%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL209-3 : 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 : n008.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 01:09:36 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL209-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:11:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.48 % Refutation found
% 0.10/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.48 fof(f2,axiom,(
% 0.10/0.48 (![A,B]: (axiom(implies(A,or(B,A))) ))),
% 0.10/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f3,axiom,(
% 0.10/0.48 (![A,B]: (axiom(implies(or(A,B),or(B,A))) ))),
% 0.10/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f4,axiom,(
% 0.10/0.48 (![A,B,C]: (axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ))),
% 0.10/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f5,axiom,(
% 0.10/0.48 (![A,B,C]: (axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ))),
% 0.10/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f6,axiom,(
% 0.10/0.48 (![X,Y]: (implies(X,Y) = or(not(X),Y) ))),
% 0.10/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f7,axiom,(
% 0.10/0.48 (![X]: (( theorem(X)| ~ axiom(X) ) ))),
% 0.10/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f8,axiom,(
% 0.10/0.48 (![X,Y]: (( theorem(X)| ~ theorem(implies(Y,X))| ~ theorem(Y) ) ))),
% 0.10/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f9,negated_conjecture,(
% 0.10/0.48 ~ theorem(implies(implies(not(p),q),or(p,q))) ),
% 0.10/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.48 fof(f11,plain,(
% 0.10/0.48 ![X0,X1]: (axiom(implies(X0,or(X1,X0))))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.48 fof(f12,plain,(
% 0.10/0.48 ![X0,X1]: (axiom(implies(or(X0,X1),or(X1,X0))))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.48 fof(f13,plain,(
% 0.10/0.48 ![X0,X1,X2]: (axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.48 fof(f14,plain,(
% 0.10/0.48 ![X0,X1,X2]: (axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f5])).
% 0.10/0.48 fof(f15,plain,(
% 0.10/0.48 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.48 fof(f16,plain,(
% 0.10/0.48 ![X0]: (theorem(X0)|~axiom(X0))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.48 fof(f17,plain,(
% 0.10/0.48 ![Y]: ((![X]: (theorem(X)|~theorem(implies(Y,X))))|~theorem(Y))),
% 0.10/0.48 inference(miniscoping,[status(thm)],[f8])).
% 0.10/0.48 fof(f18,plain,(
% 0.10/0.48 ![X0,X1]: (theorem(X0)|~theorem(implies(X1,X0))|~theorem(X1))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f17])).
% 0.10/0.48 fof(f19,plain,(
% 0.10/0.48 ~theorem(implies(implies(not(p),q),or(p,q)))),
% 0.10/0.48 inference(cnf_transformation,[status(thm)],[f9])).
% 0.10/0.48 fof(f27,plain,(
% 0.10/0.48 ![X0,X1]: (theorem(implies(X0,or(X1,X0))))),
% 0.10/0.48 inference(resolution,[status(thm)],[f11,f16])).
% 0.10/0.48 fof(f30,plain,(
% 0.10/0.48 ![X0,X1]: (theorem(implies(X0,implies(X1,X0))))),
% 0.10/0.48 inference(paramodulation,[status(thm)],[f15,f27])).
% 0.10/0.48 fof(f41,definition,(
% 0.10/0.48 ![X1]: (sQ1_spl <=> (~theorem(X1)))),
% 0.10/0.48 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.48 fof(f42,plain,(
% 0.10/0.48 ![X0]: (~theorem(X0)|~sQ1_spl)),
% 0.10/0.48 inference(component_clause,[status(thm)],[f41])).
% 0.10/0.48 fof(f46,plain,(
% 0.10/0.48 ![X0,X1]: (theorem(implies(or(X0,X1),or(X1,X0))))),
% 0.10/0.48 inference(resolution,[status(thm)],[f12,f16])).
% 0.10/0.48 fof(f47,plain,(
% 0.10/0.48 ![X0,X1]: (axiom(implies(implies(X0,X1),or(X1,not(X0)))))),
% 0.10/0.48 inference(paramodulation,[status(thm)],[f15,f12])).
% 0.10/0.48 fof(f50,plain,(
% 0.10/0.48 ![X0,X1]: (theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 0.10/0.48 inference(paramodulation,[status(thm)],[f15,f46])).
% 0.10/0.48 fof(f58,plain,(
% 0.10/0.48 ![X0,X1,X2]: (theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 0.10/0.48 inference(resolution,[status(thm)],[f13,f16])).
% 0.10/0.48 fof(f59,plain,(
% 0.10/0.48 ![X0,X1,X2]: (axiom(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))))),
% 0.10/0.48 inference(paramodulation,[status(thm)],[f15,f13])).
% 0.10/0.48 fof(f63,plain,(
% 0.10/0.48 ![X0,X1,X2]: (axiom(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))))),
% 0.10/0.48 inference(forward_demodulation,[status(thm)],[f15,f59])).
% 0.10/0.48 fof(f67,plain,(
% 0.10/0.48 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 0.10/0.48 inference(resolution,[status(thm)],[f14,f16])).
% 0.10/0.48 fof(f77,plain,(
% 0.10/0.48 ![X0,X1]: (theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))))),
% 0.10/0.48 inference(paramodulation,[status(thm)],[f15,f50])).
% 0.10/0.48 fof(f80,plain,(
% 0.10/0.48 ![X0,X1,X2]: (theorem(or(X0,or(X1,X2)))|~theorem(or(X1,or(X0,X2))))),
% 0.10/0.48 inference(resolution,[status(thm)],[f58,f18])).
% 0.10/0.48 fof(f99,plain,(
% 0.10/0.49 ![X0,X1,X2]: (axiom(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))))),
% 0.10/0.49 inference(paramodulation,[status(thm)],[f15,f63])).
% 0.10/0.49 fof(f101,plain,(
% 0.10/0.49 ![X0,X1,X2]: (axiom(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))))),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f15,f99])).
% 0.10/0.49 fof(f146,plain,(
% 0.10/0.49 ![X0,X1,X2]: (theorem(implies(or(X0,X1),or(X0,X2)))|~theorem(implies(X1,X2)))),
% 0.10/0.49 inference(resolution,[status(thm)],[f67,f18])).
% 0.10/0.49 fof(f186,plain,(
% 0.10/0.49 $false|~sQ1_spl),
% 0.10/0.49 inference(backward_subsumption_resolution,[status(thm)],[f77,f42])).
% 0.10/0.49 fof(f195,plain,(
% 0.10/0.49 ~sQ1_spl),
% 0.10/0.49 inference(contradiction_clause,[status(thm)],[f186])).
% 0.10/0.49 fof(f197,plain,(
% 0.10/0.49 ![X0,X1]: (~axiom(implies(X0,X1))|theorem(X1)|~theorem(X0))),
% 0.10/0.49 inference(resolution,[status(thm)],[f16,f18])).
% 0.10/0.49 fof(f278,plain,(
% 0.10/0.49 ![X0,X1,X2]: (~axiom(implies(implies(X0,implies(X1,X0)),X2))|theorem(X2))),
% 0.10/0.49 inference(resolution,[status(thm)],[f197,f30])).
% 0.10/0.49 fof(f316,plain,(
% 0.10/0.49 ![X0,X1,X2]: (theorem(or(not(X0),or(X1,X2)))|~theorem(or(X1,implies(X0,X2))))),
% 0.10/0.49 inference(paramodulation,[status(thm)],[f15,f80])).
% 0.10/0.49 fof(f318,plain,(
% 0.10/0.49 ![X0,X1,X2]: (theorem(implies(X0,or(X1,X2)))|~theorem(or(X1,implies(X0,X2))))),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f15,f316])).
% 0.10/0.49 fof(f494,plain,(
% 0.10/0.49 ![X0,X1,X2]: (~theorem(implies(X0,X1))|theorem(or(X2,X1))|~theorem(or(X2,X0)))),
% 0.10/0.49 inference(resolution,[status(thm)],[f146,f18])).
% 0.10/0.49 fof(f704,plain,(
% 0.10/0.49 ![X0,X1]: (theorem(implies(X0,implies(X1,X1))))),
% 0.10/0.49 inference(resolution,[status(thm)],[f278,f101])).
% 0.10/0.49 fof(f710,plain,(
% 0.10/0.49 ![X0,X1]: (theorem(implies(X0,X0))|~theorem(X1))),
% 0.10/0.49 inference(resolution,[status(thm)],[f704,f18])).
% 0.10/0.49 fof(f715,definition,(
% 0.10/0.49 ![X0]: (sQ16_spl <=> (theorem(implies(X0,X0))))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f716,plain,(
% 0.10/0.49 ![X0]: (theorem(implies(X0,X0))|~sQ16_spl)),
% 0.10/0.49 inference(component_clause,[status(thm)],[f715])).
% 0.10/0.49 fof(f718,plain,(
% 0.10/0.49 sQ16_spl|sQ1_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f710,f715,f41])).
% 0.10/0.49 fof(f720,plain,(
% 0.10/0.49 ![X0,X1]: (~axiom(implies(implies(X0,X0),X1))|theorem(X1)|~sQ16_spl)),
% 0.10/0.49 inference(resolution,[status(thm)],[f716,f197])).
% 0.10/0.49 fof(f780,plain,(
% 0.10/0.49 ![X0,X1]: (theorem(implies(X0,implies(implies(X0,X1),X1)))|~sQ16_spl)),
% 0.10/0.49 inference(resolution,[status(thm)],[f720,f101])).
% 0.10/0.49 fof(f783,plain,(
% 0.10/0.49 ![X0]: (theorem(or(X0,not(X0)))|~sQ16_spl)),
% 0.10/0.49 inference(resolution,[status(thm)],[f720,f47])).
% 0.10/0.49 fof(f1454,plain,(
% 0.10/0.49 ~theorem(or(p,implies(implies(not(p),q),q)))),
% 0.10/0.49 inference(resolution,[status(thm)],[f318,f19])).
% 0.10/0.49 fof(f1959,plain,(
% 0.10/0.49 ![X0]: (~theorem(implies(X0,implies(implies(not(p),q),q)))|~theorem(or(p,X0)))),
% 0.10/0.49 inference(resolution,[status(thm)],[f494,f1454])).
% 0.10/0.49 fof(f2160,plain,(
% 0.10/0.49 ~theorem(or(p,not(p)))|~sQ16_spl),
% 0.10/0.49 inference(resolution,[status(thm)],[f1959,f780])).
% 0.10/0.49 fof(f2168,plain,(
% 0.10/0.49 $false|~sQ16_spl),
% 0.10/0.49 inference(forward_subsumption_resolution,[status(thm)],[f2160,f783])).
% 0.10/0.49 fof(f2169,plain,(
% 0.10/0.49 ~sQ16_spl),
% 0.10/0.49 inference(contradiction_clause,[status(thm)],[f2168])).
% 0.10/0.49 fof(f2170,plain,(
% 0.10/0.49 $false),
% 0.10/0.49 inference(sat_refutation,[status(thm)],[f195,f718,f2169])).
% 0.10/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.51 % Elapsed time: 0.121756 seconds
% 0.10/0.51 % CPU time: 0.761517 seconds
% 0.10/0.51 % Total memory used: 81.529 MB
% 0.10/0.51 % Net memory used: 80.158 MB
%------------------------------------------------------------------------------