%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL240-3 : 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 : n006.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 01:09:42 PM UTC 2026
% Result : Unsatisfiable 37.36s 5.27s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL240-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n006.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 00:13:58 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 37.36/5.27 % Refutation found
% 37.36/5.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 37.36/5.27 % SZS output start CNFRefutation for theBenchmark
% 37.36/5.27 fof(f1,axiom,(
% 37.36/5.27 (![A]: (axiom(implies(or(A,A),A)) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f2,axiom,(
% 37.36/5.27 (![A,B]: (axiom(implies(A,or(B,A))) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f3,axiom,(
% 37.36/5.27 (![A,B]: (axiom(implies(or(A,B),or(B,A))) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f4,axiom,(
% 37.36/5.27 (![A,B,C]: (axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f5,axiom,(
% 37.36/5.27 (![A,B,C]: (axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f6,axiom,(
% 37.36/5.27 (![X,Y]: (implies(X,Y) = or(not(X),Y) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f7,axiom,(
% 37.36/5.27 (![X]: (( theorem(X)| ~ axiom(X) ) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f8,axiom,(
% 37.36/5.27 (![X,Y]: (( theorem(X)| ~ theorem(implies(Y,X))| ~ theorem(Y) ) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f9,axiom,(
% 37.36/5.27 (![P,Q]: (and(P,Q) = not(or(not(P),not(Q))) ))),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f10,negated_conjecture,(
% 37.36/5.27 ~ theorem(implies(and(p,q),p)) ),
% 37.36/5.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 37.36/5.27 fof(f11,plain,(
% 37.36/5.27 ![X0]: (axiom(implies(or(X0,X0),X0)))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f1])).
% 37.36/5.27 fof(f12,plain,(
% 37.36/5.27 ![X0,X1]: (axiom(implies(X0,or(X1,X0))))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f2])).
% 37.36/5.27 fof(f13,plain,(
% 37.36/5.27 ![X0,X1]: (axiom(implies(or(X0,X1),or(X1,X0))))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f3])).
% 37.36/5.27 fof(f14,plain,(
% 37.36/5.27 ![X0,X1,X2]: (axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f4])).
% 37.36/5.27 fof(f15,plain,(
% 37.36/5.27 ![X0,X1,X2]: (axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f5])).
% 37.36/5.27 fof(f16,plain,(
% 37.36/5.27 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f6])).
% 37.36/5.27 fof(f17,plain,(
% 37.36/5.27 ![X0]: (theorem(X0)|~axiom(X0))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f7])).
% 37.36/5.27 fof(f18,plain,(
% 37.36/5.27 ![Y]: ((![X]: (theorem(X)|~theorem(implies(Y,X))))|~theorem(Y))),
% 37.36/5.27 inference(miniscoping,[status(thm)],[f8])).
% 37.36/5.27 fof(f19,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(X0)|~theorem(implies(X1,X0))|~theorem(X1))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f18])).
% 37.36/5.27 fof(f20,plain,(
% 37.36/5.27 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1))))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f9])).
% 37.36/5.27 fof(f21,plain,(
% 37.36/5.27 ~theorem(implies(and(p,q),p))),
% 37.36/5.27 inference(cnf_transformation,[status(thm)],[f10])).
% 37.36/5.27 fof(f36,plain,(
% 37.36/5.27 ![X0]: (theorem(implies(or(X0,X0),X0)))),
% 37.36/5.27 inference(resolution,[status(thm)],[f11,f17])).
% 37.36/5.27 fof(f37,plain,(
% 37.36/5.27 ![X0]: (theorem(X0)|~theorem(or(X0,X0)))),
% 37.36/5.27 inference(resolution,[status(thm)],[f36,f19])).
% 37.36/5.27 fof(f38,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(implies(X0,or(X1,X0))))),
% 37.36/5.27 inference(resolution,[status(thm)],[f12,f17])).
% 37.36/5.27 fof(f39,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(X0,X1))|~theorem(X1))),
% 37.36/5.27 inference(resolution,[status(thm)],[f38,f19])).
% 37.36/5.27 fof(f41,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(or(X0,implies(X1,or(X2,X1)))))),
% 37.36/5.27 inference(resolution,[status(thm)],[f39,f38])).
% 37.36/5.27 fof(f48,plain,(
% 37.36/5.27 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 37.36/5.27 inference(backward_demodulation,[status(thm)],[f16,f20])).
% 37.36/5.27 fof(f67,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(implies(or(X0,X1),or(X1,X0))))),
% 37.36/5.27 inference(resolution,[status(thm)],[f13,f17])).
% 37.36/5.27 fof(f71,plain,(
% 37.36/5.27 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2))),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f48,f16])).
% 37.36/5.27 fof(f87,definition,(
% 37.36/5.27 ![X0,X1]: (sQ2_spl <=> (theorem(implies(X0,or(X1,X0)))))),
% 37.36/5.27 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 37.36/5.27 fof(f88,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(implies(X0,or(X1,X0)))|~sQ2_spl)),
% 37.36/5.27 inference(component_clause,[status(thm)],[f87])).
% 37.36/5.27 fof(f106,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 37.36/5.27 inference(resolution,[status(thm)],[f14,f17])).
% 37.36/5.27 fof(f115,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 37.36/5.27 inference(resolution,[status(thm)],[f15,f17])).
% 37.36/5.27 fof(f145,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(X0,X1))|~theorem(or(X1,X0)))),
% 37.36/5.27 inference(resolution,[status(thm)],[f67,f19])).
% 37.36/5.27 fof(f148,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f16,f67])).
% 37.36/5.27 fof(f149,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f16,f67])).
% 37.36/5.27 fof(f197,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(X0,not(X1)))|~theorem(implies(X1,X0)))),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f16,f145])).
% 37.36/5.27 fof(f256,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(X0)|~theorem(or(and(X1,X2),X0))|~theorem(implies(X1,not(X2))))),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f71,f19])).
% 37.36/5.27 fof(f265,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(or(X0,or(X1,X2)))|~theorem(or(X1,or(X0,X2))))),
% 37.36/5.27 inference(resolution,[status(thm)],[f106,f19])).
% 37.36/5.27 fof(f368,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(and(X0,X1),or(not(X1),not(X0)))))),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f71,f148])).
% 37.36/5.27 fof(f373,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(and(X0,X1),implies(X1,not(X0)))))),
% 37.36/5.27 inference(forward_demodulation,[status(thm)],[f16,f368])).
% 37.36/5.27 fof(f395,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(implies(X0,X1))|~theorem(or(X1,not(X0))))),
% 37.36/5.27 inference(resolution,[status(thm)],[f149,f19])).
% 37.36/5.27 fof(f417,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(or(X0,X1),not(X1)))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f197,f88])).
% 37.36/5.27 fof(f421,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(implies(or(X0,X1),or(X0,X2)))|~theorem(implies(X1,X2)))),
% 37.36/5.27 inference(resolution,[status(thm)],[f115,f19])).
% 37.36/5.27 fof(f427,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))))),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f16,f115])).
% 37.36/5.27 fof(f429,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))))),
% 37.36/5.27 inference(forward_demodulation,[status(thm)],[f16,f427])).
% 37.36/5.27 fof(f452,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(or(X0,or(or(X1,X2),not(X2))))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f417,f39])).
% 37.36/5.27 fof(f1624,plain,(
% 37.36/5.27 ![X0,X1,X2,X3]: (theorem(implies(X0,or(X1,X0)))|~theorem(implies(X2,not(X3))))),
% 37.36/5.27 inference(resolution,[status(thm)],[f256,f41])).
% 37.36/5.27 fof(f1632,definition,(
% 37.36/5.27 ![X2,X3]: (sQ22_spl <=> (~theorem(implies(X2,not(X3)))))),
% 37.36/5.27 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 37.36/5.27 fof(f1633,plain,(
% 37.36/5.27 ![X0,X1]: (~theorem(implies(X0,not(X1)))|~sQ22_spl)),
% 37.36/5.27 inference(component_clause,[status(thm)],[f1632])).
% 37.36/5.27 fof(f1650,plain,(
% 37.36/5.27 sQ2_spl|sQ22_spl),
% 37.36/5.27 inference(split_clause,[status(thm)],[f1624,f87,f1632])).
% 37.36/5.27 fof(f1736,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(or(or(X0,X1),or(X2,not(X1))))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f265,f452])).
% 37.36/5.27 fof(f1795,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(or(or(X0,not(X1)),or(X2,X1)))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f1736,f145])).
% 37.36/5.27 fof(f2055,plain,(
% 37.36/5.27 ![X0,X1,X2]: (theorem(or(X0,or(or(X1,not(X2)),X2)))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f1795,f265])).
% 37.36/5.27 fof(f2292,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(or(X0,not(X1)),X1))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f2055,f37])).
% 37.36/5.27 fof(f2308,plain,(
% 37.36/5.27 $false|~sQ22_spl),
% 37.36/5.27 inference(resolution,[status(thm)],[f1633,f36])).
% 37.36/5.27 fof(f2316,plain,(
% 37.36/5.27 ~sQ22_spl),
% 37.36/5.27 inference(contradiction_clause,[status(thm)],[f2308])).
% 37.36/5.27 fof(f2319,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(X0,or(X1,not(X0))))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f2292,f145])).
% 37.36/5.27 fof(f2355,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(X0,or(X1,not(X1))))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f2319,f265])).
% 37.36/5.27 fof(f2363,plain,(
% 37.36/5.27 ![X0,X1]: (theorem(or(X0,implies(X1,not(X0))))|~sQ2_spl)),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f16,f2319])).
% 37.36/5.27 fof(f2385,plain,(
% 37.36/5.27 ![X0]: (theorem(or(X0,not(X0)))|~sQ2_spl)),
% 37.36/5.27 inference(resolution,[status(thm)],[f2355,f37])).
% 37.36/5.27 fof(f2404,plain,(
% 37.36/5.27 ![X0]: (theorem(implies(X0,not(not(X0))))|~sQ2_spl)),
% 37.36/5.27 inference(paramodulation,[status(thm)],[f16,f2385])).
% 10.08/5.35 fof(f2606,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(implies(or(X0,X1),or(X0,not(not(X1)))))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f421,f2404])).
% 10.08/5.35 fof(f2884,plain,(
% 10.08/5.35 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(X0,X2)))|~theorem(implies(X1,X2)))),
% 10.08/5.35 inference(resolution,[status(thm)],[f429,f19])).
% 10.08/5.35 fof(f85161,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(or(X0,not(not(X1))))|~theorem(or(X0,X1))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f2606,f19])).
% 10.08/5.35 fof(f130310,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(or(and(X0,X1),not(not(implies(X1,not(X0))))))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f85161,f373])).
% 10.08/5.35 fof(f130609,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(or(X0,not(not(implies(X1,not(X0))))))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f85161,f2363])).
% 10.08/5.35 fof(f130650,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(or(and(X0,X1),not(and(X1,X0))))|~sQ2_spl)),
% 10.08/5.35 inference(forward_demodulation,[status(thm)],[f48,f130310])).
% 10.08/5.35 fof(f130666,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(or(X0,not(and(X1,X0))))|~sQ2_spl)),
% 10.08/5.35 inference(forward_demodulation,[status(thm)],[f48,f130609])).
% 10.08/5.35 fof(f130677,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(implies(and(X0,X1),X1))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f130666,f395])).
% 10.08/5.35 fof(f130772,plain,(
% 10.08/5.35 ![X0,X1,X2]: (theorem(implies(implies(X0,and(X1,X2)),implies(X0,X2)))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f130677,f2884])).
% 10.08/5.35 fof(f133173,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(implies(and(X0,X1),and(X1,X0)))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f130650,f395])).
% 10.08/5.35 fof(f136240,plain,(
% 10.08/5.35 ![X0,X1,X2]: (theorem(implies(X0,X1))|~theorem(implies(X0,and(X2,X1)))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f130772,f19])).
% 10.08/5.35 fof(f145242,plain,(
% 10.08/5.35 ![X0,X1]: (theorem(implies(and(X0,X1),X0))|~sQ2_spl)),
% 10.08/5.35 inference(resolution,[status(thm)],[f136240,f133173])).
% 10.08/5.35 fof(f145327,plain,(
% 10.08/5.35 $false|~sQ2_spl),
% 10.08/5.35 inference(backward_subsumption_resolution,[status(thm)],[f21,f145242])).
% 10.08/5.35 fof(f145414,plain,(
% 10.08/5.35 ~sQ2_spl),
% 10.08/5.35 inference(contradiction_clause,[status(thm)],[f145327])).
% 10.08/5.35 fof(f145415,plain,(
% 10.08/5.35 $false),
% 10.08/5.35 inference(sat_refutation,[status(thm)],[f1650,f2316,f145414])).
% 10.08/5.35 % SZS output end CNFRefutation for theBenchmark.p
% 10.08/5.38 % Elapsed time: 4.905267 seconds
% 10.08/5.38 % CPU time: 38.123609 seconds
% 10.08/5.38 % Total memory used: 354.718 MB
% 10.08/5.38 % Net memory used: 330.700 MB
%------------------------------------------------------------------------------