%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC118-1 : 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 : n003.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 02:41:38 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC118-1 : 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 : n003.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 07:59:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.47 fof(f8,axiom,(
% 0.14/0.47 ssList(nil) ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f85,axiom,(
% 0.14/0.47 (![U,V]: (( ~ ssList(U)| ~ ssList(V)| ssList(app(V,U)) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f100,axiom,(
% 0.14/0.47 (![U,V]: (( ~ ssList(U)| ~ ssList(V)| neq(V,U)| V = U ) ))),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f173,axiom,(
% 0.14/0.47 (![U,V,W,X]: (( app(app(U,V),W) != X| ~ ssList(W)| ~ ssList(U)| ~ ssList(V)| ~ ssList(X)| segmentP(X,V) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f186,negated_conjecture,(
% 0.14/0.47 ssList(sk1) ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f190,negated_conjecture,(
% 0.14/0.47 sk2 = sk4 ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f191,negated_conjecture,(
% 0.14/0.47 sk1 = sk3 ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f192,negated_conjecture,(
% 0.14/0.47 ssList(sk5) ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f193,negated_conjecture,(
% 0.14/0.47 ssList(sk6) ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f194,negated_conjecture,(
% 0.14/0.47 app(app(sk5,sk3),sk6) = sk4 ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f198,negated_conjecture,(
% 0.14/0.47 ( nil = sk4| nil != sk3 ) ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f199,negated_conjecture,(
% 0.14/0.47 ( nil != sk2| nil != sk1 ) ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f200,negated_conjecture,(
% 0.14/0.47 ( ~ neq(sk1,nil)| ~ segmentP(sk2,sk1) ) ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f208,plain,(
% 0.14/0.47 ssList(nil)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.47 fof(f286,plain,(
% 0.14/0.47 ![X0,X1]: (~ssList(X0)|~ssList(X1)|ssList(app(X1,X0)))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f85])).
% 0.14/0.47 fof(f303,plain,(
% 0.14/0.47 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X1,X0)|X1=X0)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f100])).
% 0.14/0.47 fof(f406,plain,(
% 0.14/0.47 ![V,X]: ((((![U]: ((![W]: (~app(app(U,V),W)=X|~ssList(W)))|~ssList(U)))|~ssList(V))|~ssList(X))|segmentP(X,V))),
% 0.14/0.47 inference(miniscoping,[status(thm)],[f173])).
% 0.14/0.47 fof(f407,plain,(
% 0.14/0.47 ![X0,X1,X2,X3]: (~app(app(X0,X1),X2)=X3|~ssList(X2)|~ssList(X0)|~ssList(X1)|~ssList(X3)|segmentP(X3,X1))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f406])).
% 0.14/0.47 fof(f431,plain,(
% 0.14/0.47 ssList(sk1)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f186])).
% 0.14/0.47 fof(f435,plain,(
% 0.14/0.47 sk2=sk4),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f190])).
% 0.14/0.47 fof(f436,plain,(
% 0.14/0.47 sk1=sk3),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f191])).
% 0.14/0.47 fof(f437,plain,(
% 0.14/0.47 ssList(sk5)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f192])).
% 0.14/0.47 fof(f438,plain,(
% 0.14/0.47 ssList(sk6)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f193])).
% 0.14/0.47 fof(f439,plain,(
% 0.14/0.47 app(app(sk5,sk3),sk6)=sk4),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f194])).
% 0.14/0.47 fof(f445,plain,(
% 0.14/0.47 nil=sk4|~nil=sk3),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f198])).
% 0.14/0.47 fof(f446,plain,(
% 0.14/0.47 ~nil=sk2|~nil=sk1),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f199])).
% 0.14/0.47 fof(f447,plain,(
% 0.14/0.47 ~neq(sk1,nil)|~segmentP(sk2,sk1)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f200])).
% 0.14/0.47 fof(f455,definition,(
% 0.14/0.47 sQ2_spl <=> (nil=sk4)),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f456,plain,(
% 0.14/0.47 nil=sk4|~sQ2_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f455])).
% 0.14/0.47 fof(f458,definition,(
% 0.14/0.47 sQ3_spl <=> (nil=sk3)),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f460,plain,(
% 0.14/0.47 ~nil=sk3|sQ3_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f458])).
% 0.14/0.47 fof(f461,plain,(
% 0.14/0.47 sQ2_spl|~sQ3_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f445,f455,f458])).
% 0.14/0.47 fof(f462,definition,(
% 0.14/0.47 sQ4_spl <=> (nil=sk2)),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f464,plain,(
% 0.14/0.47 ~nil=sk2|sQ4_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f462])).
% 0.14/0.47 fof(f465,definition,(
% 0.14/0.47 sQ5_spl <=> (nil=sk1)),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f466,plain,(
% 0.14/0.47 nil=sk1|~sQ5_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f465])).
% 0.14/0.47 fof(f468,plain,(
% 0.14/0.47 ~sQ4_spl|~sQ5_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f446,f462,f465])).
% 0.14/0.47 fof(f469,definition,(
% 0.14/0.47 sQ6_spl <=> (neq(sk1,nil))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f471,plain,(
% 0.14/0.47 ~neq(sk1,nil)|sQ6_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f469])).
% 0.14/0.47 fof(f472,definition,(
% 0.14/0.47 sQ7_spl <=> (segmentP(sk2,sk1))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f474,plain,(
% 0.14/0.47 ~segmentP(sk2,sk1)|sQ7_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f472])).
% 0.14/0.47 fof(f475,plain,(
% 0.14/0.47 ~sQ6_spl|~sQ7_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f447,f469,f472])).
% 0.14/0.47 fof(f494,plain,(
% 0.14/0.47 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~ssList(app(app(X1,X2),X0))|segmentP(app(app(X1,X2),X0),X2))),
% 0.14/0.47 inference(destructive_equality_resolution,[status(thm)],[f407])).
% 0.14/0.47 fof(f508,plain,(
% 0.14/0.47 nil=sk2|~sQ2_spl),
% 0.14/0.47 inference(forward_demodulation,[status(thm)],[f435,f456])).
% 0.14/0.47 fof(f509,plain,(
% 0.14/0.47 $false|sQ4_spl|~sQ2_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f508,f464])).
% 0.14/0.47 fof(f510,plain,(
% 0.14/0.47 sQ4_spl|~sQ2_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f509])).
% 0.14/0.47 fof(f511,plain,(
% 0.14/0.47 ~nil=sk1|sQ3_spl),
% 0.14/0.47 inference(forward_demodulation,[status(thm)],[f436,f460])).
% 0.14/0.47 fof(f512,plain,(
% 0.14/0.47 app(app(sk5,sk1),sk6)=sk4),
% 0.14/0.47 inference(forward_demodulation,[status(thm)],[f436,f439])).
% 0.14/0.47 fof(f513,plain,(
% 0.14/0.47 app(app(sk5,sk1),sk6)=sk2),
% 0.14/0.47 inference(forward_demodulation,[status(thm)],[f435,f512])).
% 0.14/0.47 fof(f578,definition,(
% 0.14/0.47 sQ8_spl <=> (ssList(sk2))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f586,definition,(
% 0.14/0.47 sQ10_spl <=> (ssList(nil))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f588,plain,(
% 0.14/0.47 ~ssList(nil)|sQ10_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f586])).
% 0.14/0.47 fof(f596,plain,(
% 0.14/0.47 ~ssList(sk6)|~ssList(app(sk5,sk1))|ssList(sk2)),
% 0.14/0.47 inference(paramodulation,[status(thm)],[f513,f286])).
% 0.14/0.47 fof(f597,definition,(
% 0.14/0.47 sQ12_spl <=> (ssList(sk6))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f599,plain,(
% 0.14/0.47 ~ssList(sk6)|sQ12_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f597])).
% 0.14/0.47 fof(f600,definition,(
% 0.14/0.47 sQ13_spl <=> (ssList(app(sk5,sk1)))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f602,plain,(
% 0.14/0.47 ~ssList(app(sk5,sk1))|sQ13_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f600])).
% 0.14/0.47 fof(f603,plain,(
% 0.14/0.47 ~sQ12_spl|~sQ13_spl|sQ8_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f596,f597,f600,f578])).
% 0.14/0.47 fof(f606,plain,(
% 0.14/0.47 $false|sQ10_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f588,f208])).
% 0.14/0.47 fof(f607,plain,(
% 0.14/0.47 sQ10_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f606])).
% 0.14/0.47 fof(f608,plain,(
% 0.14/0.47 ~ssList(sk1)|~ssList(sk5)|sQ13_spl),
% 0.14/0.47 inference(resolution,[status(thm)],[f602,f286])).
% 0.14/0.47 fof(f609,definition,(
% 0.14/0.47 sQ14_spl <=> (ssList(sk1))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f611,plain,(
% 0.14/0.47 ~ssList(sk1)|sQ14_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f609])).
% 0.14/0.47 fof(f612,definition,(
% 0.14/0.47 sQ15_spl <=> (ssList(sk5))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f614,plain,(
% 0.14/0.47 ~ssList(sk5)|sQ15_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f612])).
% 0.14/0.47 fof(f615,plain,(
% 0.14/0.47 ~sQ14_spl|~sQ15_spl|sQ13_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f608,f609,f612,f600])).
% 0.14/0.47 fof(f616,plain,(
% 0.14/0.47 $false|sQ15_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f614,f437])).
% 0.14/0.47 fof(f617,plain,(
% 0.14/0.47 sQ15_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f616])).
% 0.14/0.47 fof(f618,plain,(
% 0.14/0.47 $false|sQ14_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f611,f431])).
% 0.14/0.47 fof(f619,plain,(
% 0.14/0.47 sQ14_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f618])).
% 0.14/0.48 fof(f620,plain,(
% 0.14/0.48 $false|sQ12_spl),
% 0.14/0.48 inference(forward_subsumption_resolution,[status(thm)],[f599,f438])).
% 0.14/0.48 fof(f621,plain,(
% 0.14/0.48 sQ12_spl),
% 0.14/0.48 inference(contradiction_clause,[status(thm)],[f620])).
% 0.14/0.48 fof(f695,plain,(
% 0.14/0.48 ~ssList(nil)|~ssList(sk1)|sk1=nil|sQ6_spl),
% 0.14/0.48 inference(resolution,[status(thm)],[f303,f471])).
% 0.14/0.48 fof(f698,plain,(
% 0.14/0.48 ~sQ10_spl|~sQ14_spl|sQ5_spl|sQ6_spl),
% 0.14/0.48 inference(split_clause,[status(thm)],[f695,f586,f609,f465,f469])).
% 0.14/0.48 fof(f699,plain,(
% 0.14/0.48 $false|sQ3_spl|~sQ5_spl),
% 0.14/0.48 inference(forward_subsumption_resolution,[status(thm)],[f466,f511])).
% 0.14/0.48 fof(f700,plain,(
% 0.14/0.48 sQ3_spl|~sQ5_spl),
% 0.14/0.48 inference(contradiction_clause,[status(thm)],[f699])).
% 0.14/0.48 fof(f1650,plain,(
% 0.14/0.48 ~ssList(sk6)|~ssList(sk5)|~ssList(sk1)|~ssList(sk2)|segmentP(app(app(sk5,sk1),sk6),sk1)),
% 0.14/0.48 inference(paramodulation,[status(thm)],[f513,f494])).
% 0.14/0.48 fof(f1663,definition,(
% 0.14/0.48 sQ34_spl <=> (segmentP(app(app(sk5,sk1),sk6),sk1))),
% 0.14/0.48 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.14/0.48 fof(f1664,plain,(
% 0.14/0.48 segmentP(app(app(sk5,sk1),sk6),sk1)|~sQ34_spl),
% 0.14/0.48 inference(component_clause,[status(thm)],[f1663])).
% 0.14/0.48 fof(f1666,plain,(
% 0.14/0.48 ~sQ12_spl|~sQ15_spl|~sQ14_spl|~sQ8_spl|sQ34_spl),
% 0.14/0.48 inference(split_clause,[status(thm)],[f1650,f597,f612,f609,f578,f1663])).
% 0.14/0.48 fof(f1714,plain,(
% 0.14/0.48 segmentP(sk2,sk1)|~sQ34_spl),
% 0.14/0.48 inference(forward_demodulation,[status(thm)],[f513,f1664])).
% 0.14/0.48 fof(f1715,plain,(
% 0.14/0.48 $false|sQ7_spl|~sQ34_spl),
% 0.14/0.48 inference(forward_subsumption_resolution,[status(thm)],[f1714,f474])).
% 0.14/0.48 fof(f1716,plain,(
% 0.14/0.48 sQ7_spl|~sQ34_spl),
% 0.14/0.48 inference(contradiction_clause,[status(thm)],[f1715])).
% 0.14/0.48 fof(f1717,plain,(
% 0.14/0.48 $false),
% 0.14/0.48 inference(sat_refutation,[status(thm)],[f461,f468,f475,f510,f603,f607,f615,f617,f619,f621,f698,f700,f1666,f1716])).
% 0.14/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.49 % Elapsed time: 0.129488 seconds
% 0.14/0.49 % CPU time: 0.650608 seconds
% 0.14/0.49 % Total memory used: 121.784 MB
% 0.14/0.49 % Net memory used: 121.161 MB
%------------------------------------------------------------------------------