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Drodi-SAT---4.1.1.THM-Ass.s

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%------------------------------------------------------------------------------
% File     : Drodi-SAT---4.1.1
% Problem  : SWC179+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n020.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 02:41:47 PM UTC 2026

% Result   : Theorem 0.16s 5.41s
% Output   : Assurance 0s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC179+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.38  % Computer : n020.cluster.edu
% 0.12/5.38  % Model    : x86_64 x86_64
% 0.12/5.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38  % Memory   : 8046.5625MB
% 0.12/5.38  % OS       : Linux 6.8.0-71-generic
% 0.12/5.38  % CPULimit : 300
% 0.12/5.38  % WCLimit  : 300
% 0.12/5.38  % DateTime : Mon Sep 21 08:02:52 UTC 2026
% 0.12/5.38  % CPUTime  : 
% 0.12/5.39  % Drodi V4.1.1
% 0.16/5.41  % Refutation found
% 0.16/5.41  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/5.41  % SZS output start CNFRefutation for theBenchmark
% 0.16/5.41  fof(f71,axiom,(
% 0.16/5.41    (! [U] :( ssItem(U)=> duplicatefreeP(cons(U,nil)) ) )),
% 0.16/5.41    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.41  fof(f72,axiom,(
% 0.16/5.41    duplicatefreeP(nil) ),
% 0.16/5.41    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.41  fof(f96,conjecture,(
% 0.16/5.41    (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| duplicatefreeP(U)| ( (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> (! [X1] :( ssList(X1)=> ( cons(Y,nil) != W| app(app(Z,W),X1) != X| (? [X2] :( ssItem(X2)& memberP(Z,X2)& lt(Y,X2) ))| (? [X3] :( ssItem(X3)& memberP(X1,X3)& lt(X3,Y) ) )) ) )) )))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 0.16/5.41    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.41  fof(f97,negated_conjecture,(
% 0.16/5.41    ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| duplicatefreeP(U)| ( (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> (! [X1] :( ssList(X1)=> ( cons(Y,nil) != W| app(app(Z,W),X1) != X| (? [X2] :( ssItem(X2)& memberP(Z,X2)& lt(Y,X2) ))| (? [X3] :( ssItem(X3)& memberP(X1,X3)& lt(X3,Y) ) )) ) )) )))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 0.16/5.41    inference(negated_conjecture,[status(cth)],[f96])).
% 0.16/5.41  fof(f357,plain,(
% 0.16/5.41    ![U]: (~ssItem(U)|duplicatefreeP(cons(U,nil)))),
% 0.16/5.41    inference(pre_NNF_transformation,[status(thm)],[f71])).
% 0.16/5.41  fof(f358,plain,(
% 0.16/5.41    ![X0]: (~ssItem(X0)|duplicatefreeP(cons(X0,nil)))),
% 0.16/5.41    inference(cnf_transformation,[status(thm)],[f357])).
% 0.16/5.41  fof(f359,plain,(
% 0.16/5.41    duplicatefreeP(nil)),
% 0.16/5.41    inference(cnf_transformation,[status(thm)],[f72])).
% 0.16/5.41  fof(f415,plain,(
% 0.16/5.41    (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((V=X&U=W)&~duplicatefreeP(U))&((?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: ((~ssItem(X2)|~memberP(Z,X2))|~lt(Y,X2))))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y))))))))))|(nil=X&nil=W)))))))))))),
% 0.16/5.41    inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.16/5.41  fof(f416,definition,(
% 0.16/5.41    ![W,X,Y]: (sP0_prd(Y,X,W)<=>(ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: ((~ssItem(X2)|~memberP(Z,X2))|~lt(Y,X2))))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y))))))))))),
% 0.16/5.41    introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.16/5.41  fof(f417,plain,(
% 0.16/5.41    ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((V=X&U=W)&~duplicatefreeP(U))&((?[Y]: sP0_prd(Y,X,W))|(nil=X&nil=W))))))))))),
% 0.16/5.41    inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.16/5.41  fof(f418,plain,(
% 0.16/5.41    (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&~duplicatefreeP(sK47_skl))&(sP0_prd(sK51_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))))))),
% 0.16/5.41    inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f417])).
% 0.16/5.41  fof(f424,plain,(
% 0.16/5.41    sK47_skl=sK49_skl),
% 0.16/5.41    inference(cnf_transformation,[status(thm)],[f418])).
% 0.16/5.41  fof(f425,plain,(
% 0.16/5.41    ~duplicatefreeP(sK47_skl)),
% 0.16/5.41    inference(cnf_transformation,[status(thm)],[f418])).
% 0.16/5.41  fof(f426,plain,(
% 0.16/5.41    sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK50_skl),
% 0.16/5.41    inference(cnf_transformation,[status(thm)],[f418])).
% 0.16/5.41  fof(f427,plain,(
% 0.16/5.41    sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK49_skl),
% 0.16/5.41    inference(cnf_transformation,[status(thm)],[f418])).
% 0.16/5.41  fof(f428,definition,(
% 0.16/5.41    ![Y,Z,X2]: (sP1_prd(X2,Z,Y)<=>((~ssItem(X2)|~memberP(Z,X2))|~lt(Y,X2)))),
% 0.16/5.41    introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.16/5.41  fof(f429,plain,(
% 0.16/5.41    ![W,X,Y]: (sP0_prd(Y,X,W)<=>(ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: sP1_prd(X2,Z,Y)))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y))))))))))),
% 0.16/5.41    inference(formula_renaming,[status(thm)],[f416,f428])).
% 0.16/5.41  fof(f430,plain,(
% 0.16/5.41    ![W,X,Y]: ((~sP0_prd(Y,X,W)|(ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: sP1_prd(X2,Z,Y)))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y))))))))))&(sP0_prd(Y,X,W)|(~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: (~ssList(X1)|(((~cons(Y,nil)=W|~app(app(Z,W),X1)=X)|(?[X2]: ~sP1_prd(X2,Z,Y)))|(?[X3]: ((ssItem(X3)&memberP(X1,X3))&lt(X3,Y)))))))))))),
% 0.16/5.41    inference(NNF_transformation,[status(thm)],[f429])).
% 0.16/5.41  fof(f431,plain,(
% 0.16/5.41    (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: sP1_prd(X2,Z,Y)))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y)))))))))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: (~ssList(X1)|(((~cons(Y,nil)=W|~app(app(Z,W),X1)=X)|(?[X2]: ~sP1_prd(X2,Z,Y)))|(?[X3]: ((ssItem(X3)&memberP(X1,X3))&lt(X3,Y)))))))))))),
% 0.16/5.41    inference(miniscoping,[status(thm)],[f430])).
% 0.16/5.41  fof(f432,plain,(
% 0.16/5.41    (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&(ssList(sK52_skl(Y,X,W))&(ssList(sK53_skl(Y,X,W))&(((cons(Y,nil)=W&app(app(sK52_skl(Y,X,W),W),sK53_skl(Y,X,W))=X)&(![X2]: sP1_prd(X2,sK52_skl(Y,X,W),Y)))&(![X3]: ((~ssItem(X3)|~memberP(sK53_skl(Y,X,W),X3))|~lt(X3,Y)))))))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: (~ssList(X1)|(((~cons(Y,nil)=W|~app(app(Z,W),X1)=X)|~sP1_prd(sK54_skl(X1,Z,Y,X,W),Z,Y))|((ssItem(sK55_skl(X1,Z,Y,X,W))&memberP(X1,sK55_skl(X1,Z,Y,X,W)))&lt(sK55_skl(X1,Z,Y,X,W),Y))))))))))),
% 0.16/5.41    inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(Z,sK52_skl(Y,X,W)),skolemize(X1,sK53_skl(Y,X,W)),skolemize(X2,sK54_skl(X1,Z,Y,X,W)),skolemize(X3,sK55_skl(X1,Z,Y,X,W))],[f431])).
% 0.16/5.41  fof(f433,plain,(
% 0.16/5.41    ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 0.16/5.41    inference(cnf_transformation,[status(thm)],[f432])).
% 0.16/5.41  fof(f436,plain,(
% 0.16/5.41    ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 0.16/5.41    inference(cnf_transformation,[status(thm)],[f432])).
% 0.16/5.41  fof(f449,definition,(
% 0.16/5.41    sQ0_spl <=> (sP0_prd(sK51_skl,sK50_skl,sK49_skl))),
% 0.16/5.41    introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.16/5.41  fof(f450,plain,(
% 0.16/5.41    sP0_prd(sK51_skl,sK50_skl,sK49_skl)|~sQ0_spl),
% 0.16/5.41    inference(component_clause,[status(thm)],[f449])).
% 0.16/5.41  fof(f452,definition,(
% 0.16/5.41    sQ1_spl <=> (nil=sK50_skl)),
% 0.16/5.41    introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.16/5.41  fof(f453,plain,(
% 0.16/5.41    nil=sK50_skl|~sQ1_spl),
% 0.16/5.41    inference(component_clause,[status(thm)],[f452])).
% 0.16/5.41  fof(f455,plain,(
% 0.16/5.41    sQ0_spl|sQ1_spl),
% 0.16/5.41    inference(split_clause,[status(thm)],[f426,f449,f452])).
% 0.16/5.41  fof(f456,definition,(
% 0.16/5.41    sQ2_spl <=> (nil=sK49_skl)),
% 0.16/5.41    introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.16/5.41  fof(f457,plain,(
% 0.16/5.41    nil=sK49_skl|~sQ2_spl),
% 0.16/5.41    inference(component_clause,[status(thm)],[f456])).
% 0.16/5.41  fof(f459,plain,(
% 0.16/5.41    sQ0_spl|sQ2_spl),
% 0.16/5.41    inference(split_clause,[status(thm)],[f427,f449,f456])).
% 0.16/5.41  fof(f495,plain,(
% 0.16/5.41    ~duplicatefreeP(sK49_skl)),
% 0.16/5.41    inference(forward_demodulation,[status(thm)],[f424,f425])).
% 0.16/5.41  fof(f496,plain,(
% 0.16/5.41    ssItem(sK51_skl)|~sQ0_spl),
% 0.16/5.41    inference(resolution,[status(thm)],[f450,f433])).
% 0.16/5.41  fof(f503,plain,(
% 0.16/5.41    cons(sK51_skl,nil)=sK49_skl|~sQ0_spl),
% 0.16/5.41    inference(resolution,[status(thm)],[f436,f450])).
% 0.16/5.41  fof(f538,plain,(
% 0.16/5.41    duplicatefreeP(sK50_skl)|~sQ1_spl),
% 0.16/5.41    inference(backward_demodulation,[status(thm)],[f453,f359])).
% 0.16/5.41  fof(f540,plain,(
% 0.16/5.41    ~duplicatefreeP(sK50_skl)|~sQ1_spl|~sQ2_spl),
% 0.16/5.41    inference(backward_demodulation,[status(thm)],[f543,f495])).
% 0.16/5.41  fof(f543,plain,(
% 0.16/5.41    sK50_skl=sK49_skl|~sQ1_spl|~sQ2_spl),
% 0.16/5.41    inference(forward_demodulation,[status(thm)],[f453,f457])).
% 0.16/5.41  fof(f545,plain,(
% 0.16/5.41    $false|~sQ1_spl|~sQ2_spl),
% 0.16/5.41    inference(forward_subsumption_resolution,[status(thm)],[f540,f538])).
% 0.16/5.41  fof(f546,plain,(
% 0.16/5.41    ~sQ1_spl|~sQ2_spl),
% 0.16/5.41    inference(contradiction_clause,[status(thm)],[f545])).
% 0.16/5.41  fof(f726,plain,(
% 0.16/5.41    duplicatefreeP(cons(sK51_skl,nil))|~sQ0_spl),
% 0.16/5.41    inference(resolution,[status(thm)],[f358,f496])).
% 0.16/5.41  fof(f729,plain,(
% 0.16/5.41    duplicatefreeP(sK49_skl)|~sQ0_spl),
% 0.16/5.41    inference(forward_demodulation,[status(thm)],[f503,f726])).
% 0.16/5.41  fof(f730,plain,(
% 0.16/5.41    $false|~sQ0_spl),
% 0.16/5.41    inference(forward_subsumption_resolution,[status(thm)],[f729,f495])).
% 0.16/5.41  fof(f731,plain,(
% 0.16/5.41    ~sQ0_spl),
% 0.16/5.41    inference(contradiction_clause,[status(thm)],[f730])).
% 0.16/5.42  fof(f732,plain,(
% 0.16/5.42    $false),
% 0.16/5.42    inference(sat_refutation,[status(thm)],[f455,f459,f546,f731])).
% 0.16/5.42  % SZS output end CNFRefutation for theBenchmark.p
% 0.16/5.44  % Elapsed time: 0.048145 seconds
% 0.16/5.44  % CPU time: 0.172048 seconds
% 0.16/5.44  % Total memory used: 90.783 MB
% 0.16/5.44  % Net memory used: 90.609 MB
%------------------------------------------------------------------------------