TSTP Solution File: LCL535+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : LCL535+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 13:51:50 EST 2010
% Result : Theorem 1.93s
% Output : Solution 1.93s
% 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/SystemOnTPTP7216/LCL535+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP7216/LCL535+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP7216/LCL535+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 7312
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.01 WC
% # Preprocessing time : 0.022 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(3, axiom,axiom_5,file('/tmp/SRASS.s.p', km5_axiom_5)).
% fof(4, axiom,(axiom_m9<=>![X1]:is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))),file('/tmp/SRASS.s.p', axiom_m9)).
% fof(10, axiom,modus_ponens,file('/tmp/SRASS.s.p', hilbert_modus_ponens)).
% fof(11, axiom,modus_tollens,file('/tmp/SRASS.s.p', hilbert_modus_tollens)).
% fof(12, axiom,implies_1,file('/tmp/SRASS.s.p', hilbert_implies_1)).
% fof(13, axiom,implies_2,file('/tmp/SRASS.s.p', hilbert_implies_2)).
% fof(15, axiom,and_1,file('/tmp/SRASS.s.p', hilbert_and_1)).
% fof(17, axiom,and_3,file('/tmp/SRASS.s.p', hilbert_and_3)).
% fof(24, axiom,op_possibly,file('/tmp/SRASS.s.p', km5_op_possibly)).
% fof(25, axiom,necessitation,file('/tmp/SRASS.s.p', km5_necessitation)).
% fof(27, axiom,axiom_M,file('/tmp/SRASS.s.p', km5_axiom_M)).
% fof(29, axiom,op_strict_implies,file('/tmp/SRASS.s.p', s1_0_op_strict_implies)).
% fof(32, axiom,(axiom_M<=>![X1]:is_a_theorem(implies(necessarily(X1),X1))),file('/tmp/SRASS.s.p', axiom_M)).
% fof(39, axiom,op_or,file('/tmp/SRASS.s.p', hilbert_op_or)).
% fof(40, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(41, axiom,op_equiv,file('/tmp/SRASS.s.p', hilbert_op_equiv)).
% fof(42, axiom,substitution_of_equivalents,file('/tmp/SRASS.s.p', substitution_of_equivalents)).
% fof(46, axiom,(necessitation<=>![X1]:(is_a_theorem(X1)=>is_a_theorem(necessarily(X1)))),file('/tmp/SRASS.s.p', necessitation)).
% fof(48, axiom,(modus_ponens<=>![X1]:![X4]:((is_a_theorem(X1)&is_a_theorem(implies(X1,X4)))=>is_a_theorem(X4))),file('/tmp/SRASS.s.p', modus_ponens)).
% fof(49, axiom,(implies_1<=>![X1]:![X4]:is_a_theorem(implies(X1,implies(X4,X1)))),file('/tmp/SRASS.s.p', implies_1)).
% fof(50, axiom,(implies_2<=>![X1]:![X4]:is_a_theorem(implies(implies(X1,implies(X1,X4)),implies(X1,X4)))),file('/tmp/SRASS.s.p', implies_2)).
% fof(54, axiom,(axiom_5<=>![X1]:is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))),file('/tmp/SRASS.s.p', axiom_5)).
% fof(57, axiom,(op_possibly=>![X1]:possibly(X1)=not(necessarily(not(X1)))),file('/tmp/SRASS.s.p', op_possibly)).
% fof(59, axiom,(modus_tollens<=>![X1]:![X4]:is_a_theorem(implies(implies(not(X4),not(X1)),implies(X1,X4)))),file('/tmp/SRASS.s.p', modus_tollens)).
% fof(60, axiom,(and_1<=>![X1]:![X4]:is_a_theorem(implies(and(X1,X4),X1))),file('/tmp/SRASS.s.p', and_1)).
% fof(62, axiom,(and_3<=>![X1]:![X4]:is_a_theorem(implies(X1,implies(X4,and(X1,X4))))),file('/tmp/SRASS.s.p', and_3)).
% fof(78, axiom,(op_strict_implies=>![X1]:![X4]:strict_implies(X1,X4)=necessarily(implies(X1,X4))),file('/tmp/SRASS.s.p', op_strict_implies)).
% fof(80, axiom,(substitution_of_equivalents<=>![X1]:![X4]:(is_a_theorem(equiv(X1,X4))=>X1=X4)),file('/tmp/SRASS.s.p', substitution_of_equivalents)).
% fof(82, axiom,(op_or=>![X1]:![X4]:or(X1,X4)=not(and(not(X1),not(X4)))),file('/tmp/SRASS.s.p', op_or)).
% fof(84, axiom,(op_implies_and=>![X1]:![X4]:implies(X1,X4)=not(and(X1,not(X4)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(86, axiom,(op_equiv=>![X1]:![X4]:equiv(X1,X4)=and(implies(X1,X4),implies(X4,X1))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(88, conjecture,axiom_m9,file('/tmp/SRASS.s.p', s1_0_m6s3m9b_axiom_m9)).
% fof(89, negated_conjecture,~(axiom_m9),inference(assume_negation,[status(cth)],[88])).
% fof(90, negated_conjecture,~(axiom_m9),inference(fof_simplification,[status(thm)],[89,theory(equality)])).
% cnf(103,plain,(axiom_5),inference(split_conjunct,[status(thm)],[3])).
% fof(104, 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)],[4])).
% fof(105, 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)],[104])).
% fof(106, plain,((~(axiom_m9)|![X2]:is_a_theorem(strict_implies(possibly(possibly(X2)),possibly(X2))))&(~(is_a_theorem(strict_implies(possibly(possibly(esk4_0)),possibly(esk4_0))))|axiom_m9)),inference(skolemize,[status(esa)],[105])).
% fof(107, plain,![X2]:((is_a_theorem(strict_implies(possibly(possibly(X2)),possibly(X2)))|~(axiom_m9))&(~(is_a_theorem(strict_implies(possibly(possibly(esk4_0)),possibly(esk4_0))))|axiom_m9)),inference(shift_quantors,[status(thm)],[106])).
% cnf(108,plain,(axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(esk4_0)),possibly(esk4_0)))),inference(split_conjunct,[status(thm)],[107])).
% cnf(143,plain,(modus_ponens),inference(split_conjunct,[status(thm)],[10])).
% cnf(144,plain,(modus_tollens),inference(split_conjunct,[status(thm)],[11])).
% cnf(145,plain,(implies_1),inference(split_conjunct,[status(thm)],[12])).
% cnf(146,plain,(implies_2),inference(split_conjunct,[status(thm)],[13])).
% cnf(148,plain,(and_1),inference(split_conjunct,[status(thm)],[15])).
% cnf(150,plain,(and_3),inference(split_conjunct,[status(thm)],[17])).
% cnf(157,plain,(op_possibly),inference(split_conjunct,[status(thm)],[24])).
% cnf(158,plain,(necessitation),inference(split_conjunct,[status(thm)],[25])).
% cnf(160,plain,(axiom_M),inference(split_conjunct,[status(thm)],[27])).
% cnf(162,plain,(op_strict_implies),inference(split_conjunct,[status(thm)],[29])).
% fof(170, 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)],[32])).
% fof(171, 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)],[170])).
% fof(172, plain,((~(axiom_M)|![X2]:is_a_theorem(implies(necessarily(X2),X2)))&(~(is_a_theorem(implies(necessarily(esk16_0),esk16_0)))|axiom_M)),inference(skolemize,[status(esa)],[171])).
% fof(173, plain,![X2]:((is_a_theorem(implies(necessarily(X2),X2))|~(axiom_M))&(~(is_a_theorem(implies(necessarily(esk16_0),esk16_0)))|axiom_M)),inference(shift_quantors,[status(thm)],[172])).
% cnf(175,plain,(is_a_theorem(implies(necessarily(X1),X1))|~axiom_M),inference(split_conjunct,[status(thm)],[173])).
% cnf(212,plain,(op_or),inference(split_conjunct,[status(thm)],[39])).
% cnf(213,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[40])).
% cnf(214,plain,(op_equiv),inference(split_conjunct,[status(thm)],[41])).
% cnf(215,plain,(substitution_of_equivalents),inference(split_conjunct,[status(thm)],[42])).
% fof(224, plain,((~(necessitation)|![X1]:(~(is_a_theorem(X1))|is_a_theorem(necessarily(X1))))&(?[X1]:(is_a_theorem(X1)&~(is_a_theorem(necessarily(X1))))|necessitation)),inference(fof_nnf,[status(thm)],[46])).
% fof(225, plain,((~(necessitation)|![X2]:(~(is_a_theorem(X2))|is_a_theorem(necessarily(X2))))&(?[X3]:(is_a_theorem(X3)&~(is_a_theorem(necessarily(X3))))|necessitation)),inference(variable_rename,[status(thm)],[224])).
% fof(226, plain,((~(necessitation)|![X2]:(~(is_a_theorem(X2))|is_a_theorem(necessarily(X2))))&((is_a_theorem(esk30_0)&~(is_a_theorem(necessarily(esk30_0))))|necessitation)),inference(skolemize,[status(esa)],[225])).
% fof(227, plain,![X2]:(((~(is_a_theorem(X2))|is_a_theorem(necessarily(X2)))|~(necessitation))&((is_a_theorem(esk30_0)&~(is_a_theorem(necessarily(esk30_0))))|necessitation)),inference(shift_quantors,[status(thm)],[226])).
% fof(228, plain,![X2]:(((~(is_a_theorem(X2))|is_a_theorem(necessarily(X2)))|~(necessitation))&((is_a_theorem(esk30_0)|necessitation)&(~(is_a_theorem(necessarily(esk30_0)))|necessitation))),inference(distribute,[status(thm)],[227])).
% cnf(231,plain,(is_a_theorem(necessarily(X1))|~necessitation|~is_a_theorem(X1)),inference(split_conjunct,[status(thm)],[228])).
% fof(241, plain,((~(modus_ponens)|![X1]:![X4]:((~(is_a_theorem(X1))|~(is_a_theorem(implies(X1,X4))))|is_a_theorem(X4)))&(?[X1]:?[X4]:((is_a_theorem(X1)&is_a_theorem(implies(X1,X4)))&~(is_a_theorem(X4)))|modus_ponens)),inference(fof_nnf,[status(thm)],[48])).
% fof(242, plain,((~(modus_ponens)|![X5]:![X6]:((~(is_a_theorem(X5))|~(is_a_theorem(implies(X5,X6))))|is_a_theorem(X6)))&(?[X7]:?[X8]:((is_a_theorem(X7)&is_a_theorem(implies(X7,X8)))&~(is_a_theorem(X8)))|modus_ponens)),inference(variable_rename,[status(thm)],[241])).
% fof(243, plain,((~(modus_ponens)|![X5]:![X6]:((~(is_a_theorem(X5))|~(is_a_theorem(implies(X5,X6))))|is_a_theorem(X6)))&(((is_a_theorem(esk33_0)&is_a_theorem(implies(esk33_0,esk34_0)))&~(is_a_theorem(esk34_0)))|modus_ponens)),inference(skolemize,[status(esa)],[242])).
% fof(244, plain,![X5]:![X6]:((((~(is_a_theorem(X5))|~(is_a_theorem(implies(X5,X6))))|is_a_theorem(X6))|~(modus_ponens))&(((is_a_theorem(esk33_0)&is_a_theorem(implies(esk33_0,esk34_0)))&~(is_a_theorem(esk34_0)))|modus_ponens)),inference(shift_quantors,[status(thm)],[243])).
% fof(245, plain,![X5]:![X6]:((((~(is_a_theorem(X5))|~(is_a_theorem(implies(X5,X6))))|is_a_theorem(X6))|~(modus_ponens))&(((is_a_theorem(esk33_0)|modus_ponens)&(is_a_theorem(implies(esk33_0,esk34_0))|modus_ponens))&(~(is_a_theorem(esk34_0))|modus_ponens))),inference(distribute,[status(thm)],[244])).
% cnf(249,plain,(is_a_theorem(X1)|~modus_ponens|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)),inference(split_conjunct,[status(thm)],[245])).
% fof(250, plain,((~(implies_1)|![X1]:![X4]:is_a_theorem(implies(X1,implies(X4,X1))))&(?[X1]:?[X4]:~(is_a_theorem(implies(X1,implies(X4,X1))))|implies_1)),inference(fof_nnf,[status(thm)],[49])).
% fof(251, plain,((~(implies_1)|![X5]:![X6]:is_a_theorem(implies(X5,implies(X6,X5))))&(?[X7]:?[X8]:~(is_a_theorem(implies(X7,implies(X8,X7))))|implies_1)),inference(variable_rename,[status(thm)],[250])).
% fof(252, plain,((~(implies_1)|![X5]:![X6]:is_a_theorem(implies(X5,implies(X6,X5))))&(~(is_a_theorem(implies(esk35_0,implies(esk36_0,esk35_0))))|implies_1)),inference(skolemize,[status(esa)],[251])).
% fof(253, plain,![X5]:![X6]:((is_a_theorem(implies(X5,implies(X6,X5)))|~(implies_1))&(~(is_a_theorem(implies(esk35_0,implies(esk36_0,esk35_0))))|implies_1)),inference(shift_quantors,[status(thm)],[252])).
% cnf(255,plain,(is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1),inference(split_conjunct,[status(thm)],[253])).
% fof(256, plain,((~(implies_2)|![X1]:![X4]:is_a_theorem(implies(implies(X1,implies(X1,X4)),implies(X1,X4))))&(?[X1]:?[X4]:~(is_a_theorem(implies(implies(X1,implies(X1,X4)),implies(X1,X4))))|implies_2)),inference(fof_nnf,[status(thm)],[50])).
% fof(257, plain,((~(implies_2)|![X5]:![X6]:is_a_theorem(implies(implies(X5,implies(X5,X6)),implies(X5,X6))))&(?[X7]:?[X8]:~(is_a_theorem(implies(implies(X7,implies(X7,X8)),implies(X7,X8))))|implies_2)),inference(variable_rename,[status(thm)],[256])).
% fof(258, plain,((~(implies_2)|![X5]:![X6]:is_a_theorem(implies(implies(X5,implies(X5,X6)),implies(X5,X6))))&(~(is_a_theorem(implies(implies(esk37_0,implies(esk37_0,esk38_0)),implies(esk37_0,esk38_0))))|implies_2)),inference(skolemize,[status(esa)],[257])).
% fof(259, plain,![X5]:![X6]:((is_a_theorem(implies(implies(X5,implies(X5,X6)),implies(X5,X6)))|~(implies_2))&(~(is_a_theorem(implies(implies(esk37_0,implies(esk37_0,esk38_0)),implies(esk37_0,esk38_0))))|implies_2)),inference(shift_quantors,[status(thm)],[258])).
% cnf(261,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2),inference(split_conjunct,[status(thm)],[259])).
% fof(280, 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)],[54])).
% fof(281, 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)],[280])).
% fof(282, plain,((~(axiom_5)|![X2]:is_a_theorem(implies(possibly(X2),necessarily(possibly(X2)))))&(~(is_a_theorem(implies(possibly(esk46_0),necessarily(possibly(esk46_0)))))|axiom_5)),inference(skolemize,[status(esa)],[281])).
% fof(283, plain,![X2]:((is_a_theorem(implies(possibly(X2),necessarily(possibly(X2))))|~(axiom_5))&(~(is_a_theorem(implies(possibly(esk46_0),necessarily(possibly(esk46_0)))))|axiom_5)),inference(shift_quantors,[status(thm)],[282])).
% cnf(285,plain,(is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|~axiom_5),inference(split_conjunct,[status(thm)],[283])).
% fof(300, plain,(~(op_possibly)|![X1]:possibly(X1)=not(necessarily(not(X1)))),inference(fof_nnf,[status(thm)],[57])).
% fof(301, plain,(~(op_possibly)|![X2]:possibly(X2)=not(necessarily(not(X2)))),inference(variable_rename,[status(thm)],[300])).
% fof(302, plain,![X2]:(possibly(X2)=not(necessarily(not(X2)))|~(op_possibly)),inference(shift_quantors,[status(thm)],[301])).
% cnf(303,plain,(possibly(X1)=not(necessarily(not(X1)))|~op_possibly),inference(split_conjunct,[status(thm)],[302])).
% fof(308, plain,((~(modus_tollens)|![X1]:![X4]:is_a_theorem(implies(implies(not(X4),not(X1)),implies(X1,X4))))&(?[X1]:?[X4]:~(is_a_theorem(implies(implies(not(X4),not(X1)),implies(X1,X4))))|modus_tollens)),inference(fof_nnf,[status(thm)],[59])).
% fof(309, plain,((~(modus_tollens)|![X5]:![X6]:is_a_theorem(implies(implies(not(X6),not(X5)),implies(X5,X6))))&(?[X7]:?[X8]:~(is_a_theorem(implies(implies(not(X8),not(X7)),implies(X7,X8))))|modus_tollens)),inference(variable_rename,[status(thm)],[308])).
% fof(310, plain,((~(modus_tollens)|![X5]:![X6]:is_a_theorem(implies(implies(not(X6),not(X5)),implies(X5,X6))))&(~(is_a_theorem(implies(implies(not(esk53_0),not(esk52_0)),implies(esk52_0,esk53_0))))|modus_tollens)),inference(skolemize,[status(esa)],[309])).
% fof(311, plain,![X5]:![X6]:((is_a_theorem(implies(implies(not(X6),not(X5)),implies(X5,X6)))|~(modus_tollens))&(~(is_a_theorem(implies(implies(not(esk53_0),not(esk52_0)),implies(esk52_0,esk53_0))))|modus_tollens)),inference(shift_quantors,[status(thm)],[310])).
% cnf(313,plain,(is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens),inference(split_conjunct,[status(thm)],[311])).
% fof(314, plain,((~(and_1)|![X1]:![X4]:is_a_theorem(implies(and(X1,X4),X1)))&(?[X1]:?[X4]:~(is_a_theorem(implies(and(X1,X4),X1)))|and_1)),inference(fof_nnf,[status(thm)],[60])).
% fof(315, plain,((~(and_1)|![X5]:![X6]:is_a_theorem(implies(and(X5,X6),X5)))&(?[X7]:?[X8]:~(is_a_theorem(implies(and(X7,X8),X7)))|and_1)),inference(variable_rename,[status(thm)],[314])).
% fof(316, plain,((~(and_1)|![X5]:![X6]:is_a_theorem(implies(and(X5,X6),X5)))&(~(is_a_theorem(implies(and(esk54_0,esk55_0),esk54_0)))|and_1)),inference(skolemize,[status(esa)],[315])).
% fof(317, plain,![X5]:![X6]:((is_a_theorem(implies(and(X5,X6),X5))|~(and_1))&(~(is_a_theorem(implies(and(esk54_0,esk55_0),esk54_0)))|and_1)),inference(shift_quantors,[status(thm)],[316])).
% cnf(319,plain,(is_a_theorem(implies(and(X1,X2),X1))|~and_1),inference(split_conjunct,[status(thm)],[317])).
% fof(326, plain,((~(and_3)|![X1]:![X4]:is_a_theorem(implies(X1,implies(X4,and(X1,X4)))))&(?[X1]:?[X4]:~(is_a_theorem(implies(X1,implies(X4,and(X1,X4)))))|and_3)),inference(fof_nnf,[status(thm)],[62])).
% fof(327, plain,((~(and_3)|![X5]:![X6]:is_a_theorem(implies(X5,implies(X6,and(X5,X6)))))&(?[X7]:?[X8]:~(is_a_theorem(implies(X7,implies(X8,and(X7,X8)))))|and_3)),inference(variable_rename,[status(thm)],[326])).
% fof(328, plain,((~(and_3)|![X5]:![X6]:is_a_theorem(implies(X5,implies(X6,and(X5,X6)))))&(~(is_a_theorem(implies(esk58_0,implies(esk59_0,and(esk58_0,esk59_0)))))|and_3)),inference(skolemize,[status(esa)],[327])).
% fof(329, plain,![X5]:![X6]:((is_a_theorem(implies(X5,implies(X6,and(X5,X6))))|~(and_3))&(~(is_a_theorem(implies(esk58_0,implies(esk59_0,and(esk58_0,esk59_0)))))|and_3)),inference(shift_quantors,[status(thm)],[328])).
% cnf(331,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3),inference(split_conjunct,[status(thm)],[329])).
% fof(422, plain,(~(op_strict_implies)|![X1]:![X4]:strict_implies(X1,X4)=necessarily(implies(X1,X4))),inference(fof_nnf,[status(thm)],[78])).
% fof(423, plain,(~(op_strict_implies)|![X5]:![X6]:strict_implies(X5,X6)=necessarily(implies(X5,X6))),inference(variable_rename,[status(thm)],[422])).
% fof(424, plain,![X5]:![X6]:(strict_implies(X5,X6)=necessarily(implies(X5,X6))|~(op_strict_implies)),inference(shift_quantors,[status(thm)],[423])).
% cnf(425,plain,(strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies),inference(split_conjunct,[status(thm)],[424])).
% fof(430, plain,((~(substitution_of_equivalents)|![X1]:![X4]:(~(is_a_theorem(equiv(X1,X4)))|X1=X4))&(?[X1]:?[X4]:(is_a_theorem(equiv(X1,X4))&~(X1=X4))|substitution_of_equivalents)),inference(fof_nnf,[status(thm)],[80])).
% fof(431, plain,((~(substitution_of_equivalents)|![X5]:![X6]:(~(is_a_theorem(equiv(X5,X6)))|X5=X6))&(?[X7]:?[X8]:(is_a_theorem(equiv(X7,X8))&~(X7=X8))|substitution_of_equivalents)),inference(variable_rename,[status(thm)],[430])).
% fof(432, plain,((~(substitution_of_equivalents)|![X5]:![X6]:(~(is_a_theorem(equiv(X5,X6)))|X5=X6))&((is_a_theorem(equiv(esk90_0,esk91_0))&~(esk90_0=esk91_0))|substitution_of_equivalents)),inference(skolemize,[status(esa)],[431])).
% fof(433, plain,![X5]:![X6]:(((~(is_a_theorem(equiv(X5,X6)))|X5=X6)|~(substitution_of_equivalents))&((is_a_theorem(equiv(esk90_0,esk91_0))&~(esk90_0=esk91_0))|substitution_of_equivalents)),inference(shift_quantors,[status(thm)],[432])).
% fof(434, plain,![X5]:![X6]:(((~(is_a_theorem(equiv(X5,X6)))|X5=X6)|~(substitution_of_equivalents))&((is_a_theorem(equiv(esk90_0,esk91_0))|substitution_of_equivalents)&(~(esk90_0=esk91_0)|substitution_of_equivalents))),inference(distribute,[status(thm)],[433])).
% cnf(437,plain,(X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))),inference(split_conjunct,[status(thm)],[434])).
% fof(444, plain,(~(op_or)|![X1]:![X4]:or(X1,X4)=not(and(not(X1),not(X4)))),inference(fof_nnf,[status(thm)],[82])).
% fof(445, plain,(~(op_or)|![X5]:![X6]:or(X5,X6)=not(and(not(X5),not(X6)))),inference(variable_rename,[status(thm)],[444])).
% fof(446, plain,![X5]:![X6]:(or(X5,X6)=not(and(not(X5),not(X6)))|~(op_or)),inference(shift_quantors,[status(thm)],[445])).
% cnf(447,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[446])).
% fof(452, plain,(~(op_implies_and)|![X1]:![X4]:implies(X1,X4)=not(and(X1,not(X4)))),inference(fof_nnf,[status(thm)],[84])).
% fof(453, plain,(~(op_implies_and)|![X5]:![X6]:implies(X5,X6)=not(and(X5,not(X6)))),inference(variable_rename,[status(thm)],[452])).
% fof(454, plain,![X5]:![X6]:(implies(X5,X6)=not(and(X5,not(X6)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[453])).
% cnf(455,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[454])).
% fof(460, plain,(~(op_equiv)|![X1]:![X4]:equiv(X1,X4)=and(implies(X1,X4),implies(X4,X1))),inference(fof_nnf,[status(thm)],[86])).
% fof(461, plain,(~(op_equiv)|![X5]:![X6]:equiv(X5,X6)=and(implies(X5,X6),implies(X6,X5))),inference(variable_rename,[status(thm)],[460])).
% fof(462, plain,![X5]:![X6]:(equiv(X5,X6)=and(implies(X5,X6),implies(X6,X5))|~(op_equiv)),inference(shift_quantors,[status(thm)],[461])).
% cnf(463,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[462])).
% cnf(465,negated_conjecture,(~axiom_m9),inference(split_conjunct,[status(thm)],[90])).
% cnf(475,plain,(is_a_theorem(necessarily(X1))|$false|~is_a_theorem(X1)),inference(rw,[status(thm)],[231,158,theory(equality)])).
% cnf(476,plain,(is_a_theorem(necessarily(X1))|~is_a_theorem(X1)),inference(cn,[status(thm)],[475,theory(equality)])).
% cnf(477,plain,(~is_a_theorem(strict_implies(possibly(possibly(esk4_0)),possibly(esk4_0)))),inference(sr,[status(thm)],[108,465,theory(equality)])).
% cnf(485,plain,(X1=X2|$false|~is_a_theorem(equiv(X1,X2))),inference(rw,[status(thm)],[437,215,theory(equality)])).
% cnf(486,plain,(X1=X2|~is_a_theorem(equiv(X1,X2))),inference(cn,[status(thm)],[485,theory(equality)])).
% cnf(487,plain,(is_a_theorem(implies(necessarily(X1),X1))|$false),inference(rw,[status(thm)],[175,160,theory(equality)])).
% cnf(488,plain,(is_a_theorem(implies(necessarily(X1),X1))),inference(cn,[status(thm)],[487,theory(equality)])).
% cnf(492,plain,(not(necessarily(not(X1)))=possibly(X1)|$false),inference(rw,[status(thm)],[303,157,theory(equality)])).
% cnf(493,plain,(not(necessarily(not(X1)))=possibly(X1)),inference(cn,[status(thm)],[492,theory(equality)])).
% cnf(494,plain,(not(necessarily(possibly(X1)))=possibly(necessarily(not(X1)))),inference(spm,[status(thm)],[493,493,theory(equality)])).
% cnf(496,plain,(is_a_theorem(implies(X1,implies(X2,X1)))|$false),inference(rw,[status(thm)],[255,145,theory(equality)])).
% cnf(497,plain,(is_a_theorem(implies(X1,implies(X2,X1)))),inference(cn,[status(thm)],[496,theory(equality)])).
% cnf(507,plain,(is_a_theorem(implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[319,148,theory(equality)])).
% cnf(508,plain,(is_a_theorem(implies(and(X1,X2),X1))),inference(cn,[status(thm)],[507,theory(equality)])).
% cnf(512,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(rw,[status(thm)],[249,143,theory(equality)])).
% cnf(513,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(cn,[status(thm)],[512,theory(equality)])).
% cnf(514,plain,(is_a_theorem(X1)|~is_a_theorem(necessarily(X1))),inference(spm,[status(thm)],[513,488,theory(equality)])).
% cnf(520,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)|$false),inference(rw,[status(thm)],[425,162,theory(equality)])).
% cnf(521,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)),inference(cn,[status(thm)],[520,theory(equality)])).
% cnf(522,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(implies(X1,X2))),inference(spm,[status(thm)],[476,521,theory(equality)])).
% cnf(524,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[455,213,theory(equality)])).
% cnf(525,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[524,theory(equality)])).
% cnf(530,plain,(is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|$false),inference(rw,[status(thm)],[285,103,theory(equality)])).
% cnf(531,plain,(is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))),inference(cn,[status(thm)],[530,theory(equality)])).
% cnf(535,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[447,525,theory(equality)])).
% cnf(536,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[535,212,theory(equality)])).
% cnf(537,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[536,theory(equality)])).
% cnf(541,plain,(necessarily(or(X1,X2))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[521,537,theory(equality)])).
% cnf(562,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|$false),inference(rw,[status(thm)],[331,150,theory(equality)])).
% cnf(563,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))),inference(cn,[status(thm)],[562,theory(equality)])).
% cnf(564,plain,(is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)),inference(spm,[status(thm)],[513,563,theory(equality)])).
% cnf(576,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[463,214,theory(equality)])).
% cnf(577,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[576,theory(equality)])).
% cnf(578,plain,(X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))),inference(spm,[status(thm)],[486,577,theory(equality)])).
% cnf(590,plain,(is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))|~modus_tollens),inference(rw,[status(thm)],[313,537,theory(equality)])).
% cnf(591,plain,(is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))|$false),inference(rw,[status(thm)],[590,144,theory(equality)])).
% cnf(592,plain,(is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))),inference(cn,[status(thm)],[591,theory(equality)])).
% cnf(593,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))),inference(spm,[status(thm)],[513,592,theory(equality)])).
% cnf(597,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|$false),inference(rw,[status(thm)],[261,146,theory(equality)])).
% cnf(598,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))),inference(cn,[status(thm)],[597,theory(equality)])).
% cnf(599,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))),inference(spm,[status(thm)],[513,598,theory(equality)])).
% cnf(679,plain,(is_a_theorem(strict_implies(X1,implies(X2,X1)))),inference(spm,[status(thm)],[522,497,theory(equality)])).
% cnf(838,plain,(is_a_theorem(implies(and(X1,not(X2)),X3))|~is_a_theorem(or(X3,implies(X1,X2)))),inference(spm,[status(thm)],[593,525,theory(equality)])).
% cnf(858,plain,(is_a_theorem(or(X1,X2))|~is_a_theorem(strict_implies(not(X1),X2))),inference(spm,[status(thm)],[514,541,theory(equality)])).
% cnf(869,plain,(is_a_theorem(or(X1,implies(X2,not(X1))))),inference(spm,[status(thm)],[858,679,theory(equality)])).
% cnf(913,plain,(is_a_theorem(implies(X1,X1))),inference(spm,[status(thm)],[599,497,theory(equality)])).
% cnf(914,plain,(is_a_theorem(implies(X1,and(X1,X1)))),inference(spm,[status(thm)],[599,563,theory(equality)])).
% cnf(919,plain,(is_a_theorem(strict_implies(X1,X1))),inference(spm,[status(thm)],[522,913,theory(equality)])).
% cnf(1208,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(spm,[status(thm)],[513,564,theory(equality)])).
% cnf(1217,plain,(X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))),inference(spm,[status(thm)],[578,1208,theory(equality)])).
% cnf(1247,plain,(necessarily(possibly(X1))=possibly(X1)|~is_a_theorem(implies(necessarily(possibly(X1)),possibly(X1)))),inference(spm,[status(thm)],[1217,531,theory(equality)])).
% cnf(1252,plain,(and(X1,X1)=X1|~is_a_theorem(implies(and(X1,X1),X1))),inference(spm,[status(thm)],[1217,914,theory(equality)])).
% cnf(1259,plain,(necessarily(possibly(X1))=possibly(X1)|$false),inference(rw,[status(thm)],[1247,488,theory(equality)])).
% cnf(1260,plain,(necessarily(possibly(X1))=possibly(X1)),inference(cn,[status(thm)],[1259,theory(equality)])).
% cnf(1261,plain,(and(X1,X1)=X1|$false),inference(rw,[status(thm)],[1252,508,theory(equality)])).
% cnf(1262,plain,(and(X1,X1)=X1),inference(cn,[status(thm)],[1261,theory(equality)])).
% cnf(1307,plain,(not(possibly(X1))=possibly(necessarily(not(X1)))),inference(rw,[status(thm)],[494,1260,theory(equality)])).
% cnf(10252,plain,(is_a_theorem(implies(and(X1,not(not(X2))),X2))),inference(spm,[status(thm)],[838,869,theory(equality)])).
% cnf(10300,plain,(is_a_theorem(implies(not(not(X1)),X1))),inference(spm,[status(thm)],[10252,1262,theory(equality)])).
% cnf(10312,plain,(is_a_theorem(or(not(X1),X1))),inference(rw,[status(thm)],[10300,537,theory(equality)])).
% cnf(10334,plain,(is_a_theorem(implies(X1,not(not(X1))))),inference(spm,[status(thm)],[593,10312,theory(equality)])).
% cnf(10376,plain,(not(not(X1))=X1|~is_a_theorem(implies(not(not(X1)),X1))),inference(spm,[status(thm)],[1217,10334,theory(equality)])).
% cnf(10409,plain,(not(not(X1))=X1|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[10376,537,theory(equality)]),10312,theory(equality)])).
% cnf(10410,plain,(not(not(X1))=X1),inference(cn,[status(thm)],[10409,theory(equality)])).
% cnf(10508,plain,(not(possibly(X1))=necessarily(not(X1))),inference(spm,[status(thm)],[10410,493,theory(equality)])).
% cnf(24444,plain,(possibly(necessarily(not(X1)))=necessarily(not(X1))),inference(rw,[status(thm)],[1307,10508,theory(equality)])).
% cnf(24483,plain,(possibly(necessarily(possibly(X1)))=necessarily(possibly(X1))),inference(spm,[status(thm)],[24444,493,theory(equality)])).
% cnf(24540,plain,(possibly(possibly(X1))=necessarily(possibly(X1))),inference(rw,[status(thm)],[24483,1260,theory(equality)])).
% cnf(24541,plain,(possibly(possibly(X1))=possibly(X1)),inference(rw,[status(thm)],[24540,1260,theory(equality)])).
% cnf(24603,plain,($false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[477,24541,theory(equality)]),919,theory(equality)])).
% cnf(24604,plain,($false),inference(cn,[status(thm)],[24603,theory(equality)])).
% cnf(24605,plain,($false),24604,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 2362
% # ...of these trivial : 77
% # ...subsumed : 1668
% # ...remaining for further processing: 617
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 41
% # Backward-rewritten : 85
% # Generated clauses : 17385
% # ...of the previous two non-trivial : 15527
% # Contextual simplify-reflections : 387
% # Paramodulations : 17385
% # Factorizations : 0
% # Equation resolutions : 0
% # Current number of processed clauses: 491
% # Positive orientable unit clauses: 190
% # Positive unorientable unit clauses: 2
% # Negative unit clauses : 29
% # Non-unit-clauses : 270
% # Current number of unprocessed clauses: 11539
% # ...number of literals in the above : 26763
% # Clause-clause subsumption calls (NU) : 32479
% # Rec. Clause-clause subsumption calls : 32252
% # Unit Clause-clause subsumption calls : 1740
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 776
% # Indexed BW rewrite successes : 53
% # Backwards rewriting index: 607 leaves, 1.50+/-1.259 terms/leaf
% # Paramod-from index: 136 leaves, 1.60+/-1.368 terms/leaf
% # Paramod-into index: 548 leaves, 1.47+/-1.180 terms/leaf
% # -------------------------------------------------
% # User time : 0.526 s
% # System time : 0.013 s
% # Total time : 0.539 s
% # Maximum resident set size: 0 pages
% PrfWatch: 0.91 CPU 0.99 WC
% FINAL PrfWatch: 0.91 CPU 0.99 WC
% SZS output end Solution for /tmp/SystemOnTPTP7216/LCL535+1.tptp
%
%------------------------------------------------------------------------------