%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC256+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 : n009.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 02:41:59 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC256+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
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:09:12 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.41 fof(f4,axiom,(
% 0.14/0.41 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f15,axiom,(
% 0.14/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f17,axiom,(
% 0.14/0.41 ssList(nil) ),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f96,conjecture,(
% 0.14/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| singletonP(U)| ( (! [Y] :( ssItem(Y)=> ( cons(Y,nil) != W| ~ memberP(X,Y) ) ))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f97,negated_conjecture,(
% 0.14/0.41 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| singletonP(U)| ( (! [Y] :( ssItem(Y)=> ( cons(Y,nil) != W| ~ memberP(X,Y) ) ))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 0.14/0.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.14/0.41 fof(f113,plain,(
% 0.14/0.41 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/0.41 fof(f114,plain,(
% 0.14/0.41 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.14/0.41 inference(NNF_transformation,[status(thm)],[f113])).
% 0.14/0.41 fof(f115,plain,(
% 0.14/0.41 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.14/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.14/0.41 fof(f118,plain,(
% 0.14/0.41 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f115])).
% 0.14/0.41 fof(f217,plain,(
% 0.14/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.14/0.41 fof(f218,plain,(
% 0.14/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.14/0.41 inference(NNF_transformation,[status(thm)],[f217])).
% 0.14/0.41 fof(f219,plain,(
% 0.14/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~neq(X0,X1)|~X0=X1)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f218])).
% 0.14/0.41 fof(f223,plain,(
% 0.14/0.41 ssList(nil)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/0.41 fof(f415,plain,(
% 0.14/0.41 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&neq(V,nil))&~singletonP(U))&((?[Y]: (ssItem(Y)&(cons(Y,nil)=W&memberP(X,Y))))|(nil=X&nil=W)))))))))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.14/0.41 fof(f416,definition,(
% 0.14/0.41 ![W,X,Y]: (sP0_prd(Y,X,W)<=>(ssItem(Y)&(cons(Y,nil)=W&memberP(X,Y))))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.14/0.41 fof(f417,plain,(
% 0.14/0.41 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&neq(V,nil))&~singletonP(U))&((?[Y]: sP0_prd(Y,X,W))|(nil=X&nil=W))))))))))),
% 0.14/0.41 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.14/0.41 fof(f418,plain,(
% 0.14/0.41 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&neq(sK48_skl,nil))&~singletonP(sK47_skl))&(sP0_prd(sK51_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))))))),
% 0.14/0.41 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])).
% 0.14/0.41 fof(f419,plain,(
% 0.14/0.41 ssList(sK47_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.14/0.41 fof(f420,plain,(
% 0.14/0.41 ssList(sK48_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.14/0.41 fof(f423,plain,(
% 0.14/0.41 sK48_skl=sK50_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.14/0.41 fof(f424,plain,(
% 0.14/0.41 sK47_skl=sK49_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.14/0.41 fof(f425,plain,(
% 0.14/0.41 neq(sK48_skl,nil)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.14/0.41 fof(f426,plain,(
% 0.14/0.41 ~singletonP(sK47_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.14/0.41 fof(f427,plain,(
% 0.14/0.41 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK50_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.14/0.41 fof(f429,plain,(
% 0.14/0.41 ![W,X,Y]: ((~sP0_prd(Y,X,W)|(ssItem(Y)&(cons(Y,nil)=W&memberP(X,Y))))&(sP0_prd(Y,X,W)|(~ssItem(Y)|(~cons(Y,nil)=W|~memberP(X,Y)))))),
% 0.14/0.41 inference(NNF_transformation,[status(thm)],[f416])).
% 0.14/0.41 fof(f430,plain,(
% 0.14/0.41 (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&(cons(Y,nil)=W&memberP(X,Y)))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|(~cons(Y,nil)=W|~memberP(X,Y)))))),
% 0.14/0.41 inference(miniscoping,[status(thm)],[f429])).
% 0.14/0.41 fof(f431,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f430])).
% 0.14/0.41 fof(f432,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f430])).
% 0.14/0.41 fof(f435,definition,(
% 0.14/0.41 sQ0_spl <=> (sP0_prd(sK51_skl,sK50_skl,sK49_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f436,plain,(
% 0.14/0.41 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|~sQ0_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f435])).
% 0.14/0.41 fof(f438,definition,(
% 0.14/0.41 sQ1_spl <=> (nil=sK50_skl)),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f439,plain,(
% 0.14/0.41 nil=sK50_skl|~sQ1_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f438])).
% 0.14/0.41 fof(f441,plain,(
% 0.14/0.41 sQ0_spl|sQ1_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f427,f435,f438])).
% 0.14/0.41 fof(f449,plain,(
% 0.14/0.41 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.14/0.41 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.14/0.41 fof(f461,plain,(
% 0.14/0.41 ![X1]: (~ssList(X1)|~ssList(X1)|~neq(X1,X1))),
% 0.14/0.41 inference(destructive_equality_resolution,[status(thm)],[f219])).
% 0.14/0.41 fof(f462,plain,(
% 0.14/0.41 ![X0]: (~ssList(X0)|~neq(X0,X0))),
% 0.14/0.41 inference(duplicate_literals_removal,[status(thm)],[f461])).
% 0.14/0.41 fof(f483,plain,(
% 0.14/0.41 sP0_prd(sK51_skl,sK48_skl,sK49_skl)|~sQ0_spl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f423,f436])).
% 0.14/0.41 fof(f484,plain,(
% 0.14/0.41 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|~sQ0_spl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f424,f483])).
% 0.14/0.41 fof(f485,plain,(
% 0.14/0.41 ssItem(sK51_skl)|~sQ0_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f484,f431])).
% 0.14/0.41 fof(f488,plain,(
% 0.14/0.41 cons(sK51_skl,nil)=sK47_skl|~sQ0_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f432,f484])).
% 0.14/0.41 fof(f493,definition,(
% 0.14/0.41 sQ4_spl <=> (ssItem(sK51_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f495,plain,(
% 0.14/0.41 ~ssItem(sK51_skl)|sQ4_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f493])).
% 0.14/0.41 fof(f496,definition,(
% 0.14/0.41 sQ5_spl <=> (ssList(nil))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f498,plain,(
% 0.14/0.41 ~ssList(nil)|sQ5_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f496])).
% 0.14/0.41 fof(f500,plain,(
% 0.14/0.41 $false|sQ5_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f498,f223])).
% 0.14/0.41 fof(f501,plain,(
% 0.14/0.41 sQ5_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f500])).
% 0.14/0.41 fof(f503,plain,(
% 0.14/0.41 ~ssList(sK47_skl)|singletonP(cons(sK51_skl,nil))|~ssItem(sK51_skl)|~sQ0_spl),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f488,f449])).
% 0.14/0.41 fof(f504,definition,(
% 0.14/0.41 sQ6_spl <=> (ssList(sK47_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f506,plain,(
% 0.14/0.41 ~ssList(sK47_skl)|sQ6_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f504])).
% 0.14/0.41 fof(f507,definition,(
% 0.14/0.41 sQ7_spl <=> (singletonP(cons(sK51_skl,nil)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f508,plain,(
% 0.14/0.41 singletonP(cons(sK51_skl,nil))|~sQ7_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f507])).
% 0.14/0.41 fof(f510,plain,(
% 0.14/0.41 ~sQ6_spl|sQ7_spl|~sQ4_spl|~sQ0_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f503,f504,f507,f493,f435])).
% 0.14/0.41 fof(f511,plain,(
% 0.14/0.41 sK48_skl=nil|~sQ1_spl),
% 0.14/0.41 inference(backward_demodulation,[status(thm)],[f439,f423])).
% 0.14/0.41 fof(f513,plain,(
% 0.14/0.41 neq(nil,nil)|~sQ1_spl),
% 0.14/0.41 inference(backward_demodulation,[status(thm)],[f511,f425])).
% 0.14/0.41 fof(f517,plain,(
% 0.14/0.41 ~ssList(nil)|~sQ1_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f513,f462])).
% 0.14/0.41 fof(f518,plain,(
% 0.14/0.41 ~sQ5_spl|~sQ1_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f517,f496,f438])).
% 0.14/0.41 fof(f519,plain,(
% 0.14/0.41 $false|sQ4_spl|~sQ0_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f485,f495])).
% 0.14/0.41 fof(f520,plain,(
% 0.14/0.41 sQ4_spl|~sQ0_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f519])).
% 0.14/0.41 fof(f522,plain,(
% 0.14/0.41 $false|sQ6_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f506,f419])).
% 0.14/0.41 fof(f523,plain,(
% 0.14/0.41 sQ6_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f522])).
% 0.14/0.41 fof(f563,definition,(
% 0.14/0.41 sQ15_spl <=> (ssList(sK48_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f565,plain,(
% 0.14/0.41 ~ssList(sK48_skl)|sQ15_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f563])).
% 0.14/0.41 fof(f570,plain,(
% 0.14/0.41 $false|sQ15_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f565,f420])).
% 0.14/0.41 fof(f571,plain,(
% 0.14/0.41 sQ15_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f570])).
% 0.14/0.41 fof(f584,plain,(
% 0.14/0.41 singletonP(sK47_skl)|~sQ0_spl|~sQ7_spl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f488,f508])).
% 0.14/0.41 fof(f585,plain,(
% 0.14/0.41 $false|~sQ0_spl|~sQ7_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f584,f426])).
% 0.14/0.41 fof(f586,plain,(
% 0.14/0.41 ~sQ0_spl|~sQ7_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f585])).
% 0.14/0.41 fof(f587,plain,(
% 0.14/0.41 $false),
% 0.14/0.41 inference(sat_refutation,[status(thm)],[f441,f501,f510,f518,f520,f523,f571,f586])).
% 0.14/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.44 % Elapsed time: 0.057015 seconds
% 0.14/0.44 % CPU time: 0.216188 seconds
% 0.14/0.44 % Total memory used: 111.756 MB
% 0.14/0.44 % Net memory used: 111.501 MB
%------------------------------------------------------------------------------