%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : LCL568+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 : art05.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 14:10:55 EST 2010
% Result : Theorem 4.17s
% Output : Solution 4.17s
% 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/SystemOnTPTP9844/LCL568+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP9844/LCL568+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP9844/LCL568+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 9940
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 WC
% PrfWatch: 1.92 CPU 2.01 WC
% # Preprocessing time : 0.017 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(3, axiom,op_strict_implies,file('/tmp/SRASS.s.p', s1_0_op_strict_implies)).
% fof(4, axiom,modus_ponens_strict_implies,file('/tmp/SRASS.s.p', s1_0_modus_ponens_strict_implies)).
% fof(5, axiom,adjunction,file('/tmp/SRASS.s.p', s1_0_adjunction)).
% fof(6, axiom,(axiom_4<=>![X1]:is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))),file('/tmp/SRASS.s.p', axiom_4)).
% fof(11, axiom,op_possibly,file('/tmp/SRASS.s.p', s1_0_op_possibly)).
% fof(13, axiom,op_strict_equiv,file('/tmp/SRASS.s.p', s1_0_op_strict_equiv)).
% fof(14, axiom,axiom_m1,file('/tmp/SRASS.s.p', s1_0_axiom_m1)).
% fof(15, axiom,axiom_m2,file('/tmp/SRASS.s.p', s1_0_axiom_m2)).
% fof(17, axiom,axiom_m4,file('/tmp/SRASS.s.p', s1_0_axiom_m4)).
% fof(18, axiom,axiom_m5,file('/tmp/SRASS.s.p', s1_0_axiom_m5)).
% fof(19, axiom,axiom_m6,file('/tmp/SRASS.s.p', s1_0_m6s3m9b_axiom_m6)).
% fof(21, axiom,axiom_m9,file('/tmp/SRASS.s.p', s1_0_m6s3m9b_axiom_m9)).
% fof(22, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(25, axiom,(op_strict_implies=>![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),file('/tmp/SRASS.s.p', op_strict_implies)).
% fof(26, axiom,op_or,file('/tmp/SRASS.s.p', s1_0_op_or)).
% fof(27, axiom,substitution_strict_equiv,file('/tmp/SRASS.s.p', s1_0_substitution_strict_equiv)).
% fof(30, axiom,(axiom_m1<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),file('/tmp/SRASS.s.p', axiom_m1)).
% fof(31, axiom,(axiom_m2<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),X1))),file('/tmp/SRASS.s.p', axiom_m2)).
% fof(33, axiom,(axiom_m4<=>![X1]:is_a_theorem(strict_implies(X1,and(X1,X1)))),file('/tmp/SRASS.s.p', axiom_m4)).
% fof(34, 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(35, axiom,(axiom_m6<=>![X1]:is_a_theorem(strict_implies(X1,possibly(X1)))),file('/tmp/SRASS.s.p', axiom_m6)).
% fof(37, axiom,(axiom_m9<=>![X1]:is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))),file('/tmp/SRASS.s.p', axiom_m9)).
% fof(38, axiom,(op_or=>![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),file('/tmp/SRASS.s.p', op_or)).
% fof(40, 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(41, 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(42, axiom,(substitution_strict_equiv<=>![X1]:![X2]:(is_a_theorem(strict_equiv(X1,X2))=>X1=X2)),file('/tmp/SRASS.s.p', substitution_strict_equiv)).
% fof(43, 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,(op_possibly=>![X1]:possibly(X1)=not(necessarily(not(X1)))),file('/tmp/SRASS.s.p', op_possibly)).
% fof(51, 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(55, conjecture,axiom_4,file('/tmp/SRASS.s.p', km4b_axiom_4)).
% fof(56, negated_conjecture,~(axiom_4),inference(assume_negation,[status(cth)],[55])).
% fof(57, negated_conjecture,~(axiom_4),inference(fof_simplification,[status(thm)],[56,theory(equality)])).
% cnf(70,plain,(op_strict_implies),inference(split_conjunct,[status(thm)],[3])).
% cnf(71,plain,(modus_ponens_strict_implies),inference(split_conjunct,[status(thm)],[4])).
% cnf(72,plain,(adjunction),inference(split_conjunct,[status(thm)],[5])).
% fof(73, plain,((~(axiom_4)|![X1]:is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))))&(?[X1]:~(is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))))|axiom_4)),inference(fof_nnf,[status(thm)],[6])).
% fof(74, plain,((~(axiom_4)|![X2]:is_a_theorem(implies(necessarily(X2),necessarily(necessarily(X2)))))&(?[X3]:~(is_a_theorem(implies(necessarily(X3),necessarily(necessarily(X3)))))|axiom_4)),inference(variable_rename,[status(thm)],[73])).
% fof(75, plain,((~(axiom_4)|![X2]:is_a_theorem(implies(necessarily(X2),necessarily(necessarily(X2)))))&(~(is_a_theorem(implies(necessarily(esk4_0),necessarily(necessarily(esk4_0)))))|axiom_4)),inference(skolemize,[status(esa)],[74])).
% fof(76, plain,![X2]:((is_a_theorem(implies(necessarily(X2),necessarily(necessarily(X2))))|~(axiom_4))&(~(is_a_theorem(implies(necessarily(esk4_0),necessarily(necessarily(esk4_0)))))|axiom_4)),inference(shift_quantors,[status(thm)],[75])).
% cnf(77,plain,(axiom_4|~is_a_theorem(implies(necessarily(esk4_0),necessarily(necessarily(esk4_0))))),inference(split_conjunct,[status(thm)],[76])).
% cnf(105,plain,(op_possibly),inference(split_conjunct,[status(thm)],[11])).
% cnf(107,plain,(op_strict_equiv),inference(split_conjunct,[status(thm)],[13])).
% cnf(108,plain,(axiom_m1),inference(split_conjunct,[status(thm)],[14])).
% cnf(109,plain,(axiom_m2),inference(split_conjunct,[status(thm)],[15])).
% cnf(111,plain,(axiom_m4),inference(split_conjunct,[status(thm)],[17])).
% cnf(112,plain,(axiom_m5),inference(split_conjunct,[status(thm)],[18])).
% cnf(113,plain,(axiom_m6),inference(split_conjunct,[status(thm)],[19])).
% cnf(115,plain,(axiom_m9),inference(split_conjunct,[status(thm)],[21])).
% cnf(116,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[22])).
% fof(124, plain,(~(op_strict_implies)|![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),inference(fof_nnf,[status(thm)],[25])).
% fof(125, plain,(~(op_strict_implies)|![X3]:![X4]:strict_implies(X3,X4)=necessarily(implies(X3,X4))),inference(variable_rename,[status(thm)],[124])).
% fof(126, plain,![X3]:![X4]:(strict_implies(X3,X4)=necessarily(implies(X3,X4))|~(op_strict_implies)),inference(shift_quantors,[status(thm)],[125])).
% cnf(127,plain,(strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies),inference(split_conjunct,[status(thm)],[126])).
% cnf(128,plain,(op_or),inference(split_conjunct,[status(thm)],[26])).
% cnf(129,plain,(substitution_strict_equiv),inference(split_conjunct,[status(thm)],[27])).
% fof(137, 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)],[30])).
% fof(138, 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)],[137])).
% fof(139, plain,((~(axiom_m1)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))))&(~(is_a_theorem(strict_implies(and(esk13_0,esk14_0),and(esk14_0,esk13_0))))|axiom_m1)),inference(skolemize,[status(esa)],[138])).
% fof(140, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),and(X4,X3)))|~(axiom_m1))&(~(is_a_theorem(strict_implies(and(esk13_0,esk14_0),and(esk14_0,esk13_0))))|axiom_m1)),inference(shift_quantors,[status(thm)],[139])).
% cnf(142,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1),inference(split_conjunct,[status(thm)],[140])).
% fof(143, 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)],[31])).
% fof(144, 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)],[143])).
% fof(145, plain,((~(axiom_m2)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),X3)))&(~(is_a_theorem(strict_implies(and(esk15_0,esk16_0),esk15_0)))|axiom_m2)),inference(skolemize,[status(esa)],[144])).
% fof(146, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),X3))|~(axiom_m2))&(~(is_a_theorem(strict_implies(and(esk15_0,esk16_0),esk15_0)))|axiom_m2)),inference(shift_quantors,[status(thm)],[145])).
% cnf(148,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2),inference(split_conjunct,[status(thm)],[146])).
% fof(155, 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)],[33])).
% fof(156, 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)],[155])).
% fof(157, plain,((~(axiom_m4)|![X2]:is_a_theorem(strict_implies(X2,and(X2,X2))))&(~(is_a_theorem(strict_implies(esk20_0,and(esk20_0,esk20_0))))|axiom_m4)),inference(skolemize,[status(esa)],[156])).
% fof(158, plain,![X2]:((is_a_theorem(strict_implies(X2,and(X2,X2)))|~(axiom_m4))&(~(is_a_theorem(strict_implies(esk20_0,and(esk20_0,esk20_0))))|axiom_m4)),inference(shift_quantors,[status(thm)],[157])).
% cnf(160,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4),inference(split_conjunct,[status(thm)],[158])).
% fof(161, 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)],[34])).
% fof(162, 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)],[161])).
% fof(163, 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(esk21_0,esk22_0),strict_implies(esk22_0,esk23_0)),strict_implies(esk21_0,esk23_0))))|axiom_m5)),inference(skolemize,[status(esa)],[162])).
% fof(164, 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(esk21_0,esk22_0),strict_implies(esk22_0,esk23_0)),strict_implies(esk21_0,esk23_0))))|axiom_m5)),inference(shift_quantors,[status(thm)],[163])).
% cnf(166,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)],[164])).
% fof(167, plain,((~(axiom_m6)|![X1]:is_a_theorem(strict_implies(X1,possibly(X1))))&(?[X1]:~(is_a_theorem(strict_implies(X1,possibly(X1))))|axiom_m6)),inference(fof_nnf,[status(thm)],[35])).
% fof(168, plain,((~(axiom_m6)|![X2]:is_a_theorem(strict_implies(X2,possibly(X2))))&(?[X3]:~(is_a_theorem(strict_implies(X3,possibly(X3))))|axiom_m6)),inference(variable_rename,[status(thm)],[167])).
% fof(169, plain,((~(axiom_m6)|![X2]:is_a_theorem(strict_implies(X2,possibly(X2))))&(~(is_a_theorem(strict_implies(esk24_0,possibly(esk24_0))))|axiom_m6)),inference(skolemize,[status(esa)],[168])).
% fof(170, plain,![X2]:((is_a_theorem(strict_implies(X2,possibly(X2)))|~(axiom_m6))&(~(is_a_theorem(strict_implies(esk24_0,possibly(esk24_0))))|axiom_m6)),inference(shift_quantors,[status(thm)],[169])).
% cnf(172,plain,(is_a_theorem(strict_implies(X1,possibly(X1)))|~axiom_m6),inference(split_conjunct,[status(thm)],[170])).
% fof(179, plain,((~(axiom_m9)|![X1]:is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1))))&(?[X1]:~(is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1))))|axiom_m9)),inference(fof_nnf,[status(thm)],[37])).
% fof(180, plain,((~(axiom_m9)|![X2]:is_a_theorem(strict_implies(possibly(possibly(X2)),possibly(X2))))&(?[X3]:~(is_a_theorem(strict_implies(possibly(possibly(X3)),possibly(X3))))|axiom_m9)),inference(variable_rename,[status(thm)],[179])).
% fof(181, plain,((~(axiom_m9)|![X2]:is_a_theorem(strict_implies(possibly(possibly(X2)),possibly(X2))))&(~(is_a_theorem(strict_implies(possibly(possibly(esk27_0)),possibly(esk27_0))))|axiom_m9)),inference(skolemize,[status(esa)],[180])).
% fof(182, plain,![X2]:((is_a_theorem(strict_implies(possibly(possibly(X2)),possibly(X2)))|~(axiom_m9))&(~(is_a_theorem(strict_implies(possibly(possibly(esk27_0)),possibly(esk27_0))))|axiom_m9)),inference(shift_quantors,[status(thm)],[181])).
% cnf(184,plain,(is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))|~axiom_m9),inference(split_conjunct,[status(thm)],[182])).
% fof(185, plain,(~(op_or)|![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),inference(fof_nnf,[status(thm)],[38])).
% fof(186, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(variable_rename,[status(thm)],[185])).
% fof(187, plain,![X3]:![X4]:(or(X3,X4)=not(and(not(X3),not(X4)))|~(op_or)),inference(shift_quantors,[status(thm)],[186])).
% cnf(188,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[187])).
% fof(193, 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)],[40])).
% fof(194, 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)],[193])).
% fof(195, 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(esk28_0)&is_a_theorem(strict_implies(esk28_0,esk29_0)))&~(is_a_theorem(esk29_0)))|modus_ponens_strict_implies)),inference(skolemize,[status(esa)],[194])).
% fof(196, 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(esk28_0)&is_a_theorem(strict_implies(esk28_0,esk29_0)))&~(is_a_theorem(esk29_0)))|modus_ponens_strict_implies)),inference(shift_quantors,[status(thm)],[195])).
% fof(197, 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(esk28_0)|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(esk28_0,esk29_0))|modus_ponens_strict_implies))&(~(is_a_theorem(esk29_0))|modus_ponens_strict_implies))),inference(distribute,[status(thm)],[196])).
% cnf(201,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)],[197])).
% fof(202, 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)],[41])).
% fof(203, 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)],[202])).
% fof(204, plain,((~(adjunction)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4))))&(((is_a_theorem(esk30_0)&is_a_theorem(esk31_0))&~(is_a_theorem(and(esk30_0,esk31_0))))|adjunction)),inference(skolemize,[status(esa)],[203])).
% fof(205, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk30_0)&is_a_theorem(esk31_0))&~(is_a_theorem(and(esk30_0,esk31_0))))|adjunction)),inference(shift_quantors,[status(thm)],[204])).
% fof(206, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk30_0)|adjunction)&(is_a_theorem(esk31_0)|adjunction))&(~(is_a_theorem(and(esk30_0,esk31_0)))|adjunction))),inference(distribute,[status(thm)],[205])).
% cnf(210,plain,(is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(split_conjunct,[status(thm)],[206])).
% fof(211, 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)],[42])).
% fof(212, 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)],[211])).
% fof(213, plain,((~(substitution_strict_equiv)|![X3]:![X4]:(~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4))&((is_a_theorem(strict_equiv(esk32_0,esk33_0))&~(esk32_0=esk33_0))|substitution_strict_equiv)),inference(skolemize,[status(esa)],[212])).
% fof(214, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk32_0,esk33_0))&~(esk32_0=esk33_0))|substitution_strict_equiv)),inference(shift_quantors,[status(thm)],[213])).
% fof(215, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk32_0,esk33_0))|substitution_strict_equiv)&(~(esk32_0=esk33_0)|substitution_strict_equiv))),inference(distribute,[status(thm)],[214])).
% cnf(218,plain,(X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2))),inference(split_conjunct,[status(thm)],[215])).
% fof(219, plain,(~(op_implies_and)|![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),inference(fof_nnf,[status(thm)],[43])).
% fof(220, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(variable_rename,[status(thm)],[219])).
% fof(221, plain,![X3]:![X4]:(implies(X3,X4)=not(and(X3,not(X4)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[220])).
% cnf(222,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[221])).
% fof(249, plain,(~(op_possibly)|![X1]:possibly(X1)=not(necessarily(not(X1)))),inference(fof_nnf,[status(thm)],[49])).
% fof(250, plain,(~(op_possibly)|![X2]:possibly(X2)=not(necessarily(not(X2)))),inference(variable_rename,[status(thm)],[249])).
% fof(251, plain,![X2]:(possibly(X2)=not(necessarily(not(X2)))|~(op_possibly)),inference(shift_quantors,[status(thm)],[250])).
% cnf(252,plain,(possibly(X1)=not(necessarily(not(X1)))|~op_possibly),inference(split_conjunct,[status(thm)],[251])).
% fof(257, plain,(~(op_strict_equiv)|![X1]:![X2]:strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))),inference(fof_nnf,[status(thm)],[51])).
% fof(258, plain,(~(op_strict_equiv)|![X3]:![X4]:strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))),inference(variable_rename,[status(thm)],[257])).
% fof(259, plain,![X3]:![X4]:(strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))|~(op_strict_equiv)),inference(shift_quantors,[status(thm)],[258])).
% cnf(260,plain,(strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv),inference(split_conjunct,[status(thm)],[259])).
% cnf(264,negated_conjecture,(~axiom_4),inference(split_conjunct,[status(thm)],[57])).
% cnf(274,plain,(~is_a_theorem(implies(necessarily(esk4_0),necessarily(necessarily(esk4_0))))),inference(sr,[status(thm)],[77,264,theory(equality)])).
% cnf(279,plain,(X1=X2|$false|~is_a_theorem(strict_equiv(X1,X2))),inference(rw,[status(thm)],[218,129,theory(equality)])).
% cnf(280,plain,(X1=X2|~is_a_theorem(strict_equiv(X1,X2))),inference(cn,[status(thm)],[279,theory(equality)])).
% cnf(281,plain,(is_a_theorem(strict_implies(X1,possibly(X1)))|$false),inference(rw,[status(thm)],[172,113,theory(equality)])).
% cnf(282,plain,(is_a_theorem(strict_implies(X1,possibly(X1)))),inference(cn,[status(thm)],[281,theory(equality)])).
% cnf(283,plain,(not(necessarily(not(X1)))=possibly(X1)|$false),inference(rw,[status(thm)],[252,105,theory(equality)])).
% cnf(284,plain,(not(necessarily(not(X1)))=possibly(X1)),inference(cn,[status(thm)],[283,theory(equality)])).
% cnf(288,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|$false),inference(rw,[status(thm)],[160,111,theory(equality)])).
% cnf(289,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))),inference(cn,[status(thm)],[288,theory(equality)])).
% cnf(290,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[148,109,theory(equality)])).
% cnf(291,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))),inference(cn,[status(thm)],[290,theory(equality)])).
% cnf(292,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(rw,[status(thm)],[201,71,theory(equality)])).
% cnf(293,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(cn,[status(thm)],[292,theory(equality)])).
% cnf(294,plain,(is_a_theorem(X1)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[293,291,theory(equality)])).
% cnf(297,plain,(is_a_theorem(and(X1,X2))|$false|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(rw,[status(thm)],[210,72,theory(equality)])).
% cnf(298,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(cn,[status(thm)],[297,theory(equality)])).
% cnf(299,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)|$false),inference(rw,[status(thm)],[127,70,theory(equality)])).
% cnf(300,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)),inference(cn,[status(thm)],[299,theory(equality)])).
% cnf(301,plain,(is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))|$false),inference(rw,[status(thm)],[184,115,theory(equality)])).
% cnf(302,plain,(is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))),inference(cn,[status(thm)],[301,theory(equality)])).
% cnf(304,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[222,116,theory(equality)])).
% cnf(305,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[304,theory(equality)])).
% cnf(306,plain,(not(necessarily(implies(X1,X2)))=possibly(and(X1,not(X2)))),inference(spm,[status(thm)],[284,305,theory(equality)])).
% cnf(308,plain,(not(and(X1,possibly(X2)))=implies(X1,necessarily(not(X2)))),inference(spm,[status(thm)],[305,284,theory(equality)])).
% cnf(309,plain,(not(strict_implies(X1,X2))=possibly(and(X1,not(X2)))),inference(rw,[status(thm)],[306,300,theory(equality)])).
% cnf(311,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[142,108,theory(equality)])).
% cnf(312,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[311,theory(equality)])).
% cnf(317,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[188,305,theory(equality)])).
% cnf(318,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[317,128,theory(equality)])).
% cnf(319,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[318,theory(equality)])).
% cnf(320,plain,(necessarily(or(X1,X2))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[300,319,theory(equality)])).
% cnf(334,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)|$false),inference(rw,[status(thm)],[260,107,theory(equality)])).
% cnf(335,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)),inference(cn,[status(thm)],[334,theory(equality)])).
% cnf(336,plain,(is_a_theorem(strict_equiv(X1,X2))|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(strict_implies(X1,X2))),inference(spm,[status(thm)],[298,335,theory(equality)])).
% cnf(355,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|$false),inference(rw,[status(thm)],[166,112,theory(equality)])).
% cnf(356,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))),inference(cn,[status(thm)],[355,theory(equality)])).
% cnf(357,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))),inference(spm,[status(thm)],[293,356,theory(equality)])).
% cnf(360,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_equiv(X1,X2))),inference(spm,[status(thm)],[294,335,theory(equality)])).
% cnf(421,plain,(is_a_theorem(strict_equiv(possibly(X1),possibly(possibly(X1))))|~is_a_theorem(strict_implies(possibly(X1),possibly(possibly(X1))))),inference(spm,[status(thm)],[336,302,theory(equality)])).
% cnf(423,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)],[336,312,theory(equality)])).
% cnf(427,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|~is_a_theorem(strict_implies(and(X1,X1),X1))),inference(spm,[status(thm)],[336,289,theory(equality)])).
% cnf(428,plain,(is_a_theorem(strict_equiv(possibly(X1),possibly(possibly(X1))))|$false),inference(rw,[status(thm)],[421,282,theory(equality)])).
% cnf(429,plain,(is_a_theorem(strict_equiv(possibly(X1),possibly(possibly(X1))))),inference(cn,[status(thm)],[428,theory(equality)])).
% cnf(430,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[423,312,theory(equality)])).
% cnf(431,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[430,theory(equality)])).
% cnf(432,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|$false),inference(rw,[status(thm)],[427,291,theory(equality)])).
% cnf(433,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))),inference(cn,[status(thm)],[432,theory(equality)])).
% cnf(434,plain,(and(X1,X1)=X1),inference(spm,[status(thm)],[280,433,theory(equality)])).
% cnf(453,plain,(strict_implies(X1,X1)=strict_equiv(X1,X1)),inference(spm,[status(thm)],[335,434,theory(equality)])).
% cnf(457,plain,(not(not(X1))=implies(not(X1),X1)),inference(spm,[status(thm)],[305,434,theory(equality)])).
% cnf(470,plain,(is_a_theorem(strict_equiv(X1,X1))),inference(rw,[status(thm)],[433,434,theory(equality)])).
% cnf(474,plain,(not(not(X1))=or(X1,X1)),inference(rw,[status(thm)],[457,319,theory(equality)])).
% cnf(479,plain,(is_a_theorem(strict_implies(X1,X1))),inference(spm,[status(thm)],[360,470,theory(equality)])).
% cnf(492,plain,(possibly(X1)=possibly(possibly(X1))),inference(spm,[status(thm)],[280,429,theory(equality)])).
% cnf(528,plain,(not(and(X1,possibly(X2)))=implies(X1,necessarily(not(possibly(X2))))),inference(spm,[status(thm)],[308,492,theory(equality)])).
% cnf(534,plain,(implies(X1,necessarily(not(X2)))=implies(X1,necessarily(not(possibly(X2))))),inference(rw,[status(thm)],[528,308,theory(equality)])).
% cnf(541,plain,(and(X1,X2)=and(X2,X1)),inference(spm,[status(thm)],[280,431,theory(equality)])).
% cnf(560,plain,(and(strict_implies(X2,X1),strict_implies(X1,X2))=strict_equiv(X1,X2)),inference(spm,[status(thm)],[335,541,theory(equality)])).
% cnf(564,plain,(not(and(not(X2),X1))=implies(X1,X2)),inference(spm,[status(thm)],[305,541,theory(equality)])).
% cnf(565,plain,(possibly(and(not(X2),X1))=not(strict_implies(X1,X2))),inference(spm,[status(thm)],[309,541,theory(equality)])).
% cnf(572,plain,(is_a_theorem(X1)|~is_a_theorem(and(X2,X1))),inference(spm,[status(thm)],[294,541,theory(equality)])).
% cnf(602,plain,(strict_equiv(X2,X1)=strict_equiv(X1,X2)),inference(rw,[status(thm)],[560,335,theory(equality)])).
% cnf(787,plain,(implies(not(X2),X1)=implies(not(X1),X2)),inference(spm,[status(thm)],[305,564,theory(equality)])).
% cnf(803,plain,(or(X2,X1)=implies(not(X1),X2)),inference(rw,[status(thm)],[787,319,theory(equality)])).
% cnf(804,plain,(or(X2,X1)=or(X1,X2)),inference(rw,[status(thm)],[803,319,theory(equality)])).
% cnf(813,plain,(necessarily(or(X2,X1))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[320,804,theory(equality)])).
% cnf(819,plain,(strict_implies(not(X2),X1)=strict_implies(not(X1),X2)),inference(rw,[status(thm)],[813,320,theory(equality)])).
% cnf(1177,plain,(and(strict_implies(not(X2),X1),strict_implies(X2,not(X1)))=strict_equiv(not(X1),X2)),inference(spm,[status(thm)],[335,819,theory(equality)])).
% cnf(1203,plain,(strict_implies(not(X1),not(X2))=strict_implies(or(X2,X2),X1)),inference(spm,[status(thm)],[819,474,theory(equality)])).
% cnf(1761,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)],[357,298,theory(equality)])).
% cnf(6140,plain,(necessarily(implies(X1,necessarily(not(X2))))=strict_implies(X1,necessarily(not(possibly(X2))))),inference(spm,[status(thm)],[300,534,theory(equality)])).
% cnf(6187,plain,(strict_implies(X1,necessarily(not(X2)))=strict_implies(X1,necessarily(not(possibly(X2))))),inference(rw,[status(thm)],[6140,300,theory(equality)])).
% cnf(11373,plain,(is_a_theorem(strict_implies(necessarily(not(possibly(X1))),necessarily(not(X1))))),inference(spm,[status(thm)],[479,6187,theory(equality)])).
% cnf(11601,plain,(is_a_theorem(strict_equiv(necessarily(not(X1)),necessarily(not(possibly(X1)))))|~is_a_theorem(strict_implies(necessarily(not(X1)),necessarily(not(possibly(X1)))))),inference(spm,[status(thm)],[336,11373,theory(equality)])).
% cnf(11634,plain,(is_a_theorem(strict_equiv(necessarily(not(X1)),necessarily(not(possibly(X1)))))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[11601,6187,theory(equality)]),479,theory(equality)])).
% cnf(11635,plain,(is_a_theorem(strict_equiv(necessarily(not(X1)),necessarily(not(possibly(X1)))))),inference(cn,[status(thm)],[11634,theory(equality)])).
% cnf(11693,plain,(necessarily(not(X1))=necessarily(not(possibly(X1)))),inference(spm,[status(thm)],[280,11635,theory(equality)])).
% cnf(11782,plain,(necessarily(not(not(strict_implies(X2,X1))))=necessarily(not(and(not(X1),X2)))),inference(spm,[status(thm)],[11693,565,theory(equality)])).
% cnf(11856,plain,(necessarily(not(not(strict_implies(X2,X1))))=strict_implies(X2,X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[11782,564,theory(equality)]),300,theory(equality)])).
% cnf(25795,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(not(X1),X2)),inference(rw,[status(thm)],[1177,541,theory(equality)])).
% cnf(25829,plain,(is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(strict_equiv(not(X2),X1))),inference(spm,[status(thm)],[572,25795,theory(equality)])).
% cnf(25956,plain,(is_a_theorem(strict_implies(not(X1),not(X2)))|~is_a_theorem(strict_equiv(or(X2,X2),X1))),inference(spm,[status(thm)],[25829,474,theory(equality)])).
% cnf(26273,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)],[25956,453,theory(equality)])).
% cnf(26312,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))|$false),inference(rw,[status(thm)],[26273,479,theory(equality)])).
% cnf(26313,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(cn,[status(thm)],[26312,theory(equality)])).
% cnf(26314,plain,(is_a_theorem(strict_implies(not(not(X1)),or(X1,X1)))),inference(rw,[status(thm)],[26313,819,theory(equality)])).
% cnf(28008,plain,(is_a_theorem(strict_implies(or(X1,X1),X1))),inference(spm,[status(thm)],[479,1203,theory(equality)])).
% cnf(28173,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|~is_a_theorem(strict_implies(X1,or(X1,X1)))),inference(spm,[status(thm)],[336,28008,theory(equality)])).
% cnf(50340,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,or(X2,X2)))),inference(spm,[status(thm)],[1761,28008,theory(equality)])).
% cnf(50409,plain,(is_a_theorem(strict_implies(X1,possibly(X2)))|~is_a_theorem(strict_implies(X1,X2))),inference(spm,[status(thm)],[1761,282,theory(equality)])).
% cnf(50451,plain,(is_a_theorem(strict_implies(or(or(X1,X1),or(X1,X1)),X1))),inference(spm,[status(thm)],[50340,28008,theory(equality)])).
% cnf(50889,plain,(is_a_theorem(strict_implies(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[50451,474,theory(equality)]),819,theory(equality)])).
% cnf(50891,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|~is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(spm,[status(thm)],[336,50889,theory(equality)])).
% cnf(50948,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[50891,819,theory(equality)]),26314,theory(equality)])).
% cnf(50949,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))),inference(cn,[status(thm)],[50948,theory(equality)])).
% cnf(50990,plain,(is_a_theorem(strict_equiv(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[50949,602,theory(equality)])).
% cnf(50991,plain,(not(X1)=not(or(X1,X1))),inference(spm,[status(thm)],[280,50990,theory(equality)])).
% cnf(51083,plain,(not(necessarily(not(X1)))=possibly(or(X1,X1))),inference(spm,[status(thm)],[284,50991,theory(equality)])).
% cnf(51086,plain,(not(and(not(X1),X2))=implies(X2,or(X1,X1))),inference(spm,[status(thm)],[564,50991,theory(equality)])).
% cnf(51502,plain,(possibly(X1)=possibly(or(X1,X1))),inference(rw,[status(thm)],[51083,284,theory(equality)])).
% cnf(51505,plain,(implies(X2,X1)=implies(X2,or(X1,X1))),inference(rw,[status(thm)],[51086,564,theory(equality)])).
% cnf(68707,plain,(is_a_theorem(strict_implies(not(not(X1)),possibly(or(X1,X1))))),inference(spm,[status(thm)],[50409,26314,theory(equality)])).
% cnf(68872,plain,(is_a_theorem(strict_implies(not(possibly(X1)),not(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[68707,51502,theory(equality)]),819,theory(equality)])).
% cnf(68885,plain,(is_a_theorem(not(X1))|~is_a_theorem(not(possibly(X1)))),inference(spm,[status(thm)],[293,68872,theory(equality)])).
% cnf(69197,plain,(is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(not(not(strict_implies(X2,X1))))),inference(spm,[status(thm)],[68885,565,theory(equality)])).
% cnf(69212,plain,(is_a_theorem(implies(X2,X1))|~is_a_theorem(not(not(strict_implies(X2,X1))))),inference(rw,[status(thm)],[69197,564,theory(equality)])).
% cnf(76249,plain,(necessarily(implies(X1,X2))=strict_implies(X1,or(X2,X2))),inference(spm,[status(thm)],[300,51505,theory(equality)])).
% cnf(76380,plain,(strict_implies(X1,X2)=strict_implies(X1,or(X2,X2))),inference(rw,[status(thm)],[76249,300,theory(equality)])).
% cnf(79485,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[28173,76380,theory(equality)]),479,theory(equality)])).
% cnf(79486,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))),inference(cn,[status(thm)],[79485,theory(equality)])).
% cnf(79738,plain,(X1=or(X1,X1)),inference(spm,[status(thm)],[280,79486,theory(equality)])).
% cnf(79860,plain,(necessarily(X1)=strict_implies(not(X1),X1)),inference(spm,[status(thm)],[320,79738,theory(equality)])).
% cnf(79978,plain,(not(not(X1))=X1),inference(rw,[status(thm)],[474,79738,theory(equality)])).
% cnf(80496,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(strict_implies(X1,X2))),inference(rw,[status(thm)],[69212,79978,theory(equality)])).
% cnf(80515,plain,(necessarily(strict_implies(X1,X2))=strict_implies(X1,X2)),inference(rw,[status(thm)],[11856,79978,theory(equality)])).
% cnf(82827,plain,(is_a_theorem(implies(X1,X1))),inference(spm,[status(thm)],[80496,479,theory(equality)])).
% cnf(85101,plain,(necessarily(necessarily(X1))=necessarily(X1)),inference(spm,[status(thm)],[80515,79860,theory(equality)])).
% cnf(85140,plain,($false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[274,85101,theory(equality)]),82827,theory(equality)])).
% cnf(85141,plain,($false),inference(cn,[status(thm)],[85140,theory(equality)])).
% cnf(85142,plain,($false),85141,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 6324
% # ...of these trivial : 318
% # ...subsumed : 4708
% # ...remaining for further processing: 1298
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 53
% # Backward-rewritten : 539
% # Generated clauses : 57312
% # ...of the previous two non-trivial : 50476
% # Contextual simplify-reflections : 406
% # Paramodulations : 57312
% # Factorizations : 0
% # Equation resolutions : 0
% # Current number of processed clauses: 706
% # Positive orientable unit clauses: 278
% # Positive unorientable unit clauses: 11
% # Negative unit clauses : 1
% # Non-unit-clauses : 416
% # Current number of unprocessed clauses: 15096
% # ...number of literals in the above : 25158
% # Clause-clause subsumption calls (NU) : 87194
% # Rec. Clause-clause subsumption calls : 85921
% # Unit Clause-clause subsumption calls : 696
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 7841
% # Indexed BW rewrite successes : 310
% # Backwards rewriting index: 641 leaves, 2.56+/-4.622 terms/leaf
% # Paramod-from index: 156 leaves, 2.01+/-3.864 terms/leaf
% # Paramod-into index: 572 leaves, 2.50+/-4.835 terms/leaf
% # -------------------------------------------------
% # User time : 1.969 s
% # System time : 0.073 s
% # Total time : 2.042 s
% # Maximum resident set size: 0 pages
% PrfWatch: 3.28 CPU 3.76 WC
% FINAL PrfWatch: 3.28 CPU 3.76 WC
% SZS output end Solution for /tmp/SystemOnTPTP9844/LCL568+1.tptp
%
%------------------------------------------------------------------------------