TSTP Solution File: LCL542+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 : Wed May 31 12:19:34 EDT 2023
% Result : Theorem 0.21s 0.38s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:39:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 0.21/0.38 % Refutation found
% 0.21/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.21/0.38 fof(f7,axiom,(
% 0.21/0.38 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.38 fof(f40,axiom,(
% 0.21/0.38 and_1 ),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.38 fof(f50,axiom,(
% 0.21/0.38 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.38 fof(f64,axiom,(
% 0.21/0.38 ( axiom_m2<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) )) ),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.38 fof(f75,axiom,(
% 0.21/0.38 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.38 fof(f78,axiom,(
% 0.21/0.38 necessitation ),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.38 fof(f86,axiom,(
% 0.21/0.38 op_strict_implies ),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.38 fof(f89,conjecture,(
% 0.21/0.38 axiom_m2 ),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.38 fof(f90,negated_conjecture,(
% 0.21/0.38 ~(axiom_m2 )),
% 0.21/0.38 inference(negated_conjecture,[status(cth)],[f89])).
% 0.21/0.38 fof(f121,plain,(
% 0.21/0.38 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 0.21/0.38 inference(NNF_transformation,[status(esa)],[f7])).
% 0.21/0.38 fof(f122,plain,(
% 0.21/0.38 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sk0_13,sk0_14),sk0_13)))),
% 0.21/0.38 inference(skolemization,[status(esa)],[f121])).
% 0.21/0.38 fof(f123,plain,(
% 0.21/0.38 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 0.21/0.38 inference(cnf_transformation,[status(esa)],[f122])).
% 0.21/0.38 fof(f219,plain,(
% 0.21/0.38 and_1),
% 0.21/0.38 inference(cnf_transformation,[status(esa)],[f40])).
% 0.21/0.38 fof(f229,plain,(
% 0.21/0.38 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 0.21/0.38 inference(pre_NNF_transformation,[status(esa)],[f50])).
% 0.21/0.38 fof(f230,plain,(
% 0.21/0.38 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 0.21/0.38 inference(NNF_transformation,[status(esa)],[f229])).
% 0.21/0.38 fof(f231,plain,(
% 0.21/0.38 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sk0_55)&~is_a_theorem(necessarily(sk0_55))))),
% 0.21/0.38 inference(skolemization,[status(esa)],[f230])).
% 0.21/0.38 fof(f232,plain,(
% 0.21/0.38 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.21/0.38 inference(cnf_transformation,[status(esa)],[f231])).
% 0.21/0.38 fof(f296,plain,(
% 0.21/0.38 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),X))))),
% 0.21/0.38 inference(NNF_transformation,[status(esa)],[f64])).
% 0.21/0.38 fof(f297,plain,(
% 0.21/0.38 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|~is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78)))),
% 0.21/0.38 inference(skolemization,[status(esa)],[f296])).
% 0.21/0.38 fof(f299,plain,(
% 0.21/0.38 axiom_m2|~is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78))),
% 0.21/0.38 inference(cnf_transformation,[status(esa)],[f297])).
% 0.21/0.38 fof(f336,plain,(
% 0.21/0.38 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.21/0.38 inference(pre_NNF_transformation,[status(esa)],[f75])).
% 0.21/0.38 fof(f337,plain,(
% 0.21/0.38 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.21/0.38 inference(cnf_transformation,[status(esa)],[f336])).
% 0.21/0.38 fof(f341,plain,(
% 0.21/0.38 necessitation),
% 0.21/0.38 inference(cnf_transformation,[status(esa)],[f78])).
% 0.21/0.38 fof(f349,plain,(
% 0.21/0.38 op_strict_implies),
% 0.21/0.38 inference(cnf_transformation,[status(esa)],[f86])).
% 0.21/0.38 fof(f352,plain,(
% 0.21/0.38 ~axiom_m2),
% 0.21/0.38 inference(cnf_transformation,[status(esa)],[f90])).
% 0.21/0.38 fof(f431,plain,(
% 0.21/0.38 spl0_21 <=> and_1),
% 0.21/0.38 introduced(split_symbol_definition)).
% 0.21/0.38 fof(f433,plain,(
% 0.21/0.38 ~and_1|spl0_21),
% 0.21/0.38 inference(component_clause,[status(thm)],[f431])).
% 0.21/0.38 fof(f434,plain,(
% 0.21/0.38 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 0.21/0.38 introduced(split_symbol_definition)).
% 0.21/0.38 fof(f435,plain,(
% 0.21/0.38 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 0.21/0.38 inference(component_clause,[status(thm)],[f434])).
% 0.21/0.38 fof(f437,plain,(
% 0.32/0.63 ~spl0_21|spl0_22),
% 0.32/0.63 inference(split_clause,[status(thm)],[f123,f431,f434])).
% 0.32/0.63 fof(f677,plain,(
% 0.32/0.63 spl0_88 <=> necessitation),
% 0.32/0.63 introduced(split_symbol_definition)).
% 0.32/0.63 fof(f679,plain,(
% 0.32/0.63 ~necessitation|spl0_88),
% 0.32/0.63 inference(component_clause,[status(thm)],[f677])).
% 0.32/0.63 fof(f680,plain,(
% 0.32/0.63 spl0_89 <=> ~is_a_theorem(X0)|is_a_theorem(necessarily(X0))),
% 0.32/0.63 introduced(split_symbol_definition)).
% 0.32/0.63 fof(f681,plain,(
% 0.32/0.63 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0))|~spl0_89)),
% 0.32/0.63 inference(component_clause,[status(thm)],[f680])).
% 0.32/0.63 fof(f683,plain,(
% 0.32/0.63 ~spl0_88|spl0_89),
% 0.32/0.63 inference(split_clause,[status(thm)],[f232,f677,f680])).
% 0.32/0.63 fof(f855,plain,(
% 0.32/0.63 spl0_136 <=> axiom_m2),
% 0.32/0.63 introduced(split_symbol_definition)).
% 0.32/0.63 fof(f856,plain,(
% 0.32/0.63 axiom_m2|~spl0_136),
% 0.32/0.63 inference(component_clause,[status(thm)],[f855])).
% 0.32/0.63 fof(f862,plain,(
% 0.32/0.63 spl0_138 <=> is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78))),
% 0.32/0.63 introduced(split_symbol_definition)).
% 0.32/0.63 fof(f864,plain,(
% 0.32/0.63 ~is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78))|spl0_138),
% 0.32/0.63 inference(component_clause,[status(thm)],[f862])).
% 0.32/0.63 fof(f865,plain,(
% 0.32/0.63 spl0_136|~spl0_138),
% 0.32/0.63 inference(split_clause,[status(thm)],[f299,f855,f862])).
% 0.32/0.63 fof(f968,plain,(
% 0.32/0.63 spl0_167 <=> op_strict_implies),
% 0.32/0.63 introduced(split_symbol_definition)).
% 0.32/0.63 fof(f970,plain,(
% 0.32/0.63 ~op_strict_implies|spl0_167),
% 0.32/0.63 inference(component_clause,[status(thm)],[f968])).
% 0.32/0.63 fof(f971,plain,(
% 0.32/0.63 spl0_168 <=> strict_implies(X0,X1)=necessarily(implies(X0,X1))),
% 0.32/0.63 introduced(split_symbol_definition)).
% 0.32/0.63 fof(f972,plain,(
% 0.32/0.63 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~spl0_168)),
% 0.32/0.63 inference(component_clause,[status(thm)],[f971])).
% 0.32/0.63 fof(f974,plain,(
% 0.32/0.63 ~spl0_167|spl0_168),
% 0.32/0.63 inference(split_clause,[status(thm)],[f337,f968,f971])).
% 0.32/0.63 fof(f986,plain,(
% 0.32/0.63 $false|spl0_88),
% 0.32/0.63 inference(forward_subsumption_resolution,[status(thm)],[f679,f341])).
% 0.32/0.63 fof(f987,plain,(
% 0.32/0.63 spl0_88),
% 0.32/0.63 inference(contradiction_clause,[status(thm)],[f986])).
% 0.32/0.63 fof(f990,plain,(
% 0.32/0.63 $false|spl0_167),
% 0.32/0.63 inference(forward_subsumption_resolution,[status(thm)],[f970,f349])).
% 0.32/0.63 fof(f991,plain,(
% 0.32/0.63 spl0_167),
% 0.32/0.63 inference(contradiction_clause,[status(thm)],[f990])).
% 0.32/0.63 fof(f1009,plain,(
% 0.32/0.63 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~spl0_89|~spl0_168)),
% 0.32/0.63 inference(paramodulation,[status(thm)],[f972,f681])).
% 0.32/0.63 fof(f1029,plain,(
% 0.32/0.63 $false|spl0_21),
% 0.32/0.63 inference(forward_subsumption_resolution,[status(thm)],[f433,f219])).
% 0.32/0.63 fof(f1030,plain,(
% 0.32/0.63 spl0_21),
% 0.32/0.63 inference(contradiction_clause,[status(thm)],[f1029])).
% 0.32/0.63 fof(f1144,plain,(
% 0.32/0.63 ~is_a_theorem(implies(and(sk0_78,sk0_79),sk0_78))|spl0_138|~spl0_89|~spl0_168),
% 0.32/0.63 inference(resolution,[status(thm)],[f864,f1009])).
% 0.32/0.63 fof(f1145,plain,(
% 0.32/0.63 $false|~spl0_22|spl0_138|~spl0_89|~spl0_168),
% 0.32/0.63 inference(forward_subsumption_resolution,[status(thm)],[f1144,f435])).
% 0.32/0.63 fof(f1146,plain,(
% 0.32/0.63 ~spl0_22|spl0_138|~spl0_89|~spl0_168),
% 0.32/0.63 inference(contradiction_clause,[status(thm)],[f1145])).
% 0.32/0.63 fof(f1147,plain,(
% 0.32/0.63 $false|~spl0_136),
% 0.32/0.63 inference(forward_subsumption_resolution,[status(thm)],[f856,f352])).
% 0.32/0.63 fof(f1148,plain,(
% 0.32/0.63 ~spl0_136),
% 0.32/0.63 inference(contradiction_clause,[status(thm)],[f1147])).
% 0.32/0.63 fof(f1149,plain,(
% 0.32/0.63 $false),
% 0.32/0.63 inference(sat_refutation,[status(thm)],[f437,f683,f865,f974,f987,f991,f1030,f1146,f1148])).
% 0.32/0.63 % SZS output end CNFRefutation for theBenchmark.p
% 0.32/0.63 % Elapsed time: 0.063624 seconds
% 0.32/0.63 % CPU time: 0.043817 seconds
% 0.32/0.63 % Memory used: 3.508 MB
%------------------------------------------------------------------------------