%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP776+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:37:19 PM UTC 2026
% Result : Theorem 0.10s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP776+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:45:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.48 % Refutation found
% 0.10/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.48 fof(f2,axiom,(
% 0.10/0.48 (! [A] :( g(A)=> g(inv(A)) ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f3,axiom,(
% 0.10/0.48 g(eh) ),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f5,axiom,(
% 0.10/0.48 (! [A] :( g(A)=> product(eh,A) = A ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f7,axiom,(
% 0.10/0.48 (! [A] :( g(A)=> product(A,inv(A)) = eh ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f10,axiom,(
% 0.10/0.48 (! [B,A] :( h(A)=> h(opp(B)) ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f11,axiom,(
% 0.10/0.48 h(eg) ),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f12,axiom,(
% 0.10/0.48 (! [C,B,A] :( ( h(A)& h(B)& h(C) )=> sum(sum(A,B),C) = sum(A,sum(B,C)) ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f13,axiom,(
% 0.10/0.48 (! [A] :( h(A)=> sum(eg,A) = A ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f14,axiom,(
% 0.10/0.48 (! [A] :( h(A)=> sum(A,eg) = A ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f16,axiom,(
% 0.10/0.48 (! [A] :( h(A)=> sum(opp(A),A) = eg ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f17,axiom,(
% 0.10/0.48 (! [A] :( g(A)=> h(f(A)) ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f18,axiom,(
% 0.10/0.48 (! [B,A] : f(product(A,B)) = sum(f(A),f(B)) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f19,conjecture,(
% 0.10/0.48 (! [X0] :( f(eh) = eg& ( ~ g(X0)| f(inv(X0)) = opp(f(X0)) ) ) )),
% 0.10/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f20,negated_conjecture,(
% 0.10/0.48 ~((! [X0] :( f(eh) = eg& ( ~ g(X0)| f(inv(X0)) = opp(f(X0)) ) ) ))),
% 0.10/0.48 inference(negated_conjecture,[status(cth)],[f19])).
% 0.10/0.48 fof(f23,plain,(
% 0.10/0.48 ![A]: (~g(A)|g(inv(A)))),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.10/0.48 fof(f24,plain,(
% 0.10/0.48 ![X0]: (~g(X0)|g(inv(X0)))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f23])).
% 0.10/0.48 fof(f25,plain,(
% 0.10/0.48 g(eh)),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.48 fof(f28,plain,(
% 0.10/0.48 ![A]: (~g(A)|product(eh,A)=A)),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.10/0.48 fof(f29,plain,(
% 0.10/0.48 ![X0]: (~g(X0)|product(eh,X0)=X0)),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f28])).
% 0.10/0.48 fof(f32,plain,(
% 0.10/0.48 ![A]: (~g(A)|product(A,inv(A))=eh)),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.10/0.48 fof(f33,plain,(
% 0.10/0.48 ![X0]: (~g(X0)|product(X0,inv(X0))=eh)),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f32])).
% 0.10/0.48 fof(f38,plain,(
% 0.10/0.48 ![B,A]: (~h(A)|h(opp(B)))),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.10/0.48 fof(f39,plain,(
% 0.10/0.48 (![A]: ~h(A))|(![B]: h(opp(B)))),
% 0.10/0.48 inference(miniscoping,[status(thm)],[f38])).
% 0.10/0.48 fof(f40,plain,(
% 0.10/0.48 ![X0,X1]: (~h(X0)|h(opp(X1)))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f39])).
% 0.10/0.48 fof(f41,plain,(
% 0.10/0.48 h(eg)),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f11])).
% 0.10/0.48 fof(f42,plain,(
% 0.10/0.48 ![C,B,A]: (((~h(A)|~h(B))|~h(C))|sum(sum(A,B),C)=sum(A,sum(B,C)))),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.10/0.48 fof(f43,plain,(
% 0.10/0.48 ![X0,X1,X2]: (~h(X0)|~h(X1)|~h(X2)|sum(sum(X0,X1),X2)=sum(X0,sum(X1,X2)))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f42])).
% 0.10/0.48 fof(f44,plain,(
% 0.10/0.48 ![A]: (~h(A)|sum(eg,A)=A)),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.10/0.48 fof(f45,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(eg,X0)=X0)),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f44])).
% 0.10/0.48 fof(f46,plain,(
% 0.10/0.48 ![A]: (~h(A)|sum(A,eg)=A)),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.10/0.48 fof(f47,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(X0,eg)=X0)),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f46])).
% 0.10/0.48 fof(f50,plain,(
% 0.10/0.48 ![A]: (~h(A)|sum(opp(A),A)=eg)),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.10/0.48 fof(f51,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(opp(X0),X0)=eg)),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.48 fof(f52,plain,(
% 0.10/0.48 ![A]: (~g(A)|h(f(A)))),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.10/0.48 fof(f53,plain,(
% 0.10/0.48 ![X0]: (~g(X0)|h(f(X0)))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f52])).
% 0.10/0.48 fof(f54,plain,(
% 0.10/0.48 ![X0,X1]: (f(product(X0,X1))=sum(f(X0),f(X1)))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f18])).
% 0.10/0.48 fof(f55,plain,(
% 0.10/0.48 (?[X0]: (~f(eh)=eg|(g(X0)&~f(inv(X0))=opp(f(X0)))))),
% 0.10/0.48 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.10/0.48 fof(f56,plain,(
% 0.10/0.48 ~f(eh)=eg|(?[X0]: (g(X0)&~f(inv(X0))=opp(f(X0))))),
% 0.10/0.48 inference(miniscoping,[status(thm)],[f55])).
% 0.10/0.48 fof(f57,plain,(
% 0.10/0.48 ~f(eh)=eg|(g(sK0_skl)&~f(inv(sK0_skl))=opp(f(sK0_skl)))),
% 0.10/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f56])).
% 0.10/0.48 fof(f58,plain,(
% 0.10/0.48 ~f(eh)=eg|g(sK0_skl)),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f57])).
% 0.10/0.48 fof(f59,plain,(
% 0.10/0.48 ~f(eh)=eg|~f(inv(sK0_skl))=opp(f(sK0_skl))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f57])).
% 0.10/0.48 fof(f61,plain,(
% 0.10/0.48 ![X0]: (h(opp(X0)))),
% 0.10/0.48 inference(resolution,[status(thm)],[f40,f41])).
% 0.10/0.48 fof(f62,plain,(
% 0.10/0.48 product(eh,eh)=eh),
% 0.10/0.48 inference(resolution,[status(thm)],[f29,f25])).
% 0.10/0.48 fof(f63,plain,(
% 0.10/0.48 h(f(eh))),
% 0.10/0.48 inference(resolution,[status(thm)],[f53,f25])).
% 0.10/0.48 fof(f65,plain,(
% 0.10/0.48 sum(eg,f(eh))=f(eh)),
% 0.10/0.48 inference(resolution,[status(thm)],[f45,f63])).
% 0.10/0.48 fof(f69,plain,(
% 0.10/0.48 ![X0]: (sum(opp(X0),eg)=opp(X0))),
% 0.10/0.48 inference(resolution,[status(thm)],[f47,f61])).
% 0.10/0.48 fof(f71,plain,(
% 0.10/0.48 sum(opp(f(eh)),f(eh))=eg),
% 0.10/0.48 inference(resolution,[status(thm)],[f51,f63])).
% 0.10/0.48 fof(f86,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(sum(X0,f(eh)),f(eh))=sum(X0,sum(f(eh),f(eh))))),
% 0.10/0.48 inference(resolution,[status(thm)],[f43,f63])).
% 0.10/0.48 fof(f95,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(sum(X0,f(eh)),f(eh))=sum(X0,f(product(eh,eh))))),
% 0.10/0.48 inference(forward_demodulation,[status(thm)],[f54,f86])).
% 0.10/0.48 fof(f96,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(sum(X0,f(eh)),f(eh))=sum(X0,f(eh)))),
% 0.10/0.48 inference(forward_demodulation,[status(thm)],[f62,f95])).
% 0.10/0.48 fof(f99,plain,(
% 0.10/0.48 ![X0]: (sum(sum(opp(X0),f(eh)),f(eh))=sum(opp(X0),f(eh)))),
% 0.10/0.48 inference(resolution,[status(thm)],[f96,f61])).
% 0.10/0.48 fof(f113,plain,(
% 0.10/0.48 sum(eg,f(eh))=sum(opp(f(eh)),f(eh))),
% 0.10/0.48 inference(paramodulation,[status(thm)],[f71,f99])).
% 0.10/0.48 fof(f115,plain,(
% 0.10/0.48 f(eh)=sum(opp(f(eh)),f(eh))),
% 0.10/0.48 inference(forward_demodulation,[status(thm)],[f65,f113])).
% 0.10/0.48 fof(f121,plain,(
% 0.10/0.48 ~eg=eg|~f(inv(sK0_skl))=opp(f(sK0_skl))),
% 0.10/0.48 inference(backward_demodulation,[status(thm)],[f127,f59])).
% 0.10/0.48 fof(f122,plain,(
% 0.10/0.48 ~eg=eg|g(sK0_skl)),
% 0.10/0.48 inference(backward_demodulation,[status(thm)],[f127,f58])).
% 0.10/0.48 fof(f127,plain,(
% 0.10/0.48 f(eh)=eg),
% 0.10/0.48 inference(forward_demodulation,[status(thm)],[f71,f115])).
% 0.10/0.48 fof(f141,plain,(
% 0.10/0.48 ~f(inv(sK0_skl))=opp(f(sK0_skl))),
% 0.10/0.48 inference(trivial_equality_resolution,[status(thm)],[f121])).
% 0.10/0.48 fof(f142,plain,(
% 0.10/0.48 g(sK0_skl)),
% 0.10/0.48 inference(trivial_equality_resolution,[status(thm)],[f122])).
% 0.10/0.48 fof(f149,plain,(
% 0.10/0.48 ![X0]: (f(product(eh,X0))=sum(eg,f(X0)))),
% 0.10/0.48 inference(paramodulation,[status(thm)],[f127,f54])).
% 0.10/0.48 fof(f161,plain,(
% 0.10/0.48 product(sK0_skl,inv(sK0_skl))=eh),
% 0.10/0.48 inference(resolution,[status(thm)],[f142,f33])).
% 0.10/0.48 fof(f163,plain,(
% 0.10/0.48 h(f(sK0_skl))),
% 0.10/0.48 inference(resolution,[status(thm)],[f142,f53])).
% 0.10/0.48 fof(f165,plain,(
% 0.10/0.48 g(inv(sK0_skl))),
% 0.10/0.48 inference(resolution,[status(thm)],[f142,f24])).
% 0.10/0.48 fof(f170,plain,(
% 0.10/0.48 ![X0,X1]: (~h(X0)|~h(X1)|sum(sum(X0,f(sK0_skl)),X1)=sum(X0,sum(f(sK0_skl),X1)))),
% 0.10/0.48 inference(resolution,[status(thm)],[f163,f43])).
% 0.10/0.48 fof(f171,plain,(
% 0.10/0.48 sum(opp(f(sK0_skl)),f(sK0_skl))=eg),
% 0.10/0.48 inference(resolution,[status(thm)],[f163,f51])).
% 0.10/0.48 fof(f185,plain,(
% 0.10/0.48 h(f(inv(sK0_skl)))),
% 0.10/0.48 inference(resolution,[status(thm)],[f165,f53])).
% 0.10/0.48 fof(f186,plain,(
% 0.10/0.48 product(eh,inv(sK0_skl))=inv(sK0_skl)),
% 0.10/0.48 inference(resolution,[status(thm)],[f165,f29])).
% 0.10/0.48 fof(f222,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(sum(X0,f(sK0_skl)),f(inv(sK0_skl)))=sum(X0,sum(f(sK0_skl),f(inv(sK0_skl)))))),
% 0.10/0.48 inference(resolution,[status(thm)],[f170,f185])).
% 0.10/0.48 fof(f226,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(sum(X0,f(sK0_skl)),f(inv(sK0_skl)))=sum(X0,f(product(sK0_skl,inv(sK0_skl)))))),
% 0.10/0.48 inference(forward_demodulation,[status(thm)],[f54,f222])).
% 0.10/0.48 fof(f227,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(sum(X0,f(sK0_skl)),f(inv(sK0_skl)))=sum(X0,f(eh)))),
% 0.10/0.48 inference(forward_demodulation,[status(thm)],[f161,f226])).
% 0.10/0.48 fof(f228,plain,(
% 0.10/0.48 ![X0]: (~h(X0)|sum(sum(X0,f(sK0_skl)),f(inv(sK0_skl)))=sum(X0,eg))),
% 0.10/0.48 inference(forward_demodulation,[status(thm)],[f127,f227])).
% 0.10/0.48 fof(f234,plain,(
% 0.10/0.48 ![X0]: (sum(sum(opp(X0),f(sK0_skl)),f(inv(sK0_skl)))=sum(opp(X0),eg))),
% 0.10/0.49 inference(resolution,[status(thm)],[f228,f61])).
% 0.10/0.49 fof(f245,plain,(
% 0.10/0.49 ![X0]: (sum(sum(opp(X0),f(sK0_skl)),f(inv(sK0_skl)))=opp(X0))),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f69,f234])).
% 0.10/0.49 fof(f758,plain,(
% 0.10/0.49 sum(eg,f(inv(sK0_skl)))=opp(f(sK0_skl))),
% 0.10/0.49 inference(paramodulation,[status(thm)],[f171,f245])).
% 0.10/0.49 fof(f759,plain,(
% 0.10/0.49 f(product(eh,inv(sK0_skl)))=opp(f(sK0_skl))),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f149,f758])).
% 0.10/0.49 fof(f760,plain,(
% 0.10/0.49 f(inv(sK0_skl))=opp(f(sK0_skl))),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f186,f759])).
% 0.10/0.49 fof(f761,plain,(
% 0.10/0.49 $false),
% 0.10/0.49 inference(forward_subsumption_resolution,[status(thm)],[f760,f141])).
% 0.10/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.51 % Elapsed time: 0.134056 seconds
% 0.10/0.51 % CPU time: 0.761943 seconds
% 0.10/0.51 % Total memory used: 79.272 MB
% 0.10/0.51 % Net memory used: 78.029 MB
%------------------------------------------------------------------------------