TSTP Solution File: LCL537+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : LCL537+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 : art04.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 13:52:13 EST 2010
% Result : Theorem 1.64s
% Output : Solution 1.64s
% 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/SystemOnTPTP17790/LCL537+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP17790/LCL537+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP17790/LCL537+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 17886
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.01 WC
% # Preprocessing time : 0.021 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(1, axiom,(axiom_B<=>![X1]:is_a_theorem(implies(X1,necessarily(possibly(X1))))),file('/tmp/SRASS.s.p', axiom_B)).
% fof(2, axiom,modus_ponens,file('/tmp/SRASS.s.p', hilbert_modus_ponens)).
% fof(4, axiom,implies_1,file('/tmp/SRASS.s.p', hilbert_implies_1)).
% fof(5, axiom,implies_2,file('/tmp/SRASS.s.p', hilbert_implies_2)).
% fof(7, axiom,and_1,file('/tmp/SRASS.s.p', hilbert_and_1)).
% fof(9, axiom,and_3,file('/tmp/SRASS.s.p', hilbert_and_3)).
% fof(10, axiom,or_1,file('/tmp/SRASS.s.p', hilbert_or_1)).
% fof(12, axiom,or_3,file('/tmp/SRASS.s.p', hilbert_or_3)).
% fof(17, axiom,(axiom_M<=>![X1]:is_a_theorem(implies(necessarily(X1),X1))),file('/tmp/SRASS.s.p', axiom_M)).
% fof(18, axiom,(axiom_4<=>![X1]:is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))),file('/tmp/SRASS.s.p', axiom_4)).
% fof(19, axiom,op_possibly,file('/tmp/SRASS.s.p', km4b_op_possibly)).
% fof(22, axiom,axiom_M,file('/tmp/SRASS.s.p', km4b_axiom_M)).
% fof(23, axiom,axiom_4,file('/tmp/SRASS.s.p', km4b_axiom_4)).
% fof(24, axiom,axiom_B,file('/tmp/SRASS.s.p', km4b_axiom_B)).
% fof(26, axiom,(axiom_5<=>![X1]:is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))),file('/tmp/SRASS.s.p', axiom_5)).
% fof(29, axiom,(modus_ponens<=>![X1]:![X2]:((is_a_theorem(X1)&is_a_theorem(implies(X1,X2)))=>is_a_theorem(X2))),file('/tmp/SRASS.s.p', modus_ponens)).
% fof(30, axiom,(implies_1<=>![X1]:![X2]:is_a_theorem(implies(X1,implies(X2,X1)))),file('/tmp/SRASS.s.p', implies_1)).
% fof(31, axiom,(implies_2<=>![X1]:![X2]:is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))),file('/tmp/SRASS.s.p', implies_2)).
% fof(34, axiom,op_or,file('/tmp/SRASS.s.p', hilbert_op_or)).
% fof(35, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(36, axiom,op_equiv,file('/tmp/SRASS.s.p', hilbert_op_equiv)).
% fof(37, axiom,substitution_of_equivalents,file('/tmp/SRASS.s.p', substitution_of_equivalents)).
% fof(42, axiom,(op_possibly=>![X1]:possibly(X1)=not(necessarily(not(X1)))),file('/tmp/SRASS.s.p', op_possibly)).
% fof(44, axiom,(and_1<=>![X1]:![X2]:is_a_theorem(implies(and(X1,X2),X1))),file('/tmp/SRASS.s.p', and_1)).
% fof(46, axiom,(and_3<=>![X1]:![X2]:is_a_theorem(implies(X1,implies(X2,and(X1,X2))))),file('/tmp/SRASS.s.p', and_3)).
% fof(51, axiom,(or_1<=>![X1]:![X2]:is_a_theorem(implies(X1,or(X1,X2)))),file('/tmp/SRASS.s.p', or_1)).
% fof(53, axiom,(or_3<=>![X1]:![X2]:![X3]:is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3))))),file('/tmp/SRASS.s.p', or_3)).
% fof(69, axiom,(op_or=>![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),file('/tmp/SRASS.s.p', op_or)).
% fof(77, axiom,(op_implies_and=>![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(80, axiom,(op_equiv=>![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(81, axiom,(substitution_of_equivalents<=>![X1]:![X2]:(is_a_theorem(equiv(X1,X2))=>X1=X2)),file('/tmp/SRASS.s.p', substitution_of_equivalents)).
% fof(83, conjecture,axiom_5,file('/tmp/SRASS.s.p', km5_axiom_5)).
% fof(84, negated_conjecture,~(axiom_5),inference(assume_negation,[status(cth)],[83])).
% fof(85, negated_conjecture,~(axiom_5),inference(fof_simplification,[status(thm)],[84,theory(equality)])).
% fof(86, plain,((~(axiom_B)|![X1]:is_a_theorem(implies(X1,necessarily(possibly(X1)))))&(?[X1]:~(is_a_theorem(implies(X1,necessarily(possibly(X1)))))|axiom_B)),inference(fof_nnf,[status(thm)],[1])).
% fof(87, plain,((~(axiom_B)|![X2]:is_a_theorem(implies(X2,necessarily(possibly(X2)))))&(?[X3]:~(is_a_theorem(implies(X3,necessarily(possibly(X3)))))|axiom_B)),inference(variable_rename,[status(thm)],[86])).
% fof(88, plain,((~(axiom_B)|![X2]:is_a_theorem(implies(X2,necessarily(possibly(X2)))))&(~(is_a_theorem(implies(esk1_0,necessarily(possibly(esk1_0)))))|axiom_B)),inference(skolemize,[status(esa)],[87])).
% fof(89, plain,![X2]:((is_a_theorem(implies(X2,necessarily(possibly(X2))))|~(axiom_B))&(~(is_a_theorem(implies(esk1_0,necessarily(possibly(esk1_0)))))|axiom_B)),inference(shift_quantors,[status(thm)],[88])).
% cnf(91,plain,(is_a_theorem(implies(X1,necessarily(possibly(X1))))|~axiom_B),inference(split_conjunct,[status(thm)],[89])).
% cnf(92,plain,(modus_ponens),inference(split_conjunct,[status(thm)],[2])).
% cnf(94,plain,(implies_1),inference(split_conjunct,[status(thm)],[4])).
% cnf(95,plain,(implies_2),inference(split_conjunct,[status(thm)],[5])).
% cnf(97,plain,(and_1),inference(split_conjunct,[status(thm)],[7])).
% cnf(99,plain,(and_3),inference(split_conjunct,[status(thm)],[9])).
% cnf(100,plain,(or_1),inference(split_conjunct,[status(thm)],[10])).
% cnf(102,plain,(or_3),inference(split_conjunct,[status(thm)],[12])).
% fof(112, plain,((~(axiom_M)|![X1]:is_a_theorem(implies(necessarily(X1),X1)))&(?[X1]:~(is_a_theorem(implies(necessarily(X1),X1)))|axiom_M)),inference(fof_nnf,[status(thm)],[17])).
% fof(113, plain,((~(axiom_M)|![X2]:is_a_theorem(implies(necessarily(X2),X2)))&(?[X3]:~(is_a_theorem(implies(necessarily(X3),X3)))|axiom_M)),inference(variable_rename,[status(thm)],[112])).
% fof(114, plain,((~(axiom_M)|![X2]:is_a_theorem(implies(necessarily(X2),X2)))&(~(is_a_theorem(implies(necessarily(esk4_0),esk4_0)))|axiom_M)),inference(skolemize,[status(esa)],[113])).
% fof(115, plain,![X2]:((is_a_theorem(implies(necessarily(X2),X2))|~(axiom_M))&(~(is_a_theorem(implies(necessarily(esk4_0),esk4_0)))|axiom_M)),inference(shift_quantors,[status(thm)],[114])).
% cnf(117,plain,(is_a_theorem(implies(necessarily(X1),X1))|~axiom_M),inference(split_conjunct,[status(thm)],[115])).
% fof(118, 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)],[18])).
% fof(119, 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)],[118])).
% fof(120, plain,((~(axiom_4)|![X2]:is_a_theorem(implies(necessarily(X2),necessarily(necessarily(X2)))))&(~(is_a_theorem(implies(necessarily(esk5_0),necessarily(necessarily(esk5_0)))))|axiom_4)),inference(skolemize,[status(esa)],[119])).
% fof(121, plain,![X2]:((is_a_theorem(implies(necessarily(X2),necessarily(necessarily(X2))))|~(axiom_4))&(~(is_a_theorem(implies(necessarily(esk5_0),necessarily(necessarily(esk5_0)))))|axiom_4)),inference(shift_quantors,[status(thm)],[120])).
% cnf(123,plain,(is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_4),inference(split_conjunct,[status(thm)],[121])).
% cnf(124,plain,(op_possibly),inference(split_conjunct,[status(thm)],[19])).
% cnf(127,plain,(axiom_M),inference(split_conjunct,[status(thm)],[22])).
% cnf(128,plain,(axiom_4),inference(split_conjunct,[status(thm)],[23])).
% cnf(129,plain,(axiom_B),inference(split_conjunct,[status(thm)],[24])).
% fof(138, 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)],[26])).
% fof(139, 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)],[138])).
% fof(140, plain,((~(axiom_5)|![X2]:is_a_theorem(implies(possibly(X2),necessarily(possibly(X2)))))&(~(is_a_theorem(implies(possibly(esk7_0),necessarily(possibly(esk7_0)))))|axiom_5)),inference(skolemize,[status(esa)],[139])).
% fof(141, plain,![X2]:((is_a_theorem(implies(possibly(X2),necessarily(possibly(X2))))|~(axiom_5))&(~(is_a_theorem(implies(possibly(esk7_0),necessarily(possibly(esk7_0)))))|axiom_5)),inference(shift_quantors,[status(thm)],[140])).
% cnf(142,plain,(axiom_5|~is_a_theorem(implies(possibly(esk7_0),necessarily(possibly(esk7_0))))),inference(split_conjunct,[status(thm)],[141])).
% fof(156, plain,((~(modus_ponens)|![X1]:![X2]:((~(is_a_theorem(X1))|~(is_a_theorem(implies(X1,X2))))|is_a_theorem(X2)))&(?[X1]:?[X2]:((is_a_theorem(X1)&is_a_theorem(implies(X1,X2)))&~(is_a_theorem(X2)))|modus_ponens)),inference(fof_nnf,[status(thm)],[29])).
% fof(157, plain,((~(modus_ponens)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4)))&(?[X5]:?[X6]:((is_a_theorem(X5)&is_a_theorem(implies(X5,X6)))&~(is_a_theorem(X6)))|modus_ponens)),inference(variable_rename,[status(thm)],[156])).
% fof(158, plain,((~(modus_ponens)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4)))&(((is_a_theorem(esk12_0)&is_a_theorem(implies(esk12_0,esk13_0)))&~(is_a_theorem(esk13_0)))|modus_ponens)),inference(skolemize,[status(esa)],[157])).
% fof(159, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4))|~(modus_ponens))&(((is_a_theorem(esk12_0)&is_a_theorem(implies(esk12_0,esk13_0)))&~(is_a_theorem(esk13_0)))|modus_ponens)),inference(shift_quantors,[status(thm)],[158])).
% fof(160, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4))|~(modus_ponens))&(((is_a_theorem(esk12_0)|modus_ponens)&(is_a_theorem(implies(esk12_0,esk13_0))|modus_ponens))&(~(is_a_theorem(esk13_0))|modus_ponens))),inference(distribute,[status(thm)],[159])).
% cnf(164,plain,(is_a_theorem(X1)|~modus_ponens|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)),inference(split_conjunct,[status(thm)],[160])).
% fof(165, plain,((~(implies_1)|![X1]:![X2]:is_a_theorem(implies(X1,implies(X2,X1))))&(?[X1]:?[X2]:~(is_a_theorem(implies(X1,implies(X2,X1))))|implies_1)),inference(fof_nnf,[status(thm)],[30])).
% fof(166, plain,((~(implies_1)|![X3]:![X4]:is_a_theorem(implies(X3,implies(X4,X3))))&(?[X5]:?[X6]:~(is_a_theorem(implies(X5,implies(X6,X5))))|implies_1)),inference(variable_rename,[status(thm)],[165])).
% fof(167, plain,((~(implies_1)|![X3]:![X4]:is_a_theorem(implies(X3,implies(X4,X3))))&(~(is_a_theorem(implies(esk14_0,implies(esk15_0,esk14_0))))|implies_1)),inference(skolemize,[status(esa)],[166])).
% fof(168, plain,![X3]:![X4]:((is_a_theorem(implies(X3,implies(X4,X3)))|~(implies_1))&(~(is_a_theorem(implies(esk14_0,implies(esk15_0,esk14_0))))|implies_1)),inference(shift_quantors,[status(thm)],[167])).
% cnf(170,plain,(is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1),inference(split_conjunct,[status(thm)],[168])).
% fof(171, plain,((~(implies_2)|![X1]:![X2]:is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))&(?[X1]:?[X2]:~(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))|implies_2)),inference(fof_nnf,[status(thm)],[31])).
% fof(172, plain,((~(implies_2)|![X3]:![X4]:is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4))))&(?[X5]:?[X6]:~(is_a_theorem(implies(implies(X5,implies(X5,X6)),implies(X5,X6))))|implies_2)),inference(variable_rename,[status(thm)],[171])).
% fof(173, plain,((~(implies_2)|![X3]:![X4]:is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4))))&(~(is_a_theorem(implies(implies(esk16_0,implies(esk16_0,esk17_0)),implies(esk16_0,esk17_0))))|implies_2)),inference(skolemize,[status(esa)],[172])).
% fof(174, plain,![X3]:![X4]:((is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4)))|~(implies_2))&(~(is_a_theorem(implies(implies(esk16_0,implies(esk16_0,esk17_0)),implies(esk16_0,esk17_0))))|implies_2)),inference(shift_quantors,[status(thm)],[173])).
% cnf(176,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2),inference(split_conjunct,[status(thm)],[174])).
% cnf(189,plain,(op_or),inference(split_conjunct,[status(thm)],[34])).
% cnf(190,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[35])).
% cnf(191,plain,(op_equiv),inference(split_conjunct,[status(thm)],[36])).
% cnf(192,plain,(substitution_of_equivalents),inference(split_conjunct,[status(thm)],[37])).
% fof(217, plain,(~(op_possibly)|![X1]:possibly(X1)=not(necessarily(not(X1)))),inference(fof_nnf,[status(thm)],[42])).
% fof(218, plain,(~(op_possibly)|![X2]:possibly(X2)=not(necessarily(not(X2)))),inference(variable_rename,[status(thm)],[217])).
% fof(219, plain,![X2]:(possibly(X2)=not(necessarily(not(X2)))|~(op_possibly)),inference(shift_quantors,[status(thm)],[218])).
% cnf(220,plain,(possibly(X1)=not(necessarily(not(X1)))|~op_possibly),inference(split_conjunct,[status(thm)],[219])).
% fof(225, plain,((~(and_1)|![X1]:![X2]:is_a_theorem(implies(and(X1,X2),X1)))&(?[X1]:?[X2]:~(is_a_theorem(implies(and(X1,X2),X1)))|and_1)),inference(fof_nnf,[status(thm)],[44])).
% fof(226, plain,((~(and_1)|![X3]:![X4]:is_a_theorem(implies(and(X3,X4),X3)))&(?[X5]:?[X6]:~(is_a_theorem(implies(and(X5,X6),X5)))|and_1)),inference(variable_rename,[status(thm)],[225])).
% fof(227, plain,((~(and_1)|![X3]:![X4]:is_a_theorem(implies(and(X3,X4),X3)))&(~(is_a_theorem(implies(and(esk29_0,esk30_0),esk29_0)))|and_1)),inference(skolemize,[status(esa)],[226])).
% fof(228, plain,![X3]:![X4]:((is_a_theorem(implies(and(X3,X4),X3))|~(and_1))&(~(is_a_theorem(implies(and(esk29_0,esk30_0),esk29_0)))|and_1)),inference(shift_quantors,[status(thm)],[227])).
% cnf(230,plain,(is_a_theorem(implies(and(X1,X2),X1))|~and_1),inference(split_conjunct,[status(thm)],[228])).
% fof(237, plain,((~(and_3)|![X1]:![X2]:is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))&(?[X1]:?[X2]:~(is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))|and_3)),inference(fof_nnf,[status(thm)],[46])).
% fof(238, plain,((~(and_3)|![X3]:![X4]:is_a_theorem(implies(X3,implies(X4,and(X3,X4)))))&(?[X5]:?[X6]:~(is_a_theorem(implies(X5,implies(X6,and(X5,X6)))))|and_3)),inference(variable_rename,[status(thm)],[237])).
% fof(239, plain,((~(and_3)|![X3]:![X4]:is_a_theorem(implies(X3,implies(X4,and(X3,X4)))))&(~(is_a_theorem(implies(esk33_0,implies(esk34_0,and(esk33_0,esk34_0)))))|and_3)),inference(skolemize,[status(esa)],[238])).
% fof(240, plain,![X3]:![X4]:((is_a_theorem(implies(X3,implies(X4,and(X3,X4))))|~(and_3))&(~(is_a_theorem(implies(esk33_0,implies(esk34_0,and(esk33_0,esk34_0)))))|and_3)),inference(shift_quantors,[status(thm)],[239])).
% cnf(242,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3),inference(split_conjunct,[status(thm)],[240])).
% fof(270, plain,((~(or_1)|![X1]:![X2]:is_a_theorem(implies(X1,or(X1,X2))))&(?[X1]:?[X2]:~(is_a_theorem(implies(X1,or(X1,X2))))|or_1)),inference(fof_nnf,[status(thm)],[51])).
% fof(271, plain,((~(or_1)|![X3]:![X4]:is_a_theorem(implies(X3,or(X3,X4))))&(?[X5]:?[X6]:~(is_a_theorem(implies(X5,or(X5,X6))))|or_1)),inference(variable_rename,[status(thm)],[270])).
% fof(272, plain,((~(or_1)|![X3]:![X4]:is_a_theorem(implies(X3,or(X3,X4))))&(~(is_a_theorem(implies(esk42_0,or(esk42_0,esk43_0))))|or_1)),inference(skolemize,[status(esa)],[271])).
% fof(273, plain,![X3]:![X4]:((is_a_theorem(implies(X3,or(X3,X4)))|~(or_1))&(~(is_a_theorem(implies(esk42_0,or(esk42_0,esk43_0))))|or_1)),inference(shift_quantors,[status(thm)],[272])).
% cnf(275,plain,(is_a_theorem(implies(X1,or(X1,X2)))|~or_1),inference(split_conjunct,[status(thm)],[273])).
% fof(282, plain,((~(or_3)|![X1]:![X2]:![X3]:is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))))&(?[X1]:?[X2]:?[X3]:~(is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))))|or_3)),inference(fof_nnf,[status(thm)],[53])).
% fof(283, plain,((~(or_3)|![X4]:![X5]:![X6]:is_a_theorem(implies(implies(X4,X6),implies(implies(X5,X6),implies(or(X4,X5),X6)))))&(?[X7]:?[X8]:?[X9]:~(is_a_theorem(implies(implies(X7,X9),implies(implies(X8,X9),implies(or(X7,X8),X9)))))|or_3)),inference(variable_rename,[status(thm)],[282])).
% fof(284, plain,((~(or_3)|![X4]:![X5]:![X6]:is_a_theorem(implies(implies(X4,X6),implies(implies(X5,X6),implies(or(X4,X5),X6)))))&(~(is_a_theorem(implies(implies(esk46_0,esk48_0),implies(implies(esk47_0,esk48_0),implies(or(esk46_0,esk47_0),esk48_0)))))|or_3)),inference(skolemize,[status(esa)],[283])).
% fof(285, plain,![X4]:![X5]:![X6]:((is_a_theorem(implies(implies(X4,X6),implies(implies(X5,X6),implies(or(X4,X5),X6))))|~(or_3))&(~(is_a_theorem(implies(implies(esk46_0,esk48_0),implies(implies(esk47_0,esk48_0),implies(or(esk46_0,esk47_0),esk48_0)))))|or_3)),inference(shift_quantors,[status(thm)],[284])).
% cnf(287,plain,(is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))|~or_3),inference(split_conjunct,[status(thm)],[285])).
% fof(376, plain,(~(op_or)|![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),inference(fof_nnf,[status(thm)],[69])).
% fof(377, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(variable_rename,[status(thm)],[376])).
% fof(378, plain,![X3]:![X4]:(or(X3,X4)=not(and(not(X3),not(X4)))|~(op_or)),inference(shift_quantors,[status(thm)],[377])).
% cnf(379,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[378])).
% fof(418, plain,(~(op_implies_and)|![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),inference(fof_nnf,[status(thm)],[77])).
% fof(419, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(variable_rename,[status(thm)],[418])).
% fof(420, plain,![X3]:![X4]:(implies(X3,X4)=not(and(X3,not(X4)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[419])).
% cnf(421,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[420])).
% fof(435, plain,(~(op_equiv)|![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),inference(fof_nnf,[status(thm)],[80])).
% fof(436, plain,(~(op_equiv)|![X3]:![X4]:equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))),inference(variable_rename,[status(thm)],[435])).
% fof(437, plain,![X3]:![X4]:(equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))|~(op_equiv)),inference(shift_quantors,[status(thm)],[436])).
% cnf(438,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[437])).
% fof(439, plain,((~(substitution_of_equivalents)|![X1]:![X2]:(~(is_a_theorem(equiv(X1,X2)))|X1=X2))&(?[X1]:?[X2]:(is_a_theorem(equiv(X1,X2))&~(X1=X2))|substitution_of_equivalents)),inference(fof_nnf,[status(thm)],[81])).
% fof(440, plain,((~(substitution_of_equivalents)|![X3]:![X4]:(~(is_a_theorem(equiv(X3,X4)))|X3=X4))&(?[X5]:?[X6]:(is_a_theorem(equiv(X5,X6))&~(X5=X6))|substitution_of_equivalents)),inference(variable_rename,[status(thm)],[439])).
% fof(441, plain,((~(substitution_of_equivalents)|![X3]:![X4]:(~(is_a_theorem(equiv(X3,X4)))|X3=X4))&((is_a_theorem(equiv(esk91_0,esk92_0))&~(esk91_0=esk92_0))|substitution_of_equivalents)),inference(skolemize,[status(esa)],[440])).
% fof(442, plain,![X3]:![X4]:(((~(is_a_theorem(equiv(X3,X4)))|X3=X4)|~(substitution_of_equivalents))&((is_a_theorem(equiv(esk91_0,esk92_0))&~(esk91_0=esk92_0))|substitution_of_equivalents)),inference(shift_quantors,[status(thm)],[441])).
% fof(443, plain,![X3]:![X4]:(((~(is_a_theorem(equiv(X3,X4)))|X3=X4)|~(substitution_of_equivalents))&((is_a_theorem(equiv(esk91_0,esk92_0))|substitution_of_equivalents)&(~(esk91_0=esk92_0)|substitution_of_equivalents))),inference(distribute,[status(thm)],[442])).
% cnf(446,plain,(X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))),inference(split_conjunct,[status(thm)],[443])).
% cnf(455,negated_conjecture,(~axiom_5),inference(split_conjunct,[status(thm)],[85])).
% cnf(462,plain,(~is_a_theorem(implies(possibly(esk7_0),necessarily(possibly(esk7_0))))),inference(sr,[status(thm)],[142,455,theory(equality)])).
% cnf(473,plain,(X1=X2|$false|~is_a_theorem(equiv(X1,X2))),inference(rw,[status(thm)],[446,192,theory(equality)])).
% cnf(474,plain,(X1=X2|~is_a_theorem(equiv(X1,X2))),inference(cn,[status(thm)],[473,theory(equality)])).
% cnf(475,plain,(is_a_theorem(implies(necessarily(X1),X1))|$false),inference(rw,[status(thm)],[117,127,theory(equality)])).
% cnf(476,plain,(is_a_theorem(implies(necessarily(X1),X1))),inference(cn,[status(thm)],[475,theory(equality)])).
% cnf(481,plain,(not(necessarily(not(X1)))=possibly(X1)|$false),inference(rw,[status(thm)],[220,124,theory(equality)])).
% cnf(482,plain,(not(necessarily(not(X1)))=possibly(X1)),inference(cn,[status(thm)],[481,theory(equality)])).
% cnf(484,plain,(is_a_theorem(implies(X1,necessarily(possibly(X1))))|$false),inference(rw,[status(thm)],[91,129,theory(equality)])).
% cnf(485,plain,(is_a_theorem(implies(X1,necessarily(possibly(X1))))),inference(cn,[status(thm)],[484,theory(equality)])).
% cnf(486,plain,(is_a_theorem(implies(X1,implies(X2,X1)))|$false),inference(rw,[status(thm)],[170,94,theory(equality)])).
% cnf(487,plain,(is_a_theorem(implies(X1,implies(X2,X1)))),inference(cn,[status(thm)],[486,theory(equality)])).
% cnf(493,plain,(is_a_theorem(implies(X1,or(X1,X2)))|$false),inference(rw,[status(thm)],[275,100,theory(equality)])).
% cnf(494,plain,(is_a_theorem(implies(X1,or(X1,X2)))),inference(cn,[status(thm)],[493,theory(equality)])).
% cnf(497,plain,(is_a_theorem(implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[230,97,theory(equality)])).
% cnf(498,plain,(is_a_theorem(implies(and(X1,X2),X1))),inference(cn,[status(thm)],[497,theory(equality)])).
% cnf(502,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(rw,[status(thm)],[164,92,theory(equality)])).
% cnf(503,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(cn,[status(thm)],[502,theory(equality)])).
% cnf(511,plain,(is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))|$false),inference(rw,[status(thm)],[123,128,theory(equality)])).
% cnf(512,plain,(is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))),inference(cn,[status(thm)],[511,theory(equality)])).
% cnf(514,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[421,190,theory(equality)])).
% cnf(515,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[514,theory(equality)])).
% cnf(516,plain,(not(necessarily(implies(X1,X2)))=possibly(and(X1,not(X2)))),inference(spm,[status(thm)],[482,515,theory(equality)])).
% cnf(528,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[379,515,theory(equality)])).
% cnf(529,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[528,189,theory(equality)])).
% cnf(530,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[529,theory(equality)])).
% cnf(547,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|$false),inference(rw,[status(thm)],[242,99,theory(equality)])).
% cnf(548,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))),inference(cn,[status(thm)],[547,theory(equality)])).
% cnf(549,plain,(is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)),inference(spm,[status(thm)],[503,548,theory(equality)])).
% cnf(554,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[438,191,theory(equality)])).
% cnf(555,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[554,theory(equality)])).
% cnf(556,plain,(X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))),inference(spm,[status(thm)],[474,555,theory(equality)])).
% cnf(577,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|$false),inference(rw,[status(thm)],[176,95,theory(equality)])).
% cnf(578,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))),inference(cn,[status(thm)],[577,theory(equality)])).
% cnf(579,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))),inference(spm,[status(thm)],[503,578,theory(equality)])).
% cnf(608,plain,(is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))|$false),inference(rw,[status(thm)],[287,102,theory(equality)])).
% cnf(609,plain,(is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))),inference(cn,[status(thm)],[608,theory(equality)])).
% cnf(688,plain,(is_a_theorem(implies(implies(X1,X2),implies(or(X1,X1),X2)))),inference(spm,[status(thm)],[579,609,theory(equality)])).
% cnf(690,plain,(is_a_theorem(implies(X1,X1))),inference(spm,[status(thm)],[579,487,theory(equality)])).
% cnf(691,plain,(is_a_theorem(implies(X1,and(X1,X1)))),inference(spm,[status(thm)],[579,548,theory(equality)])).
% cnf(741,plain,(is_a_theorem(implies(or(X1,X1),X2))|~is_a_theorem(implies(X1,X2))),inference(spm,[status(thm)],[503,688,theory(equality)])).
% cnf(803,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(spm,[status(thm)],[503,549,theory(equality)])).
% cnf(808,plain,(X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))),inference(spm,[status(thm)],[556,803,theory(equality)])).
% cnf(839,plain,(necessarily(necessarily(X1))=necessarily(X1)|~is_a_theorem(implies(necessarily(necessarily(X1)),necessarily(X1)))),inference(spm,[status(thm)],[808,512,theory(equality)])).
% cnf(843,plain,(and(X1,X1)=X1|~is_a_theorem(implies(and(X1,X1),X1))),inference(spm,[status(thm)],[808,691,theory(equality)])).
% cnf(847,plain,(necessarily(possibly(X1))=X1|~is_a_theorem(implies(necessarily(possibly(X1)),X1))),inference(spm,[status(thm)],[808,485,theory(equality)])).
% cnf(854,plain,(necessarily(necessarily(X1))=necessarily(X1)|$false),inference(rw,[status(thm)],[839,476,theory(equality)])).
% cnf(855,plain,(necessarily(necessarily(X1))=necessarily(X1)),inference(cn,[status(thm)],[854,theory(equality)])).
% cnf(856,plain,(and(X1,X1)=X1|$false),inference(rw,[status(thm)],[843,498,theory(equality)])).
% cnf(857,plain,(and(X1,X1)=X1),inference(cn,[status(thm)],[856,theory(equality)])).
% cnf(862,plain,(possibly(not(X1))=not(necessarily(implies(not(X1),X1)))),inference(spm,[status(thm)],[516,857,theory(equality)])).
% cnf(877,plain,(possibly(not(X1))=not(necessarily(or(X1,X1)))),inference(rw,[status(thm)],[862,530,theory(equality)])).
% cnf(9234,plain,(is_a_theorem(implies(or(X1,X1),X1))),inference(spm,[status(thm)],[741,690,theory(equality)])).
% cnf(9436,plain,(X1=or(X1,X1)|~is_a_theorem(implies(X1,or(X1,X1)))),inference(spm,[status(thm)],[808,9234,theory(equality)])).
% cnf(9471,plain,(X1=or(X1,X1)|$false),inference(rw,[status(thm)],[9436,494,theory(equality)])).
% cnf(9472,plain,(X1=or(X1,X1)),inference(cn,[status(thm)],[9471,theory(equality)])).
% cnf(15155,plain,(not(necessarily(X1))=possibly(not(X1))),inference(rw,[status(thm)],[877,9472,theory(equality)])).
% cnf(15202,plain,(possibly(possibly(X1))=not(necessarily(necessarily(not(X1))))),inference(spm,[status(thm)],[15155,482,theory(equality)])).
% cnf(15238,plain,(possibly(possibly(X1))=possibly(X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[15202,855,theory(equality)]),482,theory(equality)])).
% cnf(15254,plain,(necessarily(possibly(X1))=possibly(X1)|~is_a_theorem(implies(necessarily(possibly(X1)),possibly(X1)))),inference(spm,[status(thm)],[847,15238,theory(equality)])).
% cnf(15298,plain,(necessarily(possibly(X1))=possibly(X1)|$false),inference(rw,[status(thm)],[15254,476,theory(equality)])).
% cnf(15299,plain,(necessarily(possibly(X1))=possibly(X1)),inference(cn,[status(thm)],[15298,theory(equality)])).
% cnf(15363,plain,($false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[462,15299,theory(equality)]),690,theory(equality)])).
% cnf(15364,plain,($false),inference(cn,[status(thm)],[15363,theory(equality)])).
% cnf(15365,plain,($false),15364,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 1531
% # ...of these trivial : 46
% # ...subsumed : 1089
% # ...remaining for further processing: 396
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 4
% # Backward-rewritten : 68
% # Generated clauses : 11715
% # ...of the previous two non-trivial : 10721
% # Contextual simplify-reflections : 261
% # Paramodulations : 11715
% # Factorizations : 0
% # Equation resolutions : 0
% # Current number of processed clauses: 324
% # Positive orientable unit clauses: 103
% # Positive unorientable unit clauses: 2
% # Negative unit clauses : 4
% # Non-unit-clauses : 215
% # Current number of unprocessed clauses: 7379
% # ...number of literals in the above : 19108
% # Clause-clause subsumption calls (NU) : 17099
% # Rec. Clause-clause subsumption calls : 15443
% # Unit Clause-clause subsumption calls : 909
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 420
% # Indexed BW rewrite successes : 40
% # Backwards rewriting index: 467 leaves, 1.41+/-1.133 terms/leaf
% # Paramod-from index: 127 leaves, 1.31+/-0.885 terms/leaf
% # Paramod-into index: 391 leaves, 1.35+/-1.013 terms/leaf
% # -------------------------------------------------
% # User time : 0.324 s
% # System time : 0.023 s
% # Total time : 0.347 s
% # Maximum resident set size: 0 pages
% PrfWatch: 0.64 CPU 0.73 WC
% FINAL PrfWatch: 0.64 CPU 0.73 WC
% SZS output end Solution for /tmp/SystemOnTPTP17790/LCL537+1.tptp
%
%------------------------------------------------------------------------------