TSTP Solution File: LCL518+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : LCL518+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 13:46:35 EST 2010
% Result : Theorem 4.21s
% Output : Solution 4.21s
% 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/SystemOnTPTP32410/LCL518+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP32410/LCL518+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP32410/LCL518+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 32506
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 WC
% PrfWatch: 1.91 CPU 2.01 WC
% # Preprocessing time : 0.018 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(1, axiom,(r1<=>![X1]:is_a_theorem(implies(or(X1,X1),X1))),file('/tmp/SRASS.s.p', r1)).
% fof(2, axiom,modus_ponens,file('/tmp/SRASS.s.p', rosser_modus_ponens)).
% fof(3, axiom,kn1,file('/tmp/SRASS.s.p', rosser_kn1)).
% fof(4, axiom,kn2,file('/tmp/SRASS.s.p', rosser_kn2)).
% fof(5, axiom,kn3,file('/tmp/SRASS.s.p', rosser_kn3)).
% fof(6, axiom,op_implies_or,file('/tmp/SRASS.s.p', principia_op_implies_or)).
% fof(14, axiom,op_or,file('/tmp/SRASS.s.p', rosser_op_or)).
% fof(15, axiom,op_implies_and,file('/tmp/SRASS.s.p', rosser_op_implies_and)).
% fof(16, axiom,op_equiv,file('/tmp/SRASS.s.p', rosser_op_equiv)).
% fof(17, axiom,substitution_of_equivalents,file('/tmp/SRASS.s.p', substitution_of_equivalents)).
% fof(18, axiom,op_and,file('/tmp/SRASS.s.p', principia_op_and)).
% fof(20, axiom,(modus_ponens<=>![X2]:![X3]:((is_a_theorem(X2)&is_a_theorem(implies(X2,X3)))=>is_a_theorem(X3))),file('/tmp/SRASS.s.p', modus_ponens)).
% fof(25, axiom,(op_or=>![X2]:![X3]:or(X2,X3)=not(and(not(X2),not(X3)))),file('/tmp/SRASS.s.p', op_or)).
% fof(26, axiom,(op_and=>![X2]:![X3]:and(X2,X3)=not(or(not(X2),not(X3)))),file('/tmp/SRASS.s.p', op_and)).
% fof(30, axiom,(kn1<=>![X1]:is_a_theorem(implies(X1,and(X1,X1)))),file('/tmp/SRASS.s.p', kn1)).
% fof(31, axiom,(kn2<=>![X1]:![X5]:is_a_theorem(implies(and(X1,X5),X1))),file('/tmp/SRASS.s.p', kn2)).
% fof(32, axiom,(op_implies_or=>![X2]:![X3]:implies(X2,X3)=or(not(X2),X3)),file('/tmp/SRASS.s.p', op_implies_or)).
% fof(39, axiom,(kn3<=>![X1]:![X5]:![X6]:is_a_theorem(implies(implies(X1,X5),implies(not(and(X5,X6)),not(and(X6,X1)))))),file('/tmp/SRASS.s.p', kn3)).
% fof(40, axiom,(op_implies_and=>![X2]:![X3]:implies(X2,X3)=not(and(X2,not(X3)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(41, axiom,(op_equiv=>![X2]:![X3]:equiv(X2,X3)=and(implies(X2,X3),implies(X3,X2))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(42, axiom,(substitution_of_equivalents<=>![X2]:![X3]:(is_a_theorem(equiv(X2,X3))=>X2=X3)),file('/tmp/SRASS.s.p', substitution_of_equivalents)).
% fof(43, conjecture,r1,file('/tmp/SRASS.s.p', principia_r1)).
% fof(44, negated_conjecture,~(r1),inference(assume_negation,[status(cth)],[43])).
% fof(45, negated_conjecture,~(r1),inference(fof_simplification,[status(thm)],[44,theory(equality)])).
% fof(46, plain,((~(r1)|![X1]:is_a_theorem(implies(or(X1,X1),X1)))&(?[X1]:~(is_a_theorem(implies(or(X1,X1),X1)))|r1)),inference(fof_nnf,[status(thm)],[1])).
% fof(47, plain,((~(r1)|![X2]:is_a_theorem(implies(or(X2,X2),X2)))&(?[X3]:~(is_a_theorem(implies(or(X3,X3),X3)))|r1)),inference(variable_rename,[status(thm)],[46])).
% fof(48, plain,((~(r1)|![X2]:is_a_theorem(implies(or(X2,X2),X2)))&(~(is_a_theorem(implies(or(esk1_0,esk1_0),esk1_0)))|r1)),inference(skolemize,[status(esa)],[47])).
% fof(49, plain,![X2]:((is_a_theorem(implies(or(X2,X2),X2))|~(r1))&(~(is_a_theorem(implies(or(esk1_0,esk1_0),esk1_0)))|r1)),inference(shift_quantors,[status(thm)],[48])).
% cnf(50,plain,(r1|~is_a_theorem(implies(or(esk1_0,esk1_0),esk1_0))),inference(split_conjunct,[status(thm)],[49])).
% cnf(52,plain,(modus_ponens),inference(split_conjunct,[status(thm)],[2])).
% cnf(53,plain,(kn1),inference(split_conjunct,[status(thm)],[3])).
% cnf(54,plain,(kn2),inference(split_conjunct,[status(thm)],[4])).
% cnf(55,plain,(kn3),inference(split_conjunct,[status(thm)],[5])).
% cnf(56,plain,(op_implies_or),inference(split_conjunct,[status(thm)],[6])).
% cnf(99,plain,(op_or),inference(split_conjunct,[status(thm)],[14])).
% cnf(100,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[15])).
% cnf(101,plain,(op_equiv),inference(split_conjunct,[status(thm)],[16])).
% cnf(102,plain,(substitution_of_equivalents),inference(split_conjunct,[status(thm)],[17])).
% cnf(103,plain,(op_and),inference(split_conjunct,[status(thm)],[18])).
% fof(105, plain,((~(modus_ponens)|![X2]:![X3]:((~(is_a_theorem(X2))|~(is_a_theorem(implies(X2,X3))))|is_a_theorem(X3)))&(?[X2]:?[X3]:((is_a_theorem(X2)&is_a_theorem(implies(X2,X3)))&~(is_a_theorem(X3)))|modus_ponens)),inference(fof_nnf,[status(thm)],[20])).
% fof(106, plain,((~(modus_ponens)|![X4]:![X5]:((~(is_a_theorem(X4))|~(is_a_theorem(implies(X4,X5))))|is_a_theorem(X5)))&(?[X6]:?[X7]:((is_a_theorem(X6)&is_a_theorem(implies(X6,X7)))&~(is_a_theorem(X7)))|modus_ponens)),inference(variable_rename,[status(thm)],[105])).
% fof(107, plain,((~(modus_ponens)|![X4]:![X5]:((~(is_a_theorem(X4))|~(is_a_theorem(implies(X4,X5))))|is_a_theorem(X5)))&(((is_a_theorem(esk19_0)&is_a_theorem(implies(esk19_0,esk20_0)))&~(is_a_theorem(esk20_0)))|modus_ponens)),inference(skolemize,[status(esa)],[106])).
% fof(108, plain,![X4]:![X5]:((((~(is_a_theorem(X4))|~(is_a_theorem(implies(X4,X5))))|is_a_theorem(X5))|~(modus_ponens))&(((is_a_theorem(esk19_0)&is_a_theorem(implies(esk19_0,esk20_0)))&~(is_a_theorem(esk20_0)))|modus_ponens)),inference(shift_quantors,[status(thm)],[107])).
% fof(109, plain,![X4]:![X5]:((((~(is_a_theorem(X4))|~(is_a_theorem(implies(X4,X5))))|is_a_theorem(X5))|~(modus_ponens))&(((is_a_theorem(esk19_0)|modus_ponens)&(is_a_theorem(implies(esk19_0,esk20_0))|modus_ponens))&(~(is_a_theorem(esk20_0))|modus_ponens))),inference(distribute,[status(thm)],[108])).
% cnf(113,plain,(is_a_theorem(X1)|~modus_ponens|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)),inference(split_conjunct,[status(thm)],[109])).
% fof(138, plain,(~(op_or)|![X2]:![X3]:or(X2,X3)=not(and(not(X2),not(X3)))),inference(fof_nnf,[status(thm)],[25])).
% fof(139, plain,(~(op_or)|![X4]:![X5]:or(X4,X5)=not(and(not(X4),not(X5)))),inference(variable_rename,[status(thm)],[138])).
% fof(140, plain,![X4]:![X5]:(or(X4,X5)=not(and(not(X4),not(X5)))|~(op_or)),inference(shift_quantors,[status(thm)],[139])).
% cnf(141,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[140])).
% fof(142, plain,(~(op_and)|![X2]:![X3]:and(X2,X3)=not(or(not(X2),not(X3)))),inference(fof_nnf,[status(thm)],[26])).
% fof(143, plain,(~(op_and)|![X4]:![X5]:and(X4,X5)=not(or(not(X4),not(X5)))),inference(variable_rename,[status(thm)],[142])).
% fof(144, plain,![X4]:![X5]:(and(X4,X5)=not(or(not(X4),not(X5)))|~(op_and)),inference(shift_quantors,[status(thm)],[143])).
% cnf(145,plain,(and(X1,X2)=not(or(not(X1),not(X2)))|~op_and),inference(split_conjunct,[status(thm)],[144])).
% fof(164, plain,((~(kn1)|![X1]:is_a_theorem(implies(X1,and(X1,X1))))&(?[X1]:~(is_a_theorem(implies(X1,and(X1,X1))))|kn1)),inference(fof_nnf,[status(thm)],[30])).
% fof(165, plain,((~(kn1)|![X2]:is_a_theorem(implies(X2,and(X2,X2))))&(?[X3]:~(is_a_theorem(implies(X3,and(X3,X3))))|kn1)),inference(variable_rename,[status(thm)],[164])).
% fof(166, plain,((~(kn1)|![X2]:is_a_theorem(implies(X2,and(X2,X2))))&(~(is_a_theorem(implies(esk37_0,and(esk37_0,esk37_0))))|kn1)),inference(skolemize,[status(esa)],[165])).
% fof(167, plain,![X2]:((is_a_theorem(implies(X2,and(X2,X2)))|~(kn1))&(~(is_a_theorem(implies(esk37_0,and(esk37_0,esk37_0))))|kn1)),inference(shift_quantors,[status(thm)],[166])).
% cnf(169,plain,(is_a_theorem(implies(X1,and(X1,X1)))|~kn1),inference(split_conjunct,[status(thm)],[167])).
% fof(170, plain,((~(kn2)|![X1]:![X5]:is_a_theorem(implies(and(X1,X5),X1)))&(?[X1]:?[X5]:~(is_a_theorem(implies(and(X1,X5),X1)))|kn2)),inference(fof_nnf,[status(thm)],[31])).
% fof(171, plain,((~(kn2)|![X6]:![X7]:is_a_theorem(implies(and(X6,X7),X6)))&(?[X8]:?[X9]:~(is_a_theorem(implies(and(X8,X9),X8)))|kn2)),inference(variable_rename,[status(thm)],[170])).
% fof(172, plain,((~(kn2)|![X6]:![X7]:is_a_theorem(implies(and(X6,X7),X6)))&(~(is_a_theorem(implies(and(esk38_0,esk39_0),esk38_0)))|kn2)),inference(skolemize,[status(esa)],[171])).
% fof(173, plain,![X6]:![X7]:((is_a_theorem(implies(and(X6,X7),X6))|~(kn2))&(~(is_a_theorem(implies(and(esk38_0,esk39_0),esk38_0)))|kn2)),inference(shift_quantors,[status(thm)],[172])).
% cnf(175,plain,(is_a_theorem(implies(and(X1,X2),X1))|~kn2),inference(split_conjunct,[status(thm)],[173])).
% fof(176, plain,(~(op_implies_or)|![X2]:![X3]:implies(X2,X3)=or(not(X2),X3)),inference(fof_nnf,[status(thm)],[32])).
% fof(177, plain,(~(op_implies_or)|![X4]:![X5]:implies(X4,X5)=or(not(X4),X5)),inference(variable_rename,[status(thm)],[176])).
% fof(178, plain,![X4]:![X5]:(implies(X4,X5)=or(not(X4),X5)|~(op_implies_or)),inference(shift_quantors,[status(thm)],[177])).
% cnf(179,plain,(implies(X1,X2)=or(not(X1),X2)|~op_implies_or),inference(split_conjunct,[status(thm)],[178])).
% fof(216, plain,((~(kn3)|![X1]:![X5]:![X6]:is_a_theorem(implies(implies(X1,X5),implies(not(and(X5,X6)),not(and(X6,X1))))))&(?[X1]:?[X5]:?[X6]:~(is_a_theorem(implies(implies(X1,X5),implies(not(and(X5,X6)),not(and(X6,X1))))))|kn3)),inference(fof_nnf,[status(thm)],[39])).
% fof(217, plain,((~(kn3)|![X7]:![X8]:![X9]:is_a_theorem(implies(implies(X7,X8),implies(not(and(X8,X9)),not(and(X9,X7))))))&(?[X10]:?[X11]:?[X12]:~(is_a_theorem(implies(implies(X10,X11),implies(not(and(X11,X12)),not(and(X12,X10))))))|kn3)),inference(variable_rename,[status(thm)],[216])).
% fof(218, plain,((~(kn3)|![X7]:![X8]:![X9]:is_a_theorem(implies(implies(X7,X8),implies(not(and(X8,X9)),not(and(X9,X7))))))&(~(is_a_theorem(implies(implies(esk51_0,esk52_0),implies(not(and(esk52_0,esk53_0)),not(and(esk53_0,esk51_0))))))|kn3)),inference(skolemize,[status(esa)],[217])).
% fof(219, plain,![X7]:![X8]:![X9]:((is_a_theorem(implies(implies(X7,X8),implies(not(and(X8,X9)),not(and(X9,X7)))))|~(kn3))&(~(is_a_theorem(implies(implies(esk51_0,esk52_0),implies(not(and(esk52_0,esk53_0)),not(and(esk53_0,esk51_0))))))|kn3)),inference(shift_quantors,[status(thm)],[218])).
% cnf(221,plain,(is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))|~kn3),inference(split_conjunct,[status(thm)],[219])).
% fof(222, plain,(~(op_implies_and)|![X2]:![X3]:implies(X2,X3)=not(and(X2,not(X3)))),inference(fof_nnf,[status(thm)],[40])).
% fof(223, plain,(~(op_implies_and)|![X4]:![X5]:implies(X4,X5)=not(and(X4,not(X5)))),inference(variable_rename,[status(thm)],[222])).
% fof(224, plain,![X4]:![X5]:(implies(X4,X5)=not(and(X4,not(X5)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[223])).
% cnf(225,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[224])).
% fof(226, plain,(~(op_equiv)|![X2]:![X3]:equiv(X2,X3)=and(implies(X2,X3),implies(X3,X2))),inference(fof_nnf,[status(thm)],[41])).
% fof(227, plain,(~(op_equiv)|![X4]:![X5]:equiv(X4,X5)=and(implies(X4,X5),implies(X5,X4))),inference(variable_rename,[status(thm)],[226])).
% fof(228, plain,![X4]:![X5]:(equiv(X4,X5)=and(implies(X4,X5),implies(X5,X4))|~(op_equiv)),inference(shift_quantors,[status(thm)],[227])).
% cnf(229,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[228])).
% fof(230, plain,((~(substitution_of_equivalents)|![X2]:![X3]:(~(is_a_theorem(equiv(X2,X3)))|X2=X3))&(?[X2]:?[X3]:(is_a_theorem(equiv(X2,X3))&~(X2=X3))|substitution_of_equivalents)),inference(fof_nnf,[status(thm)],[42])).
% fof(231, plain,((~(substitution_of_equivalents)|![X4]:![X5]:(~(is_a_theorem(equiv(X4,X5)))|X4=X5))&(?[X6]:?[X7]:(is_a_theorem(equiv(X6,X7))&~(X6=X7))|substitution_of_equivalents)),inference(variable_rename,[status(thm)],[230])).
% fof(232, plain,((~(substitution_of_equivalents)|![X4]:![X5]:(~(is_a_theorem(equiv(X4,X5)))|X4=X5))&((is_a_theorem(equiv(esk54_0,esk55_0))&~(esk54_0=esk55_0))|substitution_of_equivalents)),inference(skolemize,[status(esa)],[231])).
% fof(233, plain,![X4]:![X5]:(((~(is_a_theorem(equiv(X4,X5)))|X4=X5)|~(substitution_of_equivalents))&((is_a_theorem(equiv(esk54_0,esk55_0))&~(esk54_0=esk55_0))|substitution_of_equivalents)),inference(shift_quantors,[status(thm)],[232])).
% fof(234, plain,![X4]:![X5]:(((~(is_a_theorem(equiv(X4,X5)))|X4=X5)|~(substitution_of_equivalents))&((is_a_theorem(equiv(esk54_0,esk55_0))|substitution_of_equivalents)&(~(esk54_0=esk55_0)|substitution_of_equivalents))),inference(distribute,[status(thm)],[233])).
% cnf(237,plain,(X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))),inference(split_conjunct,[status(thm)],[234])).
% cnf(238,negated_conjecture,(~r1),inference(split_conjunct,[status(thm)],[45])).
% cnf(243,plain,(~is_a_theorem(implies(or(esk1_0,esk1_0),esk1_0))),inference(sr,[status(thm)],[50,238,theory(equality)])).
% cnf(248,plain,(X1=X2|$false|~is_a_theorem(equiv(X1,X2))),inference(rw,[status(thm)],[237,102,theory(equality)])).
% cnf(249,plain,(X1=X2|~is_a_theorem(equiv(X1,X2))),inference(cn,[status(thm)],[248,theory(equality)])).
% cnf(250,plain,(or(not(X1),X2)=implies(X1,X2)|$false),inference(rw,[status(thm)],[179,56,theory(equality)])).
% cnf(251,plain,(or(not(X1),X2)=implies(X1,X2)),inference(cn,[status(thm)],[250,theory(equality)])).
% cnf(252,plain,(is_a_theorem(implies(X1,and(X1,X1)))|$false),inference(rw,[status(thm)],[169,53,theory(equality)])).
% cnf(253,plain,(is_a_theorem(implies(X1,and(X1,X1)))),inference(cn,[status(thm)],[252,theory(equality)])).
% cnf(254,plain,(is_a_theorem(implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[175,54,theory(equality)])).
% cnf(255,plain,(is_a_theorem(implies(and(X1,X2),X1))),inference(cn,[status(thm)],[254,theory(equality)])).
% cnf(259,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[225,100,theory(equality)])).
% cnf(260,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[259,theory(equality)])).
% cnf(261,plain,(or(implies(X1,X2),X3)=implies(and(X1,not(X2)),X3)),inference(spm,[status(thm)],[251,260,theory(equality)])).
% cnf(262,plain,(not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))),inference(spm,[status(thm)],[260,260,theory(equality)])).
% cnf(263,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(rw,[status(thm)],[113,52,theory(equality)])).
% cnf(264,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(cn,[status(thm)],[263,theory(equality)])).
% cnf(265,plain,(is_a_theorem(X1)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[264,255,theory(equality)])).
% cnf(266,plain,(is_a_theorem(and(X1,X1))|~is_a_theorem(X1)),inference(spm,[status(thm)],[264,253,theory(equality)])).
% cnf(267,plain,(not(implies(X1,not(X2)))=and(X1,X2)|~op_and),inference(rw,[status(thm)],[145,251,theory(equality)])).
% cnf(268,plain,(not(implies(X1,not(X2)))=and(X1,X2)|$false),inference(rw,[status(thm)],[267,103,theory(equality)])).
% cnf(269,plain,(not(implies(X1,not(X2)))=and(X1,X2)),inference(cn,[status(thm)],[268,theory(equality)])).
% cnf(270,plain,(or(and(X1,X2),X3)=implies(implies(X1,not(X2)),X3)),inference(spm,[status(thm)],[251,269,theory(equality)])).
% cnf(272,plain,(not(implies(X1,and(X2,X3)))=and(X1,implies(X2,not(X3)))),inference(spm,[status(thm)],[269,269,theory(equality)])).
% cnf(274,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[141,260,theory(equality)])).
% cnf(275,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[274,99,theory(equality)])).
% cnf(276,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[275,theory(equality)])).
% cnf(278,plain,(not(or(X1,not(X2)))=and(not(X1),X2)),inference(spm,[status(thm)],[269,276,theory(equality)])).
% cnf(279,plain,(is_a_theorem(X1)|~is_a_theorem(or(X2,X1))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[264,276,theory(equality)])).
% cnf(280,plain,(implies(implies(X1,X2),X3)=or(and(X1,not(X2)),X3)),inference(spm,[status(thm)],[276,260,theory(equality)])).
% cnf(289,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[229,101,theory(equality)])).
% cnf(290,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[289,theory(equality)])).
% cnf(294,plain,(and(or(X1,X2),implies(X2,not(X1)))=equiv(not(X1),X2)),inference(spm,[status(thm)],[290,276,theory(equality)])).
% cnf(296,plain,(is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|~kn3),inference(rw,[status(thm)],[221,276,theory(equality)])).
% cnf(297,plain,(is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|$false),inference(rw,[status(thm)],[296,55,theory(equality)])).
% cnf(298,plain,(is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))),inference(cn,[status(thm)],[297,theory(equality)])).
% cnf(308,plain,(not(or(implies(X1,X2),not(X3)))=and(and(X1,not(X2)),X3)),inference(spm,[status(thm)],[269,261,theory(equality)])).
% cnf(317,plain,(is_a_theorem(equiv(X1,X1))|~is_a_theorem(implies(X1,X1))),inference(spm,[status(thm)],[266,290,theory(equality)])).
% cnf(337,plain,(not(implies(X1,not(X2)))=and(not(not(X1)),X2)),inference(spm,[status(thm)],[278,251,theory(equality)])).
% cnf(338,plain,(and(X1,X2)=and(not(not(X1)),X2)),inference(rw,[status(thm)],[337,269,theory(equality)])).
% cnf(346,plain,(is_a_theorem(X1)|~is_a_theorem(or(and(X2,implies(X3,X4)),X1))|~is_a_theorem(implies(X2,and(X3,not(X4))))),inference(spm,[status(thm)],[279,262,theory(equality)])).
% cnf(349,plain,(not(and(X1,or(X2,X3)))=implies(X1,and(not(X2),not(X3)))),inference(spm,[status(thm)],[262,276,theory(equality)])).
% cnf(356,plain,(is_a_theorem(not(not(X1)))|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[265,338,theory(equality)])).
% cnf(357,plain,(is_a_theorem(and(X1,not(not(X1))))|~is_a_theorem(not(not(X1)))),inference(spm,[status(thm)],[266,338,theory(equality)])).
% cnf(358,plain,(is_a_theorem(implies(not(not(X1)),and(X1,not(not(X1)))))),inference(spm,[status(thm)],[253,338,theory(equality)])).
% cnf(371,plain,(is_a_theorem(implies(X1,and(X1,not(not(X1)))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[358,276,theory(equality)]),251,theory(equality)])).
% cnf(374,plain,(is_a_theorem(not(not(X1)))|~is_a_theorem(X1)),inference(spm,[status(thm)],[356,266,theory(equality)])).
% cnf(378,plain,(is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X1,not(X2)))),inference(spm,[status(thm)],[374,269,theory(equality)])).
% cnf(401,plain,(is_a_theorem(not(and(and(not(X1),X2),X1)))),inference(spm,[status(thm)],[378,255,theory(equality)])).
% cnf(403,plain,(is_a_theorem(X1)|~is_a_theorem(or(and(and(not(X2),X3),X2),X1))),inference(spm,[status(thm)],[279,401,theory(equality)])).
% cnf(419,plain,(is_a_theorem(implies(implies(X1,X2),implies(implies(X2,not(X3)),not(and(X3,X1)))))),inference(rw,[status(thm)],[298,270,theory(equality)])).
% cnf(423,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(and(not(X2),X3),not(X2)),X1))),inference(rw,[status(thm)],[403,270,theory(equality)])).
% cnf(449,plain,(is_a_theorem(and(X1,not(not(X1))))|~is_a_theorem(X1)),inference(spm,[status(thm)],[357,374,theory(equality)])).
% cnf(579,plain,(is_a_theorem(X1)|~is_a_theorem(not(implies(X1,and(X2,X3))))),inference(spm,[status(thm)],[265,272,theory(equality)])).
% cnf(692,plain,(implies(implies(X1,not(not(X2))),X3)=implies(implies(X1,X2),X3)),inference(rw,[status(thm)],[280,270,theory(equality)])).
% cnf(717,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(and(not(not(X2)),X3),X2),X1))),inference(spm,[status(thm)],[423,692,theory(equality)])).
% cnf(737,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(and(X2,X3),X2),X1))),inference(rw,[status(thm)],[717,338,theory(equality)])).
% cnf(953,plain,(not(implies(or(X1,X2),and(X2,X1)))=equiv(not(X1),X2)),inference(rw,[status(thm)],[294,272,theory(equality)])).
% cnf(982,plain,(is_a_theorem(or(X1,X2))|~is_a_theorem(equiv(not(X1),X2))),inference(spm,[status(thm)],[579,953,theory(equality)])).
% cnf(1093,plain,(and(and(X1,not(X2)),X3)=and(not(implies(X1,X2)),X3)),inference(rw,[status(thm)],[308,278,theory(equality)])).
% cnf(1107,plain,(is_a_theorem(and(X1,not(X2)))|~is_a_theorem(and(not(implies(X1,X2)),X3))),inference(spm,[status(thm)],[265,1093,theory(equality)])).
% cnf(1168,plain,(is_a_theorem(and(X1,not(X2)))|~is_a_theorem(not(implies(X1,X2)))),inference(spm,[status(thm)],[1107,449,theory(equality)])).
% cnf(3235,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,not(implies(X3,X4))),X1))|~is_a_theorem(implies(X2,and(X3,not(X4))))),inference(rw,[status(thm)],[346,270,theory(equality)])).
% cnf(3253,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,not(implies(X2,not(X2)))),X1))),inference(spm,[status(thm)],[3235,371,theory(equality)])).
% cnf(3263,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,and(X2,X2)),X1))),inference(rw,[status(thm)],[3253,269,theory(equality)])).
% cnf(4253,plain,(is_a_theorem(and(X1,not(and(not(X2),not(X3)))))|~is_a_theorem(not(not(and(X1,or(X2,X3)))))),inference(spm,[status(thm)],[1168,349,theory(equality)])).
% cnf(4352,plain,(is_a_theorem(and(X1,or(X2,X3)))|~is_a_theorem(not(not(and(X1,or(X2,X3)))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[4253,260,theory(equality)]),276,theory(equality)])).
% cnf(5583,plain,(is_a_theorem(and(X1,implies(X2,X3)))|~is_a_theorem(not(not(and(X1,implies(X2,X3)))))),inference(spm,[status(thm)],[4352,251,theory(equality)])).
% cnf(5598,plain,(is_a_theorem(and(X1,implies(X2,X3)))|~is_a_theorem(not(implies(X1,and(X2,not(X3)))))),inference(rw,[status(thm)],[5583,262,theory(equality)])).
% cnf(5902,plain,(is_a_theorem(and(or(not(X1),X2),implies(X2,X1)))|~is_a_theorem(equiv(not(not(X1)),X2))),inference(spm,[status(thm)],[5598,953,theory(equality)])).
% cnf(5914,plain,(is_a_theorem(equiv(X1,X2))|~is_a_theorem(equiv(not(not(X1)),X2))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[5902,251,theory(equality)]),290,theory(equality)])).
% cnf(7666,plain,(is_a_theorem(implies(implies(and(X1,X1),not(X2)),not(and(X2,X1))))),inference(spm,[status(thm)],[3263,419,theory(equality)])).
% cnf(7880,plain,(is_a_theorem(not(and(X1,not(X1))))),inference(spm,[status(thm)],[737,7666,theory(equality)])).
% cnf(7919,plain,(is_a_theorem(implies(X1,X1))),inference(rw,[status(thm)],[7880,260,theory(equality)])).
% cnf(7983,plain,(is_a_theorem(equiv(X1,X1))|$false),inference(rw,[status(thm)],[317,7919,theory(equality)])).
% cnf(7984,plain,(is_a_theorem(equiv(X1,X1))),inference(cn,[status(thm)],[7983,theory(equality)])).
% cnf(8004,plain,(is_a_theorem(or(X1,not(X1)))),inference(spm,[status(thm)],[982,7984,theory(equality)])).
% cnf(8007,plain,(is_a_theorem(equiv(X1,not(not(X1))))),inference(spm,[status(thm)],[5914,7984,theory(equality)])).
% cnf(8528,plain,(X1=not(not(X1))),inference(spm,[status(thm)],[249,8007,theory(equality)])).
% cnf(8586,plain,(not(and(X1,X2))=implies(X1,not(X2))),inference(spm,[status(thm)],[260,8528,theory(equality)])).
% cnf(8587,plain,(not(implies(X1,X2))=and(X1,not(X2))),inference(spm,[status(thm)],[269,8528,theory(equality)])).
% cnf(10335,plain,(is_a_theorem(implies(implies(and(X1,X1),not(X2)),implies(X2,not(X1))))),inference(rw,[status(thm)],[7666,8586,theory(equality)])).
% cnf(76611,plain,(is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(implies(and(X2,X2),not(X1)))),inference(spm,[status(thm)],[264,10335,theory(equality)])).
% cnf(78473,plain,(is_a_theorem(implies(X1,not(not(X2))))|~is_a_theorem(implies(not(implies(not(X2),X2)),not(X1)))),inference(spm,[status(thm)],[76611,8587,theory(equality)])).
% cnf(78571,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(not(implies(not(X2),X2)),not(X1)))),inference(rw,[status(thm)],[78473,8528,theory(equality)])).
% cnf(78572,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(or(or(X2,X2),not(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[78571,276,theory(equality)]),276,theory(equality)])).
% cnf(82655,plain,(is_a_theorem(implies(or(X1,X1),X1))),inference(spm,[status(thm)],[78572,8004,theory(equality)])).
% cnf(82801,plain,($false),inference(rw,[status(thm)],[243,82655,theory(equality)])).
% cnf(82802,plain,($false),inference(cn,[status(thm)],[82801,theory(equality)])).
% cnf(82803,plain,($false),82802,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 4143
% # ...of these trivial : 344
% # ...subsumed : 2243
% # ...remaining for further processing: 1556
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 30
% # Backward-rewritten : 430
% # Generated clauses : 54796
% # ...of the previous two non-trivial : 40485
% # Contextual simplify-reflections : 23
% # Paramodulations : 54796
% # Factorizations : 0
% # Equation resolutions : 0
% # Current number of processed clauses: 1096
% # Positive orientable unit clauses: 654
% # Positive unorientable unit clauses: 4
% # Negative unit clauses : 2
% # Non-unit-clauses : 436
% # Current number of unprocessed clauses: 23841
% # ...number of literals in the above : 34841
% # Clause-clause subsumption calls (NU) : 31807
% # Rec. Clause-clause subsumption calls : 31807
% # Unit Clause-clause subsumption calls : 1083
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 34264
% # Indexed BW rewrite successes : 329
% # Backwards rewriting index: 653 leaves, 4.20+/-10.744 terms/leaf
% # Paramod-from index: 98 leaves, 7.09+/-16.925 terms/leaf
% # Paramod-into index: 604 leaves, 4.11+/-10.441 terms/leaf
% # -------------------------------------------------
% # User time : 2.076 s
% # System time : 0.068 s
% # Total time : 2.144 s
% # Maximum resident set size: 0 pages
% PrfWatch: 3.34 CPU 3.82 WC
% FINAL PrfWatch: 3.34 CPU 3.82 WC
% SZS output end Solution for /tmp/SystemOnTPTP32410/LCL518+1.tptp
%
%------------------------------------------------------------------------------