%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC004-1 : 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 : n020.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 0.13s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC004-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 07:49:17 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.42 fof(f8,axiom,(
% 0.13/0.42 ssList(nil) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f86,axiom,(
% 0.13/0.42 (![U,V]: (( ~ ssItem(U)| ~ ssList(V)| ssList(cons(U,V)) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f99,axiom,(
% 0.13/0.42 (![U,V]: (( cons(U,V) != V| ~ ssItem(U)| ~ ssList(V) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f100,axiom,(
% 0.13/0.42 (![U,V]: (( ~ ssList(U)| ~ ssList(V)| neq(V,U)| V = U ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f190,negated_conjecture,(
% 0.13/0.42 sk2 = sk4 ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f191,negated_conjecture,(
% 0.13/0.42 sk1 = sk3 ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f192,negated_conjecture,(
% 0.13/0.42 ( neq(sk2,nil)| neq(sk2,nil) ) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f200,negated_conjecture,(
% 0.13/0.42 (![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) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f201,negated_conjecture,(
% 0.13/0.42 ( ssItem(sk5)| ~ neq(sk4,nil) ) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f202,negated_conjecture,(
% 0.13/0.42 ( ssList(sk6)| ~ neq(sk4,nil) ) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f203,negated_conjecture,(
% 0.13/0.42 ( ssList(sk7)| ~ neq(sk4,nil) ) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f204,negated_conjecture,(
% 0.13/0.42 ( app(app(sk6,cons(sk5,nil)),sk7) = sk4| ~ neq(sk4,nil) ) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f205,negated_conjecture,(
% 0.13/0.42 ( app(sk6,sk7) = sk3| ~ neq(sk4,nil) ) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f213,plain,(
% 0.13/0.42 ssList(nil)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.42 fof(f292,plain,(
% 0.13/0.42 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|ssList(cons(X0,X1)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f86])).
% 0.13/0.42 fof(f306,plain,(
% 0.13/0.42 ![V]: ((![U]: (~cons(U,V)=V|~ssItem(U)))|~ssList(V))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f99])).
% 0.13/0.42 fof(f307,plain,(
% 0.13/0.42 ![X0,X1]: (~cons(X0,X1)=X1|~ssItem(X0)|~ssList(X1))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f306])).
% 0.13/0.42 fof(f308,plain,(
% 0.13/0.42 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X1,X0)|X1=X0)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f100])).
% 0.13/0.42 fof(f440,plain,(
% 0.13/0.42 sk2=sk4),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f190])).
% 0.13/0.42 fof(f441,plain,(
% 0.13/0.42 sk1=sk3),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f191])).
% 0.13/0.42 fof(f442,plain,(
% 0.13/0.42 neq(sk2,nil)|neq(sk2,nil)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f192])).
% 0.13/0.42 fof(f451,plain,(
% 0.13/0.42 (![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)),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f200])).
% 0.13/0.42 fof(f452,plain,(
% 0.13/0.42 ![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))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f451])).
% 0.13/0.42 fof(f453,plain,(
% 0.13/0.42 ssItem(sk5)|~neq(sk4,nil)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f201])).
% 0.13/0.42 fof(f454,plain,(
% 0.13/0.42 ssList(sk6)|~neq(sk4,nil)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f202])).
% 0.13/0.42 fof(f455,plain,(
% 0.13/0.42 ssList(sk7)|~neq(sk4,nil)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f203])).
% 0.13/0.42 fof(f456,plain,(
% 0.13/0.42 app(app(sk6,cons(sk5,nil)),sk7)=sk4|~neq(sk4,nil)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f204])).
% 0.13/0.42 fof(f457,plain,(
% 0.13/0.42 app(sk6,sk7)=sk3|~neq(sk4,nil)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f205])).
% 0.13/0.42 fof(f465,definition,(
% 0.13/0.42 sQ2_spl <=> (neq(sk2,nil))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f466,plain,(
% 0.13/0.42 neq(sk2,nil)|~sQ2_spl),
% 0.13/0.42 inference(component_clause,[status(thm)],[f465])).
% 0.13/0.42 fof(f468,plain,(
% 0.13/0.42 sQ2_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f442,f465])).
% 0.13/0.42 fof(f469,definition,(
% 0.13/0.42 sQ3_spl <=> (neq(sk4,nil))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f471,plain,(
% 0.13/0.42 ~neq(sk4,nil)|sQ3_spl),
% 0.13/0.42 inference(component_clause,[status(thm)],[f469])).
% 0.13/0.42 fof(f473,definition,(
% 0.13/0.42 ![X0,X1,X2]: (sQ4_spl <=> (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sk2|~app(X0,X2)=sk1|~neq(X1,nil)))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f474,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sk2|~app(X0,X2)=sk1|~neq(X1,nil)|~sQ4_spl)),
% 0.13/0.42 inference(component_clause,[status(thm)],[f473])).
% 0.13/0.42 fof(f477,definition,(
% 0.13/0.42 sQ5_spl <=> (ssItem(sk5))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f478,plain,(
% 0.13/0.42 ssItem(sk5)|~sQ5_spl),
% 0.13/0.42 inference(component_clause,[status(thm)],[f477])).
% 0.13/0.42 fof(f481,definition,(
% 0.13/0.42 sQ6_spl <=> (ssList(sk6))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f485,definition,(
% 0.13/0.42 sQ7_spl <=> (ssList(sk7))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f489,definition,(
% 0.13/0.42 sQ8_spl <=> (app(app(sk6,cons(sk5,nil)),sk7)=sk4)),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f490,plain,(
% 0.13/0.42 app(app(sk6,cons(sk5,nil)),sk7)=sk4|~sQ8_spl),
% 0.13/0.42 inference(component_clause,[status(thm)],[f489])).
% 0.13/0.42 fof(f493,definition,(
% 0.13/0.42 sQ9_spl <=> (app(sk6,sk7)=sk3)),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f494,plain,(
% 0.13/0.42 app(sk6,sk7)=sk3|~sQ9_spl),
% 0.13/0.42 inference(component_clause,[status(thm)],[f493])).
% 0.13/0.42 fof(f497,plain,(
% 0.13/0.42 sQ4_spl|~sQ3_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f452,f473,f469])).
% 0.13/0.42 fof(f498,plain,(
% 0.13/0.42 sQ5_spl|~sQ3_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f453,f477,f469])).
% 0.13/0.42 fof(f499,plain,(
% 0.13/0.42 sQ6_spl|~sQ3_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f454,f481,f469])).
% 0.13/0.42 fof(f500,plain,(
% 0.13/0.42 sQ7_spl|~sQ3_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f455,f485,f469])).
% 0.13/0.42 fof(f501,plain,(
% 0.13/0.42 sQ8_spl|~sQ3_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f456,f489,f469])).
% 0.13/0.42 fof(f502,plain,(
% 0.13/0.42 sQ9_spl|~sQ3_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f457,f493,f469])).
% 0.13/0.42 fof(f534,plain,(
% 0.13/0.42 neq(sk4,nil)|~sQ2_spl),
% 0.13/0.42 inference(forward_demodulation,[status(thm)],[f440,f466])).
% 0.13/0.42 fof(f535,plain,(
% 0.13/0.42 $false|~sQ2_spl|sQ3_spl),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f471,f534])).
% 0.13/0.42 fof(f536,plain,(
% 0.13/0.42 ~sQ2_spl|sQ3_spl),
% 0.13/0.42 inference(contradiction_clause,[status(thm)],[f535])).
% 0.13/0.42 fof(f537,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sk4|~app(X0,X2)=sk1|~neq(X1,nil)|~sQ4_spl)),
% 0.13/0.42 inference(forward_demodulation,[status(thm)],[f440,f474])).
% 0.13/0.42 fof(f538,plain,(
% 0.13/0.42 app(sk6,sk7)=sk1|~sQ9_spl),
% 0.13/0.42 inference(forward_demodulation,[status(thm)],[f441,f494])).
% 0.13/0.42 fof(f565,definition,(
% 0.13/0.42 sQ12_spl <=> (ssList(nil))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f567,plain,(
% 0.13/0.42 ~ssList(nil)|sQ12_spl),
% 0.13/0.42 inference(component_clause,[status(thm)],[f565])).
% 0.13/0.42 fof(f622,plain,(
% 0.13/0.42 $false|sQ12_spl),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f567,f213])).
% 0.13/0.42 fof(f623,plain,(
% 0.13/0.42 sQ12_spl),
% 0.13/0.42 inference(contradiction_clause,[status(thm)],[f622])).
% 0.13/0.42 fof(f637,plain,(
% 0.13/0.42 ![X0]: (~cons(sk5,X0)=X0|~ssList(X0)|~sQ5_spl)),
% 0.13/0.42 inference(resolution,[status(thm)],[f307,f478])).
% 0.13/0.42 fof(f681,plain,(
% 0.13/0.42 ~cons(sk5,nil)=nil|~sQ5_spl),
% 0.13/0.42 inference(resolution,[status(thm)],[f637,f213])).
% 0.13/0.42 fof(f711,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~ssList(nil)|~ssList(X0)|X0=nil|~ssList(X1)|~ssList(X0)|~ssList(X2)|~app(app(X1,X0),X2)=sk4|~app(X1,X2)=sk1|~sQ4_spl)),
% 0.13/0.42 inference(resolution,[status(thm)],[f308,f537])).
% 0.13/0.42 fof(f714,definition,(
% 0.13/0.42 ![X0,X1,X2]: (sQ18_spl <=> (~ssList(X0)|X0=nil|~ssList(X1)|~ssList(X0)|~ssList(X2)|~app(app(X1,X0),X2)=sk4|~app(X1,X2)=sk1))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f715,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~ssList(X0)|X0=nil|~ssList(X1)|~ssList(X0)|~ssList(X2)|~app(app(X1,X0),X2)=sk4|~app(X1,X2)=sk1|~sQ18_spl)),
% 0.13/0.42 inference(component_clause,[status(thm)],[f714])).
% 0.13/0.43 fof(f717,plain,(
% 0.13/0.43 ~sQ12_spl|sQ18_spl|~sQ4_spl),
% 0.13/0.43 inference(split_clause,[status(thm)],[f711,f565,f714,f473])).
% 0.13/0.43 fof(f718,plain,(
% 0.13/0.43 ![X0,X1,X2]: (~ssList(X0)|X0=nil|~ssList(X1)|~ssList(X2)|~app(app(X1,X0),X2)=sk4|~app(X1,X2)=sk1|~sQ18_spl)),
% 0.13/0.43 inference(duplicate_literals_removal,[status(thm)],[f715])).
% 0.13/0.43 fof(f792,definition,(
% 0.13/0.43 sQ21_spl <=> (ssList(cons(sk5,nil)))),
% 0.13/0.43 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.13/0.43 fof(f794,plain,(
% 0.13/0.43 ~ssList(cons(sk5,nil))|sQ21_spl),
% 0.13/0.43 inference(component_clause,[status(thm)],[f792])).
% 0.13/0.43 fof(f796,plain,(
% 0.13/0.43 ~ssItem(sk5)|~ssList(nil)|sQ21_spl),
% 0.13/0.43 inference(resolution,[status(thm)],[f794,f292])).
% 0.13/0.43 fof(f797,plain,(
% 0.13/0.43 ~sQ5_spl|~sQ12_spl|sQ21_spl),
% 0.13/0.43 inference(split_clause,[status(thm)],[f796,f477,f565,f792])).
% 0.13/0.43 fof(f977,definition,(
% 0.13/0.43 sQ33_spl <=> (nil=cons(sk5,nil))),
% 0.13/0.43 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.13/0.43 fof(f978,plain,(
% 0.13/0.43 nil=cons(sk5,nil)|~sQ33_spl),
% 0.13/0.43 inference(component_clause,[status(thm)],[f977])).
% 0.13/0.43 fof(f981,plain,(
% 0.13/0.43 ~ssList(cons(sk5,nil))|cons(sk5,nil)=nil|~ssList(sk6)|~ssList(sk7)|~app(sk6,sk7)=sk1|~sQ18_spl|~sQ8_spl),
% 0.13/0.43 inference(resolution,[status(thm)],[f718,f490])).
% 0.13/0.43 fof(f997,definition,(
% 0.13/0.43 sQ34_spl <=> (app(sk6,sk7)=sk1)),
% 0.13/0.43 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.13/0.43 fof(f999,plain,(
% 0.13/0.43 ~app(sk6,sk7)=sk1|sQ34_spl),
% 0.13/0.43 inference(component_clause,[status(thm)],[f997])).
% 0.13/0.43 fof(f1000,plain,(
% 0.13/0.43 ~sQ21_spl|sQ33_spl|~sQ6_spl|~sQ7_spl|~sQ34_spl|~sQ18_spl|~sQ8_spl),
% 0.13/0.43 inference(split_clause,[status(thm)],[f981,f792,f977,f481,f485,f997,f714,f489])).
% 0.13/0.43 fof(f1058,plain,(
% 0.13/0.43 $false|~sQ5_spl|~sQ33_spl),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f978,f681])).
% 0.13/0.43 fof(f1059,plain,(
% 0.13/0.43 ~sQ5_spl|~sQ33_spl),
% 0.13/0.43 inference(contradiction_clause,[status(thm)],[f1058])).
% 0.13/0.43 fof(f1062,plain,(
% 0.13/0.43 ~sk1=sk1|~sQ9_spl|sQ34_spl),
% 0.13/0.43 inference(forward_demodulation,[status(thm)],[f538,f999])).
% 0.13/0.43 fof(f1063,plain,(
% 0.13/0.43 $false|~sQ9_spl|sQ34_spl),
% 0.13/0.43 inference(trivial_equality_resolution,[status(thm)],[f1062])).
% 0.13/0.43 fof(f1064,plain,(
% 0.13/0.43 ~sQ9_spl|sQ34_spl),
% 0.13/0.43 inference(contradiction_clause,[status(thm)],[f1063])).
% 0.13/0.43 fof(f1065,plain,(
% 0.13/0.43 $false),
% 0.13/0.43 inference(sat_refutation,[status(thm)],[f468,f497,f498,f499,f500,f501,f502,f536,f623,f717,f797,f1000,f1059,f1064])).
% 0.13/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.45 % Elapsed time: 0.085968 seconds
% 0.13/0.45 % CPU time: 0.368822 seconds
% 0.13/0.45 % Total memory used: 107.480 MB
% 0.13/0.45 % Net memory used: 107.080 MB
%------------------------------------------------------------------------------