TSTP Solution File: LCL573+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL573+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 12:19:38 EDT 2023
% Result : Theorem 26.21s 3.73s
% Output : CNFRefutation 27.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL573+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n014.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 09:40:04 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.5.1
% 26.21/3.73 % Refutation found
% 26.21/3.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 26.21/3.73 % SZS output start CNFRefutation for theBenchmark
% 26.21/3.73 fof(f1,axiom,(
% 26.21/3.73 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f3,axiom,(
% 26.21/3.73 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f7,axiom,(
% 26.21/3.73 ( modus_ponens_strict_implies<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(strict_implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f8,axiom,(
% 26.21/3.73 ( adjunction<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(Y) )=> is_a_theorem(and(X,Y)) ) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f9,axiom,(
% 26.21/3.73 ( substitution_strict_equiv<=> (! [X,Y] :( is_a_theorem(strict_equiv(X,Y))=> X = Y ) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f14,axiom,(
% 26.21/3.73 ( axiom_5<=> (! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f19,axiom,(
% 26.21/3.73 ( axiom_m1<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f20,axiom,(
% 26.21/3.73 ( axiom_m2<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f21,axiom,(
% 26.21/3.73 ( axiom_m3<=> (! [X,Y,Z] : is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z)))) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f22,axiom,(
% 26.21/3.73 ( axiom_m4<=> (! [X] : is_a_theorem(strict_implies(X,and(X,X))) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f23,axiom,(
% 26.21/3.73 ( axiom_m5<=> (! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z))) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f28,axiom,(
% 26.21/3.73 ( axiom_m10<=> (! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f31,axiom,(
% 26.21/3.73 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f32,axiom,(
% 26.21/3.73 ( op_strict_equiv=> (! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) )) ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f34,axiom,(
% 26.21/3.73 op_or ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f36,axiom,(
% 26.21/3.73 op_strict_implies ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f38,axiom,(
% 26.21/3.73 op_strict_equiv ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f39,axiom,(
% 26.21/3.73 modus_ponens_strict_implies ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f40,axiom,(
% 26.21/3.73 substitution_strict_equiv ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f41,axiom,(
% 26.21/3.73 adjunction ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f42,axiom,(
% 26.21/3.73 axiom_m1 ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f43,axiom,(
% 26.21/3.73 axiom_m2 ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f44,axiom,(
% 26.21/3.73 axiom_m3 ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f45,axiom,(
% 26.21/3.73 axiom_m4 ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f46,axiom,(
% 26.21/3.73 axiom_m5 ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f47,axiom,(
% 26.21/3.73 axiom_m10 ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f49,axiom,(
% 26.21/3.73 op_implies_and ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f52,conjecture,(
% 26.21/3.73 axiom_5 ),
% 26.21/3.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 26.21/3.73 fof(f53,negated_conjecture,(
% 26.21/3.73 ~(axiom_5 )),
% 26.21/3.73 inference(negated_conjecture,[status(cth)],[f52])).
% 26.21/3.73 fof(f54,plain,(
% 26.21/3.73 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 26.21/3.73 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 26.21/3.73 fof(f55,plain,(
% 26.21/3.73 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f54])).
% 26.21/3.73 fof(f58,plain,(
% 26.21/3.73 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 26.21/3.73 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 26.21/3.73 fof(f59,plain,(
% 26.21/3.73 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f58])).
% 26.21/3.73 fof(f70,plain,(
% 26.21/3.73 modus_ponens_strict_implies<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y)))|is_a_theorem(Y)))),
% 26.21/3.73 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 26.21/3.73 fof(f71,plain,(
% 26.21/3.73 (~modus_ponens_strict_implies|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens_strict_implies|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(strict_implies(X,Y)))&~is_a_theorem(Y))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f70])).
% 26.21/3.73 fof(f72,plain,(
% 26.21/3.73 (~modus_ponens_strict_implies|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens_strict_implies|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(strict_implies(X,Y))))&~is_a_theorem(Y))))),
% 26.21/3.73 inference(miniscoping,[status(esa)],[f71])).
% 26.21/3.73 fof(f73,plain,(
% 26.21/3.73 (~modus_ponens_strict_implies|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens_strict_implies|((is_a_theorem(sk0_2)&is_a_theorem(strict_implies(sk0_2,sk0_1)))&~is_a_theorem(sk0_1)))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f72])).
% 26.21/3.73 fof(f74,plain,(
% 26.21/3.73 ![X0,X1]: (~modus_ponens_strict_implies|~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f73])).
% 26.21/3.73 fof(f78,plain,(
% 26.21/3.73 adjunction<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y))))),
% 26.21/3.73 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 26.21/3.73 fof(f79,plain,(
% 26.21/3.73 (~adjunction|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y)))))&(adjunction|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(Y))&~is_a_theorem(and(X,Y)))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f78])).
% 26.21/3.73 fof(f80,plain,(
% 26.21/3.73 (~adjunction|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y)))))&(adjunction|((is_a_theorem(sk0_3)&is_a_theorem(sk0_4))&~is_a_theorem(and(sk0_3,sk0_4))))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f79])).
% 26.21/3.73 fof(f81,plain,(
% 26.21/3.73 ![X0,X1]: (~adjunction|~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f80])).
% 26.21/3.73 fof(f85,plain,(
% 26.21/3.73 substitution_strict_equiv<=>(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y))),
% 26.21/3.73 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 26.21/3.73 fof(f86,plain,(
% 26.21/3.73 (~substitution_strict_equiv|(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y)))&(substitution_strict_equiv|(?[X,Y]: (is_a_theorem(strict_equiv(X,Y))&~X=Y)))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f85])).
% 26.21/3.73 fof(f87,plain,(
% 26.21/3.73 (~substitution_strict_equiv|(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y)))&(substitution_strict_equiv|(is_a_theorem(strict_equiv(sk0_5,sk0_6))&~sk0_5=sk0_6))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f86])).
% 26.21/3.73 fof(f88,plain,(
% 26.21/3.73 ![X0,X1]: (~substitution_strict_equiv|~is_a_theorem(strict_equiv(X0,X1))|X0=X1)),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f87])).
% 26.21/3.73 fof(f107,plain,(
% 26.21/3.73 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|(?[X]: ~is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f14])).
% 26.21/3.73 fof(f108,plain,(
% 26.21/3.73 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|~is_a_theorem(implies(possibly(sk0_12),necessarily(possibly(sk0_12)))))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f107])).
% 26.21/3.73 fof(f110,plain,(
% 26.21/3.73 axiom_5|~is_a_theorem(implies(possibly(sk0_12),necessarily(possibly(sk0_12))))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f108])).
% 26.21/3.73 fof(f127,plain,(
% 26.21/3.73 (~axiom_m1|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))&(axiom_m1|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f19])).
% 26.21/3.73 fof(f128,plain,(
% 26.21/3.73 (~axiom_m1|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))&(axiom_m1|~is_a_theorem(strict_implies(and(sk0_21,sk0_22),and(sk0_22,sk0_21))))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f127])).
% 26.21/3.73 fof(f129,plain,(
% 26.21/3.73 ![X0,X1]: (~axiom_m1|is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f128])).
% 26.21/3.73 fof(f131,plain,(
% 26.21/3.73 (~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))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f20])).
% 26.21/3.73 fof(f132,plain,(
% 26.21/3.73 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|~is_a_theorem(strict_implies(and(sk0_23,sk0_24),sk0_23)))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f131])).
% 26.21/3.73 fof(f133,plain,(
% 26.21/3.73 ![X0,X1]: (~axiom_m2|is_a_theorem(strict_implies(and(X0,X1),X0)))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f132])).
% 26.21/3.73 fof(f135,plain,(
% 26.21/3.73 (~axiom_m3|(![X,Y,Z]: is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))))&(axiom_m3|(?[X,Y,Z]: ~is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f21])).
% 26.21/3.73 fof(f136,plain,(
% 26.21/3.73 (~axiom_m3|(![X,Y,Z]: is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))))&(axiom_m3|~is_a_theorem(strict_implies(and(and(sk0_25,sk0_26),sk0_27),and(sk0_25,and(sk0_26,sk0_27)))))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f135])).
% 26.21/3.73 fof(f137,plain,(
% 26.21/3.73 ![X0,X1,X2]: (~axiom_m3|is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f136])).
% 26.21/3.73 fof(f139,plain,(
% 26.21/3.73 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|(?[X]: ~is_a_theorem(strict_implies(X,and(X,X)))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f22])).
% 26.21/3.73 fof(f140,plain,(
% 26.21/3.73 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|~is_a_theorem(strict_implies(sk0_28,and(sk0_28,sk0_28))))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f139])).
% 26.21/3.73 fof(f141,plain,(
% 26.21/3.73 ![X0]: (~axiom_m4|is_a_theorem(strict_implies(X0,and(X0,X0))))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f140])).
% 26.21/3.73 fof(f143,plain,(
% 26.21/3.73 (~axiom_m5|(![X,Y,Z]: is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))))&(axiom_m5|(?[X,Y,Z]: ~is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f23])).
% 26.21/3.73 fof(f144,plain,(
% 26.21/3.73 (~axiom_m5|(![X,Y,Z]: is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))))&(axiom_m5|~is_a_theorem(strict_implies(and(strict_implies(sk0_29,sk0_30),strict_implies(sk0_30,sk0_31)),strict_implies(sk0_29,sk0_31))))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f143])).
% 26.21/3.73 fof(f145,plain,(
% 26.21/3.73 ![X0,X1,X2]: (~axiom_m5|is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f144])).
% 26.21/3.73 fof(f163,plain,(
% 26.21/3.73 (~axiom_m10|(![X]: is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))))&(axiom_m10|(?[X]: ~is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))))),
% 26.21/3.73 inference(NNF_transformation,[status(esa)],[f28])).
% 26.21/3.73 fof(f164,plain,(
% 26.21/3.73 (~axiom_m10|(![X]: is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))))&(axiom_m10|~is_a_theorem(strict_implies(possibly(sk0_38),necessarily(possibly(sk0_38)))))),
% 26.21/3.73 inference(skolemization,[status(esa)],[f163])).
% 26.21/3.73 fof(f165,plain,(
% 26.21/3.73 ![X0]: (~axiom_m10|is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f164])).
% 26.21/3.73 fof(f171,plain,(
% 26.21/3.73 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 26.21/3.73 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 26.21/3.73 fof(f172,plain,(
% 26.21/3.73 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f171])).
% 26.21/3.73 fof(f173,plain,(
% 26.21/3.73 ~op_strict_equiv|(![X,Y]: strict_equiv(X,Y)=and(strict_implies(X,Y),strict_implies(Y,X)))),
% 26.21/3.73 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 26.21/3.73 fof(f174,plain,(
% 26.21/3.73 ![X0,X1]: (~op_strict_equiv|strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0)))),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f173])).
% 26.21/3.73 fof(f176,plain,(
% 26.21/3.73 op_or),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f34])).
% 26.21/3.73 fof(f178,plain,(
% 26.21/3.73 op_strict_implies),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f36])).
% 26.21/3.73 fof(f180,plain,(
% 26.21/3.73 op_strict_equiv),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f38])).
% 26.21/3.73 fof(f181,plain,(
% 26.21/3.73 modus_ponens_strict_implies),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f39])).
% 26.21/3.73 fof(f182,plain,(
% 26.21/3.73 substitution_strict_equiv),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f40])).
% 26.21/3.73 fof(f183,plain,(
% 26.21/3.73 adjunction),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f41])).
% 26.21/3.73 fof(f184,plain,(
% 26.21/3.73 axiom_m1),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f42])).
% 26.21/3.73 fof(f185,plain,(
% 26.21/3.73 axiom_m2),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f43])).
% 26.21/3.73 fof(f186,plain,(
% 26.21/3.73 axiom_m3),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f44])).
% 26.21/3.73 fof(f187,plain,(
% 26.21/3.73 axiom_m4),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f45])).
% 26.21/3.73 fof(f188,plain,(
% 26.21/3.73 axiom_m5),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f46])).
% 26.21/3.73 fof(f189,plain,(
% 26.21/3.73 axiom_m10),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f47])).
% 26.21/3.73 fof(f191,plain,(
% 26.21/3.73 op_implies_and),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f49])).
% 26.21/3.73 fof(f194,plain,(
% 26.21/3.73 ~axiom_5),
% 26.21/3.73 inference(cnf_transformation,[status(esa)],[f53])).
% 26.21/3.73 fof(f195,plain,(
% 26.21/3.73 spl0_0 <=> op_or),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f197,plain,(
% 26.21/3.73 ~op_or|spl0_0),
% 26.21/3.73 inference(component_clause,[status(thm)],[f195])).
% 26.21/3.73 fof(f198,plain,(
% 26.21/3.73 spl0_1 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f199,plain,(
% 26.21/3.73 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_1)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f198])).
% 26.21/3.73 fof(f201,plain,(
% 26.21/3.73 ~spl0_0|spl0_1),
% 26.21/3.73 inference(split_clause,[status(thm)],[f55,f195,f198])).
% 26.21/3.73 fof(f209,plain,(
% 26.21/3.73 spl0_4 <=> op_implies_and),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f211,plain,(
% 26.21/3.73 ~op_implies_and|spl0_4),
% 26.21/3.73 inference(component_clause,[status(thm)],[f209])).
% 26.21/3.73 fof(f212,plain,(
% 26.21/3.73 spl0_5 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f213,plain,(
% 26.21/3.73 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_5)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f212])).
% 26.21/3.73 fof(f215,plain,(
% 26.21/3.73 ~spl0_4|spl0_5),
% 26.21/3.73 inference(split_clause,[status(thm)],[f59,f209,f212])).
% 26.21/3.73 fof(f245,plain,(
% 26.21/3.73 spl0_14 <=> modus_ponens_strict_implies),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f247,plain,(
% 26.21/3.73 ~modus_ponens_strict_implies|spl0_14),
% 26.21/3.73 inference(component_clause,[status(thm)],[f245])).
% 26.21/3.73 fof(f248,plain,(
% 26.21/3.73 spl0_15 <=> ~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1)),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f249,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1)|~spl0_15)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f248])).
% 26.21/3.73 fof(f251,plain,(
% 26.21/3.73 ~spl0_14|spl0_15),
% 26.21/3.73 inference(split_clause,[status(thm)],[f74,f245,f248])).
% 26.21/3.73 fof(f264,plain,(
% 26.21/3.73 spl0_19 <=> adjunction),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f266,plain,(
% 26.21/3.73 ~adjunction|spl0_19),
% 26.21/3.73 inference(component_clause,[status(thm)],[f264])).
% 26.21/3.73 fof(f267,plain,(
% 26.21/3.73 spl0_20 <=> ~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f268,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~spl0_20)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f267])).
% 26.21/3.73 fof(f270,plain,(
% 26.21/3.73 ~spl0_19|spl0_20),
% 26.21/3.73 inference(split_clause,[status(thm)],[f81,f264,f267])).
% 26.21/3.73 fof(f283,plain,(
% 26.21/3.73 spl0_24 <=> substitution_strict_equiv),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f285,plain,(
% 26.21/3.73 ~substitution_strict_equiv|spl0_24),
% 26.21/3.73 inference(component_clause,[status(thm)],[f283])).
% 26.21/3.73 fof(f286,plain,(
% 26.21/3.73 spl0_25 <=> ~is_a_theorem(strict_equiv(X0,X1))|X0=X1),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f287,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_equiv(X0,X1))|X0=X1|~spl0_25)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f286])).
% 26.21/3.73 fof(f289,plain,(
% 26.21/3.73 ~spl0_24|spl0_25),
% 26.21/3.73 inference(split_clause,[status(thm)],[f88,f283,f286])).
% 26.21/3.73 fof(f342,plain,(
% 26.21/3.73 spl0_40 <=> axiom_5),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f343,plain,(
% 26.21/3.73 axiom_5|~spl0_40),
% 26.21/3.73 inference(component_clause,[status(thm)],[f342])).
% 26.21/3.73 fof(f345,plain,(
% 26.21/3.73 spl0_41 <=> is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f346,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))|~spl0_41)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f345])).
% 26.21/3.73 fof(f349,plain,(
% 26.21/3.73 spl0_42 <=> is_a_theorem(implies(possibly(sk0_12),necessarily(possibly(sk0_12))))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f351,plain,(
% 26.21/3.73 ~is_a_theorem(implies(possibly(sk0_12),necessarily(possibly(sk0_12))))|spl0_42),
% 26.21/3.73 inference(component_clause,[status(thm)],[f349])).
% 26.21/3.73 fof(f352,plain,(
% 26.21/3.73 spl0_40|~spl0_42),
% 26.21/3.73 inference(split_clause,[status(thm)],[f110,f342,f349])).
% 26.21/3.73 fof(f397,plain,(
% 26.21/3.73 spl0_55 <=> axiom_m1),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f399,plain,(
% 26.21/3.73 ~axiom_m1|spl0_55),
% 26.21/3.73 inference(component_clause,[status(thm)],[f397])).
% 26.21/3.73 fof(f400,plain,(
% 26.21/3.73 spl0_56 <=> is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f401,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))|~spl0_56)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f400])).
% 26.21/3.73 fof(f403,plain,(
% 26.21/3.73 ~spl0_55|spl0_56),
% 26.21/3.73 inference(split_clause,[status(thm)],[f129,f397,f400])).
% 26.21/3.73 fof(f408,plain,(
% 26.21/3.73 spl0_58 <=> axiom_m2),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f410,plain,(
% 26.21/3.73 ~axiom_m2|spl0_58),
% 26.21/3.73 inference(component_clause,[status(thm)],[f408])).
% 26.21/3.73 fof(f411,plain,(
% 26.21/3.73 spl0_59 <=> is_a_theorem(strict_implies(and(X0,X1),X0))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f412,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X0))|~spl0_59)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f411])).
% 26.21/3.73 fof(f414,plain,(
% 26.21/3.73 ~spl0_58|spl0_59),
% 26.21/3.73 inference(split_clause,[status(thm)],[f133,f408,f411])).
% 26.21/3.73 fof(f419,plain,(
% 26.21/3.73 spl0_61 <=> axiom_m3),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f421,plain,(
% 26.21/3.73 ~axiom_m3|spl0_61),
% 26.21/3.73 inference(component_clause,[status(thm)],[f419])).
% 26.21/3.73 fof(f422,plain,(
% 26.21/3.73 spl0_62 <=> is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f423,plain,(
% 26.21/3.73 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))|~spl0_62)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f422])).
% 26.21/3.73 fof(f425,plain,(
% 26.21/3.73 ~spl0_61|spl0_62),
% 26.21/3.73 inference(split_clause,[status(thm)],[f137,f419,f422])).
% 26.21/3.73 fof(f430,plain,(
% 26.21/3.73 spl0_64 <=> axiom_m4),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f432,plain,(
% 26.21/3.73 ~axiom_m4|spl0_64),
% 26.21/3.73 inference(component_clause,[status(thm)],[f430])).
% 26.21/3.73 fof(f433,plain,(
% 26.21/3.73 spl0_65 <=> is_a_theorem(strict_implies(X0,and(X0,X0)))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f434,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(strict_implies(X0,and(X0,X0)))|~spl0_65)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f433])).
% 26.21/3.73 fof(f436,plain,(
% 26.21/3.73 ~spl0_64|spl0_65),
% 26.21/3.73 inference(split_clause,[status(thm)],[f141,f430,f433])).
% 26.21/3.73 fof(f441,plain,(
% 26.21/3.73 spl0_67 <=> axiom_m5),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f443,plain,(
% 26.21/3.73 ~axiom_m5|spl0_67),
% 26.21/3.73 inference(component_clause,[status(thm)],[f441])).
% 26.21/3.73 fof(f444,plain,(
% 26.21/3.73 spl0_68 <=> is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f445,plain,(
% 26.21/3.73 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))|~spl0_68)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f444])).
% 26.21/3.73 fof(f447,plain,(
% 26.21/3.73 ~spl0_67|spl0_68),
% 26.21/3.73 inference(split_clause,[status(thm)],[f145,f441,f444])).
% 26.21/3.73 fof(f496,plain,(
% 26.21/3.73 spl0_82 <=> axiom_m10),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f498,plain,(
% 26.21/3.73 ~axiom_m10|spl0_82),
% 26.21/3.73 inference(component_clause,[status(thm)],[f496])).
% 26.21/3.73 fof(f499,plain,(
% 26.21/3.73 spl0_83 <=> is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f500,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))|~spl0_83)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f499])).
% 26.21/3.73 fof(f502,plain,(
% 26.21/3.73 ~spl0_82|spl0_83),
% 26.21/3.73 inference(split_clause,[status(thm)],[f165,f496,f499])).
% 26.21/3.73 fof(f521,plain,(
% 26.21/3.73 spl0_89 <=> op_strict_implies),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f523,plain,(
% 26.21/3.73 ~op_strict_implies|spl0_89),
% 26.21/3.73 inference(component_clause,[status(thm)],[f521])).
% 26.21/3.73 fof(f524,plain,(
% 26.21/3.73 spl0_90 <=> strict_implies(X0,X1)=necessarily(implies(X0,X1))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f525,plain,(
% 26.21/3.73 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~spl0_90)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f524])).
% 26.21/3.73 fof(f527,plain,(
% 26.21/3.73 ~spl0_89|spl0_90),
% 26.21/3.73 inference(split_clause,[status(thm)],[f172,f521,f524])).
% 26.21/3.73 fof(f528,plain,(
% 26.21/3.73 spl0_91 <=> op_strict_equiv),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f530,plain,(
% 26.21/3.73 ~op_strict_equiv|spl0_91),
% 26.21/3.73 inference(component_clause,[status(thm)],[f528])).
% 26.21/3.73 fof(f531,plain,(
% 26.21/3.73 spl0_92 <=> strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))),
% 26.21/3.73 introduced(split_symbol_definition)).
% 26.21/3.73 fof(f532,plain,(
% 26.21/3.73 ![X0,X1]: (strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))|~spl0_92)),
% 26.21/3.73 inference(component_clause,[status(thm)],[f531])).
% 26.21/3.73 fof(f534,plain,(
% 26.21/3.73 ~spl0_91|spl0_92),
% 26.21/3.73 inference(split_clause,[status(thm)],[f174,f528,f531])).
% 26.21/3.73 fof(f535,plain,(
% 26.21/3.73 $false|spl0_91),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f530,f180])).
% 26.21/3.73 fof(f536,plain,(
% 26.21/3.73 spl0_91),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f535])).
% 26.21/3.73 fof(f537,plain,(
% 26.21/3.73 $false|spl0_19),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f266,f183])).
% 26.21/3.73 fof(f538,plain,(
% 26.21/3.73 spl0_19),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f537])).
% 26.21/3.73 fof(f539,plain,(
% 26.21/3.73 $false|spl0_14),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f247,f181])).
% 26.21/3.73 fof(f540,plain,(
% 26.21/3.73 spl0_14),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f539])).
% 26.21/3.73 fof(f541,plain,(
% 26.21/3.73 $false|spl0_24),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f285,f182])).
% 26.21/3.73 fof(f542,plain,(
% 26.21/3.73 spl0_24),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f541])).
% 26.21/3.73 fof(f543,plain,(
% 26.21/3.73 $false|spl0_89),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f523,f178])).
% 26.21/3.73 fof(f544,plain,(
% 26.21/3.73 spl0_89),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f543])).
% 26.21/3.73 fof(f549,plain,(
% 26.21/3.73 $false|spl0_4),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f211,f191])).
% 26.21/3.73 fof(f550,plain,(
% 26.21/3.73 spl0_4),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f549])).
% 26.21/3.73 fof(f551,plain,(
% 26.21/3.73 $false|spl0_0),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f197,f176])).
% 26.21/3.73 fof(f552,plain,(
% 26.21/3.73 spl0_0),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f551])).
% 26.21/3.73 fof(f562,plain,(
% 26.21/3.73 $false|spl0_64),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f432,f187])).
% 26.21/3.73 fof(f563,plain,(
% 26.21/3.73 spl0_64),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f562])).
% 26.21/3.73 fof(f566,plain,(
% 26.21/3.73 $false|spl0_58),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f410,f185])).
% 26.21/3.73 fof(f567,plain,(
% 26.21/3.73 spl0_58),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f566])).
% 26.21/3.73 fof(f572,plain,(
% 26.21/3.73 $false|spl0_82),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f498,f189])).
% 26.21/3.73 fof(f573,plain,(
% 26.21/3.73 spl0_82),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f572])).
% 26.21/3.73 fof(f585,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(and(X1,X0))|~spl0_15|~spl0_56)),
% 26.21/3.73 inference(resolution,[status(thm)],[f249,f401])).
% 26.21/3.73 fof(f598,plain,(
% 26.21/3.73 $false|spl0_55),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f399,f184])).
% 26.21/3.73 fof(f599,plain,(
% 26.21/3.73 spl0_55),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f598])).
% 26.21/3.73 fof(f602,plain,(
% 26.21/3.73 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2)))|~spl0_5)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f213,f213])).
% 26.21/3.73 fof(f612,plain,(
% 26.21/3.73 $false|~spl0_41|spl0_42),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f351,f346])).
% 26.21/3.73 fof(f613,plain,(
% 26.21/3.73 ~spl0_41|spl0_42),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f612])).
% 26.21/3.73 fof(f628,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(strict_implies(X1,X0))|is_a_theorem(strict_equiv(X0,X1))|~spl0_20|~spl0_92)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f532,f268])).
% 26.21/3.73 fof(f629,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X1)))|~spl0_59|~spl0_92)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f532,f412])).
% 26.21/3.73 fof(f630,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0)))|~spl0_65|~spl0_92)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f532,f434])).
% 26.21/3.73 fof(f670,plain,(
% 26.21/3.73 $false|spl0_67),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f443,f188])).
% 26.21/3.73 fof(f671,plain,(
% 26.21/3.73 spl0_67),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f670])).
% 26.21/3.73 fof(f672,plain,(
% 26.21/3.73 ![X0,X1,X2]: (~is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2)))|is_a_theorem(strict_implies(X0,X2))|~spl0_68|~spl0_15)),
% 26.21/3.73 inference(resolution,[status(thm)],[f445,f249])).
% 26.21/3.73 fof(f673,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X0)))|~spl0_68|~spl0_92)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f532,f445])).
% 26.21/3.73 fof(f678,plain,(
% 26.21/3.73 $false|spl0_61),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f421,f186])).
% 26.21/3.73 fof(f679,plain,(
% 26.21/3.73 spl0_61),
% 26.21/3.73 inference(contradiction_clause,[status(thm)],[f678])).
% 26.21/3.73 fof(f692,plain,(
% 26.21/3.73 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f213,f199])).
% 26.21/3.73 fof(f693,plain,(
% 26.21/3.73 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_1|~spl0_5)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f213,f692])).
% 26.21/3.73 fof(f700,plain,(
% 26.21/3.73 ![X0,X1]: (strict_implies(not(X0),X1)=necessarily(or(X0,X1))|~spl0_90|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f692,f525])).
% 26.21/3.73 fof(f704,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(necessarily(or(X0,and(not(X0),not(X0)))))|~spl0_65|~spl0_90|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f700,f434])).
% 26.21/3.73 fof(f708,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X0,X1))))|~spl0_59|~spl0_92|~spl0_90|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f700,f629])).
% 26.21/3.73 fof(f838,plain,(
% 26.21/3.73 ![X0,X1,X2]: (or(X0,and(X1,not(X2)))=not(and(not(X0),implies(X1,X2)))|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f692,f602])).
% 26.21/3.73 fof(f854,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(strict_implies(X1,X0))|X0=X1|~spl0_20|~spl0_92|~spl0_25)),
% 26.21/3.73 inference(resolution,[status(thm)],[f628,f287])).
% 26.21/3.73 fof(f862,plain,(
% 26.21/3.73 ![X0]: (~is_a_theorem(strict_implies(strict_equiv(X0,X0),strict_implies(X0,X0)))|strict_equiv(X0,X0)=strict_implies(X0,X0)|~spl0_20|~spl0_25|~spl0_65|~spl0_92)),
% 26.21/3.73 inference(resolution,[status(thm)],[f854,f630])).
% 26.21/3.73 fof(f863,plain,(
% 26.21/3.73 ![X0]: (strict_equiv(X0,X0)=strict_implies(X0,X0)|~spl0_68|~spl0_20|~spl0_25|~spl0_65|~spl0_92)),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f862,f673])).
% 26.21/3.73 fof(f871,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))|and(X0,X1)=and(X1,X0)|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(resolution,[status(thm)],[f854,f401])).
% 26.21/3.73 fof(f872,plain,(
% 26.21/3.73 ![X0,X1]: (and(X0,X1)=and(X1,X0)|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f871,f401])).
% 26.21/3.73 fof(f873,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(X0,and(X0,X1)))|X0=and(X0,X1)|~spl0_20|~spl0_92|~spl0_25|~spl0_59)),
% 26.21/3.73 inference(resolution,[status(thm)],[f854,f412])).
% 26.21/3.73 fof(f874,plain,(
% 26.21/3.73 ![X0]: (~is_a_theorem(strict_implies(and(X0,X0),X0))|and(X0,X0)=X0|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(resolution,[status(thm)],[f854,f434])).
% 26.21/3.73 fof(f875,plain,(
% 26.21/3.73 ![X0]: (and(X0,X0)=X0|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f874,f412])).
% 26.21/3.73 fof(f877,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(necessarily(or(X0,not(X0))))|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65|~spl0_90|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(backward_demodulation,[status(thm)],[f875,f704])).
% 26.21/3.73 fof(f886,plain,(
% 26.21/3.73 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,implies(not(X1),X1)))|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f875,f602])).
% 26.21/3.73 fof(f887,plain,(
% 26.21/3.73 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,or(X1,X1)))|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f692,f886])).
% 26.21/3.73 fof(f888,plain,(
% 26.21/3.73 ![X0,X1]: (or(not(X0),X1)=implies(implies(not(X0),X0),X1)|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f875,f693])).
% 26.21/3.73 fof(f889,plain,(
% 26.21/3.73 ![X0,X1]: (or(not(X0),X1)=implies(or(X0,X0),X1)|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f692,f888])).
% 26.21/3.73 fof(f892,plain,(
% 26.21/3.73 ![X0]: (implies(not(X0),X0)=not(not(X0))|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f875,f213])).
% 26.21/3.73 fof(f893,plain,(
% 26.21/3.73 ![X0]: (or(X0,X0)=not(not(X0))|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f692,f892])).
% 26.21/3.73 fof(f910,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),and(X0,and(X0,X1))))|~spl0_62|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f875,f423])).
% 26.21/3.73 fof(f977,plain,(
% 26.21/3.73 ![X0,X1]: (implies(X0,X1)=not(and(not(X1),X0))|~spl0_5|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f872,f213])).
% 26.21/3.73 fof(f983,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X1))|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f872,f412])).
% 26.21/3.73 fof(f1095,plain,(
% 26.21/3.73 ![X0,X1]: (implies(not(X0),X1)=implies(not(X1),X0)|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_5)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f213,f977])).
% 26.21/3.73 fof(f1096,plain,(
% 26.21/3.73 ![X0,X1]: (or(X0,X1)=implies(not(X1),X0)|~spl0_1|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_5)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f692,f1095])).
% 26.21/3.73 fof(f1097,plain,(
% 26.21/3.73 ![X0,X1]: (or(X0,X1)=or(X1,X0)|~spl0_1|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_5)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f692,f1096])).
% 26.21/3.73 fof(f1137,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X1,X0))))|~spl0_59|~spl0_90|~spl0_1|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_5)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f1097,f708])).
% 26.21/3.73 fof(f1246,plain,(
% 26.21/3.73 ![X0,X1,X2]: (~is_a_theorem(and(strict_implies(X0,not(X1)),necessarily(or(X1,X2))))|is_a_theorem(strict_implies(X0,X2))|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f700,f672])).
% 26.21/3.73 fof(f1247,plain,(
% 26.21/3.73 ![X0,X1,X2]: (~is_a_theorem(and(necessarily(or(X0,X1)),strict_implies(X2,not(X0))))|is_a_theorem(strict_implies(X2,X1))|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f872,f1246])).
% 26.21/3.73 fof(f1300,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(X0,and(X1,X0)))|X0=and(X0,X1)|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f872,f873])).
% 26.21/3.73 fof(f1724,plain,(
% 26.21/3.73 ![X0]: (implies(or(X0,X0),not(X0))=not(or(X0,X0))|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f875,f887])).
% 26.21/3.73 fof(f1725,plain,(
% 26.21/3.73 ![X0]: (or(not(X0),not(X0))=not(or(X0,X0))|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f889,f1724])).
% 26.21/3.73 fof(f1726,plain,(
% 26.21/3.73 ![X0]: (not(not(not(X0)))=not(or(X0,X0))|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f893,f1725])).
% 26.21/3.73 fof(f1811,plain,(
% 26.21/3.73 ![X0,X1]: (implies(X0,not(not(X1)))=not(and(not(or(X1,X1)),X0))|~spl0_56|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f1726,f977])).
% 26.21/3.73 fof(f1812,plain,(
% 26.21/3.73 ![X0,X1]: (implies(X0,not(not(X1)))=implies(X0,or(X1,X1))|~spl0_56|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f977,f1811])).
% 26.21/3.73 fof(f1903,plain,(
% 26.21/3.73 ![X0,X1]: (and(X0,X1)=and(and(X0,X1),X0)|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(resolution,[status(thm)],[f910,f1300])).
% 26.21/3.73 fof(f1947,plain,(
% 26.21/3.73 ![X0,X1]: (and(X0,X1)=and(and(X1,X0),X0)|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f872,f1903])).
% 26.21/3.73 fof(f2085,plain,(
% 26.21/3.73 ![X0,X1]: (implies(and(X0,not(X1)),X1)=not(and(not(X1),X0))|~spl0_5|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f1947,f213])).
% 26.21/3.73 fof(f2086,plain,(
% 26.21/3.73 ![X0,X1]: (implies(and(X0,not(X1)),X1)=implies(X0,X1)|~spl0_5|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f977,f2085])).
% 26.21/3.73 fof(f2267,plain,(
% 26.21/3.73 ![X0,X1]: (strict_implies(and(X0,not(X1)),X1)=necessarily(implies(X0,X1))|~spl0_90|~spl0_5|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f2086,f525])).
% 26.21/3.73 fof(f2268,plain,(
% 26.21/3.73 ![X0,X1]: (strict_implies(and(X0,not(X1)),X1)=strict_implies(X0,X1)|~spl0_90|~spl0_5|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f525,f2267])).
% 26.21/3.73 fof(f3322,plain,(
% 26.21/3.73 ![X0,X1]: (strict_implies(X0,not(not(X1)))=necessarily(implies(X0,or(X1,X1)))|~spl0_90|~spl0_56|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f1812,f525])).
% 26.21/3.73 fof(f3323,plain,(
% 26.21/3.73 ![X0,X1]: (strict_implies(X0,not(not(X1)))=strict_implies(X0,or(X1,X1))|~spl0_90|~spl0_56|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f525,f3322])).
% 26.21/3.73 fof(f5676,plain,(
% 26.21/3.73 ![X0,X1,X2]: (or(X0,and(X1,not(X2)))=implies(implies(X1,X2),X0)|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f977,f838])).
% 26.21/3.73 fof(f5696,plain,(
% 26.21/3.73 ![X0,X1,X2]: (or(X0,and(not(X1),X2))=implies(implies(and(X2,not(X1)),X1),X0)|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f1947,f5676])).
% 26.21/3.73 fof(f5697,plain,(
% 26.21/3.73 ![X0,X1,X2]: (or(X0,and(not(X1),X2))=implies(implies(X2,X1),X0)|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f2086,f5696])).
% 26.21/3.73 fof(f6806,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_equiv(not(X0),X1))|is_a_theorem(necessarily(or(X1,X0)))|~spl0_59|~spl0_90|~spl0_1|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_5|~spl0_15)),
% 26.21/3.73 inference(resolution,[status(thm)],[f1137,f249])).
% 26.21/3.73 fof(f8047,plain,(
% 26.21/3.73 ![X0]: (~is_a_theorem(strict_implies(not(X0),not(X0)))|is_a_theorem(necessarily(or(not(X0),X0)))|~spl0_59|~spl0_90|~spl0_1|~spl0_56|~spl0_5|~spl0_15|~spl0_68|~spl0_20|~spl0_25|~spl0_65|~spl0_92)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f863,f6806])).
% 26.21/3.73 fof(f8048,plain,(
% 26.21/3.73 ![X0]: (~is_a_theorem(necessarily(or(X0,not(X0))))|is_a_theorem(necessarily(or(not(X0),X0)))|~spl0_59|~spl0_90|~spl0_1|~spl0_56|~spl0_5|~spl0_15|~spl0_68|~spl0_20|~spl0_25|~spl0_65|~spl0_92)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f700,f8047])).
% 26.21/3.73 fof(f8049,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(necessarily(or(not(X0),X0)))|~spl0_59|~spl0_90|~spl0_1|~spl0_56|~spl0_5|~spl0_15|~spl0_68|~spl0_20|~spl0_25|~spl0_65|~spl0_92)),
% 26.21/3.73 inference(forward_subsumption_resolution,[status(thm)],[f8048,f877])).
% 26.21/3.73 fof(f8541,plain,(
% 26.21/3.73 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(and(X0,strict_implies(and(X1,X2),X2)))|~spl0_59|~spl0_92|~spl0_25|~spl0_56|~spl0_20)),
% 26.21/3.73 inference(resolution,[status(thm)],[f983,f268])).
% 26.21/3.73 fof(f8591,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(X0,necessarily(or(not(X1),X1))))|~spl0_59|~spl0_90|~spl0_1|~spl0_56|~spl0_5|~spl0_15|~spl0_68|~spl0_25|~spl0_65|~spl0_92|~spl0_20)),
% 26.21/3.73 inference(resolution,[status(thm)],[f8049,f268])).
% 26.21/3.73 fof(f8592,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(necessarily(or(not(X0),X0)),X1))|is_a_theorem(X1)|~spl0_59|~spl0_90|~spl0_1|~spl0_56|~spl0_5|~spl0_68|~spl0_20|~spl0_25|~spl0_65|~spl0_92|~spl0_15)),
% 26.21/3.73 inference(resolution,[status(thm)],[f8049,f249])).
% 26.21/3.73 fof(f11838,plain,(
% 26.21/3.73 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(and(strict_implies(and(X1,X2),X2),X0))|~spl0_59|~spl0_92|~spl0_25|~spl0_20|~spl0_15|~spl0_56)),
% 26.21/3.73 inference(resolution,[status(thm)],[f8541,f585])).
% 26.21/3.73 fof(f12507,plain,(
% 26.21/3.73 ![X0,X1,X2]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(strict_implies(and(X2,X0),X1))|~spl0_59|~spl0_92|~spl0_25|~spl0_20|~spl0_56|~spl0_68|~spl0_15)),
% 26.21/3.73 inference(resolution,[status(thm)],[f11838,f672])).
% 26.21/3.73 fof(f14968,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(not(X0),X0))|is_a_theorem(strict_implies(X1,X0))|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f2268,f12507])).
% 26.21/3.73 fof(f14969,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(necessarily(or(X0,X0)))|is_a_theorem(strict_implies(X1,X0))|~spl0_1|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f700,f14968])).
% 26.21/3.73 fof(f15009,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(necessarily(not(not(X0))))|is_a_theorem(strict_implies(X1,X0))|~spl0_68|~spl0_15|~spl0_90|~spl0_62|~spl0_56|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f893,f14969])).
% 26.21/3.73 fof(f19525,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(necessarily(or(not(X1),X1)),X0))|~spl0_59|~spl0_90|~spl0_1|~spl0_5|~spl0_68|~spl0_25|~spl0_65|~spl0_92|~spl0_20|~spl0_15|~spl0_56)),
% 26.21/3.73 inference(resolution,[status(thm)],[f8591,f585])).
% 26.21/3.73 fof(f20581,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(X0,not(not(X1))))|is_a_theorem(strict_implies(X0,X1))|~spl0_59|~spl0_65|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1)),
% 26.21/3.73 inference(resolution,[status(thm)],[f19525,f1247])).
% 26.21/3.73 fof(f20956,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(and(not(not(X0)),X1),X0))|~spl0_65|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_59)),
% 26.21/3.73 inference(resolution,[status(thm)],[f20581,f412])).
% 26.21/3.73 fof(f20969,plain,(
% 26.21/3.73 ![X0,X1]: (~is_a_theorem(strict_implies(X0,or(X1,X1)))|is_a_theorem(strict_implies(X0,X1))|~spl0_68|~spl0_15|~spl0_90|~spl0_56|~spl0_1|~spl0_5|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_65)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f3323,f20581])).
% 26.21/3.73 fof(f21341,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(and(not(not(or(X0,X0))),X1),X0))|~spl0_65|~spl0_20|~spl0_92|~spl0_25|~spl0_56|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_59)),
% 26.21/3.73 inference(resolution,[status(thm)],[f20969,f20956])).
% 26.21/3.73 fof(f25728,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(strict_implies(not(not(or(X0,X0))),X0))|~spl0_68|~spl0_15|~spl0_1|~spl0_90|~spl0_5|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f2268,f21341])).
% 26.21/3.73 fof(f25729,plain,(
% 26.21/3.73 ![X0]: (is_a_theorem(necessarily(or(not(or(X0,X0)),X0)))|~spl0_68|~spl0_15|~spl0_1|~spl0_90|~spl0_5|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f700,f25728])).
% 26.21/3.73 fof(f25801,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(necessarily(implies(implies(X0,X1),not(or(and(not(X1),X0),and(not(X1),X0))))))|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(paramodulation,[status(thm)],[f5697,f25729])).
% 26.21/3.73 fof(f25802,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(implies(X0,X1),not(or(and(not(X1),X0),and(not(X1),X0)))))|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f525,f25801])).
% 26.21/3.73 fof(f25803,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(implies(X0,X1),not(not(not(and(not(X1),X0))))))|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 26.21/3.73 inference(forward_demodulation,[status(thm)],[f1726,f25802])).
% 26.21/3.73 fof(f25804,plain,(
% 26.21/3.73 ![X0,X1]: (is_a_theorem(strict_implies(implies(X0,X1),not(not(implies(X0,X1)))))|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_20|~spl0_92|~spl0_25|~spl0_56)),
% 27.05/3.87 inference(forward_demodulation,[status(thm)],[f977,f25803])).
% 27.05/3.87 fof(f35821,plain,(
% 27.05/3.87 ![X0,X1]: (~is_a_theorem(strict_implies(not(not(implies(X0,X1))),implies(X0,X1)))|not(not(implies(X0,X1)))=implies(X0,X1)|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_56|~spl0_20|~spl0_92|~spl0_25)),
% 27.05/3.87 inference(resolution,[status(thm)],[f25804,f854])).
% 27.05/3.87 fof(f35822,plain,(
% 27.05/3.87 ![X0,X1]: (~is_a_theorem(necessarily(or(not(implies(X0,X1)),implies(X0,X1))))|not(not(implies(X0,X1)))=implies(X0,X1)|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_56|~spl0_20|~spl0_92|~spl0_25)),
% 27.05/3.87 inference(forward_demodulation,[status(thm)],[f700,f35821])).
% 27.05/3.87 fof(f35823,plain,(
% 27.05/3.87 ![X0,X1]: (not(not(implies(X0,X1)))=implies(X0,X1)|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_56|~spl0_20|~spl0_92|~spl0_25)),
% 27.05/3.87 inference(forward_subsumption_resolution,[status(thm)],[f35822,f8049])).
% 27.05/3.87 fof(f35935,plain,(
% 27.05/3.87 ![X0,X1,X2]: (~is_a_theorem(necessarily(implies(X0,X1)))|is_a_theorem(strict_implies(X2,implies(X0,X1)))|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_56|~spl0_20|~spl0_92|~spl0_25)),
% 27.05/3.87 inference(paramodulation,[status(thm)],[f35823,f15009])).
% 27.05/3.87 fof(f35936,plain,(
% 27.05/3.87 ![X0,X1,X2]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(strict_implies(X2,implies(X0,X1)))|~spl0_68|~spl0_15|~spl0_90|~spl0_5|~spl0_1|~spl0_62|~spl0_65|~spl0_59|~spl0_56|~spl0_20|~spl0_92|~spl0_25)),
% 27.05/3.87 inference(forward_demodulation,[status(thm)],[f525,f35935])).
% 27.05/3.87 fof(f38719,plain,(
% 27.05/3.87 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(X0,X1))|~spl0_62|~spl0_59|~spl0_90|~spl0_1|~spl0_56|~spl0_5|~spl0_68|~spl0_20|~spl0_25|~spl0_65|~spl0_92|~spl0_15)),
% 27.05/3.87 inference(resolution,[status(thm)],[f35936,f8592])).
% 27.05/3.87 fof(f38780,plain,(
% 27.05/3.87 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))|~spl0_62|~spl0_59|~spl0_90|~spl0_1|~spl0_56|~spl0_5|~spl0_68|~spl0_20|~spl0_25|~spl0_65|~spl0_92|~spl0_15|~spl0_83)),
% 27.05/3.87 inference(resolution,[status(thm)],[f38719,f500])).
% 27.05/3.87 fof(f38781,plain,(
% 27.05/3.87 spl0_41|~spl0_62|~spl0_59|~spl0_90|~spl0_1|~spl0_56|~spl0_5|~spl0_68|~spl0_20|~spl0_25|~spl0_65|~spl0_92|~spl0_15|~spl0_83),
% 27.05/3.87 inference(split_clause,[status(thm)],[f38780,f345,f422,f411,f524,f198,f400,f212,f444,f267,f286,f433,f531,f248,f499])).
% 27.05/3.87 fof(f38936,plain,(
% 27.05/3.87 $false|~spl0_40),
% 27.05/3.87 inference(forward_subsumption_resolution,[status(thm)],[f343,f194])).
% 27.05/3.87 fof(f38937,plain,(
% 27.05/3.87 ~spl0_40),
% 27.05/3.87 inference(contradiction_clause,[status(thm)],[f38936])).
% 27.05/3.87 fof(f38938,plain,(
% 27.05/3.87 $false),
% 27.05/3.87 inference(sat_refutation,[status(thm)],[f201,f215,f251,f270,f289,f352,f403,f414,f425,f436,f447,f502,f527,f534,f536,f538,f540,f542,f544,f550,f552,f563,f567,f573,f599,f613,f671,f679,f38781,f38937])).
% 27.05/3.87 % SZS output end CNFRefutation for theBenchmark.p
% 27.05/3.87 % Elapsed time: 3.504856 seconds
% 27.05/3.87 % CPU time: 26.881143 seconds
% 27.05/3.87 % Memory used: 609.876 MB
%------------------------------------------------------------------------------