TSTP Solution File: LCL497+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL497+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:27:19 EDT 2024
% Result : Theorem 4.73s 0.96s
% Output : CNFRefutation 5.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : LCL497+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.27 % Computer : n002.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon Apr 29 20:33:54 EDT 2024
% 0.08/0.27 % CPUTime :
% 0.08/0.28 % Drodi V3.6.0
% 4.73/0.96 % Refutation found
% 4.73/0.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.73/0.96 % SZS output start CNFRefutation for theBenchmark
% 4.73/0.96 fof(f1,axiom,(
% 4.73/0.96 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f6,axiom,(
% 4.73/0.96 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f10,axiom,(
% 4.73/0.96 ( or_1<=> (! [X,Y] : is_a_theorem(implies(X,or(X,Y))) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f20,axiom,(
% 4.73/0.96 ( cn2<=> (! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f23,axiom,(
% 4.73/0.96 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f24,axiom,(
% 4.73/0.96 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f25,axiom,(
% 4.73/0.96 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f26,axiom,(
% 4.73/0.96 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f30,axiom,(
% 4.73/0.96 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f32,axiom,(
% 4.73/0.96 op_implies_or ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f35,axiom,(
% 4.73/0.96 modus_ponens ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f37,axiom,(
% 4.73/0.96 r2 ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f38,axiom,(
% 4.73/0.96 r3 ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f39,axiom,(
% 4.73/0.96 r4 ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f40,axiom,(
% 4.73/0.96 r5 ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f45,conjecture,(
% 4.73/0.96 cn2 ),
% 4.73/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.73/0.96 fof(f46,negated_conjecture,(
% 4.73/0.96 ~(cn2 )),
% 4.73/0.96 inference(negated_conjecture,[status(cth)],[f45])).
% 4.73/0.96 fof(f47,plain,(
% 4.73/0.96 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 4.73/0.96 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 4.73/0.96 fof(f48,plain,(
% 4.73/0.96 (~modus_ponens|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(implies(X,Y)))&~is_a_theorem(Y))))),
% 4.73/0.96 inference(NNF_transformation,[status(esa)],[f47])).
% 4.73/0.96 fof(f49,plain,(
% 4.73/0.96 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(implies(X,Y))))&~is_a_theorem(Y))))),
% 4.73/0.96 inference(miniscoping,[status(esa)],[f48])).
% 4.73/0.96 fof(f50,plain,(
% 4.73/0.96 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sk0_1)&is_a_theorem(implies(sk0_1,sk0_0)))&~is_a_theorem(sk0_0)))),
% 4.73/0.96 inference(skolemization,[status(esa)],[f49])).
% 4.73/0.96 fof(f51,plain,(
% 4.73/0.96 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 4.73/0.96 inference(cnf_transformation,[status(esa)],[f50])).
% 4.73/0.96 fof(f73,plain,(
% 4.73/0.96 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|(?[X,Y,Z]: ~is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))),
% 4.73/0.96 inference(NNF_transformation,[status(esa)],[f6])).
% 4.73/0.96 fof(f74,plain,(
% 4.73/0.96 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|~is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12)))))),
% 4.73/0.96 inference(skolemization,[status(esa)],[f73])).
% 4.73/0.96 fof(f75,plain,(
% 4.73/0.96 ![X0,X1,X2]: (~implies_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 4.73/0.96 inference(cnf_transformation,[status(esa)],[f74])).
% 5.15/0.97 fof(f76,plain,(
% 5.15/0.97 implies_3|~is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12))))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f74])).
% 5.15/0.97 fof(f89,plain,(
% 5.15/0.97 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|(?[X,Y]: ~is_a_theorem(implies(X,or(X,Y)))))),
% 5.15/0.97 inference(NNF_transformation,[status(esa)],[f10])).
% 5.15/0.97 fof(f90,plain,(
% 5.15/0.97 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20))))),
% 5.15/0.97 inference(skolemization,[status(esa)],[f89])).
% 5.15/0.97 fof(f91,plain,(
% 5.15/0.97 ![X0,X1]: (~or_1|is_a_theorem(implies(X0,or(X0,X1))))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f90])).
% 5.15/0.97 fof(f92,plain,(
% 5.15/0.97 or_1|~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20)))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f90])).
% 5.15/0.97 fof(f129,plain,(
% 5.15/0.97 (~cn2|(![P,Q]: is_a_theorem(implies(P,implies(not(P),Q)))))&(cn2|(?[P,Q]: ~is_a_theorem(implies(P,implies(not(P),Q)))))),
% 5.15/0.97 inference(NNF_transformation,[status(esa)],[f20])).
% 5.15/0.97 fof(f130,plain,(
% 5.15/0.97 (~cn2|(![P,Q]: is_a_theorem(implies(P,implies(not(P),Q)))))&(cn2|~is_a_theorem(implies(sk0_41,implies(not(sk0_41),sk0_42))))),
% 5.15/0.97 inference(skolemization,[status(esa)],[f129])).
% 5.15/0.97 fof(f132,plain,(
% 5.15/0.97 cn2|~is_a_theorem(implies(sk0_41,implies(not(sk0_41),sk0_42)))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f130])).
% 5.15/0.97 fof(f141,plain,(
% 5.15/0.97 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 5.15/0.97 inference(NNF_transformation,[status(esa)],[f23])).
% 5.15/0.97 fof(f142,plain,(
% 5.15/0.97 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46))))),
% 5.15/0.97 inference(skolemization,[status(esa)],[f141])).
% 5.15/0.97 fof(f143,plain,(
% 5.15/0.97 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f142])).
% 5.15/0.97 fof(f145,plain,(
% 5.15/0.97 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|(?[P,Q]: ~is_a_theorem(implies(or(P,Q),or(Q,P)))))),
% 5.15/0.97 inference(NNF_transformation,[status(esa)],[f24])).
% 5.15/0.97 fof(f146,plain,(
% 5.15/0.97 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47))))),
% 5.15/0.97 inference(skolemization,[status(esa)],[f145])).
% 5.15/0.97 fof(f147,plain,(
% 5.15/0.97 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f146])).
% 5.15/0.97 fof(f149,plain,(
% 5.15/0.97 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|(?[P,Q,R]: ~is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))),
% 5.15/0.97 inference(NNF_transformation,[status(esa)],[f25])).
% 5.15/0.97 fof(f150,plain,(
% 5.15/0.97 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|~is_a_theorem(implies(or(sk0_49,or(sk0_50,sk0_51)),or(sk0_50,or(sk0_49,sk0_51)))))),
% 5.15/0.97 inference(skolemization,[status(esa)],[f149])).
% 5.15/0.97 fof(f151,plain,(
% 5.15/0.97 ![X0,X1,X2]: (~r4|is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f150])).
% 5.15/0.97 fof(f153,plain,(
% 5.15/0.97 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|(?[P,Q,R]: ~is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))),
% 5.15/0.97 inference(NNF_transformation,[status(esa)],[f26])).
% 5.15/0.97 fof(f154,plain,(
% 5.15/0.97 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|~is_a_theorem(implies(implies(sk0_53,sk0_54),implies(or(sk0_52,sk0_53),or(sk0_52,sk0_54)))))),
% 5.15/0.97 inference(skolemization,[status(esa)],[f153])).
% 5.15/0.97 fof(f155,plain,(
% 5.15/0.97 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f154])).
% 5.15/0.97 fof(f163,plain,(
% 5.15/0.97 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 5.15/0.97 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 5.15/0.97 fof(f164,plain,(
% 5.15/0.97 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f163])).
% 5.15/0.97 fof(f167,plain,(
% 5.15/0.97 op_implies_or),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f32])).
% 5.15/0.97 fof(f170,plain,(
% 5.15/0.97 modus_ponens),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f35])).
% 5.15/0.97 fof(f172,plain,(
% 5.15/0.97 r2),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f37])).
% 5.15/0.97 fof(f173,plain,(
% 5.15/0.97 r3),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f38])).
% 5.15/0.97 fof(f174,plain,(
% 5.15/0.97 r4),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f39])).
% 5.15/0.97 fof(f175,plain,(
% 5.15/0.97 r5),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f40])).
% 5.15/0.97 fof(f180,plain,(
% 5.15/0.97 ~cn2),
% 5.15/0.97 inference(cnf_transformation,[status(esa)],[f46])).
% 5.15/0.97 fof(f181,plain,(
% 5.15/0.97 spl0_0 <=> modus_ponens),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f183,plain,(
% 5.15/0.97 ~modus_ponens|spl0_0),
% 5.15/0.97 inference(component_clause,[status(thm)],[f181])).
% 5.15/0.97 fof(f184,plain,(
% 5.15/0.97 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f185,plain,(
% 5.15/0.97 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 5.15/0.97 inference(component_clause,[status(thm)],[f184])).
% 5.15/0.97 fof(f187,plain,(
% 5.15/0.97 ~spl0_0|spl0_1),
% 5.15/0.97 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 5.15/0.97 fof(f248,plain,(
% 5.15/0.97 spl0_18 <=> implies_3),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f251,plain,(
% 5.15/0.97 spl0_19 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f252,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))|~spl0_19)),
% 5.15/0.97 inference(component_clause,[status(thm)],[f251])).
% 5.15/0.97 fof(f254,plain,(
% 5.15/0.97 ~spl0_18|spl0_19),
% 5.15/0.97 inference(split_clause,[status(thm)],[f75,f248,f251])).
% 5.15/0.97 fof(f255,plain,(
% 5.15/0.97 spl0_20 <=> is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12))))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f257,plain,(
% 5.15/0.97 ~is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12))))|spl0_20),
% 5.15/0.97 inference(component_clause,[status(thm)],[f255])).
% 5.15/0.97 fof(f258,plain,(
% 5.15/0.97 spl0_18|~spl0_20),
% 5.15/0.97 inference(split_clause,[status(thm)],[f76,f248,f255])).
% 5.15/0.97 fof(f292,plain,(
% 5.15/0.97 spl0_30 <=> or_1),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f295,plain,(
% 5.15/0.97 spl0_31 <=> is_a_theorem(implies(X0,or(X0,X1)))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f296,plain,(
% 5.15/0.97 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_31)),
% 5.15/0.97 inference(component_clause,[status(thm)],[f295])).
% 5.15/0.97 fof(f298,plain,(
% 5.15/0.97 ~spl0_30|spl0_31),
% 5.15/0.97 inference(split_clause,[status(thm)],[f91,f292,f295])).
% 5.15/0.97 fof(f299,plain,(
% 5.15/0.97 spl0_32 <=> is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20)))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f301,plain,(
% 5.15/0.97 ~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20)))|spl0_32),
% 5.15/0.97 inference(component_clause,[status(thm)],[f299])).
% 5.15/0.97 fof(f302,plain,(
% 5.15/0.97 spl0_30|~spl0_32),
% 5.15/0.97 inference(split_clause,[status(thm)],[f92,f292,f299])).
% 5.15/0.97 fof(f306,plain,(
% 5.15/0.97 spl0_34 <=> is_a_theorem(implies(X0,or(X1,X0)))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f307,plain,(
% 5.15/0.97 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_34)),
% 5.15/0.97 inference(component_clause,[status(thm)],[f306])).
% 5.15/0.97 fof(f396,plain,(
% 5.15/0.97 spl0_58 <=> cn2),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f397,plain,(
% 5.15/0.97 cn2|~spl0_58),
% 5.15/0.97 inference(component_clause,[status(thm)],[f396])).
% 5.15/0.97 fof(f403,plain,(
% 5.15/0.97 spl0_60 <=> is_a_theorem(implies(sk0_41,implies(not(sk0_41),sk0_42)))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f405,plain,(
% 5.15/0.97 ~is_a_theorem(implies(sk0_41,implies(not(sk0_41),sk0_42)))|spl0_60),
% 5.15/0.97 inference(component_clause,[status(thm)],[f403])).
% 5.15/0.97 fof(f406,plain,(
% 5.15/0.97 spl0_58|~spl0_60),
% 5.15/0.97 inference(split_clause,[status(thm)],[f132,f396,f403])).
% 5.15/0.97 fof(f429,plain,(
% 5.15/0.97 spl0_67 <=> r2),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f431,plain,(
% 5.15/0.97 ~r2|spl0_67),
% 5.15/0.97 inference(component_clause,[status(thm)],[f429])).
% 5.15/0.97 fof(f432,plain,(
% 5.15/0.97 ~spl0_67|spl0_34),
% 5.15/0.97 inference(split_clause,[status(thm)],[f143,f429,f306])).
% 5.15/0.97 fof(f437,plain,(
% 5.15/0.97 spl0_69 <=> r3),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f439,plain,(
% 5.15/0.97 ~r3|spl0_69),
% 5.15/0.97 inference(component_clause,[status(thm)],[f437])).
% 5.15/0.97 fof(f440,plain,(
% 5.15/0.97 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f441,plain,(
% 5.15/0.97 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 5.15/0.97 inference(component_clause,[status(thm)],[f440])).
% 5.15/0.97 fof(f443,plain,(
% 5.15/0.97 ~spl0_69|spl0_70),
% 5.15/0.97 inference(split_clause,[status(thm)],[f147,f437,f440])).
% 5.15/0.97 fof(f448,plain,(
% 5.15/0.97 spl0_72 <=> r4),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f450,plain,(
% 5.15/0.97 ~r4|spl0_72),
% 5.15/0.97 inference(component_clause,[status(thm)],[f448])).
% 5.15/0.97 fof(f451,plain,(
% 5.15/0.97 spl0_73 <=> is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f452,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))|~spl0_73)),
% 5.15/0.97 inference(component_clause,[status(thm)],[f451])).
% 5.15/0.97 fof(f454,plain,(
% 5.15/0.97 ~spl0_72|spl0_73),
% 5.15/0.97 inference(split_clause,[status(thm)],[f151,f448,f451])).
% 5.15/0.97 fof(f459,plain,(
% 5.15/0.97 spl0_75 <=> r5),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f461,plain,(
% 5.15/0.97 ~r5|spl0_75),
% 5.15/0.97 inference(component_clause,[status(thm)],[f459])).
% 5.15/0.97 fof(f462,plain,(
% 5.15/0.97 spl0_76 <=> is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f463,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))|~spl0_76)),
% 5.15/0.97 inference(component_clause,[status(thm)],[f462])).
% 5.15/0.97 fof(f465,plain,(
% 5.15/0.97 ~spl0_75|spl0_76),
% 5.15/0.97 inference(split_clause,[status(thm)],[f155,f459,f462])).
% 5.15/0.97 fof(f491,plain,(
% 5.15/0.97 spl0_84 <=> op_implies_or),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f493,plain,(
% 5.15/0.97 ~op_implies_or|spl0_84),
% 5.15/0.97 inference(component_clause,[status(thm)],[f491])).
% 5.15/0.97 fof(f494,plain,(
% 5.15/0.97 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 5.15/0.97 introduced(split_symbol_definition)).
% 5.15/0.97 fof(f495,plain,(
% 5.15/0.97 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 5.15/0.97 inference(component_clause,[status(thm)],[f494])).
% 5.15/0.97 fof(f497,plain,(
% 5.15/0.97 ~spl0_84|spl0_85),
% 5.15/0.97 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 5.15/0.97 fof(f507,plain,(
% 5.15/0.97 $false|spl0_0),
% 5.15/0.97 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 5.15/0.97 fof(f508,plain,(
% 5.15/0.97 spl0_0),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f507])).
% 5.15/0.97 fof(f511,plain,(
% 5.15/0.97 $false|spl0_84),
% 5.15/0.97 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 5.15/0.97 fof(f512,plain,(
% 5.15/0.97 spl0_84),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f511])).
% 5.15/0.97 fof(f517,plain,(
% 5.15/0.97 ![X0,X1]: (is_a_theorem(implies(not(X0),implies(X0,X1)))|~spl0_31|~spl0_85)),
% 5.15/0.97 inference(paramodulation,[status(thm)],[f495,f296])).
% 5.15/0.97 fof(f521,plain,(
% 5.15/0.97 $false|spl0_67),
% 5.15/0.97 inference(forward_subsumption_resolution,[status(thm)],[f431,f172])).
% 5.15/0.97 fof(f522,plain,(
% 5.15/0.97 spl0_67),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f521])).
% 5.15/0.97 fof(f552,plain,(
% 5.15/0.97 $false|spl0_69),
% 5.15/0.97 inference(forward_subsumption_resolution,[status(thm)],[f439,f173])).
% 5.15/0.97 fof(f553,plain,(
% 5.15/0.97 spl0_69),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f552])).
% 5.15/0.97 fof(f565,plain,(
% 5.15/0.97 ![X0]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,implies(sk0_19,or(sk0_19,sk0_20))))|spl0_32|~spl0_1)),
% 5.15/0.97 inference(resolution,[status(thm)],[f301,f185])).
% 5.15/0.97 fof(f592,plain,(
% 5.15/0.97 ![X0]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,implies(sk0_41,implies(not(sk0_41),sk0_42))))|spl0_60|~spl0_1)),
% 5.15/0.97 inference(resolution,[status(thm)],[f405,f185])).
% 5.15/0.97 fof(f643,plain,(
% 5.15/0.97 ![X0]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12)))))|spl0_20|~spl0_1)),
% 5.15/0.97 inference(resolution,[status(thm)],[f257,f185])).
% 5.15/0.97 fof(f673,plain,(
% 5.15/0.97 $false|spl0_75),
% 5.15/0.97 inference(forward_subsumption_resolution,[status(thm)],[f461,f175])).
% 5.15/0.97 fof(f674,plain,(
% 5.15/0.97 spl0_75),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f673])).
% 5.15/0.97 fof(f677,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1))))|~spl0_76|~spl0_85)),
% 5.15/0.97 inference(paramodulation,[status(thm)],[f495,f463])).
% 5.15/0.97 fof(f678,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))|~spl0_76|~spl0_85)),
% 5.15/0.97 inference(forward_demodulation,[status(thm)],[f495,f677])).
% 5.15/0.97 fof(f683,plain,(
% 5.15/0.97 $false|spl0_72),
% 5.15/0.97 inference(forward_subsumption_resolution,[status(thm)],[f450,f174])).
% 5.15/0.97 fof(f684,plain,(
% 5.15/0.97 spl0_72),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f683])).
% 5.15/0.97 fof(f685,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2))))|~spl0_73|~spl0_85)),
% 5.15/0.97 inference(paramodulation,[status(thm)],[f495,f452])).
% 5.15/0.97 fof(f686,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2))))|~spl0_73|~spl0_85)),
% 5.15/0.97 inference(forward_demodulation,[status(thm)],[f495,f685])).
% 5.15/0.97 fof(f707,plain,(
% 5.15/0.97 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|~is_a_theorem(implies(X1,implies(X0,implies(sk0_19,or(sk0_19,sk0_20)))))|spl0_32|~spl0_1)),
% 5.15/0.97 inference(resolution,[status(thm)],[f565,f185])).
% 5.15/0.97 fof(f1045,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2))))|~spl0_73|~spl0_85)),
% 5.15/0.97 inference(paramodulation,[status(thm)],[f495,f686])).
% 5.15/0.97 fof(f1046,plain,(
% 5.15/0.97 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))))|~spl0_73|~spl0_85)),
% 5.15/0.97 inference(forward_demodulation,[status(thm)],[f495,f1045])).
% 5.15/0.97 fof(f2088,plain,(
% 5.15/0.97 ~is_a_theorem(implies(not(sk0_41),implies(sk0_41,sk0_42)))|~spl0_73|~spl0_85|spl0_60|~spl0_1),
% 5.15/0.97 inference(resolution,[status(thm)],[f1046,f592])).
% 5.15/0.97 fof(f2090,plain,(
% 5.15/0.97 ~is_a_theorem(implies(implies(sk0_11,sk0_12),implies(implies(sk0_10,sk0_11),implies(sk0_10,sk0_12))))|~spl0_73|~spl0_85|spl0_20|~spl0_1),
% 5.15/0.97 inference(resolution,[status(thm)],[f1046,f643])).
% 5.15/0.97 fof(f2091,plain,(
% 5.15/0.97 $false|~spl0_76|~spl0_73|~spl0_85|spl0_20|~spl0_1),
% 5.15/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2090,f678])).
% 5.15/0.97 fof(f2092,plain,(
% 5.15/0.97 ~spl0_76|~spl0_73|~spl0_85|spl0_20|~spl0_1),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f2091])).
% 5.15/0.97 fof(f3967,plain,(
% 5.15/0.97 ![X0]: (~is_a_theorem(implies(X0,or(sk0_19,sk0_20)))|~is_a_theorem(implies(sk0_19,X0))|spl0_32|~spl0_1|~spl0_19)),
% 5.15/0.97 inference(resolution,[status(thm)],[f707,f252])).
% 5.15/0.97 fof(f3995,plain,(
% 5.15/0.97 ![X0]: (~is_a_theorem(implies(or(X0,sk0_19),or(sk0_19,sk0_20)))|spl0_32|~spl0_1|~spl0_19|~spl0_34)),
% 5.15/0.97 inference(resolution,[status(thm)],[f3967,f307])).
% 5.15/0.97 fof(f4000,plain,(
% 5.15/0.97 $false|spl0_32|~spl0_1|~spl0_19|~spl0_34|~spl0_70),
% 5.15/0.97 inference(resolution,[status(thm)],[f3995,f441])).
% 5.15/0.97 fof(f4001,plain,(
% 5.15/0.97 spl0_32|~spl0_1|~spl0_19|~spl0_34|~spl0_70),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f4000])).
% 5.15/0.97 fof(f4065,plain,(
% 5.15/0.97 $false|~spl0_31|~spl0_73|~spl0_85|spl0_60|~spl0_1),
% 5.15/0.97 inference(backward_subsumption_resolution,[status(thm)],[f2088,f517])).
% 5.15/0.97 fof(f4066,plain,(
% 5.15/0.97 ~spl0_31|~spl0_73|~spl0_85|spl0_60|~spl0_1),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f4065])).
% 5.15/0.97 fof(f4109,plain,(
% 5.15/0.97 $false|~spl0_58),
% 5.15/0.97 inference(forward_subsumption_resolution,[status(thm)],[f397,f180])).
% 5.15/0.97 fof(f4110,plain,(
% 5.15/0.97 ~spl0_58),
% 5.15/0.97 inference(contradiction_clause,[status(thm)],[f4109])).
% 5.15/0.97 fof(f4111,plain,(
% 5.15/0.97 $false),
% 5.15/0.97 inference(sat_refutation,[status(thm)],[f187,f254,f258,f298,f302,f406,f432,f443,f454,f465,f497,f508,f512,f522,f553,f674,f684,f2092,f4001,f4066,f4110])).
% 5.15/0.97 % SZS output end CNFRefutation for theBenchmark.p
% 5.15/0.99 % Elapsed time: 0.708270 seconds
% 5.15/0.99 % CPU time: 5.424044 seconds
% 5.15/0.99 % Total memory used: 149.610 MB
% 5.15/0.99 % Net memory used: 147.477 MB
%------------------------------------------------------------------------------