%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL259-3 : TPTP v9.3.1. Released v2.3.0.
% 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 01:09:44 PM UTC 2026
% Result : Unsatisfiable 39.14s 5.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL259-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n004.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 00:16:04 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 39.14/5.53 % Refutation found
% 39.14/5.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 39.14/5.53 % SZS output start CNFRefutation for theBenchmark
% 39.14/5.53 fof(f1,axiom,(
% 39.14/5.53 (![A]: (axiom(implies(or(A,A),A)) ))),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f2,axiom,(
% 39.14/5.53 (![A,B]: (axiom(implies(A,or(B,A))) ))),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f3,axiom,(
% 39.14/5.53 (![A,B]: (axiom(implies(or(A,B),or(B,A))) ))),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f4,axiom,(
% 39.14/5.53 (![A,B,C]: (axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ))),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f5,axiom,(
% 39.14/5.53 (![A,B,C]: (axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ))),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f6,axiom,(
% 39.14/5.53 (![X,Y]: (implies(X,Y) = or(not(X),Y) ))),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f7,axiom,(
% 39.14/5.53 (![X]: (( theorem(X)| ~ axiom(X) ) ))),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f8,axiom,(
% 39.14/5.53 (![X,Y]: (( theorem(X)| ~ theorem(implies(Y,X))| ~ theorem(Y) ) ))),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f9,negated_conjecture,(
% 39.14/5.53 ~ theorem(implies(implies(p,implies(p,q)),implies(p,q))) ),
% 39.14/5.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 39.14/5.53 fof(f10,plain,(
% 39.14/5.53 ![X0]: (axiom(implies(or(X0,X0),X0)))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f1])).
% 39.14/5.53 fof(f11,plain,(
% 39.14/5.53 ![X0,X1]: (axiom(implies(X0,or(X1,X0))))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f2])).
% 39.14/5.53 fof(f12,plain,(
% 39.14/5.53 ![X0,X1]: (axiom(implies(or(X0,X1),or(X1,X0))))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f3])).
% 39.14/5.53 fof(f13,plain,(
% 39.14/5.53 ![X0,X1,X2]: (axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f4])).
% 39.14/5.53 fof(f14,plain,(
% 39.14/5.53 ![X0,X1,X2]: (axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f5])).
% 39.14/5.53 fof(f15,plain,(
% 39.14/5.53 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f6])).
% 39.14/5.53 fof(f16,plain,(
% 39.14/5.53 ![X0]: (theorem(X0)|~axiom(X0))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f7])).
% 39.14/5.53 fof(f17,plain,(
% 39.14/5.53 ![Y]: ((![X]: (theorem(X)|~theorem(implies(Y,X))))|~theorem(Y))),
% 39.14/5.53 inference(miniscoping,[status(thm)],[f8])).
% 39.14/5.53 fof(f18,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(X0)|~theorem(implies(X1,X0))|~theorem(X1))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f17])).
% 39.14/5.53 fof(f19,plain,(
% 39.14/5.53 ~theorem(implies(implies(p,implies(p,q)),implies(p,q)))),
% 39.14/5.53 inference(cnf_transformation,[status(thm)],[f9])).
% 39.14/5.53 fof(f20,plain,(
% 39.14/5.53 ![X0]: (theorem(implies(or(X0,X0),X0)))),
% 39.14/5.53 inference(resolution,[status(thm)],[f10,f16])).
% 39.14/5.53 fof(f21,plain,(
% 39.14/5.53 ![X0]: (theorem(X0)|~theorem(or(X0,X0)))),
% 39.14/5.53 inference(resolution,[status(thm)],[f20,f18])).
% 39.14/5.53 fof(f22,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(implies(X0,or(X1,X0))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f11,f16])).
% 39.14/5.53 fof(f23,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(X0,X1))|~theorem(X1))),
% 39.14/5.53 inference(resolution,[status(thm)],[f22,f18])).
% 39.14/5.53 fof(f24,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(X0,implies(or(X1,X1),X1))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f23,f20])).
% 39.14/5.53 fof(f25,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(X0,implies(X1,or(X2,X1)))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f23,f22])).
% 39.14/5.53 fof(f27,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(X0,or(X1,implies(or(X2,X2),X2)))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f24,f23])).
% 39.14/5.53 fof(f31,plain,(
% 39.14/5.53 ![X0,X1,X2,X3]: (theorem(or(X0,or(X1,or(X2,implies(or(X3,X3),X3))))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f27,f23])).
% 39.14/5.53 fof(f49,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(implies(X0,implies(X1,or(X2,X1)))))),
% 39.14/5.53 inference(paramodulation,[status(thm)],[f15,f25])).
% 39.14/5.53 fof(f56,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(implies(X0,implies(X1,X0))))),
% 39.14/5.53 inference(paramodulation,[status(thm)],[f15,f22])).
% 39.14/5.53 fof(f73,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(implies(or(X0,X1),or(X1,X0))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f12,f16])).
% 39.14/5.53 fof(f83,definition,(
% 39.14/5.53 ![X1]: (sQ1_spl <=> (~theorem(X1)))),
% 39.14/5.53 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 39.14/5.53 fof(f84,plain,(
% 39.14/5.53 ![X0]: (~theorem(X0)|~sQ1_spl)),
% 39.14/5.53 inference(component_clause,[status(thm)],[f83])).
% 39.14/5.53 fof(f87,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(implies(X0,or(X1,X0)))|~theorem(X2))),
% 39.14/5.53 inference(resolution,[status(thm)],[f49,f18])).
% 39.14/5.53 fof(f91,definition,(
% 39.14/5.53 ![X0,X1]: (sQ2_spl <=> (theorem(implies(X0,or(X1,X0)))))),
% 39.14/5.53 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 39.14/5.53 fof(f92,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(implies(X0,or(X1,X0)))|~sQ2_spl)),
% 39.14/5.53 inference(component_clause,[status(thm)],[f91])).
% 39.14/5.53 fof(f94,plain,(
% 39.14/5.53 sQ2_spl|sQ1_spl),
% 39.14/5.53 inference(split_clause,[status(thm)],[f87,f91,f83])).
% 39.14/5.53 fof(f96,plain,(
% 39.14/5.53 $false|~sQ1_spl),
% 39.14/5.53 inference(backward_subsumption_resolution,[status(thm)],[f31,f84])).
% 39.14/5.53 fof(f107,plain,(
% 39.14/5.53 ~sQ1_spl),
% 39.14/5.53 inference(contradiction_clause,[status(thm)],[f96])).
% 39.14/5.53 fof(f115,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f13,f16])).
% 39.14/5.53 fof(f124,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f14,f16])).
% 39.14/5.53 fof(f138,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(X0,X1))|~theorem(or(X1,X0)))),
% 39.14/5.53 inference(resolution,[status(thm)],[f73,f18])).
% 39.14/5.53 fof(f142,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 39.14/5.53 inference(paramodulation,[status(thm)],[f15,f73])).
% 39.14/5.53 fof(f147,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(X0,or(X1,X2)))|~theorem(or(X1,or(X0,X2))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f115,f18])).
% 39.14/5.53 fof(f193,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(X0,not(X1)))|~theorem(implies(X1,X0)))),
% 39.14/5.53 inference(paramodulation,[status(thm)],[f15,f138])).
% 39.14/5.53 fof(f194,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(implies(or(X0,X1),or(X0,X2)))|~theorem(implies(X1,X2)))),
% 39.14/5.53 inference(resolution,[status(thm)],[f124,f18])).
% 39.14/5.53 fof(f222,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(implies(X0,X1))|~theorem(or(X1,not(X0))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f142,f18])).
% 39.14/5.53 fof(f237,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(or(X0,X1),not(X1)))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f193,f92])).
% 39.14/5.53 fof(f252,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(X0,or(or(X1,X2),not(X2))))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f237,f23])).
% 39.14/5.53 fof(f335,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(X0,or(not(X1),X2)))|~theorem(implies(X1,or(X0,X2))))),
% 39.14/5.53 inference(paramodulation,[status(thm)],[f15,f147])).
% 39.14/5.53 fof(f337,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(X0,implies(X1,X2)))|~theorem(implies(X1,or(X0,X2))))),
% 39.14/5.53 inference(forward_demodulation,[status(thm)],[f15,f335])).
% 39.14/5.53 fof(f355,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(or(X0,X1),or(X2,not(X1))))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f252,f147])).
% 39.14/5.53 fof(f426,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(or(X0,not(X1)),or(X2,X1)))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f355,f138])).
% 39.14/5.53 fof(f466,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(or(X0,or(or(X1,not(X2)),X2)))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f426,f147])).
% 39.14/5.53 fof(f493,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(or(X0,not(X1)),X1))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f466,f21])).
% 39.14/5.53 fof(f501,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(X0,or(X1,not(X0))))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f493,f138])).
% 39.14/5.53 fof(f506,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(X0,or(X1,not(X1))))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f501,f147])).
% 39.14/5.53 fof(f521,plain,(
% 39.14/5.53 ![X0]: (theorem(or(X0,not(X0)))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f506,f21])).
% 39.14/5.53 fof(f527,plain,(
% 39.14/5.53 ![X0]: (theorem(implies(X0,X0))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f521,f222])).
% 39.14/5.53 fof(f550,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(implies(or(X0,or(X1,not(X2))),or(X0,implies(X2,X1)))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f194,f142])).
% 39.14/5.53 fof(f553,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(implies(or(X0,or(X1,X1)),or(X0,X1))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f194,f20])).
% 39.14/5.53 fof(f558,plain,(
% 39.14/5.53 ![X0,X1,X2]: (theorem(implies(or(X0,X1),or(X0,implies(X2,X1)))))),
% 39.14/5.53 inference(resolution,[status(thm)],[f194,f56])).
% 39.14/5.53 fof(f1842,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(X0,implies(or(X0,X1),X1)))|~sQ2_spl)),
% 39.14/5.53 inference(resolution,[status(thm)],[f337,f527])).
% 39.14/5.53 fof(f1854,plain,(
% 39.14/5.53 ![X0,X1]: (theorem(or(implies(or(X0,X1),X1),X0))|~sQ2_spl)),
% 29.35/5.59 inference(resolution,[status(thm)],[f1842,f138])).
% 29.35/5.59 fof(f1883,plain,(
% 29.35/5.59 ![X0,X1,X2]: (theorem(or(X0,or(implies(or(X1,X2),X2),X1)))|~sQ2_spl)),
% 29.35/5.59 inference(resolution,[status(thm)],[f1854,f23])).
% 29.35/5.59 fof(f3131,plain,(
% 29.35/5.59 ![X0,X1,X2]: (theorem(or(X0,implies(X1,X2)))|~theorem(or(X0,or(X2,not(X1)))))),
% 29.35/5.59 inference(resolution,[status(thm)],[f550,f18])).
% 29.35/5.59 fof(f3199,plain,(
% 29.35/5.59 ![X0,X1]: (theorem(or(X0,X1))|~theorem(or(X0,or(X1,X1))))),
% 29.35/5.59 inference(resolution,[status(thm)],[f553,f18])).
% 29.35/5.59 fof(f5588,plain,(
% 29.35/5.59 ![X0,X1,X2]: (theorem(or(implies(or(X0,X1),X1),or(X2,X0)))|~sQ2_spl)),
% 29.35/5.59 inference(resolution,[status(thm)],[f1883,f147])).
% 29.35/5.59 fof(f6292,plain,(
% 29.35/5.59 ![X0,X1]: (theorem(or(not(X0),X1))|~theorem(implies(X0,or(X1,X1))))),
% 29.35/5.59 inference(paramodulation,[status(thm)],[f15,f3199])).
% 29.35/5.59 fof(f6294,plain,(
% 29.35/5.59 ![X0,X1]: (theorem(implies(X0,X1))|~theorem(implies(X0,or(X1,X1))))),
% 29.35/5.59 inference(forward_demodulation,[status(thm)],[f15,f6292])).
% 29.35/5.59 fof(f9153,plain,(
% 29.35/5.59 ![X0,X1]: (theorem(implies(or(implies(X0,X1),X1),implies(X0,X1))))),
% 29.35/5.59 inference(resolution,[status(thm)],[f6294,f558])).
% 29.35/5.59 fof(f13831,plain,(
% 29.35/5.59 ![X0,X1]: (theorem(implies(X0,X1))|~theorem(or(implies(X0,X1),X1)))),
% 29.35/5.59 inference(resolution,[status(thm)],[f9153,f18])).
% 29.35/5.59 fof(f31497,plain,(
% 29.35/5.59 ![X0,X1,X2]: (theorem(or(implies(or(not(X0),X1),X1),implies(X0,X2)))|~sQ2_spl)),
% 29.35/5.59 inference(resolution,[status(thm)],[f3131,f5588])).
% 29.35/5.59 fof(f31557,plain,(
% 29.35/5.59 ![X0,X1,X2]: (theorem(or(implies(implies(X0,X1),X1),implies(X0,X2)))|~sQ2_spl)),
% 29.35/5.59 inference(forward_demodulation,[status(thm)],[f15,f31497])).
% 29.35/5.59 fof(f45747,plain,(
% 29.35/5.59 ![X0,X1]: (theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~sQ2_spl)),
% 29.35/5.59 inference(resolution,[status(thm)],[f31557,f13831])).
% 29.35/5.59 fof(f59903,plain,(
% 29.35/5.59 $false|~sQ2_spl),
% 29.35/5.59 inference(backward_subsumption_resolution,[status(thm)],[f19,f45747])).
% 29.35/5.59 fof(f59952,plain,(
% 29.35/5.59 ~sQ2_spl),
% 29.35/5.59 inference(contradiction_clause,[status(thm)],[f59903])).
% 29.35/5.59 fof(f59953,plain,(
% 29.35/5.59 $false),
% 29.35/5.59 inference(sat_refutation,[status(thm)],[f94,f107,f59952])).
% 29.35/5.59 % SZS output end CNFRefutation for theBenchmark.p
% 29.35/5.62 % Elapsed time: 5.143806 seconds
% 29.35/5.62 % CPU time: 40.187728 seconds
% 29.35/5.62 % Total memory used: 268.602 MB
% 29.35/5.62 % Net memory used: 244.925 MB
%------------------------------------------------------------------------------