TSTP Solution File: GRP776+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:12:40 EDT 2023
% Result : Theorem 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n019.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:28:10 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.15/0.47 % Refutation found
% 0.15/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.47 fof(f2,axiom,(
% 0.15/0.47 (! [A] :( g(A)=> g(inv(A)) ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f3,axiom,(
% 0.15/0.47 g(eh) ),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f5,axiom,(
% 0.15/0.47 (! [A] :( g(A)=> product(eh,A) = A ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f8,axiom,(
% 0.15/0.47 (! [A] :( g(A)=> product(inv(A),A) = eh ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f10,axiom,(
% 0.15/0.47 (! [B,A] :( h(A)=> h(opp(B)) ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f12,axiom,(
% 0.15/0.47 (! [C,B,A] :( ( h(A)& h(B)& h(C) )=> sum(sum(A,B),C) = sum(A,sum(B,C)) ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f13,axiom,(
% 0.15/0.47 (! [A] :( h(A)=> sum(eg,A) = A ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f14,axiom,(
% 0.15/0.47 (! [A] :( h(A)=> sum(A,eg) = A ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f15,axiom,(
% 0.15/0.47 (! [A] :( h(A)=> sum(A,opp(A)) = eg ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f17,axiom,(
% 0.15/0.47 (! [A] :( g(A)=> h(f(A)) ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f18,axiom,(
% 0.15/0.47 (! [B,A] : f(product(A,B)) = sum(f(A),f(B)) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f19,conjecture,(
% 0.15/0.47 (! [X0] :( f(eh) = eg& ( ~ g(X0)| f(inv(X0)) = opp(f(X0)) ) ) )),
% 0.15/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.47 fof(f20,negated_conjecture,(
% 0.15/0.47 ~((! [X0] :( f(eh) = eg& ( ~ g(X0)| f(inv(X0)) = opp(f(X0)) ) ) ))),
% 0.15/0.47 inference(negated_conjecture,[status(cth)],[f19])).
% 0.15/0.47 fof(f23,plain,(
% 0.15/0.47 ![A]: (~g(A)|g(inv(A)))),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.15/0.47 fof(f24,plain,(
% 0.15/0.47 ![X0]: (~g(X0)|g(inv(X0)))),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f23])).
% 0.15/0.47 fof(f25,plain,(
% 0.15/0.47 g(eh)),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f3])).
% 0.15/0.47 fof(f28,plain,(
% 0.15/0.47 ![A]: (~g(A)|product(eh,A)=A)),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.15/0.47 fof(f29,plain,(
% 0.15/0.47 ![X0]: (~g(X0)|product(eh,X0)=X0)),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f28])).
% 0.15/0.47 fof(f34,plain,(
% 0.15/0.47 ![A]: (~g(A)|product(inv(A),A)=eh)),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 0.15/0.47 fof(f35,plain,(
% 0.15/0.47 ![X0]: (~g(X0)|product(inv(X0),X0)=eh)),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f34])).
% 0.15/0.47 fof(f38,plain,(
% 0.15/0.47 ![B,A]: (~h(A)|h(opp(B)))),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.15/0.47 fof(f39,plain,(
% 0.15/0.47 (![A]: ~h(A))|(![B]: h(opp(B)))),
% 0.15/0.47 inference(miniscoping,[status(esa)],[f38])).
% 0.15/0.47 fof(f40,plain,(
% 0.15/0.47 ![X0,X1]: (~h(X0)|h(opp(X1)))),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f39])).
% 0.15/0.47 fof(f42,plain,(
% 0.15/0.47 ![C,B,A]: (((~h(A)|~h(B))|~h(C))|sum(sum(A,B),C)=sum(A,sum(B,C)))),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.15/0.47 fof(f43,plain,(
% 0.15/0.47 ![X0,X1,X2]: (~h(X0)|~h(X1)|~h(X2)|sum(sum(X0,X1),X2)=sum(X0,sum(X1,X2)))),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f42])).
% 0.15/0.47 fof(f44,plain,(
% 0.15/0.47 ![A]: (~h(A)|sum(eg,A)=A)),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.15/0.47 fof(f45,plain,(
% 0.15/0.47 ![X0]: (~h(X0)|sum(eg,X0)=X0)),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f44])).
% 0.15/0.47 fof(f46,plain,(
% 0.15/0.47 ![A]: (~h(A)|sum(A,eg)=A)),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 0.15/0.47 fof(f47,plain,(
% 0.15/0.47 ![X0]: (~h(X0)|sum(X0,eg)=X0)),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f46])).
% 0.15/0.47 fof(f48,plain,(
% 0.15/0.47 ![A]: (~h(A)|sum(A,opp(A))=eg)),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 0.15/0.47 fof(f49,plain,(
% 0.15/0.47 ![X0]: (~h(X0)|sum(X0,opp(X0))=eg)),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f48])).
% 0.15/0.47 fof(f52,plain,(
% 0.15/0.47 ![A]: (~g(A)|h(f(A)))),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 0.15/0.47 fof(f53,plain,(
% 0.15/0.47 ![X0]: (~g(X0)|h(f(X0)))),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f52])).
% 0.15/0.47 fof(f54,plain,(
% 0.15/0.47 ![X0,X1]: (f(product(X0,X1))=sum(f(X0),f(X1)))),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f18])).
% 0.15/0.47 fof(f55,plain,(
% 0.15/0.47 (?[X0]: (~f(eh)=eg|(g(X0)&~f(inv(X0))=opp(f(X0)))))),
% 0.15/0.47 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 0.15/0.47 fof(f56,plain,(
% 0.15/0.47 ~f(eh)=eg|(?[X0]: (g(X0)&~f(inv(X0))=opp(f(X0))))),
% 0.15/0.47 inference(miniscoping,[status(esa)],[f55])).
% 0.15/0.47 fof(f57,plain,(
% 0.15/0.47 ~f(eh)=eg|(g(sk0_0)&~f(inv(sk0_0))=opp(f(sk0_0)))),
% 0.15/0.47 inference(skolemization,[status(esa)],[f56])).
% 0.15/0.47 fof(f58,plain,(
% 0.15/0.47 ~f(eh)=eg|g(sk0_0)),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f57])).
% 0.15/0.47 fof(f59,plain,(
% 0.15/0.47 ~f(eh)=eg|~f(inv(sk0_0))=opp(f(sk0_0))),
% 0.15/0.47 inference(cnf_transformation,[status(esa)],[f57])).
% 0.15/0.47 fof(f60,plain,(
% 0.15/0.47 spl0_0 <=> ~h(X0)),
% 0.15/0.47 introduced(split_symbol_definition)).
% 0.15/0.47 fof(f61,plain,(
% 0.15/0.47 ![X0]: (~h(X0)|~spl0_0)),
% 0.15/0.47 inference(component_clause,[status(thm)],[f60])).
% 0.15/0.47 fof(f63,plain,(
% 0.15/0.47 spl0_1 <=> h(opp(X1))),
% 0.15/0.47 introduced(split_symbol_definition)).
% 0.15/0.47 fof(f64,plain,(
% 0.15/0.47 ![X0]: (h(opp(X0))|~spl0_1)),
% 0.15/0.47 inference(component_clause,[status(thm)],[f63])).
% 0.15/0.47 fof(f66,plain,(
% 0.15/0.47 spl0_0|spl0_1),
% 0.15/0.47 inference(split_clause,[status(thm)],[f40,f60,f63])).
% 0.15/0.47 fof(f67,plain,(
% 0.15/0.47 spl0_2 <=> f(eh)=eg),
% 0.15/0.47 introduced(split_symbol_definition)).
% 0.15/0.47 fof(f69,plain,(
% 0.15/0.47 ~f(eh)=eg|spl0_2),
% 0.15/0.47 inference(component_clause,[status(thm)],[f67])).
% 0.15/0.47 fof(f70,plain,(
% 0.15/0.47 spl0_3 <=> g(sk0_0)),
% 0.15/0.47 introduced(split_symbol_definition)).
% 0.15/0.47 fof(f71,plain,(
% 0.15/0.47 g(sk0_0)|~spl0_3),
% 0.15/0.47 inference(component_clause,[status(thm)],[f70])).
% 0.15/0.47 fof(f73,plain,(
% 0.15/0.47 ~spl0_2|spl0_3),
% 0.15/0.47 inference(split_clause,[status(thm)],[f58,f67,f70])).
% 0.15/0.47 fof(f74,plain,(
% 0.15/0.47 spl0_4 <=> f(inv(sk0_0))=opp(f(sk0_0))),
% 0.15/0.47 introduced(split_symbol_definition)).
% 0.15/0.47 fof(f76,plain,(
% 0.15/0.47 ~f(inv(sk0_0))=opp(f(sk0_0))|spl0_4),
% 0.15/0.47 inference(component_clause,[status(thm)],[f74])).
% 0.15/0.47 fof(f77,plain,(
% 0.15/0.47 ~spl0_2|~spl0_4),
% 0.15/0.47 inference(split_clause,[status(thm)],[f59,f67,f74])).
% 0.15/0.47 fof(f79,plain,(
% 0.15/0.47 h(f(eh))),
% 0.15/0.47 inference(resolution,[status(thm)],[f53,f25])).
% 0.15/0.47 fof(f80,plain,(
% 0.15/0.47 product(eh,eh)=eh),
% 0.15/0.47 inference(resolution,[status(thm)],[f29,f25])).
% 0.15/0.47 fof(f84,plain,(
% 0.15/0.47 sum(f(eh),eg)=f(eh)),
% 0.15/0.47 inference(resolution,[status(thm)],[f47,f79])).
% 0.15/0.47 fof(f88,plain,(
% 0.15/0.47 sum(f(eh),opp(f(eh)))=eg),
% 0.15/0.47 inference(resolution,[status(thm)],[f49,f79])).
% 0.15/0.47 fof(f101,plain,(
% 0.15/0.47 ![X0,X1]: (~h(X0)|~h(X1)|sum(sum(X0,f(eh)),X1)=sum(X0,sum(f(eh),X1)))),
% 0.15/0.47 inference(resolution,[status(thm)],[f43,f79])).
% 0.15/0.47 fof(f139,plain,(
% 0.15/0.47 $false|~spl0_0),
% 0.15/0.47 inference(backward_subsumption_resolution,[status(thm)],[f79,f61])).
% 0.15/0.47 fof(f140,plain,(
% 0.15/0.47 ~spl0_0),
% 0.15/0.47 inference(contradiction_clause,[status(thm)],[f139])).
% 0.15/0.47 fof(f161,plain,(
% 0.15/0.47 ![X0]: (sum(eg,opp(X0))=opp(X0)|~spl0_1)),
% 0.15/0.47 inference(resolution,[status(thm)],[f45,f64])).
% 0.15/0.47 fof(f201,plain,(
% 0.15/0.47 ![X0,X1]: (~h(X0)|sum(sum(X0,f(eh)),opp(X1))=sum(X0,sum(f(eh),opp(X1)))|~spl0_1)),
% 0.15/0.47 inference(resolution,[status(thm)],[f101,f64])).
% 0.15/0.47 fof(f202,plain,(
% 0.15/0.47 ![X0]: (sum(sum(f(eh),f(eh)),opp(X0))=sum(f(eh),sum(f(eh),opp(X0)))|~spl0_1)),
% 0.15/0.47 inference(resolution,[status(thm)],[f201,f79])).
% 0.15/0.47 fof(f203,plain,(
% 0.15/0.47 ![X0]: (sum(f(product(eh,eh)),opp(X0))=sum(f(eh),sum(f(eh),opp(X0)))|~spl0_1)),
% 0.15/0.47 inference(forward_demodulation,[status(thm)],[f54,f202])).
% 0.15/0.47 fof(f204,plain,(
% 0.15/0.47 ![X0]: (sum(f(eh),opp(X0))=sum(f(eh),sum(f(eh),opp(X0)))|~spl0_1)),
% 0.15/0.47 inference(forward_demodulation,[status(thm)],[f80,f203])).
% 0.15/0.47 fof(f232,plain,(
% 0.15/0.47 sum(f(eh),opp(f(eh)))=sum(f(eh),eg)|~spl0_1),
% 0.15/0.47 inference(paramodulation,[status(thm)],[f88,f204])).
% 0.15/0.47 fof(f233,plain,(
% 0.15/0.47 eg=sum(f(eh),eg)|~spl0_1),
% 0.15/0.47 inference(forward_demodulation,[status(thm)],[f88,f232])).
% 0.15/0.47 fof(f234,plain,(
% 0.15/0.47 eg=f(eh)|~spl0_1),
% 0.15/0.47 inference(forward_demodulation,[status(thm)],[f84,f233])).
% 0.15/0.47 fof(f235,plain,(
% 0.15/0.47 $false|spl0_2|~spl0_1),
% 0.15/0.47 inference(forward_subsumption_resolution,[status(thm)],[f234,f69])).
% 0.15/0.47 fof(f236,plain,(
% 0.15/0.47 spl0_2|~spl0_1),
% 0.15/0.47 inference(contradiction_clause,[status(thm)],[f235])).
% 0.15/0.47 fof(f243,plain,(
% 0.15/0.47 h(f(sk0_0))|~spl0_3),
% 0.15/0.47 inference(resolution,[status(thm)],[f71,f53])).
% 0.15/0.47 fof(f251,plain,(
% 0.15/0.47 product(inv(sk0_0),sk0_0)=eh|~spl0_3),
% 0.15/0.47 inference(resolution,[status(thm)],[f71,f35])).
% 0.15/0.47 fof(f255,plain,(
% 0.15/0.47 g(inv(sk0_0))|~spl0_3),
% 0.15/0.47 inference(resolution,[status(thm)],[f71,f24])).
% 0.15/0.47 fof(f295,plain,(
% 0.15/0.47 sum(f(sk0_0),opp(f(sk0_0)))=eg|~spl0_3),
% 0.15/0.47 inference(resolution,[status(thm)],[f243,f49])).
% 0.15/0.47 fof(f356,plain,(
% 0.15/0.47 ![X0,X1,X2]: (~h(X0)|~h(X1)|sum(sum(X0,X1),opp(X2))=sum(X0,sum(X1,opp(X2)))|~spl0_1)),
% 0.15/0.48 inference(resolution,[status(thm)],[f43,f64])).
% 0.15/0.48 fof(f369,plain,(
% 0.15/0.48 h(f(inv(sk0_0)))|~spl0_3),
% 0.15/0.48 inference(resolution,[status(thm)],[f255,f53])).
% 0.15/0.48 fof(f396,plain,(
% 0.15/0.48 sum(f(inv(sk0_0)),eg)=f(inv(sk0_0))|~spl0_3),
% 0.15/0.48 inference(resolution,[status(thm)],[f369,f47])).
% 0.15/0.48 fof(f470,plain,(
% 0.15/0.48 ![X0,X1]: (~h(X0)|sum(sum(X0,f(sk0_0)),opp(X1))=sum(X0,sum(f(sk0_0),opp(X1)))|~spl0_1|~spl0_3)),
% 0.15/0.48 inference(resolution,[status(thm)],[f356,f243])).
% 0.15/0.48 fof(f653,plain,(
% 0.15/0.48 ![X0]: (sum(sum(f(inv(sk0_0)),f(sk0_0)),opp(X0))=sum(f(inv(sk0_0)),sum(f(sk0_0),opp(X0)))|~spl0_1|~spl0_3)),
% 0.15/0.48 inference(resolution,[status(thm)],[f470,f369])).
% 0.15/0.48 fof(f654,plain,(
% 0.15/0.48 ![X0]: (sum(f(product(inv(sk0_0),sk0_0)),opp(X0))=sum(f(inv(sk0_0)),sum(f(sk0_0),opp(X0)))|~spl0_1|~spl0_3)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f54,f653])).
% 0.15/0.48 fof(f655,plain,(
% 0.15/0.48 ![X0]: (sum(f(eh),opp(X0))=sum(f(inv(sk0_0)),sum(f(sk0_0),opp(X0)))|~spl0_1|~spl0_3)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f251,f654])).
% 0.15/0.48 fof(f656,plain,(
% 0.15/0.48 ![X0]: (sum(eg,opp(X0))=sum(f(inv(sk0_0)),sum(f(sk0_0),opp(X0)))|~spl0_1|~spl0_3)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f234,f655])).
% 0.15/0.48 fof(f657,plain,(
% 0.15/0.48 ![X0]: (opp(X0)=sum(f(inv(sk0_0)),sum(f(sk0_0),opp(X0)))|~spl0_1|~spl0_3)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f161,f656])).
% 0.15/0.48 fof(f663,plain,(
% 0.15/0.48 opp(f(sk0_0))=sum(f(inv(sk0_0)),eg)|~spl0_1|~spl0_3),
% 0.15/0.48 inference(paramodulation,[status(thm)],[f295,f657])).
% 0.15/0.48 fof(f664,plain,(
% 0.15/0.48 opp(f(sk0_0))=f(inv(sk0_0))|~spl0_1|~spl0_3),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f396,f663])).
% 0.15/0.48 fof(f665,plain,(
% 0.15/0.48 $false|spl0_4|~spl0_1|~spl0_3),
% 0.15/0.48 inference(forward_subsumption_resolution,[status(thm)],[f664,f76])).
% 0.15/0.48 fof(f666,plain,(
% 0.15/0.48 spl0_4|~spl0_1|~spl0_3),
% 0.15/0.48 inference(contradiction_clause,[status(thm)],[f665])).
% 0.15/0.48 fof(f667,plain,(
% 0.15/0.48 $false),
% 0.15/0.48 inference(sat_refutation,[status(thm)],[f66,f73,f77,f140,f236,f666])).
% 0.15/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.49 % Elapsed time: 0.177842 seconds
% 0.15/0.49 % CPU time: 0.626015 seconds
% 0.15/0.49 % Memory used: 50.309 MB
%------------------------------------------------------------------------------