TSTP Solution File: GRP776+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n004.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 : Tue Apr 30 20:21:35 EDT 2024
% Result : Theorem 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 30 00:10:48 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.6.0
% 0.19/0.42 % Refutation found
% 0.19/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.42 fof(f2,axiom,(
% 0.19/0.42 (! [A] :( g(A)=> g(inv(A)) ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f3,axiom,(
% 0.19/0.42 g(eh) ),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f6,axiom,(
% 0.19/0.42 (! [A] :( g(A)=> product(A,eh) = A ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f7,axiom,(
% 0.19/0.42 (! [A] :( g(A)=> product(A,inv(A)) = eh ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f10,axiom,(
% 0.19/0.42 (! [B,A] :( h(A)=> h(opp(B)) ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f11,axiom,(
% 0.19/0.42 h(eg) ),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f12,axiom,(
% 0.19/0.42 (! [C,B,A] :( ( h(A)& h(B)& h(C) )=> sum(sum(A,B),C) = sum(A,sum(B,C)) ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f13,axiom,(
% 0.19/0.42 (! [A] :( h(A)=> sum(eg,A) = A ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f14,axiom,(
% 0.19/0.42 (! [A] :( h(A)=> sum(A,eg) = A ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f16,axiom,(
% 0.19/0.42 (! [A] :( h(A)=> sum(opp(A),A) = eg ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f17,axiom,(
% 0.19/0.42 (! [A] :( g(A)=> h(f(A)) ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f18,axiom,(
% 0.19/0.42 (! [B,A] : f(product(A,B)) = sum(f(A),f(B)) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f19,conjecture,(
% 0.19/0.42 (! [X0] :( f(eh) = eg& ( ~ g(X0)| f(inv(X0)) = opp(f(X0)) ) ) )),
% 0.19/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.42 fof(f20,negated_conjecture,(
% 0.19/0.42 ~((! [X0] :( f(eh) = eg& ( ~ g(X0)| f(inv(X0)) = opp(f(X0)) ) ) ))),
% 0.19/0.42 inference(negated_conjecture,[status(cth)],[f19])).
% 0.19/0.42 fof(f23,plain,(
% 0.19/0.42 ![A]: (~g(A)|g(inv(A)))),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.19/0.42 fof(f24,plain,(
% 0.19/0.42 ![X0]: (~g(X0)|g(inv(X0)))),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f23])).
% 0.19/0.42 fof(f25,plain,(
% 0.19/0.42 g(eh)),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f3])).
% 0.19/0.42 fof(f30,plain,(
% 0.19/0.42 ![A]: (~g(A)|product(A,eh)=A)),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.19/0.42 fof(f31,plain,(
% 0.19/0.42 ![X0]: (~g(X0)|product(X0,eh)=X0)),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f30])).
% 0.19/0.42 fof(f32,plain,(
% 0.19/0.42 ![A]: (~g(A)|product(A,inv(A))=eh)),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 0.19/0.42 fof(f33,plain,(
% 0.19/0.42 ![X0]: (~g(X0)|product(X0,inv(X0))=eh)),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f32])).
% 0.19/0.42 fof(f38,plain,(
% 0.19/0.42 ![B,A]: (~h(A)|h(opp(B)))),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.19/0.42 fof(f39,plain,(
% 0.19/0.42 (![A]: ~h(A))|(![B]: h(opp(B)))),
% 0.19/0.42 inference(miniscoping,[status(esa)],[f38])).
% 0.19/0.42 fof(f40,plain,(
% 0.19/0.42 ![X0,X1]: (~h(X0)|h(opp(X1)))),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f39])).
% 0.19/0.42 fof(f41,plain,(
% 0.19/0.42 h(eg)),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f11])).
% 0.19/0.42 fof(f42,plain,(
% 0.19/0.42 ![C,B,A]: (((~h(A)|~h(B))|~h(C))|sum(sum(A,B),C)=sum(A,sum(B,C)))),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.19/0.42 fof(f43,plain,(
% 0.19/0.42 ![X0,X1,X2]: (~h(X0)|~h(X1)|~h(X2)|sum(sum(X0,X1),X2)=sum(X0,sum(X1,X2)))),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f42])).
% 0.19/0.42 fof(f44,plain,(
% 0.19/0.42 ![A]: (~h(A)|sum(eg,A)=A)),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.19/0.42 fof(f45,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(eg,X0)=X0)),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f44])).
% 0.19/0.42 fof(f46,plain,(
% 0.19/0.42 ![A]: (~h(A)|sum(A,eg)=A)),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 0.19/0.42 fof(f47,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(X0,eg)=X0)),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f46])).
% 0.19/0.42 fof(f50,plain,(
% 0.19/0.42 ![A]: (~h(A)|sum(opp(A),A)=eg)),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.19/0.42 fof(f51,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(opp(X0),X0)=eg)),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f50])).
% 0.19/0.42 fof(f52,plain,(
% 0.19/0.42 ![A]: (~g(A)|h(f(A)))),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 0.19/0.42 fof(f53,plain,(
% 0.19/0.42 ![X0]: (~g(X0)|h(f(X0)))),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f52])).
% 0.19/0.42 fof(f54,plain,(
% 0.19/0.42 ![X0,X1]: (f(product(X0,X1))=sum(f(X0),f(X1)))),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f18])).
% 0.19/0.42 fof(f55,plain,(
% 0.19/0.42 (?[X0]: (~f(eh)=eg|(g(X0)&~f(inv(X0))=opp(f(X0)))))),
% 0.19/0.42 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 0.19/0.42 fof(f56,plain,(
% 0.19/0.42 ~f(eh)=eg|(?[X0]: (g(X0)&~f(inv(X0))=opp(f(X0))))),
% 0.19/0.42 inference(miniscoping,[status(esa)],[f55])).
% 0.19/0.42 fof(f57,plain,(
% 0.19/0.42 ~f(eh)=eg|(g(sk0_0)&~f(inv(sk0_0))=opp(f(sk0_0)))),
% 0.19/0.42 inference(skolemization,[status(esa)],[f56])).
% 0.19/0.42 fof(f58,plain,(
% 0.19/0.42 ~f(eh)=eg|g(sk0_0)),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f57])).
% 0.19/0.42 fof(f59,plain,(
% 0.19/0.42 ~f(eh)=eg|~f(inv(sk0_0))=opp(f(sk0_0))),
% 0.19/0.42 inference(cnf_transformation,[status(esa)],[f57])).
% 0.19/0.42 fof(f60,plain,(
% 0.19/0.42 spl0_0 <=> ~h(X0)),
% 0.19/0.42 introduced(split_symbol_definition)).
% 0.19/0.42 fof(f61,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|~spl0_0)),
% 0.19/0.42 inference(component_clause,[status(thm)],[f60])).
% 0.19/0.42 fof(f63,plain,(
% 0.19/0.42 spl0_1 <=> h(opp(X1))),
% 0.19/0.42 introduced(split_symbol_definition)).
% 0.19/0.42 fof(f64,plain,(
% 0.19/0.42 ![X0]: (h(opp(X0))|~spl0_1)),
% 0.19/0.42 inference(component_clause,[status(thm)],[f63])).
% 0.19/0.42 fof(f66,plain,(
% 0.19/0.42 spl0_0|spl0_1),
% 0.19/0.42 inference(split_clause,[status(thm)],[f40,f60,f63])).
% 0.19/0.42 fof(f67,plain,(
% 0.19/0.42 spl0_2 <=> f(eh)=eg),
% 0.19/0.42 introduced(split_symbol_definition)).
% 0.19/0.42 fof(f69,plain,(
% 0.19/0.42 ~f(eh)=eg|spl0_2),
% 0.19/0.42 inference(component_clause,[status(thm)],[f67])).
% 0.19/0.42 fof(f70,plain,(
% 0.19/0.42 spl0_3 <=> g(sk0_0)),
% 0.19/0.42 introduced(split_symbol_definition)).
% 0.19/0.42 fof(f71,plain,(
% 0.19/0.42 g(sk0_0)|~spl0_3),
% 0.19/0.42 inference(component_clause,[status(thm)],[f70])).
% 0.19/0.42 fof(f73,plain,(
% 0.19/0.42 ~spl0_2|spl0_3),
% 0.19/0.42 inference(split_clause,[status(thm)],[f58,f67,f70])).
% 0.19/0.42 fof(f74,plain,(
% 0.19/0.42 spl0_4 <=> f(inv(sk0_0))=opp(f(sk0_0))),
% 0.19/0.42 introduced(split_symbol_definition)).
% 0.19/0.42 fof(f76,plain,(
% 0.19/0.42 ~f(inv(sk0_0))=opp(f(sk0_0))|spl0_4),
% 0.19/0.42 inference(component_clause,[status(thm)],[f74])).
% 0.19/0.42 fof(f77,plain,(
% 0.19/0.42 ~spl0_2|~spl0_4),
% 0.19/0.42 inference(split_clause,[status(thm)],[f59,f67,f74])).
% 0.19/0.42 fof(f79,plain,(
% 0.19/0.42 $false|~spl0_0),
% 0.19/0.42 inference(backward_subsumption_resolution,[status(thm)],[f41,f61])).
% 0.19/0.42 fof(f80,plain,(
% 0.19/0.42 ~spl0_0),
% 0.19/0.42 inference(contradiction_clause,[status(thm)],[f79])).
% 0.19/0.42 fof(f81,plain,(
% 0.19/0.42 h(f(eh))),
% 0.19/0.42 inference(resolution,[status(thm)],[f53,f25])).
% 0.19/0.42 fof(f85,plain,(
% 0.19/0.42 sum(eg,f(eh))=f(eh)),
% 0.19/0.42 inference(resolution,[status(thm)],[f45,f81])).
% 0.19/0.42 fof(f87,plain,(
% 0.19/0.42 product(eh,eh)=eh),
% 0.19/0.42 inference(resolution,[status(thm)],[f31,f25])).
% 0.19/0.42 fof(f89,plain,(
% 0.19/0.42 sum(opp(f(eh)),f(eh))=eg),
% 0.19/0.42 inference(resolution,[status(thm)],[f51,f81])).
% 0.19/0.42 fof(f127,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(sum(X0,f(eh)),f(eh))=sum(X0,sum(f(eh),f(eh))))),
% 0.19/0.42 inference(resolution,[status(thm)],[f43,f81])).
% 0.19/0.42 fof(f128,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(sum(X0,f(eh)),f(eh))=sum(X0,f(product(eh,eh))))),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f54,f127])).
% 0.19/0.42 fof(f129,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(sum(X0,f(eh)),f(eh))=sum(X0,f(eh)))),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f87,f128])).
% 0.19/0.42 fof(f171,plain,(
% 0.19/0.42 ![X0]: (sum(sum(opp(X0),f(eh)),f(eh))=sum(opp(X0),f(eh))|~spl0_1)),
% 0.19/0.42 inference(resolution,[status(thm)],[f64,f129])).
% 0.19/0.42 fof(f183,plain,(
% 0.19/0.42 ![X0]: (sum(opp(X0),eg)=opp(X0)|~spl0_1)),
% 0.19/0.42 inference(resolution,[status(thm)],[f64,f47])).
% 0.19/0.42 fof(f199,plain,(
% 0.19/0.42 sum(eg,f(eh))=sum(opp(f(eh)),f(eh))|~spl0_1),
% 0.19/0.42 inference(paramodulation,[status(thm)],[f89,f171])).
% 0.19/0.42 fof(f200,plain,(
% 0.19/0.42 f(eh)=sum(opp(f(eh)),f(eh))|~spl0_1),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f85,f199])).
% 0.19/0.42 fof(f201,plain,(
% 0.19/0.42 f(eh)=eg|~spl0_1),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f89,f200])).
% 0.19/0.42 fof(f202,plain,(
% 0.19/0.42 $false|spl0_2|~spl0_1),
% 0.19/0.42 inference(forward_subsumption_resolution,[status(thm)],[f201,f69])).
% 0.19/0.42 fof(f203,plain,(
% 0.19/0.42 spl0_2|~spl0_1),
% 0.19/0.42 inference(contradiction_clause,[status(thm)],[f202])).
% 0.19/0.42 fof(f245,plain,(
% 0.19/0.42 product(sk0_0,inv(sk0_0))=eh|~spl0_3),
% 0.19/0.42 inference(resolution,[status(thm)],[f71,f33])).
% 0.19/0.42 fof(f249,plain,(
% 0.19/0.42 g(inv(sk0_0))|~spl0_3),
% 0.19/0.42 inference(resolution,[status(thm)],[f71,f24])).
% 0.19/0.42 fof(f250,plain,(
% 0.19/0.42 h(f(sk0_0))|~spl0_3),
% 0.19/0.42 inference(resolution,[status(thm)],[f71,f53])).
% 0.19/0.42 fof(f265,plain,(
% 0.19/0.42 h(f(inv(sk0_0)))|~spl0_3),
% 0.19/0.42 inference(resolution,[status(thm)],[f249,f53])).
% 0.19/0.42 fof(f277,plain,(
% 0.19/0.42 ![X0,X1]: (~h(X0)|~h(X1)|sum(sum(X0,f(sk0_0)),X1)=sum(X0,sum(f(sk0_0),X1))|~spl0_3)),
% 0.19/0.42 inference(resolution,[status(thm)],[f250,f43])).
% 0.19/0.42 fof(f281,plain,(
% 0.19/0.42 sum(opp(f(sk0_0)),f(sk0_0))=eg|~spl0_3),
% 0.19/0.42 inference(resolution,[status(thm)],[f250,f51])).
% 0.19/0.42 fof(f316,plain,(
% 0.19/0.42 sum(eg,f(inv(sk0_0)))=f(inv(sk0_0))|~spl0_3),
% 0.19/0.42 inference(resolution,[status(thm)],[f265,f45])).
% 0.19/0.42 fof(f489,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(sum(X0,f(sk0_0)),f(inv(sk0_0)))=sum(X0,sum(f(sk0_0),f(inv(sk0_0))))|~spl0_3)),
% 0.19/0.42 inference(resolution,[status(thm)],[f277,f265])).
% 0.19/0.42 fof(f490,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(sum(X0,f(sk0_0)),f(inv(sk0_0)))=sum(X0,f(product(sk0_0,inv(sk0_0))))|~spl0_3)),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f54,f489])).
% 0.19/0.42 fof(f491,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(sum(X0,f(sk0_0)),f(inv(sk0_0)))=sum(X0,f(eh))|~spl0_3)),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f245,f490])).
% 0.19/0.42 fof(f492,plain,(
% 0.19/0.42 ![X0]: (~h(X0)|sum(sum(X0,f(sk0_0)),f(inv(sk0_0)))=sum(X0,eg)|~spl0_1|~spl0_3)),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f201,f491])).
% 0.19/0.42 fof(f516,plain,(
% 0.19/0.42 ![X0]: (sum(sum(opp(X0),f(sk0_0)),f(inv(sk0_0)))=sum(opp(X0),eg)|~spl0_3|~spl0_1)),
% 0.19/0.42 inference(resolution,[status(thm)],[f492,f64])).
% 0.19/0.42 fof(f517,plain,(
% 0.19/0.42 ![X0]: (sum(sum(opp(X0),f(sk0_0)),f(inv(sk0_0)))=opp(X0)|~spl0_3|~spl0_1)),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f183,f516])).
% 0.19/0.42 fof(f523,plain,(
% 0.19/0.42 sum(eg,f(inv(sk0_0)))=opp(f(sk0_0))|~spl0_1|~spl0_3),
% 0.19/0.42 inference(paramodulation,[status(thm)],[f281,f517])).
% 0.19/0.42 fof(f524,plain,(
% 0.19/0.42 f(inv(sk0_0))=opp(f(sk0_0))|~spl0_1|~spl0_3),
% 0.19/0.42 inference(forward_demodulation,[status(thm)],[f316,f523])).
% 0.19/0.42 fof(f525,plain,(
% 0.19/0.42 $false|spl0_4|~spl0_1|~spl0_3),
% 0.19/0.42 inference(forward_subsumption_resolution,[status(thm)],[f524,f76])).
% 0.19/0.42 fof(f526,plain,(
% 0.19/0.42 spl0_4|~spl0_1|~spl0_3),
% 0.19/0.42 inference(contradiction_clause,[status(thm)],[f525])).
% 0.19/0.42 fof(f527,plain,(
% 0.19/0.42 $false),
% 0.19/0.42 inference(sat_refutation,[status(thm)],[f66,f73,f77,f80,f203,f526])).
% 0.19/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.43 % Elapsed time: 0.094615 seconds
% 0.19/0.43 % CPU time: 0.656908 seconds
% 0.19/0.43 % Total memory used: 52.681 MB
% 0.19/0.43 % Net memory used: 51.759 MB
%------------------------------------------------------------------------------