,xz))),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f58,plain,(
% 0.07/0.37 ~sdtmndtplgtdt0(xx,xR,xz)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f59,plain,(
% 0.07/0.37 ~sdtmndtasgtdt0(xx,xR,xz)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f44])).
% 0.07/0.37 fof(f73,plain,(
% 0.07/0.37 ~aElement0(xy)|~sdtmndtplgtdt0(xy,xR,xz)|xx=xy|aElement0(sK1_skl)),
% 0.07/0.37 inference(resolution,[status(thm)],[f57,f45])).
% 0.07/0.37 fof(f74,plain,(
% 0.07/0.37 ~sdtmndtplgtdt0(xy,xR,xz)|xx=xy|aElement0(sK1_skl)),
% 0.07/0.37 inference(forward_subsumption_resolution,[status(thm)],[f73,f41])).
% 0.07/0.37 fof(f75,plain,(
% 0.07/0.37 xx=xy|aElement0(sK1_skl)|xy=xz),
% 0.07/0.37 inference(resolution,[status(thm)],[f74,f53])).
% 0.07/0.37 fof(f78,plain,(
% 0.07/0.37 xx=xy|aReductOfIn0(sK1_skl,xx,xR)|~aElement0(xy)|~sdtmndtplgtdt0(xy,xR,xz)),
% 0.07/0.37 inference(resolution,[status(thm)],[f46,f57])).
% 0.07/0.37 fof(f81,plain,(
% 0.07/0.37 xx=xy|aReductOfIn0(sK1_skl,xx,xR)|~sdtmndtplgtdt0(xy,xR,xz)),
% 0.07/0.37 inference(forward_subsumption_resolution,[status(thm)],[f78,f41])).
% 0.07/0.37 fof(f84,plain,(
% 0.07/0.37 xx=xy|sdtmndtplgtdt0(sK1_skl,xR,xy)|~aElement0(xy)|~sdtmndtplgtdt0(xy,xR,xz)),
% 0.07/0.37 inference(resolution,[status(thm)],[f47,f57])).
% 0.07/0.37 fof(f87,plain,(
% 0.07/0.37 xx=xy|sdtmndtplgtdt0(sK1_skl,xR,xy)|~sdtmndtplgtdt0(xy,xR,xz)),
% 0.07/0.37 inference(forward_subsumption_resolution,[status(thm)],[f84,f41])).
% 0.07/0.37 fof(f92,plain,(
% 0.07/0.37 xx=xy|aReductOfIn0(sK1_skl,xx,xR)|xy=xz),
% 0.07/0.37 inference(resolution,[status(thm)],[f81,f53])).
% 0.07/0.37 fof(f93,plain,(
% 0.07/0.37 xx=xy|sdtmndtplgtdt0(sK1_skl,xR,xy)|xy=xz),
% 0.07/0.37 inference(resolution,[status(thm)],[f87,f53])).
% 0.07/0.37 fof(f94,plain,(
% 0.07/0.37 xx=xy|xy=xz|~aElement0(sK1_skl)|~sdtmndtplgtdt0(sK1_skl,xR,xz)),
% 0.07/0.37 inference(resolution,[status(thm)],[f92,f57])).
% 0.07/0.37 fof(f97,plain,(
% 0.07/0.37 xx=xy|xy=xz|~sdtmndtplgtdt0(sK1_skl,xR,xz)),
% 0.07/0.37 inference(forward_subsumption_resolution,[status(thm)],[f94,f75])).
% 0.07/0.37 fof(f125,plain,(
% 0.07/0.37 ![X0,X1,X2]: (~aElement0(X0)|~aElement0(X1)|~aElement0(X2)|~sdtmndtplgtdt0(X0,xR,X1)|~sdtmndtplgtdt0(X1,xR,X2)|sdtmndtplgtdt0(X0,xR,X2))),
% 0.07/0.37 inference(resolution,[status(thm)],[f33,f40])).
% 0.07/0.37 fof(f127,plain,(
% 0.07/0.37 ![X0]: (~aElement0(X0)|~aElement0(xy)|~aElement0(xz)|~sdtmndtplgtdt0(X0,xR,xy)|sdtmndtplgtdt0(X0,xR,xz)|xy=xz)),
% 0.07/0.37 inference(resolution,[status(thm)],[f125,f53])).
% 0.07/0.37 fof(f131,plain,(
% 0.07/0.37 ![X0]: (~aElement0(X0)|~aElement0(xz)|~sdtmndtplgtdt0(X0,xR,xy)|sdtmndtplgtdt0(X0,xR,xz)|xy=xz)),
% 0.07/0.37 inference(forward_subsumption_resolution,[status(thm)],[f127,f41])).
% 0.07/0.37 fof(f134,plain,(
% 0.07/0.37 ![X0]: (~aElement0(X0)|~sdtmndtplgtdt0(X0,xR,xy)|sdtmndtplgtdt0(X0,xR,xz)|xy=xz)),
% 0.07/0.37 inference(resolution,[status(thm)],[f131,f42])).
% 0.07/0.37 fof(f135,plain,(
% 0.07/0.37 ~aElement0(sK1_skl)|sdtmndtplgtdt0(sK1_skl,xR,xz)|xy=xz|xx=xy|xy=xz),
% 0.07/0.37 inference(resolution,[status(thm)],[f134,f93])).
% 0.07/0.37 fof(f137,plain,(
% 0.07/0.37 ~aElement0(sK1_skl)|sdtmndtplgtdt0(sK1_skl,xR,xz)|xy=xz|xx=xy),
% 0.07/0.37 inference(duplicate_literals_removal,[status(thm)],[f135])).
% 0.07/0.37 fof(f138,plain,(
% 0.07/0.37 xx=xy|xy=xz),
% 0.07/0.37 inference(backward_subsumption_resolution,[status(thm)],[f97,f139])).
% 0.07/0.37 fof(f139,plain,(
% 0.07/0.37 sdtmndtplgtdt0(sK1_skl,xR,xz)|xy=xz|xx=xy),
% 0.07/0.37 inference(forward_subsumption_resolution,[status(thm)],[f137,f75])).
% 0.07/0.37 fof(f146,plain,(
% 0.07/0.37 ~sdtmndtasgtdt0(xy,xR,xz)|xy=xz),
% 0.07/0.37 inference(paramodulation,[status(thm)],[f138,f59])).
% 0.07/0.37 fof(f166,plain,(
% 0.07/0.37 xx=xy|sdtmndtplgtdt0(xx,xR,xz)),
% 0.07/0.37 inference(backward_demodulation,[status(thm)],[f173,f48])).
% 0.07/0.37 fof(f173,plain,(
% 0.07/0.37 xy=xz),
% 0.07/0.37 inference(forward_subsumption_resolution,[status(thm)],[f146,f54])).
% 0.07/0.37 fof(f196,plain,(
% 0.07/0.37 xx=xz|sdtmndtplgtdt0(xx,xR,xz)),
% 0.07/0.37 inference(forward_demodulation,[status(thm)],[f173,f166])).
% 0.07/0.37 fof(f198,plain,(
% 0.07/0.37 sdtmndtplgtdt0(xx,xR,xz)),
% 0.07/0.37 inference(forward_subsumption_resolution,[status(thm)],[f196,f55])).
% 0.07/0.37 fof(f199,plain,(
% 0.07/0.37 $false),
% 0.07/0.37 inference(backward_subsumption_resolution,[status(thm)],[f58,f198])).
% 0.07/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.41 % Elapsed time: 0.053229 seconds
% 0.12/0.41 % CPU time: 0.092567 seconds
% 0.12/0.41 % Total memory used: 15.844 MB
% 0.12/0.41 % Net memory used: 15.807 MB
%------------------------------------------------------------------------------