TSTP Solution File: SWC252+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC252+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 20:45:05 EDT 2024
% Result : Theorem 0.14s 0.34s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SWC252+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n008.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 Apr 30 00:04:12 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.14/0.32 % Drodi V3.6.0
% 0.14/0.34 % Refutation found
% 0.14/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.34 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.34 fof(f17,axiom,(
% 0.14/0.34 ssList(nil) ),
% 0.14/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f28,axiom,(
% 0.14/0.34 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 0.14/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f38,axiom,(
% 0.14/0.34 (! [U] :( ssItem(U)=> ~ memberP(nil,U) ) )),
% 0.14/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f84,axiom,(
% 0.14/0.34 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 0.14/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f96,conjecture,(
% 0.14/0.34 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| nil = U| (? [Y] :( ssItem(Y)& (? [Z] :( ssList(Z)& (? [X1] :( ssList(X1)& app(app(Z,cons(Y,nil)),X1) = U& (! [X2] :( ssItem(X2)=> ( ~ memberP(Z,X2)| ~ memberP(X1,X2)| ~ lt(Y,X2)| leq(Y,X2) ) ) )) )) )))| ( (! [X3] :( ssItem(X3)=> ( cons(X3,nil) != W| ~ memberP(X,X3) ) ))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 0.14/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f97,negated_conjecture,(
% 0.14/0.34 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| nil = U| (? [Y] :( ssItem(Y)& (? [Z] :( ssList(Z)& (? [X1] :( ssList(X1)& app(app(Z,cons(Y,nil)),X1) = U& (! [X2] :( ssItem(X2)=> ( ~ memberP(Z,X2)| ~ memberP(X1,X2)| ~ lt(Y,X2)| leq(Y,X2) ) ) )) )) )))| ( (! [X3] :( ssItem(X3)=> ( cons(X3,nil) != W| ~ memberP(X,X3) ) ))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 0.14/0.34 inference(negated_conjecture,[status(cth)],[f96])).
% 0.14/0.34 fof(f223,plain,(
% 0.14/0.34 ssList(nil)),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f17])).
% 0.14/0.34 fof(f248,plain,(
% 0.14/0.34 ![U]: (~ssList(U)|app(nil,U)=U)),
% 0.14/0.34 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 0.14/0.34 fof(f249,plain,(
% 0.14/0.34 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f248])).
% 0.14/0.34 fof(f278,plain,(
% 0.14/0.34 ![U]: (~ssItem(U)|~memberP(nil,U))),
% 0.14/0.34 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 0.14/0.34 fof(f279,plain,(
% 0.14/0.34 ![X0]: (~ssItem(X0)|~memberP(nil,X0))),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f278])).
% 0.14/0.34 fof(f388,plain,(
% 0.14/0.34 ![U]: (~ssList(U)|app(U,nil)=U)),
% 0.14/0.34 inference(pre_NNF_transformation,[status(esa)],[f84])).
% 0.14/0.34 fof(f389,plain,(
% 0.14/0.34 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f388])).
% 0.14/0.34 fof(f415,plain,(
% 0.14/0.34 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&~nil=U)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=U)|(?[X2]: (ssItem(X2)&(((memberP(Z,X2)&memberP(X1,X2))<(Y,X2))&~leq(Y,X2)))))))))))&((?[X3]: (ssItem(X3)&(cons(X3,nil)=W&memberP(X,X3))))|(nil=X&nil=W)))))))))))),
% 0.14/0.34 inference(pre_NNF_transformation,[status(esa)],[f97])).
% 0.14/0.34 fof(f416,plain,(
% 0.14/0.34 ![W,X,X3]: (pd0_0(X3,X,W)=>(ssItem(X3)&(cons(X3,nil)=W&memberP(X,X3))))),
% 0.14/0.34 introduced(predicate_definition,[f415])).
% 0.14/0.34 fof(f417,plain,(
% 0.14/0.34 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&~nil=U)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=U)|(?[X2]: (ssItem(X2)&(((memberP(Z,X2)&memberP(X1,X2))<(Y,X2))&~leq(Y,X2)))))))))))&((?[X3]: pd0_0(X3,X,W))|(nil=X&nil=W))))))))))),
% 0.14/0.34 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.14/0.34 fof(f418,plain,(
% 0.14/0.34 (ssList(sk0_47)&(ssList(sk0_48)&(ssList(sk0_49)&(ssList(sk0_50)&((((sk0_48=sk0_50&sk0_47=sk0_49)&~nil=sk0_47)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=sk0_47)|(ssItem(sk0_51(X1,Z,Y))&(((memberP(Z,sk0_51(X1,Z,Y))&memberP(X1,sk0_51(X1,Z,Y)))<(Y,sk0_51(X1,Z,Y)))&~leq(Y,sk0_51(X1,Z,Y)))))))))))&(pd0_0(sk0_52,sk0_50,sk0_49)|(nil=sk0_50&nil=sk0_49)))))))),
% 0.14/0.34 inference(skolemization,[status(esa)],[f417])).
% 0.14/0.34 fof(f419,plain,(
% 0.14/0.34 ssList(sk0_47)),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f418])).
% 0.14/0.34 fof(f423,plain,(
% 0.14/0.34 sk0_48=sk0_50),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f418])).
% 0.14/0.34 fof(f424,plain,(
% 0.14/0.34 sk0_47=sk0_49),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f418])).
% 0.14/0.34 fof(f425,plain,(
% 0.14/0.34 ~nil=sk0_47),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f418])).
% 0.14/0.34 fof(f426,plain,(
% 0.14/0.34 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk0_47|ssItem(sk0_51(X2,X1,X0)))),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f418])).
% 0.14/0.34 fof(f427,plain,(
% 0.14/0.34 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk0_47|memberP(X1,sk0_51(X2,X1,X0)))),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f418])).
% 0.14/0.34 fof(f432,plain,(
% 0.14/0.34 pd0_0(sk0_52,sk0_50,sk0_49)|nil=sk0_49),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f418])).
% 0.14/0.34 fof(f433,plain,(
% 0.14/0.34 ![W,X,X3]: (~pd0_0(X3,X,W)|(ssItem(X3)&(cons(X3,nil)=W&memberP(X,X3))))),
% 0.14/0.34 inference(pre_NNF_transformation,[status(esa)],[f416])).
% 0.14/0.34 fof(f434,plain,(
% 0.14/0.34 ![X0,X1,X2]: (~pd0_0(X0,X1,X2)|ssItem(X0))),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f433])).
% 0.14/0.34 fof(f435,plain,(
% 0.14/0.34 ![X0,X1,X2]: (~pd0_0(X0,X1,X2)|cons(X0,nil)=X2)),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f433])).
% 0.14/0.34 fof(f437,plain,(
% 0.14/0.34 spl0_0 <=> pd0_0(sk0_52,sk0_50,sk0_49)),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f438,plain,(
% 0.14/0.34 pd0_0(sk0_52,sk0_50,sk0_49)|~spl0_0),
% 0.14/0.34 inference(component_clause,[status(thm)],[f437])).
% 0.14/0.34 fof(f444,plain,(
% 0.14/0.34 spl0_2 <=> nil=sk0_49),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f445,plain,(
% 0.14/0.34 nil=sk0_49|~spl0_2),
% 0.14/0.34 inference(component_clause,[status(thm)],[f444])).
% 0.14/0.34 fof(f447,plain,(
% 0.14/0.34 spl0_0|spl0_2),
% 0.14/0.34 inference(split_clause,[status(thm)],[f432,f437,f444])).
% 0.14/0.34 fof(f482,plain,(
% 0.14/0.34 app(nil,sk0_47)=sk0_47),
% 0.14/0.34 inference(resolution,[status(thm)],[f249,f419])).
% 0.14/0.34 fof(f489,plain,(
% 0.14/0.34 pd0_0(sk0_52,sk0_48,sk0_49)|~spl0_0),
% 0.14/0.34 inference(forward_demodulation,[status(thm)],[f423,f438])).
% 0.14/0.34 fof(f490,plain,(
% 0.14/0.34 pd0_0(sk0_52,sk0_48,sk0_47)|~spl0_0),
% 0.14/0.34 inference(forward_demodulation,[status(thm)],[f424,f489])).
% 0.14/0.34 fof(f491,plain,(
% 0.14/0.34 ssItem(sk0_52)|~spl0_0),
% 0.14/0.34 inference(resolution,[status(thm)],[f490,f434])).
% 0.14/0.34 fof(f511,plain,(
% 0.14/0.34 nil=sk0_47|~spl0_2),
% 0.14/0.34 inference(forward_demodulation,[status(thm)],[f424,f445])).
% 0.14/0.34 fof(f512,plain,(
% 0.14/0.34 $false|~spl0_2),
% 0.14/0.34 inference(forward_subsumption_resolution,[status(thm)],[f511,f425])).
% 0.14/0.34 fof(f513,plain,(
% 0.14/0.34 ~spl0_2),
% 0.14/0.34 inference(contradiction_clause,[status(thm)],[f512])).
% 0.14/0.34 fof(f526,plain,(
% 0.14/0.34 cons(sk0_52,nil)=sk0_47|~spl0_0),
% 0.14/0.34 inference(resolution,[status(thm)],[f435,f490])).
% 0.14/0.34 fof(f527,plain,(
% 0.14/0.34 spl0_6 <=> ssList(nil)),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f529,plain,(
% 0.14/0.34 ~ssList(nil)|spl0_6),
% 0.14/0.34 inference(component_clause,[status(thm)],[f527])).
% 0.14/0.34 fof(f545,plain,(
% 0.14/0.34 $false|spl0_6),
% 0.14/0.34 inference(forward_subsumption_resolution,[status(thm)],[f529,f223])).
% 0.14/0.34 fof(f546,plain,(
% 0.14/0.34 spl0_6),
% 0.14/0.34 inference(contradiction_clause,[status(thm)],[f545])).
% 0.14/0.34 fof(f564,plain,(
% 0.14/0.34 spl0_12 <=> ~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~ssItem(sk0_51(X1,nil,X0))),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f565,plain,(
% 0.14/0.34 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~ssItem(sk0_51(X1,nil,X0))|~spl0_12)),
% 0.14/0.34 inference(component_clause,[status(thm)],[f564])).
% 0.14/0.34 fof(f567,plain,(
% 0.14/0.34 ![X0,X1]: (~ssItem(X0)|~ssList(nil)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~ssItem(sk0_51(X1,nil,X0)))),
% 0.14/0.34 inference(resolution,[status(thm)],[f427,f279])).
% 0.14/0.34 fof(f568,plain,(
% 0.14/0.34 spl0_12|~spl0_6),
% 0.14/0.34 inference(split_clause,[status(thm)],[f567,f564,f527])).
% 0.14/0.34 fof(f572,plain,(
% 0.14/0.34 spl0_13 <=> ~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f573,plain,(
% 0.14/0.34 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~spl0_13)),
% 0.14/0.34 inference(component_clause,[status(thm)],[f572])).
% 0.14/0.34 fof(f575,plain,(
% 0.14/0.34 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~ssItem(X0)|~ssList(nil)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~spl0_12)),
% 0.14/0.34 inference(resolution,[status(thm)],[f565,f426])).
% 0.14/0.34 fof(f576,plain,(
% 0.14/0.34 spl0_13|~spl0_6|~spl0_12),
% 0.14/0.34 inference(split_clause,[status(thm)],[f575,f572,f527,f564])).
% 0.14/0.34 fof(f577,plain,(
% 0.14/0.34 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sk0_47|~spl0_13)),
% 0.14/0.35 inference(duplicate_literals_removal,[status(esa)],[f573])).
% 0.14/0.35 fof(f579,plain,(
% 0.14/0.35 ![X0]: (~ssList(X0)|~app(app(nil,cons(sk0_52,nil)),X0)=sk0_47|~spl0_13|~spl0_0)),
% 0.14/0.35 inference(resolution,[status(thm)],[f577,f491])).
% 0.14/0.35 fof(f580,plain,(
% 0.14/0.35 ![X0]: (~ssList(X0)|~app(app(nil,sk0_47),X0)=sk0_47|~spl0_13|~spl0_0)),
% 0.14/0.35 inference(forward_demodulation,[status(thm)],[f526,f579])).
% 0.14/0.35 fof(f581,plain,(
% 0.14/0.35 ![X0]: (~ssList(X0)|~app(sk0_47,X0)=sk0_47|~spl0_13|~spl0_0)),
% 0.14/0.35 inference(forward_demodulation,[status(thm)],[f482,f580])).
% 0.14/0.35 fof(f592,plain,(
% 0.14/0.35 ~app(sk0_47,nil)=sk0_47|~spl0_13|~spl0_0),
% 0.14/0.35 inference(resolution,[status(thm)],[f581,f223])).
% 0.14/0.35 fof(f626,plain,(
% 0.14/0.35 app(sk0_47,nil)=sk0_47),
% 0.14/0.35 inference(resolution,[status(thm)],[f389,f419])).
% 0.14/0.35 fof(f677,plain,(
% 0.14/0.35 ~sk0_47=sk0_47|~spl0_13|~spl0_0),
% 0.14/0.35 inference(forward_demodulation,[status(thm)],[f626,f592])).
% 0.14/0.35 fof(f678,plain,(
% 0.14/0.35 $false|~spl0_13|~spl0_0),
% 0.14/0.35 inference(trivial_equality_resolution,[status(esa)],[f677])).
% 0.14/0.35 fof(f679,plain,(
% 0.14/0.35 ~spl0_13|~spl0_0),
% 0.14/0.35 inference(contradiction_clause,[status(thm)],[f678])).
% 0.14/0.35 fof(f680,plain,(
% 0.14/0.35 $false),
% 0.14/0.35 inference(sat_refutation,[status(thm)],[f447,f513,f546,f568,f576,f679])).
% 0.14/0.35 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.36 % Elapsed time: 0.040111 seconds
% 0.14/0.36 % CPU time: 0.160104 seconds
% 0.14/0.36 % Total memory used: 53.650 MB
% 0.14/0.36 % Net memory used: 53.498 MB
%------------------------------------------------------------------------------