TSTP Solution File: LCL573+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : LCL573+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art07.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Wed Dec 29 14:16:22 EST 2010
% Result : Theorem 8.17s
% Output : Solution 8.17s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP5060/LCL573+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP5060/LCL573+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP5060/LCL573+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=60 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 5156
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 WC
% PrfWatch: 1.92 CPU 2.01 WC
% PrfWatch: 3.91 CPU 4.01 WC
% # Preprocessing time : 0.017 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 5.91 CPU 6.02 WC
% # SZS output start CNFRefutation.
% fof(6, axiom,op_strict_implies,file('/tmp/SRASS.s.p', s1_0_op_strict_implies)).
% fof(7, axiom,modus_ponens_strict_implies,file('/tmp/SRASS.s.p', s1_0_modus_ponens_strict_implies)).
% fof(8, axiom,adjunction,file('/tmp/SRASS.s.p', s1_0_adjunction)).
% fof(9, axiom,axiom_m10,file('/tmp/SRASS.s.p', s1_0_m10_axiom_m10)).
% fof(10, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(13, axiom,(axiom_m10<=>![X1]:is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))),file('/tmp/SRASS.s.p', axiom_m10)).
% fof(14, axiom,(axiom_5<=>![X1]:is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))),file('/tmp/SRASS.s.p', axiom_5)).
% fof(15, axiom,op_or,file('/tmp/SRASS.s.p', s1_0_op_or)).
% fof(17, axiom,op_strict_equiv,file('/tmp/SRASS.s.p', s1_0_op_strict_equiv)).
% fof(18, axiom,substitution_strict_equiv,file('/tmp/SRASS.s.p', s1_0_substitution_strict_equiv)).
% fof(19, axiom,axiom_m1,file('/tmp/SRASS.s.p', s1_0_axiom_m1)).
% fof(20, axiom,axiom_m2,file('/tmp/SRASS.s.p', s1_0_axiom_m2)).
% fof(21, axiom,axiom_m3,file('/tmp/SRASS.s.p', s1_0_axiom_m3)).
% fof(22, axiom,axiom_m4,file('/tmp/SRASS.s.p', s1_0_axiom_m4)).
% fof(23, axiom,axiom_m5,file('/tmp/SRASS.s.p', s1_0_axiom_m5)).
% fof(30, axiom,(op_strict_implies=>![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),file('/tmp/SRASS.s.p', op_strict_implies)).
% fof(36, axiom,(axiom_m1<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),file('/tmp/SRASS.s.p', axiom_m1)).
% fof(37, axiom,(axiom_m2<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),X1))),file('/tmp/SRASS.s.p', axiom_m2)).
% fof(38, axiom,(axiom_m3<=>![X1]:![X2]:![X3]:is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))),file('/tmp/SRASS.s.p', axiom_m3)).
% fof(39, axiom,(axiom_m4<=>![X1]:is_a_theorem(strict_implies(X1,and(X1,X1)))),file('/tmp/SRASS.s.p', axiom_m4)).
% fof(40, axiom,(axiom_m5<=>![X1]:![X2]:![X3]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))),file('/tmp/SRASS.s.p', axiom_m5)).
% fof(41, axiom,(op_or=>![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),file('/tmp/SRASS.s.p', op_or)).
% fof(45, axiom,(modus_ponens_strict_implies<=>![X1]:![X2]:((is_a_theorem(X1)&is_a_theorem(strict_implies(X1,X2)))=>is_a_theorem(X2))),file('/tmp/SRASS.s.p', modus_ponens_strict_implies)).
% fof(46, axiom,(adjunction<=>![X1]:![X2]:((is_a_theorem(X1)&is_a_theorem(X2))=>is_a_theorem(and(X1,X2)))),file('/tmp/SRASS.s.p', adjunction)).
% fof(47, axiom,(op_strict_equiv=>![X1]:![X2]:strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))),file('/tmp/SRASS.s.p', op_strict_equiv)).
% fof(48, axiom,(op_implies_and=>![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(49, axiom,(substitution_strict_equiv<=>![X1]:![X2]:(is_a_theorem(strict_equiv(X1,X2))=>X1=X2)),file('/tmp/SRASS.s.p', substitution_strict_equiv)).
% fof(52, conjecture,axiom_5,file('/tmp/SRASS.s.p', km5_axiom_5)).
% fof(53, negated_conjecture,~(axiom_5),inference(assume_negation,[status(cth)],[52])).
% fof(54, negated_conjecture,~(axiom_5),inference(fof_simplification,[status(thm)],[53,theory(equality)])).
% cnf(80,plain,(op_strict_implies),inference(split_conjunct,[status(thm)],[6])).
% cnf(81,plain,(modus_ponens_strict_implies),inference(split_conjunct,[status(thm)],[7])).
% cnf(82,plain,(adjunction),inference(split_conjunct,[status(thm)],[8])).
% cnf(83,plain,(axiom_m10),inference(split_conjunct,[status(thm)],[9])).
% cnf(84,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[10])).
% fof(99, plain,((~(axiom_m10)|![X1]:is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))))&(?[X1]:~(is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))))|axiom_m10)),inference(fof_nnf,[status(thm)],[13])).
% fof(100, plain,((~(axiom_m10)|![X2]:is_a_theorem(strict_implies(possibly(X2),necessarily(possibly(X2)))))&(?[X3]:~(is_a_theorem(strict_implies(possibly(X3),necessarily(possibly(X3)))))|axiom_m10)),inference(variable_rename,[status(thm)],[99])).
% fof(101, plain,((~(axiom_m10)|![X2]:is_a_theorem(strict_implies(possibly(X2),necessarily(possibly(X2)))))&(~(is_a_theorem(strict_implies(possibly(esk10_0),necessarily(possibly(esk10_0)))))|axiom_m10)),inference(skolemize,[status(esa)],[100])).
% fof(102, plain,![X2]:((is_a_theorem(strict_implies(possibly(X2),necessarily(possibly(X2))))|~(axiom_m10))&(~(is_a_theorem(strict_implies(possibly(esk10_0),necessarily(possibly(esk10_0)))))|axiom_m10)),inference(shift_quantors,[status(thm)],[101])).
% cnf(104,plain,(is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))|~axiom_m10),inference(split_conjunct,[status(thm)],[102])).
% fof(105, plain,((~(axiom_5)|![X1]:is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))))&(?[X1]:~(is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))))|axiom_5)),inference(fof_nnf,[status(thm)],[14])).
% fof(106, plain,((~(axiom_5)|![X2]:is_a_theorem(implies(possibly(X2),necessarily(possibly(X2)))))&(?[X3]:~(is_a_theorem(implies(possibly(X3),necessarily(possibly(X3)))))|axiom_5)),inference(variable_rename,[status(thm)],[105])).
% fof(107, plain,((~(axiom_5)|![X2]:is_a_theorem(implies(possibly(X2),necessarily(possibly(X2)))))&(~(is_a_theorem(implies(possibly(esk11_0),necessarily(possibly(esk11_0)))))|axiom_5)),inference(skolemize,[status(esa)],[106])).
% fof(108, plain,![X2]:((is_a_theorem(implies(possibly(X2),necessarily(possibly(X2))))|~(axiom_5))&(~(is_a_theorem(implies(possibly(esk11_0),necessarily(possibly(esk11_0)))))|axiom_5)),inference(shift_quantors,[status(thm)],[107])).
% cnf(109,plain,(axiom_5|~is_a_theorem(implies(possibly(esk11_0),necessarily(possibly(esk11_0))))),inference(split_conjunct,[status(thm)],[108])).
% cnf(111,plain,(op_or),inference(split_conjunct,[status(thm)],[15])).
% cnf(113,plain,(op_strict_equiv),inference(split_conjunct,[status(thm)],[17])).
% cnf(114,plain,(substitution_strict_equiv),inference(split_conjunct,[status(thm)],[18])).
% cnf(115,plain,(axiom_m1),inference(split_conjunct,[status(thm)],[19])).
% cnf(116,plain,(axiom_m2),inference(split_conjunct,[status(thm)],[20])).
% cnf(117,plain,(axiom_m3),inference(split_conjunct,[status(thm)],[21])).
% cnf(118,plain,(axiom_m4),inference(split_conjunct,[status(thm)],[22])).
% cnf(119,plain,(axiom_m5),inference(split_conjunct,[status(thm)],[23])).
% fof(146, plain,(~(op_strict_implies)|![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),inference(fof_nnf,[status(thm)],[30])).
% fof(147, plain,(~(op_strict_implies)|![X3]:![X4]:strict_implies(X3,X4)=necessarily(implies(X3,X4))),inference(variable_rename,[status(thm)],[146])).
% fof(148, plain,![X3]:![X4]:(strict_implies(X3,X4)=necessarily(implies(X3,X4))|~(op_strict_implies)),inference(shift_quantors,[status(thm)],[147])).
% cnf(149,plain,(strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies),inference(split_conjunct,[status(thm)],[148])).
% fof(176, plain,((~(axiom_m1)|![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))))&(?[X1]:?[X2]:~(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))))|axiom_m1)),inference(fof_nnf,[status(thm)],[36])).
% fof(177, plain,((~(axiom_m1)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))))&(?[X5]:?[X6]:~(is_a_theorem(strict_implies(and(X5,X6),and(X6,X5))))|axiom_m1)),inference(variable_rename,[status(thm)],[176])).
% fof(178, plain,((~(axiom_m1)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))))&(~(is_a_theorem(strict_implies(and(esk23_0,esk24_0),and(esk24_0,esk23_0))))|axiom_m1)),inference(skolemize,[status(esa)],[177])).
% fof(179, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),and(X4,X3)))|~(axiom_m1))&(~(is_a_theorem(strict_implies(and(esk23_0,esk24_0),and(esk24_0,esk23_0))))|axiom_m1)),inference(shift_quantors,[status(thm)],[178])).
% cnf(181,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1),inference(split_conjunct,[status(thm)],[179])).
% fof(182, plain,((~(axiom_m2)|![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),X1)))&(?[X1]:?[X2]:~(is_a_theorem(strict_implies(and(X1,X2),X1)))|axiom_m2)),inference(fof_nnf,[status(thm)],[37])).
% fof(183, plain,((~(axiom_m2)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),X3)))&(?[X5]:?[X6]:~(is_a_theorem(strict_implies(and(X5,X6),X5)))|axiom_m2)),inference(variable_rename,[status(thm)],[182])).
% fof(184, plain,((~(axiom_m2)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),X3)))&(~(is_a_theorem(strict_implies(and(esk25_0,esk26_0),esk25_0)))|axiom_m2)),inference(skolemize,[status(esa)],[183])).
% fof(185, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),X3))|~(axiom_m2))&(~(is_a_theorem(strict_implies(and(esk25_0,esk26_0),esk25_0)))|axiom_m2)),inference(shift_quantors,[status(thm)],[184])).
% cnf(187,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2),inference(split_conjunct,[status(thm)],[185])).
% fof(188, plain,((~(axiom_m3)|![X1]:![X2]:![X3]:is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))))&(?[X1]:?[X2]:?[X3]:~(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))))|axiom_m3)),inference(fof_nnf,[status(thm)],[38])).
% fof(189, plain,((~(axiom_m3)|![X4]:![X5]:![X6]:is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X4,and(X5,X6)))))&(?[X7]:?[X8]:?[X9]:~(is_a_theorem(strict_implies(and(and(X7,X8),X9),and(X7,and(X8,X9)))))|axiom_m3)),inference(variable_rename,[status(thm)],[188])).
% fof(190, plain,((~(axiom_m3)|![X4]:![X5]:![X6]:is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X4,and(X5,X6)))))&(~(is_a_theorem(strict_implies(and(and(esk27_0,esk28_0),esk29_0),and(esk27_0,and(esk28_0,esk29_0)))))|axiom_m3)),inference(skolemize,[status(esa)],[189])).
% fof(191, plain,![X4]:![X5]:![X6]:((is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X4,and(X5,X6))))|~(axiom_m3))&(~(is_a_theorem(strict_implies(and(and(esk27_0,esk28_0),esk29_0),and(esk27_0,and(esk28_0,esk29_0)))))|axiom_m3)),inference(shift_quantors,[status(thm)],[190])).
% cnf(193,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|~axiom_m3),inference(split_conjunct,[status(thm)],[191])).
% fof(194, plain,((~(axiom_m4)|![X1]:is_a_theorem(strict_implies(X1,and(X1,X1))))&(?[X1]:~(is_a_theorem(strict_implies(X1,and(X1,X1))))|axiom_m4)),inference(fof_nnf,[status(thm)],[39])).
% fof(195, plain,((~(axiom_m4)|![X2]:is_a_theorem(strict_implies(X2,and(X2,X2))))&(?[X3]:~(is_a_theorem(strict_implies(X3,and(X3,X3))))|axiom_m4)),inference(variable_rename,[status(thm)],[194])).
% fof(196, plain,((~(axiom_m4)|![X2]:is_a_theorem(strict_implies(X2,and(X2,X2))))&(~(is_a_theorem(strict_implies(esk30_0,and(esk30_0,esk30_0))))|axiom_m4)),inference(skolemize,[status(esa)],[195])).
% fof(197, plain,![X2]:((is_a_theorem(strict_implies(X2,and(X2,X2)))|~(axiom_m4))&(~(is_a_theorem(strict_implies(esk30_0,and(esk30_0,esk30_0))))|axiom_m4)),inference(shift_quantors,[status(thm)],[196])).
% cnf(199,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4),inference(split_conjunct,[status(thm)],[197])).
% fof(200, plain,((~(axiom_m5)|![X1]:![X2]:![X3]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))))&(?[X1]:?[X2]:?[X3]:~(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))))|axiom_m5)),inference(fof_nnf,[status(thm)],[40])).
% fof(201, plain,((~(axiom_m5)|![X4]:![X5]:![X6]:is_a_theorem(strict_implies(and(strict_implies(X4,X5),strict_implies(X5,X6)),strict_implies(X4,X6))))&(?[X7]:?[X8]:?[X9]:~(is_a_theorem(strict_implies(and(strict_implies(X7,X8),strict_implies(X8,X9)),strict_implies(X7,X9))))|axiom_m5)),inference(variable_rename,[status(thm)],[200])).
% fof(202, plain,((~(axiom_m5)|![X4]:![X5]:![X6]:is_a_theorem(strict_implies(and(strict_implies(X4,X5),strict_implies(X5,X6)),strict_implies(X4,X6))))&(~(is_a_theorem(strict_implies(and(strict_implies(esk31_0,esk32_0),strict_implies(esk32_0,esk33_0)),strict_implies(esk31_0,esk33_0))))|axiom_m5)),inference(skolemize,[status(esa)],[201])).
% fof(203, plain,![X4]:![X5]:![X6]:((is_a_theorem(strict_implies(and(strict_implies(X4,X5),strict_implies(X5,X6)),strict_implies(X4,X6)))|~(axiom_m5))&(~(is_a_theorem(strict_implies(and(strict_implies(esk31_0,esk32_0),strict_implies(esk32_0,esk33_0)),strict_implies(esk31_0,esk33_0))))|axiom_m5)),inference(shift_quantors,[status(thm)],[202])).
% cnf(205,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_m5),inference(split_conjunct,[status(thm)],[203])).
% fof(206, plain,(~(op_or)|![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),inference(fof_nnf,[status(thm)],[41])).
% fof(207, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(variable_rename,[status(thm)],[206])).
% fof(208, plain,![X3]:![X4]:(or(X3,X4)=not(and(not(X3),not(X4)))|~(op_or)),inference(shift_quantors,[status(thm)],[207])).
% cnf(209,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[208])).
% fof(222, plain,((~(modus_ponens_strict_implies)|![X1]:![X2]:((~(is_a_theorem(X1))|~(is_a_theorem(strict_implies(X1,X2))))|is_a_theorem(X2)))&(?[X1]:?[X2]:((is_a_theorem(X1)&is_a_theorem(strict_implies(X1,X2)))&~(is_a_theorem(X2)))|modus_ponens_strict_implies)),inference(fof_nnf,[status(thm)],[45])).
% fof(223, plain,((~(modus_ponens_strict_implies)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(strict_implies(X3,X4))))|is_a_theorem(X4)))&(?[X5]:?[X6]:((is_a_theorem(X5)&is_a_theorem(strict_implies(X5,X6)))&~(is_a_theorem(X6)))|modus_ponens_strict_implies)),inference(variable_rename,[status(thm)],[222])).
% fof(224, plain,((~(modus_ponens_strict_implies)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(strict_implies(X3,X4))))|is_a_theorem(X4)))&(((is_a_theorem(esk34_0)&is_a_theorem(strict_implies(esk34_0,esk35_0)))&~(is_a_theorem(esk35_0)))|modus_ponens_strict_implies)),inference(skolemize,[status(esa)],[223])).
% fof(225, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(strict_implies(X3,X4))))|is_a_theorem(X4))|~(modus_ponens_strict_implies))&(((is_a_theorem(esk34_0)&is_a_theorem(strict_implies(esk34_0,esk35_0)))&~(is_a_theorem(esk35_0)))|modus_ponens_strict_implies)),inference(shift_quantors,[status(thm)],[224])).
% fof(226, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(strict_implies(X3,X4))))|is_a_theorem(X4))|~(modus_ponens_strict_implies))&(((is_a_theorem(esk34_0)|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(esk34_0,esk35_0))|modus_ponens_strict_implies))&(~(is_a_theorem(esk35_0))|modus_ponens_strict_implies))),inference(distribute,[status(thm)],[225])).
% cnf(230,plain,(is_a_theorem(X1)|~modus_ponens_strict_implies|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(X2)),inference(split_conjunct,[status(thm)],[226])).
% fof(231, plain,((~(adjunction)|![X1]:![X2]:((~(is_a_theorem(X1))|~(is_a_theorem(X2)))|is_a_theorem(and(X1,X2))))&(?[X1]:?[X2]:((is_a_theorem(X1)&is_a_theorem(X2))&~(is_a_theorem(and(X1,X2))))|adjunction)),inference(fof_nnf,[status(thm)],[46])).
% fof(232, plain,((~(adjunction)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4))))&(?[X5]:?[X6]:((is_a_theorem(X5)&is_a_theorem(X6))&~(is_a_theorem(and(X5,X6))))|adjunction)),inference(variable_rename,[status(thm)],[231])).
% fof(233, plain,((~(adjunction)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4))))&(((is_a_theorem(esk36_0)&is_a_theorem(esk37_0))&~(is_a_theorem(and(esk36_0,esk37_0))))|adjunction)),inference(skolemize,[status(esa)],[232])).
% fof(234, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk36_0)&is_a_theorem(esk37_0))&~(is_a_theorem(and(esk36_0,esk37_0))))|adjunction)),inference(shift_quantors,[status(thm)],[233])).
% fof(235, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk36_0)|adjunction)&(is_a_theorem(esk37_0)|adjunction))&(~(is_a_theorem(and(esk36_0,esk37_0)))|adjunction))),inference(distribute,[status(thm)],[234])).
% cnf(239,plain,(is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(split_conjunct,[status(thm)],[235])).
% fof(240, plain,(~(op_strict_equiv)|![X1]:![X2]:strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))),inference(fof_nnf,[status(thm)],[47])).
% fof(241, plain,(~(op_strict_equiv)|![X3]:![X4]:strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))),inference(variable_rename,[status(thm)],[240])).
% fof(242, plain,![X3]:![X4]:(strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))|~(op_strict_equiv)),inference(shift_quantors,[status(thm)],[241])).
% cnf(243,plain,(strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv),inference(split_conjunct,[status(thm)],[242])).
% fof(244, plain,(~(op_implies_and)|![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),inference(fof_nnf,[status(thm)],[48])).
% fof(245, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(variable_rename,[status(thm)],[244])).
% fof(246, plain,![X3]:![X4]:(implies(X3,X4)=not(and(X3,not(X4)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[245])).
% cnf(247,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[246])).
% fof(248, plain,((~(substitution_strict_equiv)|![X1]:![X2]:(~(is_a_theorem(strict_equiv(X1,X2)))|X1=X2))&(?[X1]:?[X2]:(is_a_theorem(strict_equiv(X1,X2))&~(X1=X2))|substitution_strict_equiv)),inference(fof_nnf,[status(thm)],[49])).
% fof(249, plain,((~(substitution_strict_equiv)|![X3]:![X4]:(~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4))&(?[X5]:?[X6]:(is_a_theorem(strict_equiv(X5,X6))&~(X5=X6))|substitution_strict_equiv)),inference(variable_rename,[status(thm)],[248])).
% fof(250, plain,((~(substitution_strict_equiv)|![X3]:![X4]:(~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4))&((is_a_theorem(strict_equiv(esk38_0,esk39_0))&~(esk38_0=esk39_0))|substitution_strict_equiv)),inference(skolemize,[status(esa)],[249])).
% fof(251, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk38_0,esk39_0))&~(esk38_0=esk39_0))|substitution_strict_equiv)),inference(shift_quantors,[status(thm)],[250])).
% fof(252, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk38_0,esk39_0))|substitution_strict_equiv)&(~(esk38_0=esk39_0)|substitution_strict_equiv))),inference(distribute,[status(thm)],[251])).
% cnf(255,plain,(X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2))),inference(split_conjunct,[status(thm)],[252])).
% cnf(258,negated_conjecture,(~axiom_5),inference(split_conjunct,[status(thm)],[54])).
% cnf(267,plain,(~is_a_theorem(implies(possibly(esk11_0),necessarily(possibly(esk11_0))))),inference(sr,[status(thm)],[109,258,theory(equality)])).
% cnf(272,plain,(X1=X2|$false|~is_a_theorem(strict_equiv(X1,X2))),inference(rw,[status(thm)],[255,114,theory(equality)])).
% cnf(273,plain,(X1=X2|~is_a_theorem(strict_equiv(X1,X2))),inference(cn,[status(thm)],[272,theory(equality)])).
% cnf(279,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|$false),inference(rw,[status(thm)],[199,118,theory(equality)])).
% cnf(280,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))),inference(cn,[status(thm)],[279,theory(equality)])).
% cnf(281,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[187,116,theory(equality)])).
% cnf(282,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))),inference(cn,[status(thm)],[281,theory(equality)])).
% cnf(283,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(rw,[status(thm)],[230,81,theory(equality)])).
% cnf(284,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(cn,[status(thm)],[283,theory(equality)])).
% cnf(285,plain,(is_a_theorem(X1)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[284,282,theory(equality)])).
% cnf(287,plain,(is_a_theorem(and(X1,X2))|$false|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(rw,[status(thm)],[239,82,theory(equality)])).
% cnf(288,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(cn,[status(thm)],[287,theory(equality)])).
% cnf(289,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)|$false),inference(rw,[status(thm)],[149,80,theory(equality)])).
% cnf(290,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)),inference(cn,[status(thm)],[289,theory(equality)])).
% cnf(291,plain,(is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))|$false),inference(rw,[status(thm)],[104,83,theory(equality)])).
% cnf(292,plain,(is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))),inference(cn,[status(thm)],[291,theory(equality)])).
% cnf(295,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[247,84,theory(equality)])).
% cnf(296,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[295,theory(equality)])).
% cnf(301,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[209,296,theory(equality)])).
% cnf(302,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[301,111,theory(equality)])).
% cnf(303,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[302,theory(equality)])).
% cnf(304,plain,(necessarily(or(X1,X2))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[290,303,theory(equality)])).
% cnf(307,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[181,115,theory(equality)])).
% cnf(308,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[307,theory(equality)])).
% cnf(309,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(and(X2,X1))),inference(spm,[status(thm)],[284,308,theory(equality)])).
% cnf(323,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)|$false),inference(rw,[status(thm)],[243,113,theory(equality)])).
% cnf(324,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)),inference(cn,[status(thm)],[323,theory(equality)])).
% cnf(325,plain,(is_a_theorem(strict_equiv(X1,X2))|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(strict_implies(X1,X2))),inference(spm,[status(thm)],[288,324,theory(equality)])).
% cnf(326,plain,(is_a_theorem(strict_implies(strict_equiv(X1,X2),strict_implies(X1,X2)))),inference(spm,[status(thm)],[282,324,theory(equality)])).
% cnf(334,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|$false),inference(rw,[status(thm)],[193,117,theory(equality)])).
% cnf(335,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))),inference(cn,[status(thm)],[334,theory(equality)])).
% cnf(336,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(and(and(X1,X2),X3))),inference(spm,[status(thm)],[284,335,theory(equality)])).
% cnf(341,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|$false),inference(rw,[status(thm)],[205,119,theory(equality)])).
% cnf(342,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))),inference(cn,[status(thm)],[341,theory(equality)])).
% cnf(343,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))),inference(spm,[status(thm)],[284,342,theory(equality)])).
% cnf(346,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_equiv(X1,X2))),inference(spm,[status(thm)],[285,324,theory(equality)])).
% cnf(400,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|~is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(spm,[status(thm)],[325,308,theory(equality)])).
% cnf(401,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(and(X1,X2),X3)))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))),inference(spm,[status(thm)],[325,335,theory(equality)])).
% cnf(404,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|~is_a_theorem(strict_implies(and(X1,X1),X1))),inference(spm,[status(thm)],[325,280,theory(equality)])).
% cnf(405,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[400,308,theory(equality)])).
% cnf(406,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[405,theory(equality)])).
% cnf(407,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|$false),inference(rw,[status(thm)],[404,282,theory(equality)])).
% cnf(408,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))),inference(cn,[status(thm)],[407,theory(equality)])).
% cnf(409,plain,(and(X1,X1)=X1),inference(spm,[status(thm)],[273,408,theory(equality)])).
% cnf(415,plain,(strict_implies(X1,X1)=strict_equiv(X1,X1)),inference(spm,[status(thm)],[324,409,theory(equality)])).
% cnf(419,plain,(not(not(X1))=implies(not(X1),X1)),inference(spm,[status(thm)],[296,409,theory(equality)])).
% cnf(431,plain,(is_a_theorem(strict_equiv(X1,X1))),inference(rw,[status(thm)],[408,409,theory(equality)])).
% cnf(435,plain,(not(not(X1))=or(X1,X1)),inference(rw,[status(thm)],[419,303,theory(equality)])).
% cnf(440,plain,(is_a_theorem(strict_implies(X1,X1))),inference(spm,[status(thm)],[346,431,theory(equality)])).
% cnf(478,plain,(and(X1,X2)=and(X2,X1)),inference(spm,[status(thm)],[273,406,theory(equality)])).
% cnf(497,plain,(and(strict_implies(X2,X1),strict_implies(X1,X2))=strict_equiv(X1,X2)),inference(spm,[status(thm)],[324,478,theory(equality)])).
% cnf(501,plain,(not(and(not(X2),X1))=implies(X1,X2)),inference(spm,[status(thm)],[296,478,theory(equality)])).
% cnf(506,plain,(is_a_theorem(X1)|~is_a_theorem(and(X2,X1))),inference(spm,[status(thm)],[285,478,theory(equality)])).
% cnf(508,plain,(is_a_theorem(strict_implies(and(X2,X1),X1))),inference(spm,[status(thm)],[282,478,theory(equality)])).
% cnf(537,plain,(strict_equiv(X2,X1)=strict_equiv(X1,X2)),inference(rw,[status(thm)],[497,324,theory(equality)])).
% cnf(578,plain,(necessarily(not(not(X1)))=strict_implies(not(X1),X1)),inference(spm,[status(thm)],[304,435,theory(equality)])).
% cnf(697,plain,(implies(not(X2),X1)=implies(not(X1),X2)),inference(spm,[status(thm)],[296,501,theory(equality)])).
% cnf(713,plain,(or(X2,X1)=implies(not(X1),X2)),inference(rw,[status(thm)],[697,303,theory(equality)])).
% cnf(714,plain,(or(X2,X1)=or(X1,X2)),inference(rw,[status(thm)],[713,303,theory(equality)])).
% cnf(722,plain,(necessarily(or(X2,X1))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[304,714,theory(equality)])).
% cnf(728,plain,(strict_implies(not(X2),X1)=strict_implies(not(X1),X2)),inference(rw,[status(thm)],[722,304,theory(equality)])).
% cnf(1008,plain,(and(strict_implies(not(X2),X1),strict_implies(X2,not(X1)))=strict_equiv(not(X1),X2)),inference(spm,[status(thm)],[324,728,theory(equality)])).
% cnf(1011,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[284,728,theory(equality)])).
% cnf(1028,plain,(strict_implies(not(X1),not(X2))=strict_implies(or(X2,X2),X1)),inference(spm,[status(thm)],[728,435,theory(equality)])).
% cnf(1030,plain,(strict_implies(not(X1),and(not(X2),X3))=strict_implies(implies(X3,X2),X1)),inference(spm,[status(thm)],[728,501,theory(equality)])).
% cnf(1049,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),and(X2,not(X3))))|~is_a_theorem(implies(X2,X3))),inference(spm,[status(thm)],[1011,296,theory(equality)])).
% cnf(1078,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(X3)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[336,288,theory(equality)])).
% cnf(1213,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X3,X2))|~is_a_theorem(strict_implies(X1,X3))),inference(spm,[status(thm)],[343,288,theory(equality)])).
% cnf(1404,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),and(not(X2),not(X3))))|~is_a_theorem(or(X2,X3))),inference(spm,[status(thm)],[1049,303,theory(equality)])).
% cnf(1997,plain,(is_a_theorem(and(strict_implies(X1,X2),and(strict_implies(X2,X1),X3)))|~is_a_theorem(strict_equiv(X1,X2))|~is_a_theorem(X3)),inference(spm,[status(thm)],[1078,324,theory(equality)])).
% cnf(2790,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))|~is_a_theorem(strict_implies(and(X1,and(X1,X2)),and(X1,X2)))),inference(spm,[status(thm)],[401,409,theory(equality)])).
% cnf(2805,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))|$false),inference(rw,[status(thm)],[2790,508,theory(equality)])).
% cnf(2806,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))),inference(cn,[status(thm)],[2805,theory(equality)])).
% cnf(2816,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X1,and(X1,X2))))),inference(rw,[status(thm)],[2806,537,theory(equality)])).
% cnf(2817,plain,(and(X1,X2)=and(X1,and(X1,X2))),inference(spm,[status(thm)],[273,2816,theory(equality)])).
% cnf(2840,plain,(not(and(not(X1),X2))=implies(and(not(X1),X2),X1)),inference(spm,[status(thm)],[501,2817,theory(equality)])).
% cnf(2893,plain,(implies(X2,X1)=implies(and(not(X1),X2),X1)),inference(rw,[status(thm)],[2840,501,theory(equality)])).
% cnf(3016,plain,(necessarily(implies(X2,X1))=strict_implies(and(not(X1),X2),X1)),inference(spm,[status(thm)],[290,2893,theory(equality)])).
% cnf(3052,plain,(strict_implies(X2,X1)=strict_implies(and(not(X1),X2),X1)),inference(rw,[status(thm)],[3016,290,theory(equality)])).
% cnf(18419,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(not(X1),X2)),inference(rw,[status(thm)],[1008,478,theory(equality)])).
% cnf(18446,plain,(is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(strict_equiv(not(X2),X1))),inference(spm,[status(thm)],[506,18419,theory(equality)])).
% cnf(18567,plain,(is_a_theorem(strict_implies(not(X1),not(X2)))|~is_a_theorem(strict_equiv(or(X2,X2),X1))),inference(spm,[status(thm)],[18446,435,theory(equality)])).
% cnf(19260,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))|~is_a_theorem(strict_implies(or(X1,X1),or(X1,X1)))),inference(spm,[status(thm)],[18567,415,theory(equality)])).
% cnf(19299,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))|$false),inference(rw,[status(thm)],[19260,440,theory(equality)])).
% cnf(19300,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(cn,[status(thm)],[19299,theory(equality)])).
% cnf(19301,plain,(is_a_theorem(strict_implies(not(not(X1)),or(X1,X1)))),inference(rw,[status(thm)],[19300,728,theory(equality)])).
% cnf(19513,plain,(is_a_theorem(strict_implies(or(X1,X1),X1))),inference(spm,[status(thm)],[440,1028,theory(equality)])).
% cnf(20193,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(or(X3,X2),X1))|~is_a_theorem(or(X2,X3))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[1404,1030,theory(equality)]),303,theory(equality)])).
% cnf(26865,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,or(X2,X2)))),inference(spm,[status(thm)],[1213,19513,theory(equality)])).
% cnf(26901,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,and(X2,X3)))),inference(spm,[status(thm)],[1213,282,theory(equality)])).
% cnf(26949,plain,(is_a_theorem(strict_implies(or(or(X1,X1),or(X1,X1)),X1))),inference(spm,[status(thm)],[26865,19513,theory(equality)])).
% cnf(27645,plain,(is_a_theorem(strict_implies(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[26949,435,theory(equality)]),728,theory(equality)])).
% cnf(27647,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|~is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(spm,[status(thm)],[325,27645,theory(equality)])).
% cnf(27699,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[27647,728,theory(equality)]),19301,theory(equality)])).
% cnf(27700,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))),inference(cn,[status(thm)],[27699,theory(equality)])).
% cnf(27735,plain,(is_a_theorem(strict_equiv(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[27700,537,theory(equality)])).
% cnf(27736,plain,(not(X1)=not(or(X1,X1))),inference(spm,[status(thm)],[273,27735,theory(equality)])).
% cnf(27838,plain,(not(and(not(X1),X2))=implies(X2,or(X1,X1))),inference(spm,[status(thm)],[501,27736,theory(equality)])).
% cnf(28090,plain,(not(not(not(X1)))=not(X1)),inference(spm,[status(thm)],[27736,435,theory(equality)])).
% cnf(28114,plain,(implies(X2,X1)=implies(X2,or(X1,X1))),inference(rw,[status(thm)],[27838,501,theory(equality)])).
% cnf(28643,plain,(not(and(not(X1),X2))=implies(X2,not(not(X1)))),inference(spm,[status(thm)],[501,28090,theory(equality)])).
% cnf(28918,plain,(implies(X2,X1)=implies(X2,not(not(X1)))),inference(rw,[status(thm)],[28643,501,theory(equality)])).
% cnf(29886,plain,(is_a_theorem(strict_implies(or(and(X1,X2),and(X1,X2)),X1))),inference(spm,[status(thm)],[26901,19513,theory(equality)])).
% cnf(29953,plain,(is_a_theorem(strict_implies(not(X1),not(and(X1,X2))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[29886,435,theory(equality)]),728,theory(equality)])).
% cnf(29988,plain,(is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1)))),inference(spm,[status(thm)],[29953,501,theory(equality)])).
% cnf(29992,plain,(is_a_theorem(strict_implies(not(X1),implies(X1,X2)))),inference(spm,[status(thm)],[29953,296,theory(equality)])).
% cnf(42420,plain,(necessarily(implies(X1,X2))=strict_implies(X1,or(X2,X2))),inference(spm,[status(thm)],[290,28114,theory(equality)])).
% cnf(42525,plain,(strict_implies(X1,X2)=strict_implies(X1,or(X2,X2))),inference(rw,[status(thm)],[42420,290,theory(equality)])).
% cnf(43434,plain,(necessarily(implies(X1,X2))=strict_implies(X1,not(not(X2)))),inference(spm,[status(thm)],[290,28918,theory(equality)])).
% cnf(43540,plain,(strict_implies(X1,X2)=strict_implies(X1,not(not(X2)))),inference(rw,[status(thm)],[43434,290,theory(equality)])).
% cnf(44253,plain,(is_a_theorem(or(X1,X1))|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(X2)),inference(spm,[status(thm)],[284,42525,theory(equality)])).
% cnf(46439,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(not(X1))),inference(spm,[status(thm)],[284,29992,theory(equality)])).
% cnf(62863,plain,(is_a_theorem(or(strict_implies(X1,X2),strict_implies(X1,X2)))|~is_a_theorem(strict_equiv(X1,X2))),inference(spm,[status(thm)],[44253,326,theory(equality)])).
% cnf(63031,plain,(is_a_theorem(not(not(strict_implies(X1,X2))))|~is_a_theorem(strict_equiv(X1,X2))),inference(rw,[status(thm)],[62863,435,theory(equality)])).
% cnf(71505,plain,(is_a_theorem(not(not(strict_implies(X1,X1))))|~is_a_theorem(strict_implies(X1,X1))),inference(spm,[status(thm)],[63031,415,theory(equality)])).
% cnf(71510,plain,(is_a_theorem(not(not(strict_implies(X1,X1))))|$false),inference(rw,[status(thm)],[71505,440,theory(equality)])).
% cnf(71511,plain,(is_a_theorem(not(not(strict_implies(X1,X1))))),inference(cn,[status(thm)],[71510,theory(equality)])).
% cnf(71516,plain,(is_a_theorem(implies(not(strict_implies(X1,X1)),X2))),inference(spm,[status(thm)],[46439,71511,theory(equality)])).
% cnf(71542,plain,(is_a_theorem(or(strict_implies(X1,X1),X2))),inference(rw,[status(thm)],[71516,303,theory(equality)])).
% cnf(71586,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(or(X2,strict_implies(X3,X3)),X1))),inference(spm,[status(thm)],[20193,71542,theory(equality)])).
% cnf(99432,plain,(is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X1,not(not(X3))))),inference(spm,[status(thm)],[1213,29988,theory(equality)])).
% cnf(99531,plain,(is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X1,X3))),inference(rw,[status(thm)],[99432,43540,theory(equality)])).
% cnf(113661,plain,(is_a_theorem(and(strict_implies(X1,X1),and(strict_implies(X1,X1),X2)))|~is_a_theorem(strict_implies(X1,X1))|~is_a_theorem(X2)),inference(spm,[status(thm)],[1997,415,theory(equality)])).
% cnf(113666,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|~is_a_theorem(strict_implies(X1,X1))|~is_a_theorem(X2)),inference(rw,[status(thm)],[113661,2817,theory(equality)])).
% cnf(113667,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|$false|~is_a_theorem(X2)),inference(rw,[status(thm)],[113666,440,theory(equality)])).
% cnf(113668,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|~is_a_theorem(X2)),inference(cn,[status(thm)],[113667,theory(equality)])).
% cnf(113756,plain,(is_a_theorem(and(X1,strict_implies(X2,X2)))|~is_a_theorem(X1)),inference(spm,[status(thm)],[309,113668,theory(equality)])).
% cnf(114781,plain,(is_a_theorem(strict_equiv(not(not(X1)),X1))|~is_a_theorem(strict_implies(X1,not(not(X1))))),inference(spm,[status(thm)],[113756,18419,theory(equality)])).
% cnf(114796,plain,(is_a_theorem(strict_equiv(not(not(X1)),X1))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[114781,43540,theory(equality)]),440,theory(equality)])).
% cnf(114797,plain,(is_a_theorem(strict_equiv(not(not(X1)),X1))),inference(cn,[status(thm)],[114796,theory(equality)])).
% cnf(114807,plain,(is_a_theorem(strict_equiv(X1,not(not(X1))))),inference(rw,[status(thm)],[114797,537,theory(equality)])).
% cnf(114810,plain,(X1=not(not(X1))),inference(spm,[status(thm)],[273,114807,theory(equality)])).
% cnf(114895,plain,(not(and(X1,X2))=implies(X2,not(X1))),inference(spm,[status(thm)],[501,114810,theory(equality)])).
% cnf(114904,plain,(strict_implies(X1,X2)=strict_implies(not(X2),not(X1))),inference(spm,[status(thm)],[728,114810,theory(equality)])).
% cnf(115428,plain,(necessarily(X1)=strict_implies(not(X1),X1)),inference(rw,[status(thm)],[578,114810,theory(equality)])).
% cnf(126326,plain,(is_a_theorem(strict_implies(not(X1),implies(X2,not(X3))))|~is_a_theorem(strict_implies(X3,X1))),inference(spm,[status(thm)],[99531,114904,theory(equality)])).
% cnf(126519,plain,(is_a_theorem(strict_implies(and(X3,X2),X1))|~is_a_theorem(strict_implies(X3,X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[126326,114895,theory(equality)]),114904,theory(equality)])).
% cnf(177550,plain,(is_a_theorem(strict_implies(and(not(X1),X2),X1))|~is_a_theorem(necessarily(X1))),inference(spm,[status(thm)],[126519,115428,theory(equality)])).
% cnf(177860,plain,(is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(necessarily(X1))),inference(rw,[status(thm)],[177550,3052,theory(equality)])).
% cnf(178198,plain,(is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X2,X3))),inference(spm,[status(thm)],[177860,290,theory(equality)])).
% cnf(183154,plain,(is_a_theorem(strict_implies(X1,implies(possibly(X2),necessarily(possibly(X2)))))),inference(spm,[status(thm)],[178198,292,theory(equality)])).
% cnf(186788,plain,(is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))),inference(spm,[status(thm)],[71586,183154,theory(equality)])).
% cnf(187126,plain,($false),inference(rw,[status(thm)],[267,186788,theory(equality)])).
% cnf(187127,plain,($false),inference(cn,[status(thm)],[187126,theory(equality)])).
% cnf(187128,plain,($false),187127,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 8977
% # ...of these trivial : 529
% # ...subsumed : 6738
% # ...remaining for further processing: 1710
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 73
% # Backward-rewritten : 562
% # Generated clauses : 125562
% # ...of the previous two non-trivial : 105354
% # Contextual simplify-reflections : 648
% # Paramodulations : 125562
% # Factorizations : 0
% # Equation resolutions : 0
% # Current number of processed clauses: 1075
% # Positive orientable unit clauses: 605
% # Positive unorientable unit clauses: 18
% # Negative unit clauses : 2
% # Non-unit-clauses : 450
% # Current number of unprocessed clauses: 47465
% # ...number of literals in the above : 71236
% # Clause-clause subsumption calls (NU) : 70385
% # Rec. Clause-clause subsumption calls : 70239
% # Unit Clause-clause subsumption calls : 918
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 17818
% # Indexed BW rewrite successes : 289
% # Backwards rewriting index: 933 leaves, 2.88+/-4.472 terms/leaf
% # Paramod-from index: 208 leaves, 3.21+/-6.418 terms/leaf
% # Paramod-into index: 824 leaves, 2.78+/-4.440 terms/leaf
% # -------------------------------------------------
% # User time : 4.248 s
% # System time : 0.159 s
% # Total time : 4.407 s
% # Maximum resident set size: 0 pages
% PrfWatch: 7.27 CPU 7.40 WC
% FINAL PrfWatch: 7.27 CPU 7.40 WC
% SZS output end Solution for /tmp/SystemOnTPTP5060/LCL573+1.tptp
%
%------------------------------------------------------------------------------