%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL220-3 : 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 : n011.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 202.86s 41.20s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL220-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.05/15.55 % CPULimit : 300
% 0.05/15.55 % WCLimit : 300
% 0.05/15.55 % DateTime : Mon Sep 21 00:12:29 UTC 2026
% 0.05/15.55 % CPUTime :
% 0.05/15.56 % Drodi V4.1.1
% 202.86/41.20 % Refutation found
% 202.86/41.20 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 202.86/41.20 % SZS output start CNFRefutation for theBenchmark
% 202.86/41.20 fof(f1,axiom,(
% 202.86/41.20 (![A]: (axiom(implies(or(A,A),A)) ))),
% 202.86/41.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.20 fof(f2,axiom,(
% 202.86/41.20 (![A,B]: (axiom(implies(A,or(B,A))) ))),
% 202.86/41.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.20 fof(f3,axiom,(
% 202.86/41.20 (![A,B]: (axiom(implies(or(A,B),or(B,A))) ))),
% 202.86/41.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.20 fof(f4,axiom,(
% 202.86/41.20 (![A,B,C]: (axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ))),
% 202.86/41.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.20 fof(f5,axiom,(
% 202.86/41.20 (![A,B,C]: (axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ))),
% 202.86/41.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.20 fof(f6,axiom,(
% 202.86/41.20 (![X,Y]: (implies(X,Y) = or(not(X),Y) ))),
% 202.86/41.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.20 fof(f7,axiom,(
% 202.86/41.20 (![X]: (( theorem(X)| ~ axiom(X) ) ))),
% 202.86/41.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.21 fof(f8,axiom,(
% 202.86/41.21 (![X,Y]: (( theorem(X)| ~ theorem(implies(Y,X))| ~ theorem(Y) ) ))),
% 202.86/41.21 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.21 fof(f9,negated_conjecture,(
% 202.86/41.21 ~ theorem(implies(implies(implies(p,q),q),implies(implies(q,p),p))) ),
% 202.86/41.21 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 202.86/41.21 fof(f10,plain,(
% 202.86/41.21 ![X0]: (axiom(implies(or(X0,X0),X0)))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f1])).
% 202.86/41.21 fof(f11,plain,(
% 202.86/41.21 ![X0,X1]: (axiom(implies(X0,or(X1,X0))))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f2])).
% 202.86/41.21 fof(f12,plain,(
% 202.86/41.21 ![X0,X1]: (axiom(implies(or(X0,X1),or(X1,X0))))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f3])).
% 202.86/41.21 fof(f13,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f4])).
% 202.86/41.21 fof(f14,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f5])).
% 202.86/41.21 fof(f15,plain,(
% 202.86/41.21 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f6])).
% 202.86/41.21 fof(f16,plain,(
% 202.86/41.21 ![X0]: (theorem(X0)|~axiom(X0))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f7])).
% 202.86/41.21 fof(f17,plain,(
% 202.86/41.21 ![Y]: ((![X]: (theorem(X)|~theorem(implies(Y,X))))|~theorem(Y))),
% 202.86/41.21 inference(miniscoping,[status(thm)],[f8])).
% 202.86/41.21 fof(f18,plain,(
% 202.86/41.21 ![X0,X1]: (theorem(X0)|~theorem(implies(X1,X0))|~theorem(X1))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f17])).
% 202.86/41.21 fof(f19,plain,(
% 202.86/41.21 ~theorem(implies(implies(implies(p,q),q),implies(implies(q,p),p)))),
% 202.86/41.21 inference(cnf_transformation,[status(thm)],[f9])).
% 202.86/41.21 fof(f20,plain,(
% 202.86/41.21 ![X0]: (theorem(implies(or(X0,X0),X0)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f10,f16])).
% 202.86/41.21 fof(f21,plain,(
% 202.86/41.21 ![X0]: (theorem(X0)|~theorem(or(X0,X0)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f20,f18])).
% 202.86/41.21 fof(f22,plain,(
% 202.86/41.21 ![X0,X1]: (theorem(implies(X0,or(X1,X0))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f11,f16])).
% 202.86/41.21 fof(f23,plain,(
% 202.86/41.21 ![X0,X1]: (theorem(or(X0,X1))|~theorem(X1))),
% 202.86/41.21 inference(resolution,[status(thm)],[f22,f18])).
% 202.86/41.21 fof(f26,plain,(
% 202.86/41.21 ![X0,X1]: (theorem(implies(X0,implies(X1,X0))))),
% 202.86/41.21 inference(paramodulation,[status(thm)],[f15,f22])).
% 202.86/41.21 fof(f29,plain,(
% 202.86/41.21 ![X0]: (theorem(implies(implies(X0,not(X0)),not(X0))))),
% 202.86/41.21 inference(paramodulation,[status(thm)],[f15,f20])).
% 202.86/41.21 fof(f45,plain,(
% 202.86/41.21 ![X0,X1]: (theorem(implies(or(X0,X1),or(X1,X0))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f12,f16])).
% 202.86/41.21 fof(f48,plain,(
% 202.86/41.21 ![X0,X1]: (theorem(or(X0,X1))|~theorem(or(X1,X0)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f45,f18])).
% 202.86/41.21 fof(f63,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f13,f16])).
% 202.86/41.21 fof(f64,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))))),
% 202.86/41.21 inference(paramodulation,[status(thm)],[f15,f13])).
% 202.86/41.21 fof(f65,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(or(X0,implies(X1,X2)),or(not(X1),or(X0,X2)))))),
% 202.86/41.21 inference(paramodulation,[status(thm)],[f15,f13])).
% 202.86/41.21 fof(f68,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))))),
% 202.86/41.21 inference(forward_demodulation,[status(thm)],[f15,f64])).
% 202.86/41.21 fof(f69,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(or(X0,implies(X1,X2)),implies(X1,or(X0,X2)))))),
% 202.86/41.21 inference(forward_demodulation,[status(thm)],[f15,f65])).
% 202.86/41.21 fof(f72,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f14,f16])).
% 202.86/41.21 fof(f73,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))))),
% 202.86/41.21 inference(paramodulation,[status(thm)],[f15,f14])).
% 202.86/41.21 fof(f75,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))))),
% 202.86/41.21 inference(forward_demodulation,[status(thm)],[f15,f73])).
% 202.86/41.21 fof(f77,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(or(X0,or(X1,X2)))|~theorem(or(X1,or(X0,X2))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f63,f18])).
% 202.86/41.21 fof(f91,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(implies(or(X0,X1),or(X0,X2)))|~theorem(implies(X1,X2)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f72,f18])).
% 202.86/41.21 fof(f116,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(or(X0,or(X1,X2)))|~theorem(or(X0,X2)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f77,f23])).
% 202.86/41.21 fof(f150,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))))),
% 202.86/41.21 inference(paramodulation,[status(thm)],[f15,f68])).
% 202.86/41.21 fof(f152,plain,(
% 202.86/41.21 ![X0,X1,X2]: (axiom(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))))),
% 202.86/41.21 inference(forward_demodulation,[status(thm)],[f15,f150])).
% 202.86/41.21 fof(f182,plain,(
% 202.86/41.21 ![X0,X1]: (theorem(X0)|~theorem(X1)|~axiom(implies(X1,X0)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f18,f16])).
% 202.86/41.21 fof(f224,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(or(X0,implies(X1,X2)))|~theorem(implies(X1,or(X0,X2))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f182,f68])).
% 202.86/41.21 fof(f226,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(X0,X2)))|~theorem(implies(X1,X2)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f182,f75])).
% 202.86/41.21 fof(f229,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(implies(X0,or(X1,X2)))|~theorem(or(X1,implies(X0,X2))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f182,f69])).
% 202.86/41.21 fof(f273,plain,(
% 202.86/41.21 ![X0,X1,X2]: (~theorem(implies(X0,X1))|theorem(or(X2,X1))|~theorem(or(X2,X0)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f91,f18])).
% 202.86/41.21 fof(f290,plain,(
% 202.86/41.21 ![X0,X1]: (~theorem(or(or(X0,X1),X1))|theorem(or(X0,X1)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f116,f21])).
% 202.86/41.21 fof(f302,plain,(
% 202.86/41.21 ![X0,X1]: (theorem(or(X0,X1))|~theorem(or(X1,or(X0,X1))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f290,f48])).
% 202.86/41.21 fof(f393,plain,(
% 202.86/41.21 ![X0,X1]: (~theorem(or(X0,or(X1,X1)))|theorem(or(X0,X1)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f77,f302])).
% 202.86/41.21 fof(f450,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(implies(X0,implies(X1,X2)))|~theorem(implies(X1,implies(X0,X2))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f152,f182])).
% 202.86/41.21 fof(f504,plain,(
% 202.86/41.21 ![X0,X1]: (~theorem(implies(X0,or(X1,X1)))|theorem(or(not(X0),X1)))),
% 202.86/41.21 inference(paramodulation,[status(thm)],[f15,f393])).
% 202.86/41.21 fof(f506,plain,(
% 202.86/41.21 ![X0,X1]: (~theorem(implies(X0,or(X1,X1)))|theorem(implies(X0,X1)))),
% 202.86/41.21 inference(forward_demodulation,[status(thm)],[f15,f504])).
% 202.86/41.21 fof(f549,plain,(
% 202.86/41.21 ![X0]: (theorem(implies(X0,X0)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f506,f22])).
% 202.86/41.21 fof(f930,plain,(
% 202.86/41.21 ![X0,X1,X2]: (~theorem(implies(X0,X1))|theorem(implies(X2,X1))|~theorem(implies(X2,X0)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f226,f18])).
% 202.86/41.21 fof(f1045,plain,(
% 202.86/41.21 ![X0,X1,X2]: (theorem(implies(X0,or(X1,X2)))|~theorem(or(implies(X0,X2),X1)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f229,f48])).
% 202.86/41.21 fof(f1381,plain,(
% 202.86/41.21 ![X0,X1,X2,X3]: (~theorem(implies(implies(X0,X1),X2))|theorem(or(X3,X2))|~theorem(implies(X0,or(X3,X1))))),
% 202.86/41.21 inference(resolution,[status(thm)],[f273,f224])).
% 202.86/41.21 fof(f1653,plain,(
% 202.86/41.21 ![X0,X1,X2]: (~theorem(implies(X0,implies(X1,X2)))|theorem(implies(X0,X2))|~theorem(X1))),
% 202.86/41.21 inference(resolution,[status(thm)],[f450,f18])).
% 202.86/41.21 fof(f1765,plain,(
% 202.86/41.21 ![X0,X1,X2,X3]: (~theorem(implies(implies(or(X0,X1),or(X0,X2)),X3))|theorem(implies(implies(X1,X2),X3)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f930,f72])).
% 202.86/41.21 fof(f1766,plain,(
% 202.86/41.21 ![X0,X1,X2,X3]: (~theorem(implies(implies(X0,X1),X2))|theorem(implies(implies(X0,X3),X2))|~theorem(implies(X3,X1)))),
% 202.86/41.21 inference(resolution,[status(thm)],[f930,f226])).
% 129.52/41.27 fof(f1774,plain,(
% 129.52/41.27 ![X0,X1,X2]: (~theorem(implies(implies(X0,X1),X2))|theorem(implies(X1,X2)))),
% 129.52/41.27 inference(resolution,[status(thm)],[f930,f26])).
% 129.52/41.27 fof(f1780,plain,(
% 129.52/41.27 ![X0,X1,X2]: (~theorem(implies(or(X0,X1),X2))|theorem(implies(X1,X2)))),
% 129.52/41.27 inference(resolution,[status(thm)],[f930,f22])).
% 129.52/41.27 fof(f2066,plain,(
% 129.52/41.27 ![X0,X1]: (theorem(implies(X0,or(X0,X1))))),
% 129.52/41.27 inference(resolution,[status(thm)],[f1780,f45])).
% 129.52/41.27 fof(f2101,plain,(
% 129.52/41.27 ![X0,X1,X2]: (theorem(implies(X0,or(implies(X1,X0),X2))))),
% 129.52/41.27 inference(resolution,[status(thm)],[f2066,f1774])).
% 129.52/41.27 fof(f2144,plain,(
% 129.52/41.27 ![X0,X1,X2]: (~theorem(implies(implies(X0,X1),X2))|theorem(or(X0,X2)))),
% 129.52/41.27 inference(resolution,[status(thm)],[f1381,f2066])).
% 129.52/41.27 fof(f2885,plain,(
% 129.52/41.27 ![X0,X1]: (theorem(implies(implies(X0,X1),X1))|~theorem(X0))),
% 129.52/41.27 inference(resolution,[status(thm)],[f1653,f549])).
% 129.52/41.27 fof(f2932,plain,(
% 129.52/41.27 ![X0,X1]: (~theorem(X0)|theorem(implies(implies(X0,or(X1,X1)),X1)))),
% 129.52/41.27 inference(resolution,[status(thm)],[f2885,f506])).
% 129.52/41.27 fof(f3290,plain,(
% 129.52/41.27 ![X0]: (theorem(or(X0,not(X0))))),
% 129.52/41.27 inference(resolution,[status(thm)],[f2144,f29])).
% 129.52/41.27 fof(f3339,plain,(
% 129.52/41.27 ![X0,X1]: (theorem(implies(X0,or(not(implies(X0,X1)),X1))))),
% 129.52/41.27 inference(resolution,[status(thm)],[f3290,f1045])).
% 129.52/41.27 fof(f3350,plain,(
% 129.52/41.27 ![X0,X1]: (theorem(implies(X0,implies(implies(X0,X1),X1))))),
% 129.52/41.27 inference(forward_demodulation,[status(thm)],[f15,f3339])).
% 129.52/41.27 fof(f4437,plain,(
% 129.52/41.27 ![X0]: (~theorem(implies(implies(implies(p,q),X0),implies(implies(q,p),p)))|~theorem(implies(q,X0)))),
% 129.52/41.27 inference(resolution,[status(thm)],[f1766,f19])).
% 129.52/41.27 fof(f5607,definition,(
% 129.52/41.27 sQ93_spl <=> (theorem(implies(q,implies(implies(q,p),p))))),
% 129.52/41.27 introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition])).
% 129.52/41.27 fof(f5609,plain,(
% 129.52/41.27 ~theorem(implies(q,implies(implies(q,p),p)))|sQ93_spl),
% 129.52/41.27 inference(component_clause,[status(thm)],[f5607])).
% 129.52/41.27 fof(f8566,plain,(
% 129.52/41.27 $false|sQ93_spl),
% 129.52/41.27 inference(forward_subsumption_resolution,[status(thm)],[f5609,f3350])).
% 129.52/41.27 fof(f8567,plain,(
% 129.52/41.27 sQ93_spl),
% 129.52/41.27 inference(contradiction_clause,[status(thm)],[f8566])).
% 129.52/41.27 fof(f13471,plain,(
% 129.52/41.27 ![X0,X1]: (~theorem(or(X0,X1))|theorem(implies(implies(X1,X0),X0)))),
% 129.52/41.27 inference(resolution,[status(thm)],[f2932,f1765])).
% 129.52/41.27 fof(f28023,plain,(
% 129.52/41.27 ![X0,X1,X2]: (theorem(or(implies(X0,X1),implies(X1,X2))))),
% 129.52/41.27 inference(resolution,[status(thm)],[f2101,f224])).
% 129.52/41.27 fof(f52285,plain,(
% 129.52/41.27 ~theorem(or(implies(implies(q,p),p),implies(p,q)))|~theorem(implies(q,implies(implies(q,p),p)))),
% 129.52/41.27 inference(resolution,[status(thm)],[f13471,f4437])).
% 129.52/41.27 fof(f52386,definition,(
% 129.52/41.27 sQ568_spl <=> (theorem(or(implies(implies(q,p),p),implies(p,q))))),
% 129.52/41.27 introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition])).
% 129.52/41.27 fof(f52388,plain,(
% 129.52/41.27 ~theorem(or(implies(implies(q,p),p),implies(p,q)))|sQ568_spl),
% 129.52/41.27 inference(component_clause,[status(thm)],[f52386])).
% 129.52/41.27 fof(f52389,plain,(
% 129.52/41.27 ~sQ568_spl|~sQ93_spl),
% 129.52/41.27 inference(split_clause,[status(thm)],[f52285,f52386,f5607])).
% 129.52/41.27 fof(f52416,plain,(
% 129.52/41.27 $false|sQ568_spl),
% 129.52/41.27 inference(forward_subsumption_resolution,[status(thm)],[f52388,f28023])).
% 129.52/41.27 fof(f52417,plain,(
% 129.52/41.27 sQ568_spl),
% 129.52/41.27 inference(contradiction_clause,[status(thm)],[f52416])).
% 129.52/41.27 fof(f52418,plain,(
% 129.52/41.27 $false),
% 129.52/41.27 inference(sat_refutation,[status(thm)],[f8567,f52389,f52417])).
% 129.52/41.27 % SZS output end CNFRefutation for theBenchmark.p
% 16.13/41.61 % Elapsed time: 25.976163 seconds
% 16.13/41.61 % CPU time: 204.816065 seconds
% 16.13/41.61 % Total memory used: 1.877 GB
% 16.13/41.61 % Net memory used: 1.703 GB
%------------------------------------------------------------------------------