%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC417-1 : 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 : n002.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 02:42:25 PM UTC 2026
% Result : Unsatisfiable 20.43s 13.03s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC417-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.39 % Computer : n002.cluster.edu
% 0.09/10.39 % Model : x86_64 x86_64
% 0.09/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.39 % Memory : 8046.5625MB
% 0.09/10.39 % OS : Linux 6.8.0-71-generic
% 0.09/10.39 % CPULimit : 300
% 0.09/10.39 % WCLimit : 300
% 0.09/10.39 % DateTime : Mon Sep 21 08:25:43 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.15/10.41 % Drodi V4.1.1
% 20.43/13.03 % Refutation found
% 20.43/13.03 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 20.43/13.03 % SZS output start CNFRefutation for theBenchmark
% 20.43/13.03 fof(f8,axiom,(
% 20.43/13.03 ssList(nil) ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f73,axiom,(
% 20.43/13.03 (![U]: (( ~ ssList(U)| app(U,nil) = U ) ))),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f74,axiom,(
% 20.43/13.03 (![U]: (( ~ ssList(U)| app(nil,U) = U ) ))),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f86,axiom,(
% 20.43/13.03 (![U,V]: (( ~ ssItem(U)| ~ ssList(V)| ssList(cons(U,V)) ) ))),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f186,negated_conjecture,(
% 20.43/13.03 ssList(sk1) ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f190,negated_conjecture,(
% 20.43/13.03 sk2 = sk4 ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f191,negated_conjecture,(
% 20.43/13.03 sk1 = sk3 ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f192,negated_conjecture,(
% 20.43/13.03 ( neq(sk2,nil)| neq(sk2,nil) ) ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f199,negated_conjecture,(
% 20.43/13.03 (![A,B,C]: (( ~ ssItem(A)| ~ ssList(B)| ~ ssList(C)| app(app(B,cons(A,nil)),C) != sk2| app(app(C,cons(A,nil)),B) != sk1| ~ neq(sk4,nil) ) ))),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f200,negated_conjecture,(
% 20.43/13.03 ( ssItem(sk5)| ~ neq(sk4,nil) ) ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f201,negated_conjecture,(
% 20.43/13.03 ( ssList(sk6)| ~ neq(sk4,nil) ) ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f202,negated_conjecture,(
% 20.43/13.03 ( app(cons(sk5,nil),sk6) = sk4| ~ neq(sk4,nil) ) ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f203,negated_conjecture,(
% 20.43/13.03 ( app(sk6,cons(sk5,nil)) = sk3| ~ neq(sk4,nil) ) ),
% 20.43/13.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.43/13.03 fof(f211,plain,(
% 20.43/13.03 ssList(nil)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f8])).
% 20.43/13.03 fof(f277,plain,(
% 20.43/13.03 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f73])).
% 20.43/13.03 fof(f278,plain,(
% 20.43/13.03 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f74])).
% 20.43/13.03 fof(f290,plain,(
% 20.43/13.03 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|ssList(cons(X0,X1)))),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f86])).
% 20.43/13.03 fof(f434,plain,(
% 20.43/13.03 ssList(sk1)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f186])).
% 20.43/13.03 fof(f438,plain,(
% 20.43/13.03 sk2=sk4),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f190])).
% 20.43/13.03 fof(f439,plain,(
% 20.43/13.03 sk1=sk3),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f191])).
% 20.43/13.03 fof(f440,plain,(
% 20.43/13.03 neq(sk2,nil)|neq(sk2,nil)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f192])).
% 20.43/13.03 fof(f448,plain,(
% 20.43/13.03 (![A,B,C]: ((((~ssItem(A)|~ssList(B))|~ssList(C))|~app(app(B,cons(A,nil)),C)=sk2)|~app(app(C,cons(A,nil)),B)=sk1))|~neq(sk4,nil)),
% 20.43/13.03 inference(miniscoping,[status(thm)],[f199])).
% 20.43/13.03 fof(f449,plain,(
% 20.43/13.03 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk2|~app(app(X2,cons(X0,nil)),X1)=sk1|~neq(sk4,nil))),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f448])).
% 20.43/13.03 fof(f450,plain,(
% 20.43/13.03 ssItem(sk5)|~neq(sk4,nil)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f200])).
% 20.43/13.03 fof(f451,plain,(
% 20.43/13.03 ssList(sk6)|~neq(sk4,nil)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f201])).
% 20.43/13.03 fof(f452,plain,(
% 20.43/13.03 app(cons(sk5,nil),sk6)=sk4|~neq(sk4,nil)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f202])).
% 20.43/13.03 fof(f453,plain,(
% 20.43/13.03 app(sk6,cons(sk5,nil))=sk3|~neq(sk4,nil)),
% 20.43/13.03 inference(cnf_transformation,[status(thm)],[f203])).
% 20.43/13.03 fof(f461,definition,(
% 20.43/13.03 sQ2_spl <=> (neq(sk2,nil))),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f462,plain,(
% 20.43/13.03 neq(sk2,nil)|~sQ2_spl),
% 20.43/13.03 inference(component_clause,[status(thm)],[f461])).
% 20.43/13.03 fof(f464,plain,(
% 20.43/13.03 sQ2_spl),
% 20.43/13.03 inference(split_clause,[status(thm)],[f440,f461])).
% 20.43/13.03 fof(f465,definition,(
% 20.43/13.03 sQ3_spl <=> (neq(sk4,nil))),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f467,plain,(
% 20.43/13.03 ~neq(sk4,nil)|sQ3_spl),
% 20.43/13.03 inference(component_clause,[status(thm)],[f465])).
% 20.43/13.03 fof(f469,definition,(
% 20.43/13.03 ![X0,X1,X2]: (sQ4_spl <=> (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk2|~app(app(X2,cons(X0,nil)),X1)=sk1))),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f470,plain,(
% 20.43/13.03 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sk2|~app(app(X2,cons(X0,nil)),X1)=sk1|~sQ4_spl)),
% 20.43/13.03 inference(component_clause,[status(thm)],[f469])).
% 20.43/13.03 fof(f473,definition,(
% 20.43/13.03 sQ5_spl <=> (ssItem(sk5))),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f474,plain,(
% 20.43/13.03 ssItem(sk5)|~sQ5_spl),
% 20.43/13.03 inference(component_clause,[status(thm)],[f473])).
% 20.43/13.03 fof(f477,definition,(
% 20.43/13.03 sQ6_spl <=> (ssList(sk6))),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f481,definition,(
% 20.43/13.03 sQ7_spl <=> (app(cons(sk5,nil),sk6)=sk4)),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f482,plain,(
% 20.43/13.03 app(cons(sk5,nil),sk6)=sk4|~sQ7_spl),
% 20.43/13.03 inference(component_clause,[status(thm)],[f481])).
% 20.43/13.03 fof(f485,definition,(
% 20.43/13.03 sQ8_spl <=> (app(sk6,cons(sk5,nil))=sk3)),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f486,plain,(
% 20.43/13.03 app(sk6,cons(sk5,nil))=sk3|~sQ8_spl),
% 20.43/13.03 inference(component_clause,[status(thm)],[f485])).
% 20.43/13.03 fof(f489,plain,(
% 20.43/13.03 sQ4_spl|~sQ3_spl),
% 20.43/13.03 inference(split_clause,[status(thm)],[f449,f469,f465])).
% 20.43/13.03 fof(f490,plain,(
% 20.43/13.03 sQ5_spl|~sQ3_spl),
% 20.43/13.03 inference(split_clause,[status(thm)],[f450,f473,f465])).
% 20.43/13.03 fof(f491,plain,(
% 20.43/13.03 sQ6_spl|~sQ3_spl),
% 20.43/13.03 inference(split_clause,[status(thm)],[f451,f477,f465])).
% 20.43/13.03 fof(f492,plain,(
% 20.43/13.03 sQ7_spl|~sQ3_spl),
% 20.43/13.03 inference(split_clause,[status(thm)],[f452,f481,f465])).
% 20.43/13.03 fof(f493,plain,(
% 20.43/13.03 sQ8_spl|~sQ3_spl),
% 20.43/13.03 inference(split_clause,[status(thm)],[f453,f485,f465])).
% 20.43/13.03 fof(f526,plain,(
% 20.43/13.03 app(sk1,nil)=sk1),
% 20.43/13.03 inference(resolution,[status(thm)],[f277,f434])).
% 20.43/13.03 fof(f574,plain,(
% 20.43/13.03 ~neq(sk2,nil)|sQ3_spl),
% 20.43/13.03 inference(forward_demodulation,[status(thm)],[f438,f467])).
% 20.43/13.03 fof(f575,plain,(
% 20.43/13.03 $false|~sQ2_spl|sQ3_spl),
% 20.43/13.03 inference(forward_subsumption_resolution,[status(thm)],[f574,f462])).
% 20.43/13.03 fof(f576,plain,(
% 20.43/13.03 ~sQ2_spl|sQ3_spl),
% 20.43/13.03 inference(contradiction_clause,[status(thm)],[f575])).
% 20.43/13.03 fof(f577,plain,(
% 20.43/13.03 app(cons(sk5,nil),sk6)=sk2|~sQ7_spl),
% 20.43/13.03 inference(forward_demodulation,[status(thm)],[f438,f482])).
% 20.43/13.03 fof(f578,plain,(
% 20.43/13.03 app(sk6,cons(sk5,nil))=sk1|~sQ8_spl),
% 20.43/13.03 inference(forward_demodulation,[status(thm)],[f439,f486])).
% 20.43/13.03 fof(f585,plain,(
% 20.43/13.03 ![X0]: (~ssItem(sk5)|~ssList(X0)|~ssList(sk6)|~app(app(X0,cons(sk5,nil)),sk6)=sk2|~app(sk1,X0)=sk1|~sQ4_spl|~sQ8_spl)),
% 20.43/13.03 inference(paramodulation,[status(thm)],[f578,f470])).
% 20.43/13.03 fof(f586,definition,(
% 20.43/13.03 ![X0]: (sQ9_spl <=> (~ssList(X0)|~app(app(X0,cons(sk5,nil)),sk6)=sk2|~app(sk1,X0)=sk1))),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f587,plain,(
% 20.43/13.03 ![X0]: (~ssList(X0)|~app(app(X0,cons(sk5,nil)),sk6)=sk2|~app(sk1,X0)=sk1|~sQ9_spl)),
% 20.43/13.03 inference(component_clause,[status(thm)],[f586])).
% 20.43/13.03 fof(f589,plain,(
% 20.43/13.03 ~sQ5_spl|sQ9_spl|~sQ6_spl|~sQ4_spl|~sQ8_spl),
% 20.43/13.03 inference(split_clause,[status(thm)],[f585,f473,f586,f477,f469,f485])).
% 20.43/13.03 fof(f601,definition,(
% 20.43/13.03 sQ10_spl <=> (ssList(nil))),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f603,plain,(
% 20.43/13.03 ~ssList(nil)|sQ10_spl),
% 20.43/13.03 inference(component_clause,[status(thm)],[f601])).
% 20.43/13.03 fof(f611,definition,(
% 20.43/13.03 sQ13_spl <=> (ssList(cons(sk5,nil)))),
% 20.43/13.03 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 20.43/13.03 fof(f612,plain,(
% 20.43/13.03 ssList(cons(sk5,nil))|~sQ13_spl),
% 20.43/13.03 inference(component_clause,[status(thm)],[f611])).
% 20.43/13.03 fof(f613,plain,(
% 20.43/13.03 ~ssList(cons(sk5,nil))|sQ13_spl),
% 20.43/13.03 inference(component_clause,[status(thm)],[f611])).
% 20.43/13.03 fof(f636,plain,(
% 20.43/13.03 $false|sQ10_spl),
% 20.43/13.03 inference(forward_subsumption_resolution,[status(thm)],[f603,f211])).
% 20.43/13.03 fof(f637,plain,(
% 20.43/13.03 sQ10_spl),
% 20.43/13.03 inference(contradiction_clause,[status(thm)],[f636])).
% 20.43/13.03 fof(f772,plain,(
% 20.43/13.03 ![X0]: (~ssList(X0)|ssList(cons(sk5,X0))|~sQ5_spl)),
% 20.43/13.03 inference(resolution,[status(thm)],[f474,f290])).
% 20.43/13.03 fof(f5116,plain,(
% 20.43/13.03 ssList(cons(sk5,nil))|~sQ5_spl),
% 20.43/13.06 inference(resolution,[status(thm)],[f772,f211])).
% 20.43/13.06 fof(f5120,plain,(
% 20.43/13.06 $false|sQ13_spl|~sQ5_spl),
% 20.43/13.06 inference(forward_subsumption_resolution,[status(thm)],[f5116,f613])).
% 20.43/13.06 fof(f5121,plain,(
% 20.43/13.06 sQ13_spl|~sQ5_spl),
% 20.43/13.06 inference(contradiction_clause,[status(thm)],[f5120])).
% 20.43/13.06 fof(f11301,plain,(
% 20.43/13.06 app(nil,cons(sk5,nil))=cons(sk5,nil)|~sQ13_spl),
% 20.43/13.06 inference(resolution,[status(thm)],[f612,f278])).
% 20.43/13.06 fof(f13377,plain,(
% 20.43/13.06 ~ssList(nil)|~app(cons(sk5,nil),sk6)=sk2|~app(sk1,nil)=sk1|~sQ9_spl|~sQ13_spl),
% 20.43/13.06 inference(paramodulation,[status(thm)],[f11301,f587])).
% 20.43/13.06 fof(f13386,definition,(
% 20.43/13.06 sQ890_spl <=> (app(cons(sk5,nil),sk6)=sk2)),
% 20.43/13.06 introduced(definition,[new_symbols(definition,[sQ890_spl])],[split_symbol_definition])).
% 20.43/13.06 fof(f13388,plain,(
% 20.43/13.06 ~app(cons(sk5,nil),sk6)=sk2|sQ890_spl),
% 20.43/13.06 inference(component_clause,[status(thm)],[f13386])).
% 20.43/13.06 fof(f13389,definition,(
% 20.43/13.06 sQ891_spl <=> (app(sk1,nil)=sk1)),
% 20.43/13.06 introduced(definition,[new_symbols(definition,[sQ891_spl])],[split_symbol_definition])).
% 20.43/13.06 fof(f13391,plain,(
% 20.43/13.06 ~app(sk1,nil)=sk1|sQ891_spl),
% 20.43/13.06 inference(component_clause,[status(thm)],[f13389])).
% 20.43/13.06 fof(f13392,plain,(
% 20.43/13.06 ~sQ10_spl|~sQ890_spl|~sQ891_spl|~sQ9_spl|~sQ13_spl),
% 20.43/13.06 inference(split_clause,[status(thm)],[f13377,f601,f13386,f13389,f586,f611])).
% 20.43/13.06 fof(f13411,plain,(
% 20.43/13.06 ~sk2=sk2|~sQ7_spl|sQ890_spl),
% 20.43/13.06 inference(forward_demodulation,[status(thm)],[f577,f13388])).
% 20.43/13.06 fof(f13412,plain,(
% 20.43/13.06 $false|~sQ7_spl|sQ890_spl),
% 20.43/13.06 inference(trivial_equality_resolution,[status(thm)],[f13411])).
% 20.43/13.06 fof(f13413,plain,(
% 20.43/13.06 ~sQ7_spl|sQ890_spl),
% 20.43/13.06 inference(contradiction_clause,[status(thm)],[f13412])).
% 20.43/13.06 fof(f13414,plain,(
% 20.43/13.06 ~sk1=sk1|sQ891_spl),
% 20.43/13.06 inference(forward_demodulation,[status(thm)],[f526,f13391])).
% 20.43/13.06 fof(f13415,plain,(
% 20.43/13.06 $false|sQ891_spl),
% 20.43/13.06 inference(trivial_equality_resolution,[status(thm)],[f13414])).
% 20.43/13.06 fof(f13416,plain,(
% 20.43/13.06 sQ891_spl),
% 20.43/13.06 inference(contradiction_clause,[status(thm)],[f13415])).
% 20.43/13.06 fof(f13417,plain,(
% 20.43/13.06 $false),
% 20.43/13.06 inference(sat_refutation,[status(thm)],[f464,f489,f490,f491,f492,f493,f576,f589,f637,f5121,f13392,f13413,f13416])).
% 20.43/13.06 % SZS output end CNFRefutation for theBenchmark.p
% 20.43/13.08 % Elapsed time: 2.673250 seconds
% 20.43/13.08 % CPU time: 20.914998 seconds
% 20.43/13.08 % Total memory used: 391.216 MB
% 20.43/13.08 % Net memory used: 373.809 MB
%------------------------------------------------------------------------------