%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC001+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:41:18 PM UTC 2026
% Result : Theorem 0.23s 0.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC001+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % Computer : n004.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 07:47:51 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.53 % Drodi V4.1.1
% 0.23/0.55 % Refutation found
% 0.23/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.55 % SZS output start CNFRefutation for theBenchmark
% 0.23/0.55 fof(f1,axiom,(
% 0.23/0.55 (! [U] :( ssItem(U)=> (! [V] :( ssItem(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.23/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.55 fof(f96,conjecture,(
% 0.23/0.55 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ duplicatefreeP(W)| (? [Y] :( ssItem(Y)& ( ( ~ memberP(X,Y)& memberP(W,Y) )| ( ~ memberP(W,Y)& memberP(X,Y) ) ) ))| ( (! [Z] :( ssItem(Z)=> ( ( ~ memberP(V,Z)& ~ memberP(U,Z) )| ( memberP(V,Z)& memberP(U,Z) ) ) ))& duplicatefreeP(U) ) ) ) )) )) )) )),
% 0.23/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.55 fof(f97,negated_conjecture,(
% 0.23/0.55 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ duplicatefreeP(W)| (? [Y] :( ssItem(Y)& ( ( ~ memberP(X,Y)& memberP(W,Y) )| ( ~ memberP(W,Y)& memberP(X,Y) ) ) ))| ( (! [Z] :( ssItem(Z)=> ( ( ~ memberP(V,Z)& ~ memberP(U,Z) )| ( memberP(V,Z)& memberP(U,Z) ) ) ))& duplicatefreeP(U) ) ) ) )) )) )) ))),
% 0.23/0.55 inference(negated_conjecture,[status(cth)],[f96])).
% 0.23/0.55 fof(f98,plain,(
% 0.23/0.55 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(neq(U,V)<=>~U=V))))),
% 0.23/0.55 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.23/0.55 fof(f99,plain,(
% 0.23/0.55 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.23/0.55 inference(NNF_transformation,[status(thm)],[f98])).
% 0.23/0.55 fof(f100,plain,(
% 0.23/0.55 ![X0,X1]: (~ssItem(X0)|~ssItem(X1)|~neq(X0,X1)|~X0=X1)),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f99])).
% 0.23/0.55 fof(f101,plain,(
% 0.23/0.55 ![X0,X1]: (~ssItem(X0)|~ssItem(X1)|neq(X0,X1)|X0=X1)),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f99])).
% 0.23/0.55 fof(f415,plain,(
% 0.23/0.55 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&duplicatefreeP(W))&(![Y]: (~ssItem(Y)|((memberP(X,Y)|~memberP(W,Y))&(memberP(W,Y)|~memberP(X,Y))))))&((?[Z]: (ssItem(Z)&((memberP(V,Z)|memberP(U,Z))&(~memberP(V,Z)|~memberP(U,Z)))))|~duplicatefreeP(U)))))))))))),
% 0.23/0.55 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.23/0.55 fof(f416,plain,(
% 0.23/0.55 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&duplicatefreeP(sK49_skl))&(![Y]: (~ssItem(Y)|((memberP(sK50_skl,Y)|~memberP(sK49_skl,Y))&(memberP(sK49_skl,Y)|~memberP(sK50_skl,Y))))))&((ssItem(sK51_skl)&((memberP(sK48_skl,sK51_skl)|memberP(sK47_skl,sK51_skl))&(~memberP(sK48_skl,sK51_skl)|~memberP(sK47_skl,sK51_skl))))|~duplicatefreeP(sK47_skl)))))))),
% 0.23/0.55 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(Z,sK51_skl)],[f415])).
% 0.23/0.55 fof(f419,plain,(
% 0.23/0.55 ssList(sK49_skl)),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f420,plain,(
% 0.23/0.55 ssList(sK50_skl)),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f421,plain,(
% 0.23/0.55 sK48_skl=sK50_skl),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f422,plain,(
% 0.23/0.55 sK47_skl=sK49_skl),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f423,plain,(
% 0.23/0.55 duplicatefreeP(sK49_skl)),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f424,plain,(
% 0.23/0.55 ![X0]: (~ssItem(X0)|memberP(sK50_skl,X0)|~memberP(sK49_skl,X0))),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f425,plain,(
% 0.23/0.55 ![X0]: (~ssItem(X0)|memberP(sK49_skl,X0)|~memberP(sK50_skl,X0))),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f426,plain,(
% 0.23/0.55 ssItem(sK51_skl)|~duplicatefreeP(sK47_skl)),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f427,plain,(
% 0.23/0.55 memberP(sK48_skl,sK51_skl)|memberP(sK47_skl,sK51_skl)|~duplicatefreeP(sK47_skl)),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f428,plain,(
% 0.23/0.55 ~memberP(sK48_skl,sK51_skl)|~memberP(sK47_skl,sK51_skl)|~duplicatefreeP(sK47_skl)),
% 0.23/0.55 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/0.55 fof(f429,definition,(
% 0.23/0.55 sQ0_spl <=> (ssItem(sK51_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f430,plain,(
% 0.23/0.55 ssItem(sK51_skl)|~sQ0_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f429])).
% 0.23/0.55 fof(f432,definition,(
% 0.23/0.55 sQ1_spl <=> (duplicatefreeP(sK47_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f434,plain,(
% 0.23/0.55 ~duplicatefreeP(sK47_skl)|sQ1_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f432])).
% 0.23/0.55 fof(f435,plain,(
% 0.23/0.55 sQ0_spl|~sQ1_spl),
% 0.23/0.55 inference(split_clause,[status(thm)],[f426,f429,f432])).
% 0.23/0.55 fof(f436,definition,(
% 0.23/0.55 sQ2_spl <=> (memberP(sK48_skl,sK51_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f437,plain,(
% 0.23/0.55 memberP(sK48_skl,sK51_skl)|~sQ2_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f436])).
% 0.23/0.55 fof(f438,plain,(
% 0.23/0.55 ~memberP(sK48_skl,sK51_skl)|sQ2_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f436])).
% 0.23/0.55 fof(f439,definition,(
% 0.23/0.55 sQ3_spl <=> (memberP(sK47_skl,sK51_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f440,plain,(
% 0.23/0.55 memberP(sK47_skl,sK51_skl)|~sQ3_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f439])).
% 0.23/0.55 fof(f441,plain,(
% 0.23/0.55 ~memberP(sK47_skl,sK51_skl)|sQ3_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f439])).
% 0.23/0.55 fof(f442,plain,(
% 0.23/0.55 sQ2_spl|sQ3_spl|~sQ1_spl),
% 0.23/0.55 inference(split_clause,[status(thm)],[f427,f436,f439,f432])).
% 0.23/0.55 fof(f443,plain,(
% 0.23/0.55 ~sQ2_spl|~sQ3_spl|~sQ1_spl),
% 0.23/0.55 inference(split_clause,[status(thm)],[f428,f436,f439,f432])).
% 0.23/0.55 fof(f444,plain,(
% 0.23/0.55 ![X1]: (~ssItem(X1)|~ssItem(X1)|~neq(X1,X1))),
% 0.23/0.55 inference(destructive_equality_resolution,[status(thm)],[f100])).
% 0.23/0.55 fof(f445,plain,(
% 0.23/0.55 ![X0]: (~ssItem(X0)|~neq(X0,X0))),
% 0.23/0.55 inference(duplicate_literals_removal,[status(thm)],[f444])).
% 0.23/0.55 fof(f476,plain,(
% 0.23/0.55 ~duplicatefreeP(sK49_skl)|sQ1_spl),
% 0.23/0.55 inference(forward_demodulation,[status(thm)],[f422,f434])).
% 0.23/0.55 fof(f477,plain,(
% 0.23/0.55 $false|sQ1_spl),
% 0.23/0.55 inference(forward_subsumption_resolution,[status(thm)],[f476,f423])).
% 0.23/0.55 fof(f478,plain,(
% 0.23/0.55 sQ1_spl),
% 0.23/0.55 inference(contradiction_clause,[status(thm)],[f477])).
% 0.23/0.55 fof(f480,plain,(
% 0.23/0.55 memberP(sK50_skl,sK51_skl)|~sQ2_spl),
% 0.23/0.55 inference(forward_demodulation,[status(thm)],[f421,f437])).
% 0.23/0.55 fof(f481,plain,(
% 0.23/0.55 ~memberP(sK49_skl,sK51_skl)|sQ3_spl),
% 0.23/0.55 inference(forward_demodulation,[status(thm)],[f422,f441])).
% 0.23/0.55 fof(f493,plain,(
% 0.23/0.55 ![X0]: (~ssItem(X0)|neq(sK51_skl,X0)|sK51_skl=X0|~sQ0_spl)),
% 0.23/0.55 inference(resolution,[status(thm)],[f101,f430])).
% 0.23/0.55 fof(f495,definition,(
% 0.23/0.55 sQ4_spl <=> (ssList(sK50_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f497,plain,(
% 0.23/0.55 ~ssList(sK50_skl)|sQ4_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f495])).
% 0.23/0.55 fof(f502,plain,(
% 0.23/0.55 $false|sQ4_spl),
% 0.23/0.55 inference(forward_subsumption_resolution,[status(thm)],[f497,f420])).
% 0.23/0.55 fof(f503,plain,(
% 0.23/0.55 sQ4_spl),
% 0.23/0.55 inference(contradiction_clause,[status(thm)],[f502])).
% 0.23/0.55 fof(f509,plain,(
% 0.23/0.55 ~memberP(sK50_skl,sK51_skl)|sQ2_spl),
% 0.23/0.55 inference(forward_demodulation,[status(thm)],[f421,f438])).
% 0.23/0.55 fof(f510,plain,(
% 0.23/0.55 memberP(sK49_skl,sK51_skl)|~sQ3_spl),
% 0.23/0.55 inference(forward_demodulation,[status(thm)],[f422,f440])).
% 0.23/0.55 fof(f513,definition,(
% 0.23/0.55 sQ7_spl <=> (ssList(sK49_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f515,plain,(
% 0.23/0.55 ~ssList(sK49_skl)|sQ7_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f513])).
% 0.23/0.55 fof(f524,plain,(
% 0.23/0.55 $false|sQ7_spl),
% 0.23/0.55 inference(forward_subsumption_resolution,[status(thm)],[f515,f419])).
% 0.23/0.55 fof(f525,plain,(
% 0.23/0.55 sQ7_spl),
% 0.23/0.55 inference(contradiction_clause,[status(thm)],[f524])).
% 0.23/0.55 fof(f526,plain,(
% 0.23/0.55 ~ssItem(sK51_skl)|memberP(sK50_skl,sK51_skl)|~sQ3_spl),
% 0.23/0.55 inference(resolution,[status(thm)],[f424,f510])).
% 0.23/0.55 fof(f527,definition,(
% 0.23/0.55 sQ10_spl <=> (memberP(sK50_skl,sK51_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f528,plain,(
% 0.23/0.55 memberP(sK50_skl,sK51_skl)|~sQ10_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f527])).
% 0.23/0.55 fof(f530,plain,(
% 0.23/0.55 ~sQ0_spl|sQ10_spl|~sQ3_spl),
% 0.23/0.55 inference(split_clause,[status(thm)],[f526,f429,f527,f439])).
% 0.23/0.55 fof(f531,plain,(
% 0.23/0.55 $false|sQ2_spl|~sQ10_spl),
% 0.23/0.55 inference(forward_subsumption_resolution,[status(thm)],[f528,f509])).
% 0.23/0.55 fof(f532,plain,(
% 0.23/0.55 sQ2_spl|~sQ10_spl),
% 0.23/0.55 inference(contradiction_clause,[status(thm)],[f531])).
% 0.23/0.55 fof(f539,plain,(
% 0.23/0.55 neq(sK51_skl,sK51_skl)|sK51_skl=sK51_skl|~sQ0_spl),
% 0.23/0.55 inference(resolution,[status(thm)],[f493,f430])).
% 0.23/0.55 fof(f554,definition,(
% 0.23/0.55 sQ15_spl <=> (neq(sK51_skl,sK51_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f555,plain,(
% 0.23/0.55 neq(sK51_skl,sK51_skl)|~sQ15_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f554])).
% 0.23/0.55 fof(f557,definition,(
% 0.23/0.55 sQ16_spl <=> (sK51_skl=sK51_skl)),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f560,plain,(
% 0.23/0.55 sQ15_spl|sQ16_spl|~sQ0_spl),
% 0.23/0.55 inference(split_clause,[status(thm)],[f539,f554,f557,f429])).
% 0.23/0.55 fof(f562,plain,(
% 0.23/0.55 ~ssItem(sK51_skl)|~sQ15_spl),
% 0.23/0.55 inference(resolution,[status(thm)],[f555,f445])).
% 0.23/0.55 fof(f563,plain,(
% 0.23/0.55 $false|~sQ0_spl|~sQ15_spl),
% 0.23/0.55 inference(forward_subsumption_resolution,[status(thm)],[f562,f430])).
% 0.23/0.55 fof(f564,plain,(
% 0.23/0.55 ~sQ0_spl|~sQ15_spl),
% 0.23/0.55 inference(contradiction_clause,[status(thm)],[f563])).
% 0.23/0.55 fof(f658,plain,(
% 0.23/0.55 ~ssItem(sK51_skl)|memberP(sK49_skl,sK51_skl)|~sQ2_spl),
% 0.23/0.55 inference(resolution,[status(thm)],[f425,f480])).
% 0.23/0.55 fof(f659,definition,(
% 0.23/0.55 sQ33_spl <=> (memberP(sK49_skl,sK51_skl))),
% 0.23/0.55 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.23/0.55 fof(f660,plain,(
% 0.23/0.55 memberP(sK49_skl,sK51_skl)|~sQ33_spl),
% 0.23/0.55 inference(component_clause,[status(thm)],[f659])).
% 0.23/0.55 fof(f662,plain,(
% 0.23/0.55 ~sQ0_spl|sQ33_spl|~sQ2_spl),
% 0.23/0.55 inference(split_clause,[status(thm)],[f658,f429,f659,f436])).
% 0.23/0.55 fof(f663,plain,(
% 0.23/0.55 $false|sQ3_spl|~sQ33_spl),
% 0.23/0.55 inference(forward_subsumption_resolution,[status(thm)],[f660,f481])).
% 0.23/0.55 fof(f664,plain,(
% 0.23/0.55 sQ3_spl|~sQ33_spl),
% 0.23/0.55 inference(contradiction_clause,[status(thm)],[f663])).
% 0.23/0.55 fof(f665,plain,(
% 0.23/0.55 $false),
% 0.23/0.55 inference(sat_refutation,[status(thm)],[f435,f442,f443,f478,f503,f525,f530,f532,f560,f564,f662,f664])).
% 0.23/0.55 % SZS output end CNFRefutation for theBenchmark.p
% 0.23/0.62 % Elapsed time: 0.119779 seconds
% 0.23/0.62 % CPU time: 0.137333 seconds
% 0.23/0.62 % Total memory used: 17.458 MB
% 0.23/0.62 % Net memory used: 17.439 MB
%------------------------------------------------------------------------------