%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC241-1 : 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 : n001.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 02:41:57 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.60s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC241-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n001.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 08:13:44 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 0.24/0.60 % Refutation found
% 0.24/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.60 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.60 fof(f103,axiom,(
% 0.24/0.60 (![U,V]: (( ~ lt(U,V)| ~ ssItem(V)| ~ ssItem(U)| leq(U,V) ) ))),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f191,negated_conjecture,(
% 0.24/0.60 sk1 = sk3 ),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f192,negated_conjecture,(
% 0.24/0.60 nil != sk1 ),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f193,negated_conjecture,(
% 0.24/0.60 (![A,B,C]: (( ~ ssItem(A)| ~ ssList(B)| ~ ssList(C)| app(app(B,cons(A,nil)),C) != sk1| ssItem(sk5(C,B,A)) ) ))),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f196,negated_conjecture,(
% 0.24/0.60 (![A,B,C]: (( ~ ssItem(A)| ~ ssList(B)| ~ ssList(C)| app(app(B,cons(A,nil)),C) != sk1| lt(A,sk5(C,B,A)) ) ))),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f197,negated_conjecture,(
% 0.24/0.60 (![A,B,C]: (( ~ ssItem(A)| ~ ssList(B)| ~ ssList(C)| app(app(B,cons(A,nil)),C) != sk1| ~ leq(A,sk5(C,B,A)) ) ))),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f198,negated_conjecture,(
% 0.24/0.60 ( nil = sk3| ssItem(sk6) ) ),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f199,negated_conjecture,(
% 0.24/0.60 ( nil = sk3| ssList(sk7) ) ),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f200,negated_conjecture,(
% 0.24/0.60 ( nil = sk3| ssList(sk8) ) ),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f201,negated_conjecture,(
% 0.24/0.60 ( nil = sk3| app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
% 0.24/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f308,plain,(
% 0.24/0.60 ![X0,X1]: (~lt(X0,X1)|~ssItem(X1)|~ssItem(X0)|leq(X0,X1))),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f103])).
% 0.24/0.60 fof(f438,plain,(
% 0.24/0.60 sk1=sk3),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f191])).
% 0.24/0.60 fof(f439,plain,(
% 0.24/0.60 ~nil=sk1),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f192])).
% 0.24/0.60 fof(f440,plain,(
% 0.24/0.60 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk1|ssItem(sk5(X2,X1,X0)))),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f193])).
% 0.24/0.60 fof(f443,plain,(
% 0.24/0.60 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk1|lt(X0,sk5(X2,X1,X0)))),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f196])).
% 0.24/0.60 fof(f444,plain,(
% 0.24/0.60 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk1|~leq(X0,sk5(X2,X1,X0)))),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f197])).
% 0.24/0.60 fof(f445,plain,(
% 0.24/0.60 nil=sk3|ssItem(sk6)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f198])).
% 0.24/0.60 fof(f446,plain,(
% 0.24/0.60 nil=sk3|ssList(sk7)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f199])).
% 0.24/0.60 fof(f447,plain,(
% 0.24/0.60 nil=sk3|ssList(sk8)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f200])).
% 0.24/0.60 fof(f448,plain,(
% 0.24/0.60 nil=sk3|app(app(sk7,cons(sk6,nil)),sk8)=sk3),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f201])).
% 0.24/0.60 fof(f457,definition,(
% 0.24/0.60 sQ2_spl <=> (nil=sk3)),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f458,plain,(
% 0.24/0.60 nil=sk3|~sQ2_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f457])).
% 0.24/0.60 fof(f460,definition,(
% 0.24/0.60 sQ3_spl <=> (ssItem(sk6))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f463,plain,(
% 0.24/0.60 sQ2_spl|sQ3_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f445,f457,f460])).
% 0.24/0.60 fof(f464,definition,(
% 0.24/0.60 sQ4_spl <=> (ssList(sk7))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f467,plain,(
% 0.24/0.60 sQ2_spl|sQ4_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f446,f457,f464])).
% 0.24/0.60 fof(f468,definition,(
% 0.24/0.60 sQ5_spl <=> (ssList(sk8))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f471,plain,(
% 0.24/0.60 sQ2_spl|sQ5_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f447,f457,f468])).
% 0.24/0.60 fof(f472,definition,(
% 0.24/0.60 sQ6_spl <=> (app(app(sk7,cons(sk6,nil)),sk8)=sk3)),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f473,plain,(
% 0.24/0.60 app(app(sk7,cons(sk6,nil)),sk8)=sk3|~sQ6_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f472])).
% 0.24/0.60 fof(f475,plain,(
% 0.24/0.60 sQ2_spl|sQ6_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f448,f457,f472])).
% 0.24/0.60 fof(f559,definition,(
% 0.24/0.60 sQ22_spl <=> (nil=sk1)),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f560,plain,(
% 0.24/0.60 nil=sk1|~sQ22_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f559])).
% 0.24/0.60 fof(f1219,plain,(
% 0.24/0.60 ~nil=sk3),
% 0.24/0.60 inference(forward_demodulation,[status(thm)],[f438,f439])).
% 0.24/0.60 fof(f1220,plain,(
% 0.24/0.60 $false|~sQ2_spl),
% 0.24/0.60 inference(forward_subsumption_resolution,[status(thm)],[f458,f1219])).
% 0.24/0.60 fof(f1221,plain,(
% 0.24/0.60 ~sQ2_spl),
% 0.24/0.60 inference(contradiction_clause,[status(thm)],[f1220])).
% 0.24/0.60 fof(f1230,plain,(
% 0.24/0.60 nil=sk3|~sQ22_spl),
% 0.24/0.60 inference(forward_demodulation,[status(thm)],[f438,f560])).
% 0.24/0.60 fof(f1231,plain,(
% 0.24/0.60 $false|~sQ22_spl),
% 0.24/0.60 inference(forward_subsumption_resolution,[status(thm)],[f1230,f1219])).
% 0.24/0.60 fof(f1232,plain,(
% 0.24/0.60 ~sQ22_spl),
% 0.24/0.60 inference(contradiction_clause,[status(thm)],[f1231])).
% 0.24/0.60 fof(f1341,plain,(
% 0.24/0.60 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk3|ssItem(sk5(X2,X1,X0)))),
% 0.24/0.61 inference(forward_demodulation,[status(thm)],[f438,f440])).
% 0.24/0.61 fof(f1366,plain,(
% 0.24/0.61 ~ssItem(sk6)|~ssList(sk7)|~ssList(sk8)|ssItem(sk5(sk8,sk7,sk6))|~sQ6_spl),
% 0.24/0.61 inference(resolution,[status(thm)],[f473,f1341])).
% 0.24/0.61 fof(f1374,definition,(
% 0.24/0.61 sQ170_spl <=> (ssItem(sk5(sk8,sk7,sk6)))),
% 0.24/0.61 introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition])).
% 0.24/0.61 fof(f1377,plain,(
% 0.24/0.61 ~sQ3_spl|~sQ4_spl|~sQ5_spl|sQ170_spl|~sQ6_spl),
% 0.24/0.61 inference(split_clause,[status(thm)],[f1366,f460,f464,f468,f1374,f472])).
% 0.24/0.61 fof(f1420,definition,(
% 0.24/0.61 sQ174_spl <=> (leq(sk6,sk5(sk8,sk7,sk6)))),
% 0.24/0.61 introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition])).
% 0.24/0.61 fof(f1424,definition,(
% 0.24/0.61 sQ175_spl <=> (lt(sk6,sk5(sk8,sk7,sk6)))),
% 0.24/0.61 introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition])).
% 0.24/0.61 fof(f1425,plain,(
% 0.24/0.61 lt(sk6,sk5(sk8,sk7,sk6))|~sQ175_spl),
% 0.24/0.61 inference(component_clause,[status(thm)],[f1424])).
% 0.24/0.61 fof(f1869,plain,(
% 0.24/0.61 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk3|~leq(X0,sk5(X2,X1,X0)))),
% 0.24/0.61 inference(forward_demodulation,[status(thm)],[f438,f444])).
% 0.24/0.61 fof(f1870,plain,(
% 0.24/0.61 ~ssItem(sk6)|~ssList(sk7)|~ssList(sk8)|~leq(sk6,sk5(sk8,sk7,sk6))|~sQ6_spl),
% 0.24/0.61 inference(resolution,[status(thm)],[f1869,f473])).
% 0.24/0.61 fof(f1872,plain,(
% 0.24/0.61 ~sQ3_spl|~sQ4_spl|~sQ5_spl|~sQ174_spl|~sQ6_spl),
% 0.24/0.61 inference(split_clause,[status(thm)],[f1870,f460,f464,f468,f1420,f472])).
% 0.24/0.61 fof(f1874,plain,(
% 0.24/0.61 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk3|lt(X0,sk5(X2,X1,X0)))),
% 0.24/0.61 inference(forward_demodulation,[status(thm)],[f438,f443])).
% 0.24/0.61 fof(f1875,plain,(
% 0.24/0.61 ~ssItem(sk6)|~ssList(sk7)|~ssList(sk8)|lt(sk6,sk5(sk8,sk7,sk6))|~sQ6_spl),
% 0.24/0.61 inference(resolution,[status(thm)],[f1874,f473])).
% 0.24/0.61 fof(f1877,plain,(
% 0.24/0.61 ~sQ3_spl|~sQ4_spl|~sQ5_spl|sQ175_spl|~sQ6_spl),
% 0.24/0.61 inference(split_clause,[status(thm)],[f1875,f460,f464,f468,f1424,f472])).
% 0.24/0.61 fof(f2038,plain,(
% 0.24/0.61 ~ssItem(sk5(sk8,sk7,sk6))|~ssItem(sk6)|leq(sk6,sk5(sk8,sk7,sk6))|~sQ175_spl),
% 0.24/0.61 inference(resolution,[status(thm)],[f1425,f308])).
% 0.24/0.61 fof(f2039,plain,(
% 0.24/0.61 ~sQ170_spl|~sQ3_spl|sQ174_spl|~sQ175_spl),
% 0.24/0.61 inference(split_clause,[status(thm)],[f2038,f1374,f460,f1420,f1424])).
% 0.24/0.61 fof(f2040,plain,(
% 0.24/0.61 $false),
% 0.24/0.61 inference(sat_refutation,[status(thm)],[f463,f467,f471,f475,f1221,f1232,f1377,f1872,f1877,f2039])).
% 0.24/0.61 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.64 % Elapsed time: 0.170726 seconds
% 0.24/0.64 % CPU time: 0.703976 seconds
% 0.24/0.64 % Total memory used: 86.061 MB
% 0.24/0.64 % Net memory used: 85.504 MB
%------------------------------------------------------------------------------