%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC024-1 : 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 : n002.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 02:41:22 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC024-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 07:52:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.43 fof(f8,axiom,(
% 0.14/0.43 ssList(nil) ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f61,axiom,(
% 0.14/0.43 (![U]: (( ~ ssList(U)| frontsegP(U,U) ) ))),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f85,axiom,(
% 0.14/0.43 (![U,V]: (( ~ ssList(U)| ~ ssList(V)| ssList(app(V,U)) ) ))),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f100,axiom,(
% 0.14/0.43 (![U,V]: (( ~ ssList(U)| ~ ssList(V)| neq(V,U)| V = U ) ))),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f115,axiom,(
% 0.14/0.43 (![U,V]: (( U != V| ~ neq(U,V)| ~ ssList(V)| ~ ssList(U) ) ))),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f144,axiom,(
% 0.14/0.43 (![U,V,W]: (( app(U,V) != W| ~ ssList(V)| ~ ssList(U)| ~ ssList(W)| frontsegP(W,U) ) ))),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f186,negated_conjecture,(
% 0.14/0.43 ssList(sk1) ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f187,negated_conjecture,(
% 0.14/0.43 ssList(sk2) ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f190,negated_conjecture,(
% 0.14/0.43 sk2 = sk4 ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f191,negated_conjecture,(
% 0.14/0.43 sk1 = sk3 ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f192,negated_conjecture,(
% 0.14/0.43 neq(sk2,nil) ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f193,negated_conjecture,(
% 0.14/0.43 (![A]: (( ~ ssList(A)| ~ neq(A,nil)| ~ frontsegP(sk2,A)| ~ frontsegP(sk1,A) ) ))),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f194,negated_conjecture,(
% 0.14/0.43 ssList(sk5) ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f195,negated_conjecture,(
% 0.14/0.43 app(sk3,sk5) = sk4 ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f198,negated_conjecture,(
% 0.14/0.43 ( nil = sk4| nil != sk3 ) ),
% 0.14/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.43 fof(f206,plain,(
% 0.14/0.43 ssList(nil)),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.43 fof(f259,plain,(
% 0.14/0.43 ![X0]: (~ssList(X0)|frontsegP(X0,X0))),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f61])).
% 0.14/0.43 fof(f284,plain,(
% 0.14/0.43 ![X0,X1]: (~ssList(X0)|~ssList(X1)|ssList(app(X1,X0)))),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f85])).
% 0.14/0.43 fof(f301,plain,(
% 0.14/0.43 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X1,X0)|X1=X0)),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f100])).
% 0.14/0.43 fof(f319,plain,(
% 0.14/0.43 ![U]: ((![V]: ((~U=V|~neq(U,V))|~ssList(V)))|~ssList(U))),
% 0.14/0.43 inference(miniscoping,[status(thm)],[f115])).
% 0.14/0.43 fof(f320,plain,(
% 0.14/0.43 ![X0,X1]: (~X0=X1|~neq(X0,X1)|~ssList(X1)|~ssList(X0))),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f319])).
% 0.14/0.43 fof(f358,plain,(
% 0.14/0.43 ![U,W]: ((((![V]: (~app(U,V)=W|~ssList(V)))|~ssList(U))|~ssList(W))|frontsegP(W,U))),
% 0.14/0.43 inference(miniscoping,[status(thm)],[f144])).
% 0.14/0.43 fof(f359,plain,(
% 0.14/0.43 ![X0,X1,X2]: (~app(X0,X1)=X2|~ssList(X1)|~ssList(X0)|~ssList(X2)|frontsegP(X2,X0))),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f358])).
% 0.14/0.43 fof(f429,plain,(
% 0.14/0.43 ssList(sk1)),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f186])).
% 0.14/0.43 fof(f430,plain,(
% 0.14/0.43 ssList(sk2)),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f187])).
% 0.14/0.43 fof(f433,plain,(
% 0.14/0.43 sk2=sk4),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f190])).
% 0.14/0.43 fof(f434,plain,(
% 0.14/0.43 sk1=sk3),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f191])).
% 0.14/0.43 fof(f435,plain,(
% 0.14/0.43 neq(sk2,nil)),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f192])).
% 0.14/0.43 fof(f436,plain,(
% 0.14/0.43 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sk2,X0)|~frontsegP(sk1,X0))),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f193])).
% 0.14/0.43 fof(f437,plain,(
% 0.14/0.43 ssList(sk5)),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f194])).
% 0.14/0.43 fof(f438,plain,(
% 0.14/0.43 app(sk3,sk5)=sk4),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f195])).
% 0.14/0.43 fof(f442,plain,(
% 0.14/0.43 nil=sk4|~nil=sk3),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f198])).
% 0.14/0.43 fof(f450,definition,(
% 0.14/0.43 sQ2_spl <=> (nil=sk4)),
% 0.14/0.43 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.43 fof(f451,plain,(
% 0.14/0.43 nil=sk4|~sQ2_spl),
% 0.14/0.43 inference(component_clause,[status(thm)],[f450])).
% 0.14/0.43 fof(f453,definition,(
% 0.14/0.43 sQ3_spl <=> (nil=sk3)),
% 0.14/0.43 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/0.43 fof(f455,plain,(
% 0.14/0.43 ~nil=sk3|sQ3_spl),
% 0.14/0.43 inference(component_clause,[status(thm)],[f453])).
% 0.14/0.43 fof(f456,plain,(
% 0.14/0.43 sQ2_spl|~sQ3_spl),
% 0.14/0.43 inference(split_clause,[status(thm)],[f442,f450,f453])).
% 0.14/0.43 fof(f464,plain,(
% 0.14/0.43 ![X1]: (~neq(X1,X1)|~ssList(X1)|~ssList(X1))),
% 0.14/0.43 inference(destructive_equality_resolution,[status(thm)],[f320])).
% 0.14/0.43 fof(f465,plain,(
% 0.14/0.43 ![X0]: (~neq(X0,X0)|~ssList(X0))),
% 0.14/0.43 inference(duplicate_literals_removal,[status(thm)],[f464])).
% 0.14/0.43 fof(f472,plain,(
% 0.14/0.43 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~ssList(app(X1,X0))|frontsegP(app(X1,X0),X1))),
% 0.14/0.43 inference(destructive_equality_resolution,[status(thm)],[f359])).
% 0.14/0.43 fof(f499,plain,(
% 0.14/0.43 nil=sk2|~sQ2_spl),
% 0.14/0.43 inference(forward_demodulation,[status(thm)],[f433,f451])).
% 0.14/0.43 fof(f500,plain,(
% 0.14/0.43 neq(sk2,sk2)|~sQ2_spl),
% 0.14/0.43 inference(forward_demodulation,[status(thm)],[f499,f435])).
% 0.14/0.43 fof(f515,plain,(
% 0.14/0.43 app(sk1,sk5)=sk4),
% 0.14/0.43 inference(forward_demodulation,[status(thm)],[f434,f438])).
% 0.14/0.43 fof(f516,plain,(
% 0.14/0.43 app(sk1,sk5)=sk2),
% 0.14/0.43 inference(forward_demodulation,[status(thm)],[f433,f515])).
% 0.14/0.43 fof(f529,plain,(
% 0.14/0.43 ~nil=sk1|sQ3_spl),
% 0.14/0.43 inference(forward_demodulation,[status(thm)],[f434,f455])).
% 0.14/0.43 fof(f565,definition,(
% 0.14/0.43 sQ7_spl <=> (ssList(nil))),
% 0.14/0.43 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/0.43 fof(f567,plain,(
% 0.14/0.43 ~ssList(nil)|sQ7_spl),
% 0.14/0.43 inference(component_clause,[status(thm)],[f565])).
% 0.14/0.43 fof(f573,plain,(
% 0.14/0.43 $false|sQ7_spl),
% 0.14/0.43 inference(forward_subsumption_resolution,[status(thm)],[f567,f206])).
% 0.14/0.43 fof(f574,plain,(
% 0.14/0.43 sQ7_spl),
% 0.14/0.43 inference(contradiction_clause,[status(thm)],[f573])).
% 0.14/0.43 fof(f585,definition,(
% 0.14/0.43 sQ9_spl <=> (ssList(sk5))),
% 0.14/0.43 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.14/0.43 fof(f587,plain,(
% 0.14/0.43 ~ssList(sk5)|sQ9_spl),
% 0.14/0.43 inference(component_clause,[status(thm)],[f585])).
% 0.14/0.43 fof(f590,definition,(
% 0.14/0.43 sQ10_spl <=> (ssList(sk1))),
% 0.14/0.43 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.14/0.43 fof(f592,plain,(
% 0.14/0.43 ~ssList(sk1)|sQ10_spl),
% 0.14/0.43 inference(component_clause,[status(thm)],[f590])).
% 0.14/0.43 fof(f597,plain,(
% 0.14/0.43 $false|sQ10_spl),
% 0.14/0.43 inference(forward_subsumption_resolution,[status(thm)],[f592,f429])).
% 0.14/0.43 fof(f598,plain,(
% 0.14/0.43 sQ10_spl),
% 0.14/0.43 inference(contradiction_clause,[status(thm)],[f597])).
% 0.14/0.43 fof(f599,plain,(
% 0.14/0.43 $false|sQ9_spl),
% 0.14/0.43 inference(forward_subsumption_resolution,[status(thm)],[f587,f437])).
% 0.14/0.43 fof(f600,plain,(
% 0.14/0.43 sQ9_spl),
% 0.14/0.43 inference(contradiction_clause,[status(thm)],[f599])).
% 0.14/0.43 fof(f775,plain,(
% 0.14/0.43 ![X0]: (~ssList(nil)|~ssList(X0)|X0=nil|~ssList(X0)|~frontsegP(sk2,X0)|~frontsegP(sk1,X0))),
% 0.14/0.43 inference(resolution,[status(thm)],[f301,f436])).
% 0.14/0.43 fof(f778,definition,(
% 0.14/0.43 ![X0]: (sQ18_spl <=> (~ssList(X0)|X0=nil|~ssList(X0)|~frontsegP(sk2,X0)|~frontsegP(sk1,X0)))),
% 0.14/0.43 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.14/0.43 fof(f779,plain,(
% 0.14/0.43 ![X0]: (~ssList(X0)|X0=nil|~ssList(X0)|~frontsegP(sk2,X0)|~frontsegP(sk1,X0)|~sQ18_spl)),
% 0.14/0.43 inference(component_clause,[status(thm)],[f778])).
% 0.14/0.43 fof(f781,plain,(
% 0.14/0.43 ~sQ7_spl|sQ18_spl),
% 0.14/0.43 inference(split_clause,[status(thm)],[f775,f565,f778])).
% 0.14/0.43 fof(f782,plain,(
% 0.14/0.43 ![X0]: (~ssList(X0)|X0=nil|~frontsegP(sk2,X0)|~frontsegP(sk1,X0)|~sQ18_spl)),
% 0.14/0.43 inference(duplicate_literals_removal,[status(thm)],[f779])).
% 0.14/0.43 fof(f827,plain,(
% 0.14/0.43 ~ssList(sk1)|sk1=nil|~frontsegP(sk2,sk1)|~ssList(sk1)|~sQ18_spl),
% 0.14/0.43 inference(resolution,[status(thm)],[f782,f259])).
% 0.14/0.43 fof(f832,definition,(
% 0.14/0.43 sQ22_spl <=> (sk1=nil)),
% 0.14/0.43 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.14/0.43 fof(f833,plain,(
% 0.14/0.43 sk1=nil|~sQ22_spl),
% 0.14/0.43 inference(component_clause,[status(thm)],[f832])).
% 0.14/0.43 fof(f835,definition,(
% 0.14/0.43 sQ23_spl <=> (frontsegP(sk2,sk1))),
% 0.14/0.43 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.14/0.43 fof(f838,plain,(
% 0.14/0.43 ~sQ10_spl|sQ22_spl|~sQ23_spl|~sQ18_spl),
% 0.14/0.43 inference(split_clause,[status(thm)],[f827,f590,f832,f835,f778])).
% 0.14/0.43 fof(f839,plain,(
% 0.14/0.43 $false|sQ3_spl|~sQ22_spl),
% 0.14/0.43 inference(forward_subsumption_resolution,[status(thm)],[f833,f529])).
% 0.14/0.44 fof(f840,plain,(
% 0.14/0.44 sQ3_spl|~sQ22_spl),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f839])).
% 0.14/0.44 fof(f948,plain,(
% 0.14/0.44 ~ssList(sk2)|~sQ2_spl),
% 0.14/0.44 inference(resolution,[status(thm)],[f500,f465])).
% 0.14/0.44 fof(f949,plain,(
% 0.14/0.44 $false|~sQ2_spl),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f948,f430])).
% 0.14/0.44 fof(f950,plain,(
% 0.14/0.44 ~sQ2_spl),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f949])).
% 0.14/0.44 fof(f959,plain,(
% 0.14/0.44 ![X0,X1]: (~ssList(X0)|~ssList(X1)|frontsegP(app(X1,X0),X1))),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f472,f284])).
% 0.14/0.44 fof(f962,plain,(
% 0.14/0.44 ~ssList(sk5)|~ssList(sk1)|frontsegP(sk2,sk1)),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f516,f959])).
% 0.14/0.44 fof(f967,plain,(
% 0.14/0.44 ~sQ9_spl|~sQ10_spl|sQ23_spl),
% 0.14/0.44 inference(split_clause,[status(thm)],[f962,f585,f590,f835])).
% 0.14/0.44 fof(f968,plain,(
% 0.14/0.44 $false),
% 0.14/0.44 inference(sat_refutation,[status(thm)],[f456,f574,f598,f600,f781,f838,f840,f950,f967])).
% 0.14/0.44 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.47 % Elapsed time: 0.089514 seconds
% 0.14/0.47 % CPU time: 0.387731 seconds
% 0.14/0.47 % Total memory used: 114.420 MB
% 0.14/0.47 % Net memory used: 114.081 MB
%------------------------------------------------------------------------------