%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC218-1 : 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 : n019.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 02:41:54 PM UTC 2026
% Result : Unsatisfiable 6.12s 1.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC218-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 % Computer : n019.cluster.edu
% 0.19/0.48 % Model : x86_64 x86_64
% 0.19/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.48 % Memory : 8046.5625MB
% 0.19/0.48 % OS : Linux 6.8.0-71-generic
% 0.19/0.48 % CPULimit : 300
% 0.19/0.48 % WCLimit : 300
% 0.19/0.48 % DateTime : Mon Sep 21 08:05:50 UTC 2026
% 0.19/0.48 % CPUTime :
% 0.19/0.54 % Drodi V4.1.1
% 6.12/1.51 % Refutation found
% 6.12/1.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.12/1.51 % SZS output start CNFRefutation for theBenchmark
% 6.12/1.51 fof(f8,axiom,(
% 6.12/1.51 ssList(nil) ),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f85,axiom,(
% 6.12/1.51 (![U,V]: (( ~ ssList(U)| ~ ssList(V)| ssList(app(V,U)) ) ))),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f86,axiom,(
% 6.12/1.51 (![U,V]: (( ~ ssItem(U)| ~ ssList(V)| ssList(cons(U,V)) ) ))),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f99,axiom,(
% 6.12/1.51 (![U,V]: (( cons(U,V) != V| ~ ssItem(U)| ~ ssList(V) ) ))),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f100,axiom,(
% 6.12/1.51 (![U,V]: (( ~ ssList(U)| ~ ssList(V)| neq(V,U)| V = U ) ))),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f118,axiom,(
% 6.12/1.51 (![U,V]: (( app(U,V) != nil| ~ ssList(V)| ~ ssList(U)| nil = U ) ))),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f119,axiom,(
% 6.12/1.51 (![U,V]: (( app(U,V) != nil| ~ ssList(V)| ~ ssList(U)| nil = V ) ))),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f191,negated_conjecture,(
% 6.12/1.51 sk1 = sk3 ),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f192,negated_conjecture,(
% 6.12/1.51 ssList(sk5) ),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f193,negated_conjecture,(
% 6.12/1.51 ssList(sk6) ),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f195,negated_conjecture,(
% 6.12/1.51 ssItem(sk7) ),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f196,negated_conjecture,(
% 6.12/1.51 app(app(sk5,cons(sk7,nil)),sk6) = sk3 ),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f197,negated_conjecture,(
% 6.12/1.51 ~ neq(sk1,nil) ),
% 6.12/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.12/1.51 fof(f205,plain,(
% 6.12/1.51 ssList(nil)),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f8])).
% 6.12/1.51 fof(f283,plain,(
% 6.12/1.51 ![X0,X1]: (~ssList(X0)|~ssList(X1)|ssList(app(X1,X0)))),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f85])).
% 6.12/1.51 fof(f284,plain,(
% 6.12/1.51 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|ssList(cons(X0,X1)))),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f86])).
% 6.12/1.51 fof(f298,plain,(
% 6.12/1.51 ![V]: ((![U]: (~cons(U,V)=V|~ssItem(U)))|~ssList(V))),
% 6.12/1.51 inference(miniscoping,[status(thm)],[f99])).
% 6.12/1.51 fof(f299,plain,(
% 6.12/1.51 ![X0,X1]: (~cons(X0,X1)=X1|~ssItem(X0)|~ssList(X1))),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f298])).
% 6.12/1.51 fof(f300,plain,(
% 6.12/1.51 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X1,X0)|X1=X0)),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f100])).
% 6.12/1.51 fof(f324,plain,(
% 6.12/1.51 ![U]: (((![V]: (~app(U,V)=nil|~ssList(V)))|~ssList(U))|nil=U)),
% 6.12/1.51 inference(miniscoping,[status(thm)],[f118])).
% 6.12/1.51 fof(f325,plain,(
% 6.12/1.51 ![X0,X1]: (~app(X0,X1)=nil|~ssList(X1)|~ssList(X0)|nil=X0)),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f324])).
% 6.12/1.51 fof(f326,plain,(
% 6.12/1.51 ![V]: ((![U]: ((~app(U,V)=nil|~ssList(V))|~ssList(U)))|nil=V)),
% 6.12/1.51 inference(miniscoping,[status(thm)],[f119])).
% 6.12/1.51 fof(f327,plain,(
% 6.12/1.51 ![X0,X1]: (~app(X0,X1)=nil|~ssList(X1)|~ssList(X0)|nil=X1)),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f326])).
% 6.12/1.51 fof(f433,plain,(
% 6.12/1.51 sk1=sk3),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f191])).
% 6.12/1.51 fof(f434,plain,(
% 6.12/1.51 ssList(sk5)),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f192])).
% 6.12/1.51 fof(f435,plain,(
% 6.12/1.51 ssList(sk6)),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f193])).
% 6.12/1.51 fof(f437,plain,(
% 6.12/1.51 ssItem(sk7)),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f195])).
% 6.12/1.51 fof(f438,plain,(
% 6.12/1.51 app(app(sk5,cons(sk7,nil)),sk6)=sk3),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f196])).
% 6.12/1.51 fof(f439,plain,(
% 6.12/1.51 ~neq(sk1,nil)),
% 6.12/1.51 inference(cnf_transformation,[status(thm)],[f197])).
% 6.12/1.51 fof(f506,definition,(
% 6.12/1.51 sQ2_spl <=> (ssList(nil))),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f508,plain,(
% 6.12/1.51 ~ssList(nil)|sQ2_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f506])).
% 6.12/1.51 fof(f509,definition,(
% 6.12/1.51 sQ3_spl <=> (ssList(sk5))),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f511,plain,(
% 6.12/1.51 ~ssList(sk5)|sQ3_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f509])).
% 6.12/1.51 fof(f513,definition,(
% 6.12/1.51 sQ4_spl <=> (ssList(sk6))),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f515,plain,(
% 6.12/1.51 ~ssList(sk6)|sQ4_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f513])).
% 6.12/1.51 fof(f517,plain,(
% 6.12/1.51 ![X0]: (~ssList(X0)|ssList(cons(sk7,X0)))),
% 6.12/1.51 inference(resolution,[status(thm)],[f284,f437])).
% 6.12/1.51 fof(f551,definition,(
% 6.12/1.51 sQ7_spl <=> (ssList(sk1))),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f558,plain,(
% 6.12/1.51 ![X0]: (~cons(sk7,X0)=X0|~ssList(X0))),
% 6.12/1.51 inference(resolution,[status(thm)],[f299,f437])).
% 6.12/1.51 fof(f575,plain,(
% 6.12/1.51 app(app(sk5,cons(sk7,nil)),sk6)=sk1),
% 6.12/1.51 inference(forward_demodulation,[status(thm)],[f433,f438])).
% 6.12/1.51 fof(f576,plain,(
% 6.12/1.51 ~ssList(sk6)|~ssList(app(sk5,cons(sk7,nil)))|ssList(sk1)),
% 6.12/1.51 inference(paramodulation,[status(thm)],[f575,f283])).
% 6.12/1.51 fof(f577,definition,(
% 6.12/1.51 sQ8_spl <=> (ssList(app(sk5,cons(sk7,nil))))),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f578,plain,(
% 6.12/1.51 ssList(app(sk5,cons(sk7,nil)))|~sQ8_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f577])).
% 6.12/1.51 fof(f579,plain,(
% 6.12/1.51 ~ssList(app(sk5,cons(sk7,nil)))|sQ8_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f577])).
% 6.12/1.51 fof(f580,plain,(
% 6.12/1.51 ~sQ4_spl|~sQ8_spl|sQ7_spl),
% 6.12/1.51 inference(split_clause,[status(thm)],[f576,f513,f577,f551])).
% 6.12/1.51 fof(f583,plain,(
% 6.12/1.51 $false|sQ4_spl),
% 6.12/1.51 inference(forward_subsumption_resolution,[status(thm)],[f515,f435])).
% 6.12/1.51 fof(f584,plain,(
% 6.12/1.51 sQ4_spl),
% 6.12/1.51 inference(contradiction_clause,[status(thm)],[f583])).
% 6.12/1.51 fof(f585,plain,(
% 6.12/1.51 $false|sQ3_spl),
% 6.12/1.51 inference(forward_subsumption_resolution,[status(thm)],[f511,f434])).
% 6.12/1.51 fof(f586,plain,(
% 6.12/1.51 sQ3_spl),
% 6.12/1.51 inference(contradiction_clause,[status(thm)],[f585])).
% 6.12/1.51 fof(f599,plain,(
% 6.12/1.51 ~ssList(nil)|~ssList(sk1)|sk1=nil),
% 6.12/1.51 inference(resolution,[status(thm)],[f300,f439])).
% 6.12/1.51 fof(f602,definition,(
% 6.12/1.51 sQ9_spl <=> (sk1=nil)),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f603,plain,(
% 6.12/1.51 sk1=nil|~sQ9_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f602])).
% 6.12/1.51 fof(f605,plain,(
% 6.12/1.51 ~sQ2_spl|~sQ7_spl|sQ9_spl),
% 6.12/1.51 inference(split_clause,[status(thm)],[f599,f506,f551,f602])).
% 6.12/1.51 fof(f668,plain,(
% 6.12/1.51 $false|sQ2_spl),
% 6.12/1.51 inference(forward_subsumption_resolution,[status(thm)],[f508,f205])).
% 6.12/1.51 fof(f669,plain,(
% 6.12/1.51 sQ2_spl),
% 6.12/1.51 inference(contradiction_clause,[status(thm)],[f668])).
% 6.12/1.51 fof(f681,plain,(
% 6.12/1.51 ![X0]: (~app(X0,sk6)=nil|~ssList(X0)|nil=X0)),
% 6.12/1.51 inference(resolution,[status(thm)],[f325,f435])).
% 6.12/1.51 fof(f766,plain,(
% 6.12/1.51 ~ssList(cons(sk7,nil))|~ssList(sk5)|sQ8_spl),
% 6.12/1.51 inference(resolution,[status(thm)],[f579,f283])).
% 6.12/1.51 fof(f767,definition,(
% 6.12/1.51 sQ22_spl <=> (ssList(cons(sk7,nil)))),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f768,plain,(
% 6.12/1.51 ssList(cons(sk7,nil))|~sQ22_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f767])).
% 6.12/1.51 fof(f769,plain,(
% 6.12/1.51 ~ssList(cons(sk7,nil))|sQ22_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f767])).
% 6.12/1.51 fof(f770,plain,(
% 6.12/1.51 ~sQ22_spl|~sQ3_spl|sQ8_spl),
% 6.12/1.51 inference(split_clause,[status(thm)],[f766,f767,f509,f577])).
% 6.12/1.51 fof(f771,plain,(
% 6.12/1.51 ~ssList(nil)|sQ22_spl),
% 6.12/1.51 inference(resolution,[status(thm)],[f769,f517])).
% 6.12/1.51 fof(f772,plain,(
% 6.12/1.51 ~sQ2_spl|sQ22_spl),
% 6.12/1.51 inference(split_clause,[status(thm)],[f771,f506,f767])).
% 6.12/1.51 fof(f773,plain,(
% 6.12/1.51 ![X0]: (~app(X0,cons(sk7,nil))=nil|~ssList(X0)|nil=cons(sk7,nil)|~sQ22_spl)),
% 6.12/1.51 inference(resolution,[status(thm)],[f768,f327])).
% 6.12/1.51 fof(f782,definition,(
% 6.12/1.51 ![X0]: (sQ23_spl <=> (~app(X0,cons(sk7,nil))=nil|~ssList(X0)))),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f783,plain,(
% 6.12/1.51 ![X0]: (~app(X0,cons(sk7,nil))=nil|~ssList(X0)|~sQ23_spl)),
% 6.12/1.51 inference(component_clause,[status(thm)],[f782])).
% 6.12/1.51 fof(f785,definition,(
% 6.12/1.51 sQ24_spl <=> (nil=cons(sk7,nil))),
% 6.12/1.51 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 6.12/1.51 fof(f786,plain,(
% 6.12/1.51 nil=cons(sk7,nil)|~sQ24_spl),
% 6.12/1.51 inference(component_clause,[status(thm)],[f785])).
% 6.12/1.51 fof(f788,plain,(
% 6.12/1.51 sQ23_spl|sQ24_spl|~sQ22_spl),
% 6.12/1.51 inference(split_clause,[status(thm)],[f773,f782,f785,f767])).
% 6.12/1.51 fof(f904,definition,(
% 6.12/1.52 sQ29_spl <=> (nil=app(sk5,cons(sk7,nil)))),
% 6.12/1.52 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 6.12/1.52 fof(f905,plain,(
% 6.12/1.52 nil=app(sk5,cons(sk7,nil))|~sQ29_spl),
% 6.12/1.52 inference(component_clause,[status(thm)],[f904])).
% 6.12/1.52 fof(f957,plain,(
% 6.12/1.52 ~app(sk5,cons(sk7,nil))=nil|~sQ23_spl),
% 6.12/1.52 inference(resolution,[status(thm)],[f783,f434])).
% 6.12/1.52 fof(f1880,plain,(
% 6.12/1.52 app(app(sk5,cons(sk7,nil)),sk6)=nil|~sQ9_spl),
% 6.12/1.52 inference(backward_demodulation,[status(thm)],[f603,f575])).
% 6.12/1.52 fof(f2087,plain,(
% 6.12/1.52 ~app(app(sk5,cons(sk7,nil)),sk6)=nil|nil=app(sk5,cons(sk7,nil))|~sQ8_spl),
% 6.12/1.52 inference(resolution,[status(thm)],[f681,f578])).
% 6.12/1.52 fof(f2103,definition,(
% 6.12/1.52 sQ45_spl <=> (app(app(sk5,cons(sk7,nil)),sk6)=nil)),
% 6.12/1.52 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 6.12/1.52 fof(f2105,plain,(
% 6.12/1.52 ~app(app(sk5,cons(sk7,nil)),sk6)=nil|sQ45_spl),
% 6.12/1.52 inference(component_clause,[status(thm)],[f2103])).
% 6.12/1.52 fof(f2106,plain,(
% 6.12/1.52 ~sQ45_spl|sQ29_spl|~sQ8_spl),
% 6.12/1.52 inference(split_clause,[status(thm)],[f2087,f2103,f904,f577])).
% 6.12/1.52 fof(f2782,plain,(
% 6.12/1.52 ~cons(sk7,nil)=nil),
% 6.12/1.52 inference(resolution,[status(thm)],[f558,f205])).
% 6.12/1.52 fof(f2783,plain,(
% 6.12/1.52 ~nil=nil|~sQ24_spl),
% 6.12/1.52 inference(forward_demodulation,[status(thm)],[f786,f2782])).
% 6.12/1.52 fof(f2784,plain,(
% 6.12/1.52 $false|~sQ24_spl),
% 6.12/1.52 inference(trivial_equality_resolution,[status(thm)],[f2783])).
% 6.12/1.52 fof(f2785,plain,(
% 6.12/1.52 ~sQ24_spl),
% 6.12/1.52 inference(contradiction_clause,[status(thm)],[f2784])).
% 6.12/1.52 fof(f4239,plain,(
% 6.12/1.52 $false|~sQ23_spl|~sQ29_spl),
% 6.12/1.52 inference(forward_subsumption_resolution,[status(thm)],[f905,f957])).
% 6.12/1.52 fof(f4240,plain,(
% 6.12/1.52 ~sQ23_spl|~sQ29_spl),
% 6.12/1.52 inference(contradiction_clause,[status(thm)],[f4239])).
% 6.12/1.52 fof(f4241,plain,(
% 6.12/1.52 ~nil=nil|~sQ9_spl|sQ45_spl),
% 6.12/1.52 inference(forward_demodulation,[status(thm)],[f1880,f2105])).
% 6.12/1.52 fof(f4242,plain,(
% 6.12/1.52 $false|~sQ9_spl|sQ45_spl),
% 6.12/1.52 inference(trivial_equality_resolution,[status(thm)],[f4241])).
% 6.12/1.52 fof(f4243,plain,(
% 6.12/1.52 ~sQ9_spl|sQ45_spl),
% 6.12/1.52 inference(contradiction_clause,[status(thm)],[f4242])).
% 6.12/1.52 fof(f4244,plain,(
% 6.12/1.52 $false),
% 6.12/1.52 inference(sat_refutation,[status(thm)],[f580,f584,f586,f605,f669,f770,f772,f788,f2106,f2785,f4240,f4243])).
% 6.12/1.52 % SZS output end CNFRefutation for theBenchmark.p
% 6.12/1.56 % Elapsed time: 1.055457 seconds
% 6.12/1.56 % CPU time: 7.675663 seconds
% 6.12/1.56 % Total memory used: 196.717 MB
% 6.12/1.56 % Net memory used: 191.486 MB
%------------------------------------------------------------------------------