%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC012-1 : 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 : n015.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 02:41:20 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC012-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n015.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 07:52:11 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.39 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/5.41 fof(f8,axiom,(
% 0.14/5.41 ssList(nil) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f73,axiom,(
% 0.14/5.41 (![U]: (( ~ ssList(U)| app(U,nil) = U ) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f188,negated_conjecture,(
% 0.14/5.41 ssList(sk3) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f189,negated_conjecture,(
% 0.14/5.41 ssList(sk4) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f190,negated_conjecture,(
% 0.14/5.41 sk2 = sk4 ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f191,negated_conjecture,(
% 0.14/5.41 sk1 = sk3 ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f192,negated_conjecture,(
% 0.14/5.41 ( neq(sk2,nil)| neq(sk2,nil) ) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f197,negated_conjecture,(
% 0.14/5.41 (![A,B,C]: (( ~ ssItem(A)| ~ ssList(B)| ~ ssList(C)| app(app(B,cons(A,nil)),C) != sk2| app(B,C) != sk1| ~ neq(sk4,nil) ) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f198,negated_conjecture,(
% 0.14/5.41 ( ssItem(sk5)| ~ neq(sk4,nil) ) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f199,negated_conjecture,(
% 0.14/5.41 ( app(sk3,cons(sk5,nil)) = sk4| ~ neq(sk4,nil) ) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f207,plain,(
% 0.14/5.41 ssList(nil)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/5.41 fof(f273,plain,(
% 0.14/5.41 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f73])).
% 0.14/5.41 fof(f432,plain,(
% 0.14/5.41 ssList(sk3)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f188])).
% 0.14/5.41 fof(f433,plain,(
% 0.14/5.41 ssList(sk4)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f189])).
% 0.14/5.41 fof(f434,plain,(
% 0.14/5.41 sk2=sk4),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f190])).
% 0.14/5.41 fof(f435,plain,(
% 0.14/5.41 sk1=sk3),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f191])).
% 0.14/5.41 fof(f436,plain,(
% 0.14/5.41 neq(sk2,nil)|neq(sk2,nil)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f192])).
% 0.14/5.41 fof(f442,plain,(
% 0.14/5.41 (![B,C]: ((![A]: (((~ssItem(A)|~ssList(B))|~ssList(C))|~app(app(B,cons(A,nil)),C)=sk2))|~app(B,C)=sk1))|~neq(sk4,nil)),
% 0.14/5.41 inference(miniscoping,[status(thm)],[f197])).
% 0.14/5.41 fof(f443,plain,(
% 0.14/5.41 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk2|~app(X1,X2)=sk1|~neq(sk4,nil))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f442])).
% 0.14/5.41 fof(f444,plain,(
% 0.14/5.41 ssItem(sk5)|~neq(sk4,nil)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f198])).
% 0.14/5.41 fof(f445,plain,(
% 0.14/5.41 app(sk3,cons(sk5,nil))=sk4|~neq(sk4,nil)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f199])).
% 0.14/5.41 fof(f453,definition,(
% 0.14/5.41 sQ2_spl <=> (neq(sk2,nil))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f454,plain,(
% 0.14/5.41 neq(sk2,nil)|~sQ2_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f453])).
% 0.14/5.41 fof(f456,plain,(
% 0.14/5.41 sQ2_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f436,f453])).
% 0.14/5.41 fof(f457,definition,(
% 0.14/5.41 sQ3_spl <=> (neq(sk4,nil))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f459,plain,(
% 0.14/5.41 ~neq(sk4,nil)|sQ3_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f457])).
% 0.14/5.41 fof(f461,definition,(
% 0.14/5.41 ![X0,X1,X2]: (sQ4_spl <=> (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk2|~app(X1,X2)=sk1))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f462,plain,(
% 0.14/5.41 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk2|~app(X1,X2)=sk1|~sQ4_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f461])).
% 0.14/5.41 fof(f465,definition,(
% 0.14/5.41 sQ5_spl <=> (ssItem(sk5))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f469,definition,(
% 0.14/5.41 sQ6_spl <=> (app(sk3,cons(sk5,nil))=sk4)),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f470,plain,(
% 0.14/5.41 app(sk3,cons(sk5,nil))=sk4|~sQ6_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f469])).
% 0.14/5.41 fof(f473,plain,(
% 0.14/5.41 sQ4_spl|~sQ3_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f443,f461,f457])).
% 0.14/5.41 fof(f474,plain,(
% 0.14/5.41 sQ5_spl|~sQ3_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f444,f465,f457])).
% 0.14/5.41 fof(f475,plain,(
% 0.14/5.41 sQ6_spl|~sQ3_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f445,f469,f457])).
% 0.14/5.41 fof(f507,plain,(
% 0.14/5.41 neq(sk4,nil)|~sQ2_spl),
% 0.14/5.41 inference(forward_demodulation,[status(thm)],[f434,f454])).
% 0.14/5.41 fof(f508,plain,(
% 0.14/5.41 $false|~sQ2_spl|sQ3_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f459,f507])).
% 0.14/5.41 fof(f509,plain,(
% 0.14/5.41 ~sQ2_spl|sQ3_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f508])).
% 0.14/5.41 fof(f510,plain,(
% 0.14/5.41 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk4|~app(X1,X2)=sk1|~sQ4_spl)),
% 0.14/5.41 inference(forward_demodulation,[status(thm)],[f434,f462])).
% 0.14/5.41 fof(f511,plain,(
% 0.14/5.41 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk4|~app(X1,X2)=sk3|~sQ4_spl)),
% 0.14/5.41 inference(forward_demodulation,[status(thm)],[f435,f510])).
% 0.14/5.41 fof(f513,plain,(
% 0.14/5.41 app(sk4,nil)=sk4),
% 0.14/5.41 inference(resolution,[status(thm)],[f273,f433])).
% 0.14/5.41 fof(f514,plain,(
% 0.14/5.41 app(sk3,nil)=sk3),
% 0.14/5.41 inference(resolution,[status(thm)],[f273,f432])).
% 0.14/5.41 fof(f728,plain,(
% 0.14/5.41 ![X0]: (~ssItem(sk5)|~ssList(sk3)|~ssList(X0)|~app(sk4,X0)=sk4|~app(sk3,X0)=sk3|~sQ4_spl|~sQ6_spl)),
% 0.14/5.41 inference(paramodulation,[status(thm)],[f470,f511])).
% 0.14/5.41 fof(f729,definition,(
% 0.14/5.41 sQ7_spl <=> (ssList(sk3))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f731,plain,(
% 0.14/5.41 ~ssList(sk3)|sQ7_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f729])).
% 0.14/5.41 fof(f732,definition,(
% 0.14/5.41 ![X0]: (sQ8_spl <=> (~ssList(X0)|~app(sk4,X0)=sk4|~app(sk3,X0)=sk3))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f733,plain,(
% 0.14/5.41 ![X0]: (~ssList(X0)|~app(sk4,X0)=sk4|~app(sk3,X0)=sk3|~sQ8_spl)),
% 0.14/5.41 inference(component_clause,[status(thm)],[f732])).
% 0.14/5.41 fof(f735,plain,(
% 0.14/5.41 ~sQ5_spl|~sQ7_spl|sQ8_spl|~sQ4_spl|~sQ6_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f728,f465,f729,f732,f461,f469])).
% 0.14/5.41 fof(f736,plain,(
% 0.14/5.41 $false|sQ7_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f731,f432])).
% 0.14/5.41 fof(f737,plain,(
% 0.14/5.41 sQ7_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f736])).
% 0.14/5.41 fof(f1140,definition,(
% 0.14/5.41 sQ9_spl <=> (ssList(nil))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f1142,plain,(
% 0.14/5.41 ~ssList(nil)|sQ9_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f1140])).
% 0.14/5.41 fof(f1165,plain,(
% 0.14/5.41 $false|sQ9_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f1142,f207])).
% 0.14/5.41 fof(f1166,plain,(
% 0.14/5.41 sQ9_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f1165])).
% 0.14/5.41 fof(f1443,plain,(
% 0.14/5.41 ~ssList(nil)|~app(sk4,nil)=sk4|~sQ8_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f733,f514])).
% 0.14/5.41 fof(f1446,definition,(
% 0.14/5.41 sQ15_spl <=> (app(sk4,nil)=sk4)),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f1448,plain,(
% 0.14/5.41 ~app(sk4,nil)=sk4|sQ15_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f1446])).
% 0.14/5.41 fof(f1449,plain,(
% 0.14/5.41 ~sQ9_spl|~sQ15_spl|~sQ8_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f1443,f1140,f1446,f732])).
% 0.14/5.41 fof(f1463,plain,(
% 0.14/5.41 ~sk4=sk4|sQ15_spl),
% 0.14/5.41 inference(forward_demodulation,[status(thm)],[f513,f1448])).
% 0.14/5.41 fof(f1464,plain,(
% 0.14/5.41 $false|sQ15_spl),
% 0.14/5.41 inference(trivial_equality_resolution,[status(thm)],[f1463])).
% 0.14/5.41 fof(f1465,plain,(
% 0.14/5.41 sQ15_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f1464])).
% 0.14/5.41 fof(f1466,plain,(
% 0.14/5.41 $false),
% 0.14/5.41 inference(sat_refutation,[status(thm)],[f456,f473,f474,f475,f509,f735,f737,f1166,f1449,f1465])).
% 0.14/5.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.44 % Elapsed time: 0.058377 seconds
% 0.14/5.44 % CPU time: 0.166634 seconds
% 0.14/5.44 % Total memory used: 65.633 MB
% 0.14/5.44 % Net memory used: 65.506 MB
%------------------------------------------------------------------------------