%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC003-1 : 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 : n004.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 02:41:18 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC003-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n004.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 07:48:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.42 fof(f8,axiom,(
% 0.12/0.42 ssList(nil) ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f86,axiom,(
% 0.12/0.42 (![U,V]: (( ~ ssItem(U)| ~ ssList(V)| ssList(cons(U,V)) ) ))),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f98,axiom,(
% 0.12/0.42 (![U,V]: (( cons(U,V) != nil| ~ ssItem(U)| ~ ssList(V) ) ))),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f100,axiom,(
% 0.12/0.42 (![U,V]: (( ~ ssList(U)| ~ ssList(V)| neq(V,U)| V = U ) ))),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f190,negated_conjecture,(
% 0.12/0.42 sk2 = sk4 ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f191,negated_conjecture,(
% 0.12/0.42 sk1 = sk3 ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f192,negated_conjecture,(
% 0.12/0.42 ( neq(sk2,nil)| neq(sk2,nil) ) ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f201,negated_conjecture,(
% 0.12/0.42 (![A,B,C]: (( ~ ssList(A)| ~ ssList(B)| ~ ssList(C)| app(app(A,B),C) != sk2| app(A,C) != sk1| ~ neq(B,nil)| ~ neq(sk4,nil) ) ))),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f202,negated_conjecture,(
% 0.12/0.42 ( ssItem(sk5)| ~ neq(sk4,nil) ) ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f203,negated_conjecture,(
% 0.12/0.42 ( ssList(sk6)| ~ neq(sk4,nil) ) ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f204,negated_conjecture,(
% 0.12/0.42 ( ssList(sk7)| ~ neq(sk4,nil) ) ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f205,negated_conjecture,(
% 0.12/0.42 ( app(app(sk6,cons(sk5,nil)),sk7) = sk4| ~ neq(sk4,nil) ) ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f206,negated_conjecture,(
% 0.12/0.42 ( app(sk6,sk7) = sk3| ~ neq(sk4,nil) ) ),
% 0.12/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f215,plain,(
% 0.12/0.42 ssList(nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/0.42 fof(f294,plain,(
% 0.12/0.42 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|ssList(cons(X0,X1)))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f86])).
% 0.12/0.42 fof(f306,plain,(
% 0.12/0.42 ![V]: ((![U]: (~cons(U,V)=nil|~ssItem(U)))|~ssList(V))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f98])).
% 0.12/0.42 fof(f307,plain,(
% 0.12/0.42 ![X0,X1]: (~cons(X0,X1)=nil|~ssItem(X0)|~ssList(X1))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f306])).
% 0.12/0.42 fof(f310,plain,(
% 0.12/0.42 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X1,X0)|X1=X0)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f100])).
% 0.12/0.42 fof(f442,plain,(
% 0.12/0.42 sk2=sk4),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f190])).
% 0.12/0.42 fof(f443,plain,(
% 0.12/0.42 sk1=sk3),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f191])).
% 0.12/0.42 fof(f444,plain,(
% 0.12/0.42 neq(sk2,nil)|neq(sk2,nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f192])).
% 0.12/0.42 fof(f455,plain,(
% 0.12/0.42 (![B]: ((![A,C]: ((((~ssList(A)|~ssList(B))|~ssList(C))|~app(app(A,B),C)=sk2)|~app(A,C)=sk1))|~neq(B,nil)))|~neq(sk4,nil)),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f201])).
% 0.12/0.42 fof(f456,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sk2|~app(X0,X2)=sk1|~neq(X1,nil)|~neq(sk4,nil))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f455])).
% 0.12/0.42 fof(f457,plain,(
% 0.12/0.42 ssItem(sk5)|~neq(sk4,nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f202])).
% 0.12/0.42 fof(f458,plain,(
% 0.12/0.42 ssList(sk6)|~neq(sk4,nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f203])).
% 0.12/0.42 fof(f459,plain,(
% 0.12/0.42 ssList(sk7)|~neq(sk4,nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f204])).
% 0.12/0.42 fof(f460,plain,(
% 0.12/0.42 app(app(sk6,cons(sk5,nil)),sk7)=sk4|~neq(sk4,nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f205])).
% 0.12/0.42 fof(f461,plain,(
% 0.12/0.42 app(sk6,sk7)=sk3|~neq(sk4,nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f206])).
% 0.12/0.42 fof(f471,definition,(
% 0.12/0.42 sQ2_spl <=> (neq(sk2,nil))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f472,plain,(
% 0.12/0.42 neq(sk2,nil)|~sQ2_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f471])).
% 0.12/0.42 fof(f474,plain,(
% 0.12/0.42 sQ2_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f444,f471])).
% 0.12/0.42 fof(f475,definition,(
% 0.12/0.42 sQ3_spl <=> (neq(sk4,nil))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f477,plain,(
% 0.12/0.42 ~neq(sk4,nil)|sQ3_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f475])).
% 0.12/0.42 fof(f479,definition,(
% 0.12/0.42 ![X0,X1,X2]: (sQ4_spl <=> (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sk2|~app(X0,X2)=sk1|~neq(X1,nil)))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f480,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sk2|~app(X0,X2)=sk1|~neq(X1,nil)|~sQ4_spl)),
% 0.12/0.42 inference(component_clause,[status(thm)],[f479])).
% 0.12/0.42 fof(f483,definition,(
% 0.12/0.42 sQ5_spl <=> (ssItem(sk5))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f484,plain,(
% 0.12/0.42 ssItem(sk5)|~sQ5_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f483])).
% 0.12/0.42 fof(f487,definition,(
% 0.12/0.42 sQ6_spl <=> (ssList(sk6))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f491,definition,(
% 0.12/0.42 sQ7_spl <=> (ssList(sk7))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f495,definition,(
% 0.12/0.42 sQ8_spl <=> (app(app(sk6,cons(sk5,nil)),sk7)=sk4)),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f496,plain,(
% 0.12/0.42 app(app(sk6,cons(sk5,nil)),sk7)=sk4|~sQ8_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f495])).
% 0.12/0.42 fof(f499,definition,(
% 0.12/0.42 sQ9_spl <=> (app(sk6,sk7)=sk3)),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f500,plain,(
% 0.12/0.42 app(sk6,sk7)=sk3|~sQ9_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f499])).
% 0.12/0.42 fof(f507,plain,(
% 0.12/0.42 sQ4_spl|~sQ3_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f456,f479,f475])).
% 0.12/0.42 fof(f508,plain,(
% 0.12/0.42 sQ5_spl|~sQ3_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f457,f483,f475])).
% 0.12/0.42 fof(f509,plain,(
% 0.12/0.42 sQ6_spl|~sQ3_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f458,f487,f475])).
% 0.12/0.42 fof(f510,plain,(
% 0.12/0.42 sQ7_spl|~sQ3_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f459,f491,f475])).
% 0.12/0.42 fof(f511,plain,(
% 0.12/0.42 sQ8_spl|~sQ3_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f460,f495,f475])).
% 0.12/0.42 fof(f512,plain,(
% 0.12/0.42 sQ9_spl|~sQ3_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f461,f499,f475])).
% 0.12/0.42 fof(f545,plain,(
% 0.12/0.42 ~neq(sk2,nil)|sQ3_spl),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f442,f477])).
% 0.12/0.42 fof(f546,plain,(
% 0.12/0.42 $false|~sQ2_spl|sQ3_spl),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f545,f472])).
% 0.12/0.42 fof(f547,plain,(
% 0.12/0.42 ~sQ2_spl|sQ3_spl),
% 0.12/0.42 inference(contradiction_clause,[status(thm)],[f546])).
% 0.12/0.42 fof(f548,plain,(
% 0.12/0.42 app(app(sk6,cons(sk5,nil)),sk7)=sk2|~sQ8_spl),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f442,f496])).
% 0.12/0.42 fof(f549,plain,(
% 0.12/0.42 app(sk6,sk7)=sk1|~sQ9_spl),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f443,f500])).
% 0.12/0.42 fof(f578,definition,(
% 0.12/0.42 sQ13_spl <=> (ssList(nil))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f580,plain,(
% 0.12/0.42 ~ssList(nil)|sQ13_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f578])).
% 0.12/0.42 fof(f626,plain,(
% 0.12/0.42 $false|sQ13_spl),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f580,f215])).
% 0.12/0.42 fof(f627,plain,(
% 0.12/0.42 sQ13_spl),
% 0.12/0.42 inference(contradiction_clause,[status(thm)],[f626])).
% 0.12/0.42 fof(f643,plain,(
% 0.12/0.42 ![X0]: (~cons(sk5,X0)=nil|~ssList(X0)|~sQ5_spl)),
% 0.12/0.42 inference(resolution,[status(thm)],[f307,f484])).
% 0.12/0.42 fof(f681,plain,(
% 0.12/0.42 ~cons(sk5,nil)=nil|~sQ5_spl),
% 0.12/0.42 inference(resolution,[status(thm)],[f643,f215])).
% 0.12/0.42 fof(f697,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~ssList(nil)|~ssList(X0)|X0=nil|~ssList(X1)|~ssList(X0)|~ssList(X2)|~app(app(X1,X0),X2)=sk2|~app(X1,X2)=sk1|~sQ4_spl)),
% 0.12/0.42 inference(resolution,[status(thm)],[f310,f480])).
% 0.12/0.42 fof(f700,definition,(
% 0.12/0.42 ![X0,X1,X2]: (sQ18_spl <=> (~ssList(X0)|X0=nil|~ssList(X1)|~ssList(X0)|~ssList(X2)|~app(app(X1,X0),X2)=sk2|~app(X1,X2)=sk1))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f701,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~ssList(X0)|X0=nil|~ssList(X1)|~ssList(X0)|~ssList(X2)|~app(app(X1,X0),X2)=sk2|~app(X1,X2)=sk1|~sQ18_spl)),
% 0.12/0.42 inference(component_clause,[status(thm)],[f700])).
% 0.12/0.42 fof(f703,plain,(
% 0.12/0.42 ~sQ13_spl|sQ18_spl|~sQ4_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f697,f578,f700,f479])).
% 0.12/0.42 fof(f704,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~ssList(X0)|X0=nil|~ssList(X1)|~ssList(X2)|~app(app(X1,X0),X2)=sk2|~app(X1,X2)=sk1|~sQ18_spl)),
% 0.12/0.42 inference(duplicate_literals_removal,[status(thm)],[f701])).
% 0.12/0.42 fof(f801,definition,(
% 0.12/0.42 sQ22_spl <=> (ssList(cons(sk5,nil)))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f803,plain,(
% 0.12/0.42 ~ssList(cons(sk5,nil))|sQ22_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f801])).
% 0.12/0.42 fof(f805,plain,(
% 0.12/0.42 ~ssItem(sk5)|~ssList(nil)|sQ22_spl),
% 0.12/0.42 inference(resolution,[status(thm)],[f803,f294])).
% 0.12/0.42 fof(f806,plain,(
% 0.12/0.42 ~sQ5_spl|~sQ13_spl|sQ22_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f805,f483,f578,f801])).
% 0.12/0.42 fof(f955,definition,(
% 0.12/0.42 sQ24_spl <=> (nil=cons(sk5,nil))),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f956,plain,(
% 0.12/0.42 nil=cons(sk5,nil)|~sQ24_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f955])).
% 0.12/0.42 fof(f1015,plain,(
% 0.12/0.42 ~ssList(cons(sk5,nil))|cons(sk5,nil)=nil|~ssList(sk6)|~ssList(sk7)|~app(sk6,sk7)=sk1|~sQ18_spl|~sQ8_spl),
% 0.12/0.42 inference(resolution,[status(thm)],[f704,f548])).
% 0.12/0.42 fof(f1031,definition,(
% 0.12/0.42 sQ35_spl <=> (app(sk6,sk7)=sk1)),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f1033,plain,(
% 0.12/0.42 ~app(sk6,sk7)=sk1|sQ35_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f1031])).
% 0.12/0.42 fof(f1034,plain,(
% 0.12/0.42 ~sQ22_spl|sQ24_spl|~sQ6_spl|~sQ7_spl|~sQ35_spl|~sQ18_spl|~sQ8_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f1015,f801,f955,f487,f491,f1031,f700,f495])).
% 0.12/0.42 fof(f1092,plain,(
% 0.12/0.42 $false|~sQ5_spl|~sQ24_spl),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f956,f681])).
% 0.12/0.42 fof(f1093,plain,(
% 0.12/0.42 ~sQ5_spl|~sQ24_spl),
% 0.12/0.42 inference(contradiction_clause,[status(thm)],[f1092])).
% 0.12/0.42 fof(f1096,plain,(
% 0.12/0.42 ~sk1=sk1|~sQ9_spl|sQ35_spl),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f549,f1033])).
% 0.12/0.42 fof(f1097,plain,(
% 0.12/0.42 $false|~sQ9_spl|sQ35_spl),
% 0.12/0.42 inference(trivial_equality_resolution,[status(thm)],[f1096])).
% 0.12/0.42 fof(f1098,plain,(
% 0.12/0.42 ~sQ9_spl|sQ35_spl),
% 0.12/0.42 inference(contradiction_clause,[status(thm)],[f1097])).
% 0.12/0.42 fof(f1099,plain,(
% 0.12/0.42 $false),
% 0.12/0.42 inference(sat_refutation,[status(thm)],[f474,f507,f508,f509,f510,f511,f512,f547,f627,f703,f806,f1034,f1093,f1098])).
% 0.12/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.086322 seconds
% 0.12/0.44 % CPU time: 0.369655 seconds
% 0.12/0.44 % Total memory used: 115.147 MB
% 0.12/0.44 % Net memory used: 114.828 MB
%------------------------------------------------------------------------------