TSTP Solution File: LCL531+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL531+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 12:19:32 EDT 2023
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL531+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 09:43:13 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.40 fof(f1,axiom,(
% 0.12/0.40 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f5,axiom,(
% 0.12/0.40 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f9,axiom,(
% 0.12/0.40 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f35,axiom,(
% 0.12/0.40 modus_ponens ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f38,axiom,(
% 0.12/0.40 implies_2 ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f42,axiom,(
% 0.12/0.40 and_3 ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f50,axiom,(
% 0.12/0.40 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f66,axiom,(
% 0.12/0.40 ( axiom_m4<=> (! [X] : is_a_theorem(strict_implies(X,and(X,X))) )) ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f75,axiom,(
% 0.12/0.40 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f78,axiom,(
% 0.12/0.40 necessitation ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f85,axiom,(
% 0.12/0.40 op_strict_implies ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f88,conjecture,(
% 0.12/0.40 axiom_m4 ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f89,negated_conjecture,(
% 0.12/0.40 ~(axiom_m4 )),
% 0.12/0.40 inference(negated_conjecture,[status(cth)],[f88])).
% 0.12/0.40 fof(f90,plain,(
% 0.12/0.40 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.12/0.40 fof(f91,plain,(
% 0.12/0.40 (~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))))),
% 0.12/0.40 inference(NNF_transformation,[status(esa)],[f90])).
% 0.12/0.40 fof(f92,plain,(
% 0.12/0.40 (~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))))),
% 0.12/0.40 inference(miniscoping,[status(esa)],[f91])).
% 0.12/0.40 fof(f93,plain,(
% 0.12/0.40 (~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)))),
% 0.12/0.40 inference(skolemization,[status(esa)],[f92])).
% 0.12/0.40 fof(f94,plain,(
% 0.12/0.40 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f93])).
% 0.12/0.40 fof(f112,plain,(
% 0.12/0.40 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|(?[X,Y]: ~is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))),
% 0.12/0.40 inference(NNF_transformation,[status(esa)],[f5])).
% 0.12/0.40 fof(f113,plain,(
% 0.12/0.40 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9))))),
% 0.12/0.40 inference(skolemization,[status(esa)],[f112])).
% 0.12/0.40 fof(f114,plain,(
% 0.12/0.40 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f113])).
% 0.12/0.40 fof(f128,plain,(
% 0.12/0.40 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,and(X,Y))))))),
% 0.12/0.40 inference(NNF_transformation,[status(esa)],[f9])).
% 0.12/0.40 fof(f129,plain,(
% 0.12/0.40 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sk0_17,implies(sk0_18,and(sk0_17,sk0_18)))))),
% 0.12/0.40 inference(skolemization,[status(esa)],[f128])).
% 0.12/0.40 fof(f130,plain,(
% 0.12/0.40 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f129])).
% 0.12/0.40 fof(f213,plain,(
% 0.12/0.40 modus_ponens),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f35])).
% 0.12/0.40 fof(f216,plain,(
% 0.12/0.40 implies_2),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f38])).
% 0.12/0.40 fof(f220,plain,(
% 0.12/0.40 and_3),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f42])).
% 0.12/0.40 fof(f228,plain,(
% 0.12/0.40 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(esa)],[f50])).
% 0.12/0.40 fof(f229,plain,(
% 0.12/0.40 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 0.12/0.40 inference(NNF_transformation,[status(esa)],[f228])).
% 0.12/0.40 fof(f230,plain,(
% 0.12/0.40 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sk0_55)&~is_a_theorem(necessarily(sk0_55))))),
% 0.12/0.40 inference(skolemization,[status(esa)],[f229])).
% 0.12/0.40 fof(f231,plain,(
% 0.12/0.40 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f230])).
% 0.12/0.40 fof(f303,plain,(
% 0.12/0.40 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|(?[X]: ~is_a_theorem(strict_implies(X,and(X,X)))))),
% 0.12/0.40 inference(NNF_transformation,[status(esa)],[f66])).
% 0.12/0.40 fof(f304,plain,(
% 0.12/0.40 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|~is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83))))),
% 0.12/0.40 inference(skolemization,[status(esa)],[f303])).
% 0.12/0.40 fof(f306,plain,(
% 0.12/0.40 axiom_m4|~is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83)))),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f304])).
% 0.12/0.40 fof(f335,plain,(
% 0.12/0.40 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(esa)],[f75])).
% 0.12/0.40 fof(f336,plain,(
% 0.12/0.40 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f335])).
% 0.12/0.40 fof(f340,plain,(
% 0.12/0.40 necessitation),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f78])).
% 0.12/0.40 fof(f347,plain,(
% 0.12/0.40 op_strict_implies),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f85])).
% 0.12/0.40 fof(f350,plain,(
% 0.12/0.40 ~axiom_m4),
% 0.12/0.40 inference(cnf_transformation,[status(esa)],[f89])).
% 0.12/0.40 fof(f351,plain,(
% 0.12/0.40 spl0_0 <=> modus_ponens),
% 0.12/0.40 introduced(split_symbol_definition)).
% 0.12/0.40 fof(f353,plain,(
% 0.12/0.40 ~modus_ponens|spl0_0),
% 0.12/0.40 inference(component_clause,[status(thm)],[f351])).
% 0.12/0.40 fof(f354,plain,(
% 0.12/0.40 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 0.12/0.40 introduced(split_symbol_definition)).
% 0.12/0.40 fof(f355,plain,(
% 0.12/0.40 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 0.12/0.40 inference(component_clause,[status(thm)],[f354])).
% 0.12/0.40 fof(f357,plain,(
% 0.12/0.40 ~spl0_0|spl0_1),
% 0.12/0.40 inference(split_clause,[status(thm)],[f94,f351,f354])).
% 0.12/0.40 fof(f407,plain,(
% 0.12/0.40 spl0_15 <=> implies_2),
% 0.12/0.40 introduced(split_symbol_definition)).
% 0.12/0.40 fof(f409,plain,(
% 0.12/0.40 ~implies_2|spl0_15),
% 0.12/0.40 inference(component_clause,[status(thm)],[f407])).
% 0.12/0.40 fof(f410,plain,(
% 0.12/0.40 spl0_16 <=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))),
% 0.12/0.40 introduced(split_symbol_definition)).
% 0.12/0.40 fof(f411,plain,(
% 0.12/0.40 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~spl0_16)),
% 0.12/0.40 inference(component_clause,[status(thm)],[f410])).
% 0.12/0.40 fof(f413,plain,(
% 0.12/0.40 ~spl0_15|spl0_16),
% 0.12/0.40 inference(split_clause,[status(thm)],[f114,f407,f410])).
% 0.12/0.40 fof(f451,plain,(
% 0.12/0.40 spl0_27 <=> and_3),
% 0.12/0.40 introduced(split_symbol_definition)).
% 0.12/0.40 fof(f453,plain,(
% 0.12/0.40 ~and_3|spl0_27),
% 0.12/0.40 inference(component_clause,[status(thm)],[f451])).
% 0.12/0.40 fof(f454,plain,(
% 0.12/0.40 spl0_28 <=> is_a_theorem(implies(X0,implies(X1,and(X0,X1))))),
% 0.12/0.40 introduced(split_symbol_definition)).
% 0.12/0.40 fof(f455,plain,(
% 0.12/0.40 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))|~spl0_28)),
% 0.12/0.40 inference(component_clause,[status(thm)],[f454])).
% 0.12/0.40 fof(f457,plain,(
% 0.12/0.40 ~spl0_27|spl0_28),
% 0.12/0.40 inference(split_clause,[status(thm)],[f130,f451,f454])).
% 0.12/0.40 fof(f675,plain,(
% 0.12/0.40 spl0_88 <=> necessitation),
% 0.12/0.40 introduced(split_symbol_definition)).
% 0.12/0.40 fof(f677,plain,(
% 0.12/0.40 ~necessitation|spl0_88),
% 0.12/0.40 inference(component_clause,[status(thm)],[f675])).
% 0.12/0.40 fof(f678,plain,(
% 0.12/0.40 spl0_89 <=> ~is_a_theorem(X0)|is_a_theorem(necessarily(X0))),
% 0.12/0.40 introduced(split_symbol_definition)).
% 0.12/0.40 fof(f679,plain,(
% 0.12/0.41 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0))|~spl0_89)),
% 0.12/0.41 inference(component_clause,[status(thm)],[f678])).
% 0.12/0.41 fof(f681,plain,(
% 0.12/0.41 ~spl0_88|spl0_89),
% 0.12/0.41 inference(split_clause,[status(thm)],[f231,f675,f678])).
% 0.12/0.41 fof(f875,plain,(
% 0.12/0.41 spl0_142 <=> axiom_m4),
% 0.12/0.41 introduced(split_symbol_definition)).
% 0.12/0.41 fof(f876,plain,(
% 0.12/0.41 axiom_m4|~spl0_142),
% 0.12/0.41 inference(component_clause,[status(thm)],[f875])).
% 0.12/0.41 fof(f882,plain,(
% 0.12/0.41 spl0_144 <=> is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83)))),
% 0.12/0.41 introduced(split_symbol_definition)).
% 0.12/0.41 fof(f884,plain,(
% 0.12/0.41 ~is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83)))|spl0_144),
% 0.12/0.41 inference(component_clause,[status(thm)],[f882])).
% 0.12/0.41 fof(f885,plain,(
% 0.12/0.41 spl0_142|~spl0_144),
% 0.12/0.41 inference(split_clause,[status(thm)],[f306,f875,f882])).
% 0.12/0.41 fof(f966,plain,(
% 0.12/0.41 spl0_167 <=> op_strict_implies),
% 0.12/0.41 introduced(split_symbol_definition)).
% 0.12/0.41 fof(f968,plain,(
% 0.12/0.41 ~op_strict_implies|spl0_167),
% 0.12/0.41 inference(component_clause,[status(thm)],[f966])).
% 0.12/0.41 fof(f969,plain,(
% 0.12/0.41 spl0_168 <=> strict_implies(X0,X1)=necessarily(implies(X0,X1))),
% 0.12/0.41 introduced(split_symbol_definition)).
% 0.12/0.41 fof(f970,plain,(
% 0.12/0.41 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~spl0_168)),
% 0.12/0.41 inference(component_clause,[status(thm)],[f969])).
% 0.12/0.41 fof(f972,plain,(
% 0.12/0.41 ~spl0_167|spl0_168),
% 0.12/0.41 inference(split_clause,[status(thm)],[f336,f966,f969])).
% 0.12/0.41 fof(f982,plain,(
% 0.12/0.41 $false|spl0_167),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f968,f347])).
% 0.12/0.41 fof(f983,plain,(
% 0.12/0.41 spl0_167),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f982])).
% 0.12/0.41 fof(f992,plain,(
% 0.12/0.41 $false|spl0_0),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f353,f213])).
% 0.12/0.41 fof(f993,plain,(
% 0.12/0.41 spl0_0),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f992])).
% 0.12/0.41 fof(f994,plain,(
% 0.12/0.41 $false|spl0_88),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f677,f340])).
% 0.12/0.41 fof(f995,plain,(
% 0.12/0.41 spl0_88),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f994])).
% 0.12/0.41 fof(f1100,plain,(
% 0.12/0.41 $false|spl0_27),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f453,f220])).
% 0.12/0.41 fof(f1101,plain,(
% 0.12/0.41 spl0_27),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f1100])).
% 0.12/0.41 fof(f1104,plain,(
% 0.12/0.41 $false|spl0_15),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f409,f216])).
% 0.12/0.41 fof(f1105,plain,(
% 0.12/0.41 spl0_15),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f1104])).
% 0.12/0.41 fof(f1117,plain,(
% 0.12/0.41 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~spl0_89|~spl0_168)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f970,f679])).
% 0.12/0.41 fof(f1192,plain,(
% 0.12/0.41 ~is_a_theorem(implies(sk0_83,and(sk0_83,sk0_83)))|~spl0_89|~spl0_168|spl0_144),
% 0.12/0.41 inference(resolution,[status(thm)],[f1117,f884])).
% 0.12/0.41 fof(f1444,plain,(
% 0.12/0.41 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1))|~spl0_16|~spl0_1)),
% 0.12/0.41 inference(resolution,[status(thm)],[f411,f355])).
% 0.12/0.41 fof(f1835,plain,(
% 0.12/0.41 ~is_a_theorem(implies(sk0_83,implies(sk0_83,and(sk0_83,sk0_83))))|~spl0_16|~spl0_1|~spl0_89|~spl0_168|spl0_144),
% 0.12/0.41 inference(resolution,[status(thm)],[f1444,f1192])).
% 0.12/0.41 fof(f1836,plain,(
% 0.12/0.41 $false|~spl0_28|~spl0_16|~spl0_1|~spl0_89|~spl0_168|spl0_144),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1835,f455])).
% 0.12/0.41 fof(f1837,plain,(
% 0.12/0.41 ~spl0_28|~spl0_16|~spl0_1|~spl0_89|~spl0_168|spl0_144),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f1836])).
% 0.12/0.41 fof(f1841,plain,(
% 0.12/0.41 $false|~spl0_142),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f876,f350])).
% 0.12/0.41 fof(f1842,plain,(
% 0.12/0.41 ~spl0_142),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f1841])).
% 0.12/0.41 fof(f1843,plain,(
% 0.12/0.41 $false),
% 0.12/0.41 inference(sat_refutation,[status(thm)],[f357,f413,f457,f681,f885,f972,f983,f993,f995,f1101,f1105,f1837,f1842])).
% 0.12/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/0.45 % Elapsed time: 0.095276 seconds
% 0.20/0.45 % CPU time: 0.345870 seconds
% 0.20/0.45 % Memory used: 27.435 MB
%------------------------------------------------------------------------------