%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL219-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 01:09:38 PM UTC 2026
% Result : Unsatisfiable 85.06s 11.22s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL219-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 00:11:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 85.06/11.22 % Refutation found
% 85.06/11.22 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 85.06/11.22 % SZS output start CNFRefutation for theBenchmark
% 85.06/11.22 fof(f1,axiom,(
% 85.06/11.22 (![A]: (axiom(implies(or(A,A),A)) ))),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f2,axiom,(
% 85.06/11.22 (![A,B]: (axiom(implies(A,or(B,A))) ))),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f3,axiom,(
% 85.06/11.22 (![A,B]: (axiom(implies(or(A,B),or(B,A))) ))),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f4,axiom,(
% 85.06/11.22 (![A,B,C]: (axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ))),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f5,axiom,(
% 85.06/11.22 (![A,B,C]: (axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ))),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f6,axiom,(
% 85.06/11.22 (![X,Y]: (implies(X,Y) = or(not(X),Y) ))),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f7,axiom,(
% 85.06/11.22 (![X]: (( theorem(X)| ~ axiom(X) ) ))),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f8,axiom,(
% 85.06/11.22 (![X,Y]: (( theorem(X)| ~ theorem(implies(Y,X))| ~ theorem(Y) ) ))),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f9,negated_conjecture,(
% 85.06/11.22 ~ theorem(implies(implies(implies(p,q),q),or(p,q))) ),
% 85.06/11.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 85.06/11.22 fof(f10,plain,(
% 85.06/11.22 ![X0]: (axiom(implies(or(X0,X0),X0)))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f1])).
% 85.06/11.22 fof(f11,plain,(
% 85.06/11.22 ![X0,X1]: (axiom(implies(X0,or(X1,X0))))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f2])).
% 85.06/11.22 fof(f12,plain,(
% 85.06/11.22 ![X0,X1]: (axiom(implies(or(X0,X1),or(X1,X0))))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f3])).
% 85.06/11.22 fof(f13,plain,(
% 85.06/11.22 ![X0,X1,X2]: (axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f4])).
% 85.06/11.22 fof(f14,plain,(
% 85.06/11.22 ![X0,X1,X2]: (axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f5])).
% 85.06/11.22 fof(f15,plain,(
% 85.06/11.22 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f6])).
% 85.06/11.22 fof(f16,plain,(
% 85.06/11.22 ![X0]: (theorem(X0)|~axiom(X0))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f7])).
% 85.06/11.22 fof(f17,plain,(
% 85.06/11.22 ![Y]: ((![X]: (theorem(X)|~theorem(implies(Y,X))))|~theorem(Y))),
% 85.06/11.22 inference(miniscoping,[status(thm)],[f8])).
% 85.06/11.22 fof(f18,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(X0)|~theorem(implies(X1,X0))|~theorem(X1))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f17])).
% 85.06/11.22 fof(f19,plain,(
% 85.06/11.22 ~theorem(implies(implies(implies(p,q),q),or(p,q)))),
% 85.06/11.22 inference(cnf_transformation,[status(thm)],[f9])).
% 85.06/11.22 fof(f20,plain,(
% 85.06/11.22 ![X0]: (theorem(implies(or(X0,X0),X0)))),
% 85.06/11.22 inference(resolution,[status(thm)],[f10,f16])).
% 85.06/11.22 fof(f21,plain,(
% 85.06/11.22 ![X0]: (theorem(X0)|~theorem(or(X0,X0)))),
% 85.06/11.22 inference(resolution,[status(thm)],[f20,f18])).
% 85.06/11.22 fof(f22,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(implies(X0,or(X1,X0))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f11,f16])).
% 85.06/11.22 fof(f23,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(X0,X1))|~theorem(X1))),
% 85.06/11.22 inference(resolution,[status(thm)],[f22,f18])).
% 85.06/11.22 fof(f24,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(X0,implies(or(X1,X1),X1))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f23,f20])).
% 85.06/11.22 fof(f25,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(X0,implies(X1,or(X2,X1)))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f23,f22])).
% 85.06/11.22 fof(f27,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(X0,or(X1,implies(or(X2,X2),X2)))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f24,f23])).
% 85.06/11.22 fof(f31,plain,(
% 85.06/11.22 ![X0,X1,X2,X3]: (theorem(or(X0,or(X1,or(X2,implies(or(X3,X3),X3))))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f27,f23])).
% 85.06/11.22 fof(f49,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(implies(X0,implies(X1,or(X2,X1)))))),
% 85.06/11.22 inference(paramodulation,[status(thm)],[f15,f25])).
% 85.06/11.22 fof(f73,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(implies(or(X0,X1),or(X1,X0))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f12,f16])).
% 85.06/11.22 fof(f83,definition,(
% 85.06/11.22 ![X1]: (sQ1_spl <=> (~theorem(X1)))),
% 85.06/11.22 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 85.06/11.22 fof(f84,plain,(
% 85.06/11.22 ![X0]: (~theorem(X0)|~sQ1_spl)),
% 85.06/11.22 inference(component_clause,[status(thm)],[f83])).
% 85.06/11.22 fof(f87,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(implies(X0,or(X1,X0)))|~theorem(X2))),
% 85.06/11.22 inference(resolution,[status(thm)],[f49,f18])).
% 85.06/11.22 fof(f91,definition,(
% 85.06/11.22 ![X0,X1]: (sQ2_spl <=> (theorem(implies(X0,or(X1,X0)))))),
% 85.06/11.22 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 85.06/11.22 fof(f92,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(implies(X0,or(X1,X0)))|~sQ2_spl)),
% 85.06/11.22 inference(component_clause,[status(thm)],[f91])).
% 85.06/11.22 fof(f94,plain,(
% 85.06/11.22 sQ2_spl|sQ1_spl),
% 85.06/11.22 inference(split_clause,[status(thm)],[f87,f91,f83])).
% 85.06/11.22 fof(f96,plain,(
% 85.06/11.22 $false|~sQ1_spl),
% 85.06/11.22 inference(backward_subsumption_resolution,[status(thm)],[f31,f84])).
% 85.06/11.22 fof(f107,plain,(
% 85.06/11.22 ~sQ1_spl),
% 85.06/11.22 inference(contradiction_clause,[status(thm)],[f96])).
% 85.06/11.22 fof(f115,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f13,f16])).
% 85.06/11.22 fof(f124,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f14,f16])).
% 85.06/11.22 fof(f138,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(X0,X1))|~theorem(or(X1,X0)))),
% 85.06/11.22 inference(resolution,[status(thm)],[f73,f18])).
% 85.06/11.22 fof(f142,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 85.06/11.22 inference(paramodulation,[status(thm)],[f15,f73])).
% 85.06/11.22 fof(f147,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(X0,or(X1,X2)))|~theorem(or(X1,or(X0,X2))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f115,f18])).
% 85.06/11.22 fof(f193,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(X0,not(X1)))|~theorem(implies(X1,X0)))),
% 85.06/11.22 inference(paramodulation,[status(thm)],[f15,f138])).
% 85.06/11.22 fof(f194,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(implies(or(X0,X1),or(X0,X2)))|~theorem(implies(X1,X2)))),
% 85.06/11.22 inference(resolution,[status(thm)],[f124,f18])).
% 85.06/11.22 fof(f222,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(implies(X0,X1))|~theorem(or(X1,not(X0))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f142,f18])).
% 85.06/11.22 fof(f237,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(or(X0,X1),not(X1)))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f193,f92])).
% 85.06/11.22 fof(f252,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(X0,or(or(X1,X2),not(X2))))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f237,f23])).
% 85.06/11.22 fof(f335,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(X0,or(not(X1),X2)))|~theorem(implies(X1,or(X0,X2))))),
% 85.06/11.22 inference(paramodulation,[status(thm)],[f15,f147])).
% 85.06/11.22 fof(f337,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(X0,implies(X1,X2)))|~theorem(implies(X1,or(X0,X2))))),
% 85.06/11.22 inference(forward_demodulation,[status(thm)],[f15,f335])).
% 85.06/11.22 fof(f355,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(or(X0,X1),or(X2,not(X1))))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f252,f147])).
% 85.06/11.22 fof(f426,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(or(X0,not(X1)),or(X2,X1)))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f355,f138])).
% 85.06/11.22 fof(f466,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(X0,or(or(X1,not(X2)),X2)))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f426,f147])).
% 85.06/11.22 fof(f493,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(or(X0,not(X1)),X1))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f466,f21])).
% 85.06/11.22 fof(f501,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(X0,or(X1,not(X0))))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f493,f138])).
% 85.06/11.22 fof(f506,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(X0,or(X1,not(X1))))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f501,f147])).
% 85.06/11.22 fof(f521,plain,(
% 85.06/11.22 ![X0]: (theorem(or(X0,not(X0)))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f506,f21])).
% 85.06/11.22 fof(f527,plain,(
% 85.06/11.22 ![X0]: (theorem(implies(X0,X0))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f521,f222])).
% 85.06/11.22 fof(f550,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(implies(or(X0,or(X1,not(X2))),or(X0,implies(X2,X1)))))),
% 85.06/11.22 inference(resolution,[status(thm)],[f194,f142])).
% 85.06/11.22 fof(f1842,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(or(X0,implies(or(X0,X1),X1)))|~sQ2_spl)),
% 85.06/11.22 inference(resolution,[status(thm)],[f337,f527])).
% 85.06/11.22 fof(f1843,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(or(not(X0),implies(X1,X2)))|~theorem(implies(X1,implies(X0,X2))))),
% 85.06/11.22 inference(paramodulation,[status(thm)],[f15,f337])).
% 85.06/11.22 fof(f1844,plain,(
% 85.06/11.22 ![X0,X1,X2]: (theorem(implies(X0,implies(X1,X2)))|~theorem(implies(X1,implies(X0,X2))))),
% 85.06/11.22 inference(forward_demodulation,[status(thm)],[f15,f1843])).
% 85.06/11.22 fof(f1861,plain,(
% 85.06/11.22 ![X0,X1]: (theorem(implies(X0,implies(or(not(X0),X1),X1)))|~sQ2_spl)),
% 85.06/11.22 inference(paramodulation,[status(thm)],[f15,f1842])).
% 13.17/11.30 fof(f1863,plain,(
% 13.17/11.30 ![X0,X1]: (theorem(implies(X0,implies(implies(X0,X1),X1)))|~sQ2_spl)),
% 13.17/11.30 inference(forward_demodulation,[status(thm)],[f15,f1861])).
% 13.17/11.30 fof(f1888,plain,(
% 13.17/11.30 ![X0,X1]: (theorem(implies(implies(X0,X1),X1))|~theorem(X0)|~sQ2_spl)),
% 13.17/11.30 inference(resolution,[status(thm)],[f1863,f18])).
% 13.17/11.30 fof(f3131,plain,(
% 13.17/11.30 ![X0,X1,X2]: (theorem(or(X0,implies(X1,X2)))|~theorem(or(X0,or(X2,not(X1)))))),
% 13.17/11.30 inference(resolution,[status(thm)],[f550,f18])).
% 13.17/11.30 fof(f9390,plain,(
% 13.17/11.30 ![X0,X1,X2]: (theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))))),
% 13.17/11.30 inference(resolution,[status(thm)],[f1844,f124])).
% 13.17/11.30 fof(f31553,plain,(
% 13.17/11.30 ![X0,X1]: (theorem(or(X0,implies(X0,X1)))|~sQ2_spl)),
% 13.17/11.30 inference(resolution,[status(thm)],[f3131,f501])).
% 13.17/11.30 fof(f31670,plain,(
% 13.17/11.30 ![X0,X1,X2]: (theorem(implies(implies(or(X0,implies(X0,X1)),X2),X2))|~sQ2_spl)),
% 13.17/11.30 inference(resolution,[status(thm)],[f31553,f1888])).
% 13.17/11.30 fof(f46453,plain,(
% 13.17/11.30 ![X0,X1,X2]: (theorem(X0)|~theorem(implies(or(X1,implies(X1,X2)),X0))|~sQ2_spl)),
% 13.17/11.30 inference(resolution,[status(thm)],[f31670,f18])).
% 13.17/11.30 fof(f131089,plain,(
% 13.17/11.30 ![X0,X1,X2]: (theorem(implies(implies(implies(X0,X1),X2),or(X0,X2)))|~sQ2_spl)),
% 13.17/11.30 inference(resolution,[status(thm)],[f9390,f46453])).
% 13.17/11.30 fof(f136477,plain,(
% 13.17/11.30 $false|~sQ2_spl),
% 13.17/11.30 inference(backward_subsumption_resolution,[status(thm)],[f19,f131089])).
% 13.17/11.30 fof(f136573,plain,(
% 13.17/11.30 ~sQ2_spl),
% 13.17/11.30 inference(contradiction_clause,[status(thm)],[f136477])).
% 13.17/11.30 fof(f136574,plain,(
% 13.17/11.30 $false),
% 13.17/11.30 inference(sat_refutation,[status(thm)],[f94,f107,f136573])).
% 13.17/11.30 % SZS output end CNFRefutation for theBenchmark.p
% 13.17/11.33 % Elapsed time: 10.946587 seconds
% 13.17/11.33 % CPU time: 86.049808 seconds
% 13.17/11.33 % Total memory used: 606.106 MB
% 13.17/11.33 % Net memory used: 538.394 MB
%------------------------------------------------------------------------------