TSTP Solution File: LCL546+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : LCL546+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 : art09.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 13:54:08 EST 2010
% Result : Theorem 2.40s
% Output : Solution 2.40s
% 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/SystemOnTPTP28003/LCL546+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP28003/LCL546+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP28003/LCL546+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 28099
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 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_B,file('/tmp/SRASS.s.p', km4b_axiom_B)).
% fof(4, axiom,(axiom_m6<=>![X3]:is_a_theorem(strict_implies(X3,possibly(X3)))),file('/tmp/SRASS.s.p', axiom_m6)).
% 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', km4b_op_possibly)).
% fof(25, axiom,necessitation,file('/tmp/SRASS.s.p', km4b_necessitation)).
% fof(27, axiom,axiom_M,file('/tmp/SRASS.s.p', km4b_axiom_M)).
% fof(28, axiom,axiom_4,file('/tmp/SRASS.s.p', km4b_axiom_4)).
% fof(30, axiom,op_strict_implies,file('/tmp/SRASS.s.p', s1_0_op_strict_implies)).
% fof(33, axiom,(axiom_M<=>![X3]:is_a_theorem(implies(necessarily(X3),X3))),file('/tmp/SRASS.s.p', axiom_M)).
% fof(34, axiom,(axiom_4<=>![X3]:is_a_theorem(implies(necessarily(X3),necessarily(necessarily(X3))))),file('/tmp/SRASS.s.p', axiom_4)).
% fof(40, axiom,op_or,file('/tmp/SRASS.s.p', hilbert_op_or)).
% fof(41, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(42, axiom,op_equiv,file('/tmp/SRASS.s.p', hilbert_op_equiv)).
% fof(43, axiom,substitution_of_equivalents,file('/tmp/SRASS.s.p', substitution_of_equivalents)).
% fof(47, axiom,(necessitation<=>![X3]:(is_a_theorem(X3)=>is_a_theorem(necessarily(X3)))),file('/tmp/SRASS.s.p', necessitation)).
% fof(49, axiom,(axiom_B<=>![X3]:is_a_theorem(implies(X3,necessarily(possibly(X3))))),file('/tmp/SRASS.s.p', axiom_B)).
% fof(50, axiom,(modus_ponens<=>![X3]:![X4]:((is_a_theorem(X3)&is_a_theorem(implies(X3,X4)))=>is_a_theorem(X4))),file('/tmp/SRASS.s.p', modus_ponens)).
% fof(51, axiom,(implies_1<=>![X3]:![X4]:is_a_theorem(implies(X3,implies(X4,X3)))),file('/tmp/SRASS.s.p', implies_1)).
% fof(52, axiom,(implies_2<=>![X3]:![X4]:is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4)))),file('/tmp/SRASS.s.p', implies_2)).
% fof(58, axiom,(op_possibly=>![X3]:possibly(X3)=not(necessarily(not(X3)))),file('/tmp/SRASS.s.p', op_possibly)).
% fof(60, axiom,(modus_tollens<=>![X3]:![X4]:is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4)))),file('/tmp/SRASS.s.p', modus_tollens)).
% fof(61, axiom,(and_1<=>![X3]:![X4]:is_a_theorem(implies(and(X3,X4),X3))),file('/tmp/SRASS.s.p', and_1)).
% fof(63, axiom,(and_3<=>![X3]:![X4]:is_a_theorem(implies(X3,implies(X4,and(X3,X4))))),file('/tmp/SRASS.s.p', and_3)).
% fof(79, axiom,(op_strict_implies=>![X3]:![X4]:strict_implies(X3,X4)=necessarily(implies(X3,X4))),file('/tmp/SRASS.s.p', op_strict_implies)).
% fof(81, axiom,(substitution_of_equivalents<=>![X3]:![X4]:(is_a_theorem(equiv(X3,X4))=>X3=X4)),file('/tmp/SRASS.s.p', substitution_of_equivalents)).
% fof(83, axiom,(op_implies_and=>![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(84, axiom,(op_or=>![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),file('/tmp/SRASS.s.p', op_or)).
% fof(87, axiom,(op_equiv=>![X3]:![X4]:equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(89, conjecture,axiom_m6,file('/tmp/SRASS.s.p', s1_0_m6s3m9b_axiom_m6)).
% fof(90, negated_conjecture,~(axiom_m6),inference(assume_negation,[status(cth)],[89])).
% fof(91, negated_conjecture,~(axiom_m6),inference(fof_simplification,[status(thm)],[90,theory(equality)])).
% cnf(104,plain,(axiom_B),inference(split_conjunct,[status(thm)],[3])).
% fof(105, plain,((~(axiom_m6)|![X3]:is_a_theorem(strict_implies(X3,possibly(X3))))&(?[X3]:~(is_a_theorem(strict_implies(X3,possibly(X3))))|axiom_m6)),inference(fof_nnf,[status(thm)],[4])).
% fof(106, plain,((~(axiom_m6)|![X4]:is_a_theorem(strict_implies(X4,possibly(X4))))&(?[X5]:~(is_a_theorem(strict_implies(X5,possibly(X5))))|axiom_m6)),inference(variable_rename,[status(thm)],[105])).
% fof(107, plain,((~(axiom_m6)|![X4]:is_a_theorem(strict_implies(X4,possibly(X4))))&(~(is_a_theorem(strict_implies(esk4_0,possibly(esk4_0))))|axiom_m6)),inference(skolemize,[status(esa)],[106])).
% fof(108, plain,![X4]:((is_a_theorem(strict_implies(X4,possibly(X4)))|~(axiom_m6))&(~(is_a_theorem(strict_implies(esk4_0,possibly(esk4_0))))|axiom_m6)),inference(shift_quantors,[status(thm)],[107])).
% cnf(109,plain,(axiom_m6|~is_a_theorem(strict_implies(esk4_0,possibly(esk4_0)))),inference(split_conjunct,[status(thm)],[108])).
% cnf(144,plain,(modus_ponens),inference(split_conjunct,[status(thm)],[10])).
% cnf(145,plain,(modus_tollens),inference(split_conjunct,[status(thm)],[11])).
% cnf(146,plain,(implies_1),inference(split_conjunct,[status(thm)],[12])).
% cnf(147,plain,(implies_2),inference(split_conjunct,[status(thm)],[13])).
% cnf(149,plain,(and_1),inference(split_conjunct,[status(thm)],[15])).
% cnf(151,plain,(and_3),inference(split_conjunct,[status(thm)],[17])).
% cnf(158,plain,(op_possibly),inference(split_conjunct,[status(thm)],[24])).
% cnf(159,plain,(necessitation),inference(split_conjunct,[status(thm)],[25])).
% cnf(161,plain,(axiom_M),inference(split_conjunct,[status(thm)],[27])).
% cnf(162,plain,(axiom_4),inference(split_conjunct,[status(thm)],[28])).
% cnf(164,plain,(op_strict_implies),inference(split_conjunct,[status(thm)],[30])).
% fof(172, plain,((~(axiom_M)|![X3]:is_a_theorem(implies(necessarily(X3),X3)))&(?[X3]:~(is_a_theorem(implies(necessarily(X3),X3)))|axiom_M)),inference(fof_nnf,[status(thm)],[33])).
% fof(173, plain,((~(axiom_M)|![X4]:is_a_theorem(implies(necessarily(X4),X4)))&(?[X5]:~(is_a_theorem(implies(necessarily(X5),X5)))|axiom_M)),inference(variable_rename,[status(thm)],[172])).
% fof(174, plain,((~(axiom_M)|![X4]:is_a_theorem(implies(necessarily(X4),X4)))&(~(is_a_theorem(implies(necessarily(esk16_0),esk16_0)))|axiom_M)),inference(skolemize,[status(esa)],[173])).
% fof(175, plain,![X4]:((is_a_theorem(implies(necessarily(X4),X4))|~(axiom_M))&(~(is_a_theorem(implies(necessarily(esk16_0),esk16_0)))|axiom_M)),inference(shift_quantors,[status(thm)],[174])).
% cnf(177,plain,(is_a_theorem(implies(necessarily(X1),X1))|~axiom_M),inference(split_conjunct,[status(thm)],[175])).
% fof(178, plain,((~(axiom_4)|![X3]:is_a_theorem(implies(necessarily(X3),necessarily(necessarily(X3)))))&(?[X3]:~(is_a_theorem(implies(necessarily(X3),necessarily(necessarily(X3)))))|axiom_4)),inference(fof_nnf,[status(thm)],[34])).
% fof(179, plain,((~(axiom_4)|![X4]:is_a_theorem(implies(necessarily(X4),necessarily(necessarily(X4)))))&(?[X5]:~(is_a_theorem(implies(necessarily(X5),necessarily(necessarily(X5)))))|axiom_4)),inference(variable_rename,[status(thm)],[178])).
% fof(180, plain,((~(axiom_4)|![X4]:is_a_theorem(implies(necessarily(X4),necessarily(necessarily(X4)))))&(~(is_a_theorem(implies(necessarily(esk17_0),necessarily(necessarily(esk17_0)))))|axiom_4)),inference(skolemize,[status(esa)],[179])).
% fof(181, plain,![X4]:((is_a_theorem(implies(necessarily(X4),necessarily(necessarily(X4))))|~(axiom_4))&(~(is_a_theorem(implies(necessarily(esk17_0),necessarily(necessarily(esk17_0)))))|axiom_4)),inference(shift_quantors,[status(thm)],[180])).
% cnf(183,plain,(is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_4),inference(split_conjunct,[status(thm)],[181])).
% cnf(214,plain,(op_or),inference(split_conjunct,[status(thm)],[40])).
% cnf(215,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[41])).
% cnf(216,plain,(op_equiv),inference(split_conjunct,[status(thm)],[42])).
% cnf(217,plain,(substitution_of_equivalents),inference(split_conjunct,[status(thm)],[43])).
% fof(226, plain,((~(necessitation)|![X3]:(~(is_a_theorem(X3))|is_a_theorem(necessarily(X3))))&(?[X3]:(is_a_theorem(X3)&~(is_a_theorem(necessarily(X3))))|necessitation)),inference(fof_nnf,[status(thm)],[47])).
% fof(227, plain,((~(necessitation)|![X4]:(~(is_a_theorem(X4))|is_a_theorem(necessarily(X4))))&(?[X5]:(is_a_theorem(X5)&~(is_a_theorem(necessarily(X5))))|necessitation)),inference(variable_rename,[status(thm)],[226])).
% fof(228, plain,((~(necessitation)|![X4]:(~(is_a_theorem(X4))|is_a_theorem(necessarily(X4))))&((is_a_theorem(esk30_0)&~(is_a_theorem(necessarily(esk30_0))))|necessitation)),inference(skolemize,[status(esa)],[227])).
% fof(229, plain,![X4]:(((~(is_a_theorem(X4))|is_a_theorem(necessarily(X4)))|~(necessitation))&((is_a_theorem(esk30_0)&~(is_a_theorem(necessarily(esk30_0))))|necessitation)),inference(shift_quantors,[status(thm)],[228])).
% fof(230, plain,![X4]:(((~(is_a_theorem(X4))|is_a_theorem(necessarily(X4)))|~(necessitation))&((is_a_theorem(esk30_0)|necessitation)&(~(is_a_theorem(necessarily(esk30_0)))|necessitation))),inference(distribute,[status(thm)],[229])).
% cnf(233,plain,(is_a_theorem(necessarily(X1))|~necessitation|~is_a_theorem(X1)),inference(split_conjunct,[status(thm)],[230])).
% fof(243, plain,((~(axiom_B)|![X3]:is_a_theorem(implies(X3,necessarily(possibly(X3)))))&(?[X3]:~(is_a_theorem(implies(X3,necessarily(possibly(X3)))))|axiom_B)),inference(fof_nnf,[status(thm)],[49])).
% fof(244, plain,((~(axiom_B)|![X4]:is_a_theorem(implies(X4,necessarily(possibly(X4)))))&(?[X5]:~(is_a_theorem(implies(X5,necessarily(possibly(X5)))))|axiom_B)),inference(variable_rename,[status(thm)],[243])).
% fof(245, plain,((~(axiom_B)|![X4]:is_a_theorem(implies(X4,necessarily(possibly(X4)))))&(~(is_a_theorem(implies(esk33_0,necessarily(possibly(esk33_0)))))|axiom_B)),inference(skolemize,[status(esa)],[244])).
% fof(246, plain,![X4]:((is_a_theorem(implies(X4,necessarily(possibly(X4))))|~(axiom_B))&(~(is_a_theorem(implies(esk33_0,necessarily(possibly(esk33_0)))))|axiom_B)),inference(shift_quantors,[status(thm)],[245])).
% cnf(248,plain,(is_a_theorem(implies(X1,necessarily(possibly(X1))))|~axiom_B),inference(split_conjunct,[status(thm)],[246])).
% fof(249, plain,((~(modus_ponens)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4)))&(?[X3]:?[X4]:((is_a_theorem(X3)&is_a_theorem(implies(X3,X4)))&~(is_a_theorem(X4)))|modus_ponens)),inference(fof_nnf,[status(thm)],[50])).
% fof(250, 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)],[249])).
% fof(251, plain,((~(modus_ponens)|![X5]:![X6]:((~(is_a_theorem(X5))|~(is_a_theorem(implies(X5,X6))))|is_a_theorem(X6)))&(((is_a_theorem(esk34_0)&is_a_theorem(implies(esk34_0,esk35_0)))&~(is_a_theorem(esk35_0)))|modus_ponens)),inference(skolemize,[status(esa)],[250])).
% fof(252, plain,![X5]:![X6]:((((~(is_a_theorem(X5))|~(is_a_theorem(implies(X5,X6))))|is_a_theorem(X6))|~(modus_ponens))&(((is_a_theorem(esk34_0)&is_a_theorem(implies(esk34_0,esk35_0)))&~(is_a_theorem(esk35_0)))|modus_ponens)),inference(shift_quantors,[status(thm)],[251])).
% fof(253, plain,![X5]:![X6]:((((~(is_a_theorem(X5))|~(is_a_theorem(implies(X5,X6))))|is_a_theorem(X6))|~(modus_ponens))&(((is_a_theorem(esk34_0)|modus_ponens)&(is_a_theorem(implies(esk34_0,esk35_0))|modus_ponens))&(~(is_a_theorem(esk35_0))|modus_ponens))),inference(distribute,[status(thm)],[252])).
% cnf(257,plain,(is_a_theorem(X1)|~modus_ponens|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)),inference(split_conjunct,[status(thm)],[253])).
% fof(258, plain,((~(implies_1)|![X3]:![X4]:is_a_theorem(implies(X3,implies(X4,X3))))&(?[X3]:?[X4]:~(is_a_theorem(implies(X3,implies(X4,X3))))|implies_1)),inference(fof_nnf,[status(thm)],[51])).
% fof(259, 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)],[258])).
% fof(260, plain,((~(implies_1)|![X5]:![X6]:is_a_theorem(implies(X5,implies(X6,X5))))&(~(is_a_theorem(implies(esk36_0,implies(esk37_0,esk36_0))))|implies_1)),inference(skolemize,[status(esa)],[259])).
% fof(261, plain,![X5]:![X6]:((is_a_theorem(implies(X5,implies(X6,X5)))|~(implies_1))&(~(is_a_theorem(implies(esk36_0,implies(esk37_0,esk36_0))))|implies_1)),inference(shift_quantors,[status(thm)],[260])).
% cnf(263,plain,(is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1),inference(split_conjunct,[status(thm)],[261])).
% fof(264, plain,((~(implies_2)|![X3]:![X4]:is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4))))&(?[X3]:?[X4]:~(is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4))))|implies_2)),inference(fof_nnf,[status(thm)],[52])).
% fof(265, 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)],[264])).
% fof(266, plain,((~(implies_2)|![X5]:![X6]:is_a_theorem(implies(implies(X5,implies(X5,X6)),implies(X5,X6))))&(~(is_a_theorem(implies(implies(esk38_0,implies(esk38_0,esk39_0)),implies(esk38_0,esk39_0))))|implies_2)),inference(skolemize,[status(esa)],[265])).
% fof(267, plain,![X5]:![X6]:((is_a_theorem(implies(implies(X5,implies(X5,X6)),implies(X5,X6)))|~(implies_2))&(~(is_a_theorem(implies(implies(esk38_0,implies(esk38_0,esk39_0)),implies(esk38_0,esk39_0))))|implies_2)),inference(shift_quantors,[status(thm)],[266])).
% cnf(269,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2),inference(split_conjunct,[status(thm)],[267])).
% fof(302, plain,(~(op_possibly)|![X3]:possibly(X3)=not(necessarily(not(X3)))),inference(fof_nnf,[status(thm)],[58])).
% fof(303, plain,(~(op_possibly)|![X4]:possibly(X4)=not(necessarily(not(X4)))),inference(variable_rename,[status(thm)],[302])).
% fof(304, plain,![X4]:(possibly(X4)=not(necessarily(not(X4)))|~(op_possibly)),inference(shift_quantors,[status(thm)],[303])).
% cnf(305,plain,(possibly(X1)=not(necessarily(not(X1)))|~op_possibly),inference(split_conjunct,[status(thm)],[304])).
% fof(310, plain,((~(modus_tollens)|![X3]:![X4]:is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4))))&(?[X3]:?[X4]:~(is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4))))|modus_tollens)),inference(fof_nnf,[status(thm)],[60])).
% fof(311, 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)],[310])).
% fof(312, 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)],[311])).
% fof(313, 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)],[312])).
% cnf(315,plain,(is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))|~modus_tollens),inference(split_conjunct,[status(thm)],[313])).
% fof(316, plain,((~(and_1)|![X3]:![X4]:is_a_theorem(implies(and(X3,X4),X3)))&(?[X3]:?[X4]:~(is_a_theorem(implies(and(X3,X4),X3)))|and_1)),inference(fof_nnf,[status(thm)],[61])).
% fof(317, 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)],[316])).
% fof(318, 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)],[317])).
% fof(319, 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)],[318])).
% cnf(321,plain,(is_a_theorem(implies(and(X1,X2),X1))|~and_1),inference(split_conjunct,[status(thm)],[319])).
% fof(328, plain,((~(and_3)|![X3]:![X4]:is_a_theorem(implies(X3,implies(X4,and(X3,X4)))))&(?[X3]:?[X4]:~(is_a_theorem(implies(X3,implies(X4,and(X3,X4)))))|and_3)),inference(fof_nnf,[status(thm)],[63])).
% fof(329, 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)],[328])).
% fof(330, 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)],[329])).
% fof(331, 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)],[330])).
% cnf(333,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3),inference(split_conjunct,[status(thm)],[331])).
% fof(424, plain,(~(op_strict_implies)|![X3]:![X4]:strict_implies(X3,X4)=necessarily(implies(X3,X4))),inference(fof_nnf,[status(thm)],[79])).
% fof(425, plain,(~(op_strict_implies)|![X5]:![X6]:strict_implies(X5,X6)=necessarily(implies(X5,X6))),inference(variable_rename,[status(thm)],[424])).
% fof(426, plain,![X5]:![X6]:(strict_implies(X5,X6)=necessarily(implies(X5,X6))|~(op_strict_implies)),inference(shift_quantors,[status(thm)],[425])).
% cnf(427,plain,(strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies),inference(split_conjunct,[status(thm)],[426])).
% fof(432, plain,((~(substitution_of_equivalents)|![X3]:![X4]:(~(is_a_theorem(equiv(X3,X4)))|X3=X4))&(?[X3]:?[X4]:(is_a_theorem(equiv(X3,X4))&~(X3=X4))|substitution_of_equivalents)),inference(fof_nnf,[status(thm)],[81])).
% fof(433, 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)],[432])).
% fof(434, 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)],[433])).
% fof(435, 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)],[434])).
% fof(436, 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)],[435])).
% cnf(439,plain,(X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))),inference(split_conjunct,[status(thm)],[436])).
% fof(446, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(fof_nnf,[status(thm)],[83])).
% fof(447, plain,(~(op_implies_and)|![X5]:![X6]:implies(X5,X6)=not(and(X5,not(X6)))),inference(variable_rename,[status(thm)],[446])).
% fof(448, plain,![X5]:![X6]:(implies(X5,X6)=not(and(X5,not(X6)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[447])).
% cnf(449,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[448])).
% fof(450, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(fof_nnf,[status(thm)],[84])).
% fof(451, plain,(~(op_or)|![X5]:![X6]:or(X5,X6)=not(and(not(X5),not(X6)))),inference(variable_rename,[status(thm)],[450])).
% fof(452, plain,![X5]:![X6]:(or(X5,X6)=not(and(not(X5),not(X6)))|~(op_or)),inference(shift_quantors,[status(thm)],[451])).
% cnf(453,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[452])).
% fof(462, plain,(~(op_equiv)|![X3]:![X4]:equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))),inference(fof_nnf,[status(thm)],[87])).
% fof(463, plain,(~(op_equiv)|![X5]:![X6]:equiv(X5,X6)=and(implies(X5,X6),implies(X6,X5))),inference(variable_rename,[status(thm)],[462])).
% fof(464, plain,![X5]:![X6]:(equiv(X5,X6)=and(implies(X5,X6),implies(X6,X5))|~(op_equiv)),inference(shift_quantors,[status(thm)],[463])).
% cnf(465,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[464])).
% cnf(467,negated_conjecture,(~axiom_m6),inference(split_conjunct,[status(thm)],[91])).
% cnf(476,plain,(~is_a_theorem(strict_implies(esk4_0,possibly(esk4_0)))),inference(sr,[status(thm)],[109,467,theory(equality)])).
% cnf(477,plain,(is_a_theorem(necessarily(X1))|$false|~is_a_theorem(X1)),inference(rw,[status(thm)],[233,159,theory(equality)])).
% cnf(478,plain,(is_a_theorem(necessarily(X1))|~is_a_theorem(X1)),inference(cn,[status(thm)],[477,theory(equality)])).
% cnf(488,plain,(X1=X2|$false|~is_a_theorem(equiv(X1,X2))),inference(rw,[status(thm)],[439,217,theory(equality)])).
% cnf(489,plain,(X1=X2|~is_a_theorem(equiv(X1,X2))),inference(cn,[status(thm)],[488,theory(equality)])).
% cnf(490,plain,(is_a_theorem(implies(necessarily(X1),X1))|$false),inference(rw,[status(thm)],[177,161,theory(equality)])).
% cnf(491,plain,(is_a_theorem(implies(necessarily(X1),X1))),inference(cn,[status(thm)],[490,theory(equality)])).
% cnf(495,plain,(not(necessarily(not(X1)))=possibly(X1)|$false),inference(rw,[status(thm)],[305,158,theory(equality)])).
% cnf(496,plain,(not(necessarily(not(X1)))=possibly(X1)),inference(cn,[status(thm)],[495,theory(equality)])).
% cnf(499,plain,(is_a_theorem(implies(X1,necessarily(possibly(X1))))|$false),inference(rw,[status(thm)],[248,104,theory(equality)])).
% cnf(500,plain,(is_a_theorem(implies(X1,necessarily(possibly(X1))))),inference(cn,[status(thm)],[499,theory(equality)])).
% cnf(501,plain,(is_a_theorem(implies(X1,implies(X2,X1)))|$false),inference(rw,[status(thm)],[263,146,theory(equality)])).
% cnf(502,plain,(is_a_theorem(implies(X1,implies(X2,X1)))),inference(cn,[status(thm)],[501,theory(equality)])).
% cnf(512,plain,(is_a_theorem(implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[321,149,theory(equality)])).
% cnf(513,plain,(is_a_theorem(implies(and(X1,X2),X1))),inference(cn,[status(thm)],[512,theory(equality)])).
% cnf(517,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(rw,[status(thm)],[257,144,theory(equality)])).
% cnf(518,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(cn,[status(thm)],[517,theory(equality)])).
% cnf(519,plain,(is_a_theorem(X1)|~is_a_theorem(necessarily(X1))),inference(spm,[status(thm)],[518,491,theory(equality)])).
% cnf(526,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)|$false),inference(rw,[status(thm)],[427,164,theory(equality)])).
% cnf(527,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)),inference(cn,[status(thm)],[526,theory(equality)])).
% cnf(528,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(implies(X1,X2))),inference(spm,[status(thm)],[478,527,theory(equality)])).
% cnf(530,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[449,215,theory(equality)])).
% cnf(531,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[530,theory(equality)])).
% cnf(536,plain,(is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))|$false),inference(rw,[status(thm)],[183,162,theory(equality)])).
% cnf(537,plain,(is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))),inference(cn,[status(thm)],[536,theory(equality)])).
% cnf(543,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[453,531,theory(equality)])).
% cnf(544,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[543,214,theory(equality)])).
% cnf(545,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[544,theory(equality)])).
% cnf(550,plain,(necessarily(or(X1,X2))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[527,545,theory(equality)])).
% cnf(571,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|$false),inference(rw,[status(thm)],[333,151,theory(equality)])).
% cnf(572,plain,(is_a_theorem(implies(X1,implies(X2,and(X1,X2))))),inference(cn,[status(thm)],[571,theory(equality)])).
% cnf(573,plain,(is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)),inference(spm,[status(thm)],[518,572,theory(equality)])).
% cnf(585,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[465,216,theory(equality)])).
% cnf(586,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[585,theory(equality)])).
% cnf(587,plain,(X1=X2|~is_a_theorem(and(implies(X1,X2),implies(X2,X1)))),inference(spm,[status(thm)],[489,586,theory(equality)])).
% cnf(599,plain,(is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))|~modus_tollens),inference(rw,[status(thm)],[315,545,theory(equality)])).
% cnf(600,plain,(is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))|$false),inference(rw,[status(thm)],[599,145,theory(equality)])).
% cnf(601,plain,(is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))),inference(cn,[status(thm)],[600,theory(equality)])).
% cnf(602,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))),inference(spm,[status(thm)],[518,601,theory(equality)])).
% cnf(606,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|$false),inference(rw,[status(thm)],[269,147,theory(equality)])).
% cnf(607,plain,(is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))),inference(cn,[status(thm)],[606,theory(equality)])).
% cnf(608,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))),inference(spm,[status(thm)],[518,607,theory(equality)])).
% cnf(694,plain,(is_a_theorem(strict_implies(X1,implies(X2,X1)))),inference(spm,[status(thm)],[528,502,theory(equality)])).
% cnf(696,plain,(is_a_theorem(strict_implies(X1,necessarily(possibly(X1))))),inference(spm,[status(thm)],[528,500,theory(equality)])).
% cnf(859,plain,(is_a_theorem(implies(and(X1,not(X2)),X3))|~is_a_theorem(or(X3,implies(X1,X2)))),inference(spm,[status(thm)],[602,531,theory(equality)])).
% cnf(875,plain,(is_a_theorem(or(X1,X2))|~is_a_theorem(strict_implies(not(X1),X2))),inference(spm,[status(thm)],[519,550,theory(equality)])).
% cnf(889,plain,(is_a_theorem(or(X1,implies(X2,not(X1))))),inference(spm,[status(thm)],[875,694,theory(equality)])).
% cnf(948,plain,(is_a_theorem(implies(X1,and(X1,X1)))),inference(spm,[status(thm)],[608,572,theory(equality)])).
% cnf(1334,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(spm,[status(thm)],[518,573,theory(equality)])).
% cnf(1343,plain,(X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))),inference(spm,[status(thm)],[587,1334,theory(equality)])).
% cnf(1425,plain,(necessarily(necessarily(X1))=necessarily(X1)|~is_a_theorem(implies(necessarily(necessarily(X1)),necessarily(X1)))),inference(spm,[status(thm)],[1343,537,theory(equality)])).
% cnf(1437,plain,(necessarily(possibly(X1))=X1|~is_a_theorem(implies(necessarily(possibly(X1)),X1))),inference(spm,[status(thm)],[1343,500,theory(equality)])).
% cnf(1438,plain,(and(X1,X1)=X1|~is_a_theorem(implies(and(X1,X1),X1))),inference(spm,[status(thm)],[1343,948,theory(equality)])).
% cnf(1446,plain,(necessarily(necessarily(X1))=necessarily(X1)|$false),inference(rw,[status(thm)],[1425,491,theory(equality)])).
% cnf(1447,plain,(necessarily(necessarily(X1))=necessarily(X1)),inference(cn,[status(thm)],[1446,theory(equality)])).
% cnf(1450,plain,(and(X1,X1)=X1|$false),inference(rw,[status(thm)],[1438,513,theory(equality)])).
% cnf(1451,plain,(and(X1,X1)=X1),inference(cn,[status(thm)],[1450,theory(equality)])).
% cnf(12519,plain,(is_a_theorem(implies(and(X1,not(not(X2))),X2))),inference(spm,[status(thm)],[859,889,theory(equality)])).
% cnf(14656,plain,(is_a_theorem(implies(not(not(X1)),X1))),inference(spm,[status(thm)],[12519,1451,theory(equality)])).
% cnf(14671,plain,(is_a_theorem(or(not(X1),X1))),inference(rw,[status(thm)],[14656,545,theory(equality)])).
% cnf(14697,plain,(is_a_theorem(implies(X1,not(not(X1))))),inference(spm,[status(thm)],[602,14671,theory(equality)])).
% cnf(14748,plain,(not(not(X1))=X1|~is_a_theorem(implies(not(not(X1)),X1))),inference(spm,[status(thm)],[1343,14697,theory(equality)])).
% cnf(14787,plain,(not(not(X1))=X1|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[14748,545,theory(equality)]),14671,theory(equality)])).
% cnf(14788,plain,(not(not(X1))=X1),inference(cn,[status(thm)],[14787,theory(equality)])).
% cnf(14806,plain,(not(necessarily(X1))=possibly(not(X1))),inference(spm,[status(thm)],[496,14788,theory(equality)])).
% cnf(15316,plain,(possibly(possibly(X1))=not(necessarily(necessarily(not(X1))))),inference(spm,[status(thm)],[14806,496,theory(equality)])).
% cnf(15364,plain,(possibly(possibly(X1))=possibly(X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[15316,1447,theory(equality)]),496,theory(equality)])).
% cnf(35459,plain,(necessarily(possibly(X1))=possibly(X1)|~is_a_theorem(implies(necessarily(possibly(X1)),possibly(X1)))),inference(spm,[status(thm)],[1437,15364,theory(equality)])).
% cnf(35497,plain,(necessarily(possibly(X1))=possibly(X1)|$false),inference(rw,[status(thm)],[35459,491,theory(equality)])).
% cnf(35498,plain,(necessarily(possibly(X1))=possibly(X1)),inference(cn,[status(thm)],[35497,theory(equality)])).
% cnf(35644,plain,(is_a_theorem(strict_implies(X1,possibly(X1)))),inference(rw,[status(thm)],[696,35498,theory(equality)])).
% cnf(37971,plain,($false),inference(rw,[status(thm)],[476,35644,theory(equality)])).
% cnf(37972,plain,($false),inference(cn,[status(thm)],[37971,theory(equality)])).
% cnf(37973,plain,($false),37972,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 3248
% # ...of these trivial : 102
% # ...subsumed : 2412
% # ...remaining for further processing: 734
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 18
% # Backward-rewritten : 170
% # Generated clauses : 26946
% # ...of the previous two non-trivial : 23707
% # Contextual simplify-reflections : 645
% # Paramodulations : 26946
% # Factorizations : 0
% # Equation resolutions : 0
% # Current number of processed clauses: 546
% # Positive orientable unit clauses: 212
% # Positive unorientable unit clauses: 2
% # Negative unit clauses : 4
% # Non-unit-clauses : 328
% # Current number of unprocessed clauses: 14787
% # ...number of literals in the above : 37322
% # Clause-clause subsumption calls (NU) : 54942
% # Rec. Clause-clause subsumption calls : 54799
% # Unit Clause-clause subsumption calls : 1789
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 1135
% # Indexed BW rewrite successes : 68
% # Backwards rewriting index: 629 leaves, 1.56+/-1.361 terms/leaf
% # Paramod-from index: 158 leaves, 1.62+/-1.561 terms/leaf
% # Paramod-into index: 559 leaves, 1.53+/-1.311 terms/leaf
% # -------------------------------------------------
% # User time : 0.812 s
% # System time : 0.030 s
% # Total time : 0.842 s
% # Maximum resident set size: 0 pages
% PrfWatch: 1.36 CPU 1.46 WC
% FINAL PrfWatch: 1.36 CPU 1.46 WC
% SZS output end Solution for /tmp/SystemOnTPTP28003/LCL546+1.tptp
%
%------------------------------------------------------------------------------