TSTP Solution File: LCL486+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL486+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 20:27:18 EDT 2024
% Result : Theorem 5.91s 1.04s
% Output : CNFRefutation 5.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.07 % Problem : LCL486+1 : TPTP v8.1.2. Released v3.3.0.
% 0.01/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n027.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 20:43:01 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.10/0.27 % Drodi V3.6.0
% 5.91/1.04 % Refutation found
% 5.91/1.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.91/1.04 % SZS output start CNFRefutation for theBenchmark
% 5.91/1.04 fof(f1,axiom,(
% 5.91/1.04 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f6,axiom,(
% 5.91/1.04 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f25,axiom,(
% 5.91/1.04 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f26,axiom,(
% 5.91/1.04 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f30,axiom,(
% 5.91/1.04 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f32,axiom,(
% 5.91/1.04 op_implies_or ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f35,axiom,(
% 5.91/1.04 modus_ponens ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f39,axiom,(
% 5.91/1.04 r4 ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f40,axiom,(
% 5.91/1.04 r5 ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f45,conjecture,(
% 5.91/1.04 implies_3 ),
% 5.91/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.91/1.04 fof(f46,negated_conjecture,(
% 5.91/1.04 ~(implies_3 )),
% 5.91/1.04 inference(negated_conjecture,[status(cth)],[f45])).
% 5.91/1.04 fof(f47,plain,(
% 5.91/1.04 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 5.91/1.04 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 5.91/1.04 fof(f48,plain,(
% 5.91/1.04 (~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))))),
% 5.91/1.04 inference(NNF_transformation,[status(esa)],[f47])).
% 5.91/1.04 fof(f49,plain,(
% 5.91/1.04 (~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))))),
% 5.91/1.04 inference(miniscoping,[status(esa)],[f48])).
% 5.91/1.04 fof(f50,plain,(
% 5.91/1.04 (~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)))),
% 5.91/1.04 inference(skolemization,[status(esa)],[f49])).
% 5.91/1.04 fof(f51,plain,(
% 5.91/1.04 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f50])).
% 5.91/1.04 fof(f73,plain,(
% 5.91/1.04 (~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))))))),
% 5.91/1.04 inference(NNF_transformation,[status(esa)],[f6])).
% 5.91/1.04 fof(f74,plain,(
% 5.91/1.04 (~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)))))),
% 5.91/1.04 inference(skolemization,[status(esa)],[f73])).
% 5.91/1.04 fof(f76,plain,(
% 5.91/1.04 implies_3|~is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12))))),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f74])).
% 5.91/1.04 fof(f149,plain,(
% 5.91/1.04 (~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))))))),
% 5.91/1.04 inference(NNF_transformation,[status(esa)],[f25])).
% 5.91/1.04 fof(f150,plain,(
% 5.91/1.04 (~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)))))),
% 5.91/1.04 inference(skolemization,[status(esa)],[f149])).
% 5.91/1.04 fof(f151,plain,(
% 5.91/1.04 ![X0,X1,X2]: (~r4|is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f150])).
% 5.91/1.04 fof(f153,plain,(
% 5.91/1.04 (~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))))))),
% 5.91/1.04 inference(NNF_transformation,[status(esa)],[f26])).
% 5.91/1.04 fof(f154,plain,(
% 5.91/1.04 (~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)))))),
% 5.91/1.04 inference(skolemization,[status(esa)],[f153])).
% 5.91/1.04 fof(f155,plain,(
% 5.91/1.04 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f154])).
% 5.91/1.04 fof(f163,plain,(
% 5.91/1.04 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 5.91/1.04 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 5.91/1.04 fof(f164,plain,(
% 5.91/1.04 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f163])).
% 5.91/1.04 fof(f167,plain,(
% 5.91/1.04 op_implies_or),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f32])).
% 5.91/1.04 fof(f170,plain,(
% 5.91/1.04 modus_ponens),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f35])).
% 5.91/1.04 fof(f174,plain,(
% 5.91/1.04 r4),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f39])).
% 5.91/1.04 fof(f175,plain,(
% 5.91/1.04 r5),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f40])).
% 5.91/1.04 fof(f180,plain,(
% 5.91/1.04 ~implies_3),
% 5.91/1.04 inference(cnf_transformation,[status(esa)],[f46])).
% 5.91/1.04 fof(f181,plain,(
% 5.91/1.04 spl0_0 <=> modus_ponens),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f183,plain,(
% 5.91/1.04 ~modus_ponens|spl0_0),
% 5.91/1.04 inference(component_clause,[status(thm)],[f181])).
% 5.91/1.04 fof(f184,plain,(
% 5.91/1.04 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f185,plain,(
% 5.91/1.04 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 5.91/1.04 inference(component_clause,[status(thm)],[f184])).
% 5.91/1.04 fof(f187,plain,(
% 5.91/1.04 ~spl0_0|spl0_1),
% 5.91/1.04 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 5.91/1.04 fof(f248,plain,(
% 5.91/1.04 spl0_18 <=> implies_3),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f249,plain,(
% 5.91/1.04 implies_3|~spl0_18),
% 5.91/1.04 inference(component_clause,[status(thm)],[f248])).
% 5.91/1.04 fof(f251,plain,(
% 5.91/1.04 spl0_19 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f252,plain,(
% 5.91/1.04 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))|~spl0_19)),
% 5.91/1.04 inference(component_clause,[status(thm)],[f251])).
% 5.91/1.04 fof(f255,plain,(
% 5.91/1.04 spl0_20 <=> is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12))))),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f257,plain,(
% 5.91/1.04 ~is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12))))|spl0_20),
% 5.91/1.04 inference(component_clause,[status(thm)],[f255])).
% 5.91/1.04 fof(f258,plain,(
% 5.91/1.04 spl0_18|~spl0_20),
% 5.91/1.04 inference(split_clause,[status(thm)],[f76,f248,f255])).
% 5.91/1.04 fof(f448,plain,(
% 5.91/1.04 spl0_72 <=> r4),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f450,plain,(
% 5.91/1.04 ~r4|spl0_72),
% 5.91/1.04 inference(component_clause,[status(thm)],[f448])).
% 5.91/1.04 fof(f451,plain,(
% 5.91/1.04 spl0_73 <=> is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f452,plain,(
% 5.91/1.04 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))|~spl0_73)),
% 5.91/1.04 inference(component_clause,[status(thm)],[f451])).
% 5.91/1.04 fof(f454,plain,(
% 5.91/1.04 ~spl0_72|spl0_73),
% 5.91/1.04 inference(split_clause,[status(thm)],[f151,f448,f451])).
% 5.91/1.04 fof(f459,plain,(
% 5.91/1.04 spl0_75 <=> r5),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f461,plain,(
% 5.91/1.04 ~r5|spl0_75),
% 5.91/1.04 inference(component_clause,[status(thm)],[f459])).
% 5.91/1.04 fof(f462,plain,(
% 5.91/1.04 spl0_76 <=> is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f463,plain,(
% 5.91/1.04 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))|~spl0_76)),
% 5.91/1.04 inference(component_clause,[status(thm)],[f462])).
% 5.91/1.04 fof(f465,plain,(
% 5.91/1.04 ~spl0_75|spl0_76),
% 5.91/1.04 inference(split_clause,[status(thm)],[f155,f459,f462])).
% 5.91/1.04 fof(f491,plain,(
% 5.91/1.04 spl0_84 <=> op_implies_or),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.04 fof(f493,plain,(
% 5.91/1.04 ~op_implies_or|spl0_84),
% 5.91/1.04 inference(component_clause,[status(thm)],[f491])).
% 5.91/1.04 fof(f494,plain,(
% 5.91/1.04 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 5.91/1.04 introduced(split_symbol_definition)).
% 5.91/1.07 fof(f495,plain,(
% 5.91/1.07 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 5.91/1.07 inference(component_clause,[status(thm)],[f494])).
% 5.91/1.07 fof(f497,plain,(
% 5.91/1.07 ~spl0_84|spl0_85),
% 5.91/1.07 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 5.91/1.07 fof(f507,plain,(
% 5.91/1.07 $false|spl0_84),
% 5.91/1.07 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 5.91/1.07 fof(f508,plain,(
% 5.91/1.07 spl0_84),
% 5.91/1.07 inference(contradiction_clause,[status(thm)],[f507])).
% 5.91/1.07 fof(f515,plain,(
% 5.91/1.07 $false|spl0_0),
% 5.91/1.07 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 5.91/1.07 fof(f516,plain,(
% 5.91/1.07 spl0_0),
% 5.91/1.07 inference(contradiction_clause,[status(thm)],[f515])).
% 5.91/1.07 fof(f522,plain,(
% 5.91/1.07 $false|~spl0_19|spl0_20),
% 5.91/1.07 inference(backward_subsumption_resolution,[status(thm)],[f257,f252])).
% 5.91/1.07 fof(f523,plain,(
% 5.91/1.07 ~spl0_19|spl0_20),
% 5.91/1.07 inference(contradiction_clause,[status(thm)],[f522])).
% 5.91/1.07 fof(f568,plain,(
% 5.91/1.07 $false|spl0_75),
% 5.91/1.07 inference(forward_subsumption_resolution,[status(thm)],[f461,f175])).
% 5.91/1.07 fof(f569,plain,(
% 5.91/1.07 spl0_75),
% 5.91/1.07 inference(contradiction_clause,[status(thm)],[f568])).
% 5.91/1.07 fof(f570,plain,(
% 5.91/1.07 $false|spl0_72),
% 5.91/1.07 inference(forward_subsumption_resolution,[status(thm)],[f450,f174])).
% 5.91/1.07 fof(f571,plain,(
% 5.91/1.07 spl0_72),
% 5.91/1.07 inference(contradiction_clause,[status(thm)],[f570])).
% 5.91/1.07 fof(f837,plain,(
% 5.91/1.07 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1))))|~spl0_76|~spl0_85)),
% 5.91/1.07 inference(paramodulation,[status(thm)],[f495,f463])).
% 5.91/1.07 fof(f838,plain,(
% 5.91/1.07 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))|~spl0_76|~spl0_85)),
% 5.91/1.07 inference(forward_demodulation,[status(thm)],[f495,f837])).
% 5.91/1.07 fof(f850,plain,(
% 5.91/1.07 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,implies(X1,X2)),or(not(X1),or(X0,X2))))|~spl0_73|~spl0_85)),
% 5.91/1.07 inference(paramodulation,[status(thm)],[f495,f452])).
% 5.91/1.07 fof(f851,plain,(
% 5.91/1.07 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,implies(X1,X2)),implies(X1,or(X0,X2))))|~spl0_73|~spl0_85)),
% 5.91/1.07 inference(forward_demodulation,[status(thm)],[f495,f850])).
% 5.91/1.07 fof(f7890,plain,(
% 5.91/1.07 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,or(not(X0),X2))))|~spl0_73|~spl0_85)),
% 5.91/1.07 inference(paramodulation,[status(thm)],[f495,f851])).
% 5.91/1.07 fof(f7891,plain,(
% 5.91/1.07 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))))|~spl0_73|~spl0_85)),
% 5.91/1.07 inference(forward_demodulation,[status(thm)],[f495,f7890])).
% 5.91/1.07 fof(f7975,plain,(
% 5.91/1.07 ![X0,X1,X2]: (~is_a_theorem(implies(X0,implies(X1,X2)))|is_a_theorem(implies(X1,implies(X0,X2)))|~spl0_73|~spl0_85|~spl0_1)),
% 5.91/1.07 inference(resolution,[status(thm)],[f7891,f185])).
% 5.91/1.07 fof(f8021,plain,(
% 5.91/1.07 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))|~spl0_73|~spl0_1|~spl0_76|~spl0_85)),
% 5.91/1.07 inference(resolution,[status(thm)],[f7975,f838])).
% 5.91/1.07 fof(f8022,plain,(
% 5.91/1.07 spl0_19|~spl0_73|~spl0_1|~spl0_76|~spl0_85),
% 5.91/1.07 inference(split_clause,[status(thm)],[f8021,f251,f451,f184,f462,f494])).
% 5.91/1.07 fof(f8047,plain,(
% 5.91/1.07 $false|~spl0_18),
% 5.91/1.07 inference(forward_subsumption_resolution,[status(thm)],[f249,f180])).
% 5.91/1.07 fof(f8048,plain,(
% 5.91/1.07 ~spl0_18),
% 5.91/1.07 inference(contradiction_clause,[status(thm)],[f8047])).
% 5.91/1.07 fof(f8049,plain,(
% 5.91/1.07 $false),
% 5.91/1.07 inference(sat_refutation,[status(thm)],[f187,f258,f454,f465,f497,f508,f516,f523,f569,f571,f8022,f8048])).
% 5.91/1.07 % SZS output end CNFRefutation for theBenchmark.p
% 5.91/1.09 % Elapsed time: 0.815239 seconds
% 5.91/1.09 % CPU time: 6.320103 seconds
% 5.91/1.09 % Total memory used: 204.768 MB
% 5.91/1.09 % Net memory used: 199.050 MB
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