TSTP Solution File: LCL472+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : LCL472+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 : art03.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 13:31:12 EST 2010
% Result : Theorem 212.40s
% Output : Solution 291.91s
% 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/SystemOnTPTP11992/LCL472+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% not found
% Adding ~C to TBU ... ~hilbert_equivalence_1:
% ---- Iteration 1 (0 axioms selected)
% Looking for TBU SAT ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... equivalence_1:
% CSA axiom equivalence_1 found
% Looking for CSA axiom ... luka_op_equiv:
% CSA axiom luka_op_equiv found
% Looking for CSA axiom ... luka_modus_ponens: CSA axiom luka_modus_ponens found
% ---- Iteration 2 (3 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... luka_cn1:
% CSA axiom luka_cn1 found
% Looking for CSA axiom ... luka_cn2:
% CSA axiom luka_cn2 found
% Looking for CSA axiom ... luka_cn3:
% CSA axiom luka_cn3 found
% ---- Iteration 3 (6 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... substitution_of_equivalents:
% CSA axiom substitution_of_equivalents found
% Looking for CSA axiom ... hilbert_op_equiv:
% equivalence_2:
% CSA axiom equivalence_2 found
% Looking for CSA axiom ... equivalence_3:
% CSA axiom equivalence_3 found
% ---- Iteration 4 (9 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% luka_op_or:
% CSA axiom luka_op_or found
% Looking for CSA axiom ... hilbert_op_or:
% CSA axiom hilbert_op_or found
% Looking for CSA axiom ... hilbert_op_implies_and:
% CSA axiom hilbert_op_implies_and found
% ---- Iteration 5 (12 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% modus_ponens:
% CSA axiom modus_ponens found
% Looking for CSA axiom ... substitution_of_equivalents:implies_1:
% CSA axiom implies_1 found
% Looking for CSA axiom ... implies_2:
% CSA axiom implies_2 found
% ---- Iteration 6 (15 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% substitution_of_equivalents:implies_3:
% CSA axiom implies_3 found
% Looking for CSA axiom ... cn1:
% CSA axiom cn1 found
% Looking for CSA axiom ... op_implies_and:
% CSA axiom op_implies_and found
% ---- Iteration 7 (18 axioms selected)
% Looking for TBU SAT ... yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% substitution_of_equivalents:op_equiv:
% CSA axiom op_equiv found
% Looking for CSA axiom ... and_1:
% CSA axiom and_1 found
% Looking for CSA axiom ... and_2:
% CSA axiom and_2 found
% ---- Iteration 8 (21 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% substitution_of_equivalents:and_3:
% CSA axiom and_3 found
% Looking for CSA axiom ... or_1:
% CSA axiom or_1 found
% Looking for CSA axiom ... or_2:
% CSA axiom or_2 found
% ---- Iteration 9 (24 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% substitution_of_equivalents:or_3:
% CSA axiom or_3 found
% Looking for CSA axiom ... kn1:
% CSA axiom kn1 found
% Looking for CSA axiom ... kn2:
% CSA axiom kn2 found
% ---- Iteration 10 (27 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% substitution_of_equivalents:r1:
% CSA axiom r1 found
% Looking for CSA axiom ... r2:
% CSA axiom r2 found
% Looking for CSA axiom ... r3:
% CSA axiom r3 found
% ---- Iteration 11 (30 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% substitution_of_equivalents:r4:
% CSA axiom r4 found
% Looking for CSA axiom ... r5:
% CSA axiom r5 found
% Looking for CSA axiom ... modus_tollens:
% CSA axiom modus_tollens found
% ---- Iteration 12 (33 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_equiv:
% substitution_of_equivalents:cn2:
% CSA axiom cn2 found
% Looking for CSA axiom ... cn3:
% CSA axiom cn3 found
% Looking for CSA axiom ... op_or:
% CSA axiom op_or found
% ---- Iteration 13 (36 axioms selected)
% Looking for TBU SAT ...
% no
% Looking for TBU UNS ...
% yes - theorem proved
% ---- Selection completed
% Selected axioms are ... :op_or:cn3:cn2:modus_tollens:r5:r4:r3:r2:r1:kn2:kn1:or_3:or_2:or_1:and_3:and_2:and_1:op_equiv:op_implies_and:cn1:implies_3:implies_2:implies_1:modus_ponens:hilbert_op_implies_and:hilbert_op_or:luka_op_or:equivalence_3:equivalence_2:substitution_of_equivalents:luka_cn3:luka_cn2:luka_cn1:luka_modus_ponens:luka_op_equiv:equivalence_1 (36)
% Unselected axioms are ... :hilbert_op_equiv:substitution_of_equivalents:op_and:kn3:op_implies_or:luka_op_implies (6)
% SZS status THM for /tmp/SystemOnTPTP11992/LCL472+1.tptp
% Looking for THM ...
% found
% SZS output start Solution for /tmp/SystemOnTPTP11992/LCL472+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=600 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 600s
% TreeLimitedRun: WC time limit is 1200s
% TreeLimitedRun: PID is 19105
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 WC
% PrfWatch: 1.92 CPU 2.01 WC
% PrfWatch: 3.91 CPU 4.01 WC
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% PrfWatch: 56.96 CPU 58.14 WC
% PrfWatch: 58.96 CPU 60.15 WC
% # Preprocessing time : 0.016 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 60.92 CPU 62.15 WC
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% PrfWatch: 74.86 CPU 76.18 WC
% PrfWatch: 76.79 CPU 78.25 WC
% PrfWatch: 78.38 CPU 80.31 WC
% # SZS output start CNFRefutation.
% fof(1, axiom,(op_or=>![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),file('/tmp/SRASS.s.p', op_or)).
% fof(2, axiom,(cn3<=>![X3]:is_a_theorem(implies(implies(not(X3),X3),X3))),file('/tmp/SRASS.s.p', cn3)).
% fof(3, axiom,(cn2<=>![X3]:![X4]:is_a_theorem(implies(X3,implies(not(X3),X4)))),file('/tmp/SRASS.s.p', cn2)).
% fof(18, axiom,(op_equiv=>![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(19, axiom,(op_implies_and=>![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(20, axiom,(cn1<=>![X3]:![X4]:![X5]:is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5))))),file('/tmp/SRASS.s.p', cn1)).
% fof(24, axiom,(modus_ponens<=>![X1]:![X2]:((is_a_theorem(X1)&is_a_theorem(implies(X1,X2)))=>is_a_theorem(X2))),file('/tmp/SRASS.s.p', modus_ponens)).
% fof(25, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(26, axiom,op_or,file('/tmp/SRASS.s.p', hilbert_op_or)).
% fof(31, axiom,cn3,file('/tmp/SRASS.s.p', luka_cn3)).
% fof(32, axiom,cn2,file('/tmp/SRASS.s.p', luka_cn2)).
% fof(33, axiom,cn1,file('/tmp/SRASS.s.p', luka_cn1)).
% fof(34, axiom,modus_ponens,file('/tmp/SRASS.s.p', luka_modus_ponens)).
% fof(35, axiom,op_equiv,file('/tmp/SRASS.s.p', luka_op_equiv)).
% fof(36, axiom,(equivalence_1<=>![X1]:![X2]:is_a_theorem(implies(equiv(X1,X2),implies(X1,X2)))),file('/tmp/SRASS.s.p', equivalence_1)).
% fof(37, conjecture,equivalence_1,file('/tmp/SRASS.s.p', hilbert_equivalence_1)).
% fof(38, negated_conjecture,~(equivalence_1),inference(assume_negation,[status(cth)],[37])).
% fof(39, negated_conjecture,~(equivalence_1),inference(fof_simplification,[status(thm)],[38,theory(equality)])).
% fof(40, plain,(~(op_or)|![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),inference(fof_nnf,[status(thm)],[1])).
% fof(41, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(variable_rename,[status(thm)],[40])).
% fof(42, plain,![X3]:![X4]:(or(X3,X4)=not(and(not(X3),not(X4)))|~(op_or)),inference(shift_quantors,[status(thm)],[41])).
% cnf(43,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[42])).
% fof(44, plain,((~(cn3)|![X3]:is_a_theorem(implies(implies(not(X3),X3),X3)))&(?[X3]:~(is_a_theorem(implies(implies(not(X3),X3),X3)))|cn3)),inference(fof_nnf,[status(thm)],[2])).
% fof(45, plain,((~(cn3)|![X4]:is_a_theorem(implies(implies(not(X4),X4),X4)))&(?[X5]:~(is_a_theorem(implies(implies(not(X5),X5),X5)))|cn3)),inference(variable_rename,[status(thm)],[44])).
% fof(46, plain,((~(cn3)|![X4]:is_a_theorem(implies(implies(not(X4),X4),X4)))&(~(is_a_theorem(implies(implies(not(esk1_0),esk1_0),esk1_0)))|cn3)),inference(skolemize,[status(esa)],[45])).
% fof(47, plain,![X4]:((is_a_theorem(implies(implies(not(X4),X4),X4))|~(cn3))&(~(is_a_theorem(implies(implies(not(esk1_0),esk1_0),esk1_0)))|cn3)),inference(shift_quantors,[status(thm)],[46])).
% cnf(49,plain,(is_a_theorem(implies(implies(not(X1),X1),X1))|~cn3),inference(split_conjunct,[status(thm)],[47])).
% fof(50, plain,((~(cn2)|![X3]:![X4]:is_a_theorem(implies(X3,implies(not(X3),X4))))&(?[X3]:?[X4]:~(is_a_theorem(implies(X3,implies(not(X3),X4))))|cn2)),inference(fof_nnf,[status(thm)],[3])).
% fof(51, plain,((~(cn2)|![X5]:![X6]:is_a_theorem(implies(X5,implies(not(X5),X6))))&(?[X7]:?[X8]:~(is_a_theorem(implies(X7,implies(not(X7),X8))))|cn2)),inference(variable_rename,[status(thm)],[50])).
% fof(52, plain,((~(cn2)|![X5]:![X6]:is_a_theorem(implies(X5,implies(not(X5),X6))))&(~(is_a_theorem(implies(esk2_0,implies(not(esk2_0),esk3_0))))|cn2)),inference(skolemize,[status(esa)],[51])).
% fof(53, plain,![X5]:![X6]:((is_a_theorem(implies(X5,implies(not(X5),X6)))|~(cn2))&(~(is_a_theorem(implies(esk2_0,implies(not(esk2_0),esk3_0))))|cn2)),inference(shift_quantors,[status(thm)],[52])).
% cnf(55,plain,(is_a_theorem(implies(X1,implies(not(X1),X2)))|~cn2),inference(split_conjunct,[status(thm)],[53])).
% fof(140, plain,(~(op_equiv)|![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),inference(fof_nnf,[status(thm)],[18])).
% fof(141, plain,(~(op_equiv)|![X3]:![X4]:equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))),inference(variable_rename,[status(thm)],[140])).
% fof(142, plain,![X3]:![X4]:(equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))|~(op_equiv)),inference(shift_quantors,[status(thm)],[141])).
% cnf(143,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[142])).
% fof(144, plain,(~(op_implies_and)|![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),inference(fof_nnf,[status(thm)],[19])).
% fof(145, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(variable_rename,[status(thm)],[144])).
% fof(146, plain,![X3]:![X4]:(implies(X3,X4)=not(and(X3,not(X4)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[145])).
% cnf(147,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[146])).
% fof(148, plain,((~(cn1)|![X3]:![X4]:![X5]:is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))))&(?[X3]:?[X4]:?[X5]:~(is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))))|cn1)),inference(fof_nnf,[status(thm)],[20])).
% fof(149, plain,((~(cn1)|![X6]:![X7]:![X8]:is_a_theorem(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8)))))&(?[X9]:?[X10]:?[X11]:~(is_a_theorem(implies(implies(X9,X10),implies(implies(X10,X11),implies(X9,X11)))))|cn1)),inference(variable_rename,[status(thm)],[148])).
% fof(150, plain,((~(cn1)|![X6]:![X7]:![X8]:is_a_theorem(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8)))))&(~(is_a_theorem(implies(implies(esk33_0,esk34_0),implies(implies(esk34_0,esk35_0),implies(esk33_0,esk35_0)))))|cn1)),inference(skolemize,[status(esa)],[149])).
% fof(151, plain,![X6]:![X7]:![X8]:((is_a_theorem(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))))|~(cn1))&(~(is_a_theorem(implies(implies(esk33_0,esk34_0),implies(implies(esk34_0,esk35_0),implies(esk33_0,esk35_0)))))|cn1)),inference(shift_quantors,[status(thm)],[150])).
% cnf(153,plain,(is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~cn1),inference(split_conjunct,[status(thm)],[151])).
% fof(172, plain,((~(modus_ponens)|![X1]:![X2]:((~(is_a_theorem(X1))|~(is_a_theorem(implies(X1,X2))))|is_a_theorem(X2)))&(?[X1]:?[X2]:((is_a_theorem(X1)&is_a_theorem(implies(X1,X2)))&~(is_a_theorem(X2)))|modus_ponens)),inference(fof_nnf,[status(thm)],[24])).
% fof(173, plain,((~(modus_ponens)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4)))&(?[X5]:?[X6]:((is_a_theorem(X5)&is_a_theorem(implies(X5,X6)))&~(is_a_theorem(X6)))|modus_ponens)),inference(variable_rename,[status(thm)],[172])).
% fof(174, plain,((~(modus_ponens)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4)))&(((is_a_theorem(esk43_0)&is_a_theorem(implies(esk43_0,esk44_0)))&~(is_a_theorem(esk44_0)))|modus_ponens)),inference(skolemize,[status(esa)],[173])).
% fof(175, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4))|~(modus_ponens))&(((is_a_theorem(esk43_0)&is_a_theorem(implies(esk43_0,esk44_0)))&~(is_a_theorem(esk44_0)))|modus_ponens)),inference(shift_quantors,[status(thm)],[174])).
% fof(176, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(implies(X3,X4))))|is_a_theorem(X4))|~(modus_ponens))&(((is_a_theorem(esk43_0)|modus_ponens)&(is_a_theorem(implies(esk43_0,esk44_0))|modus_ponens))&(~(is_a_theorem(esk44_0))|modus_ponens))),inference(distribute,[status(thm)],[175])).
% cnf(180,plain,(is_a_theorem(X1)|~modus_ponens|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)),inference(split_conjunct,[status(thm)],[176])).
% cnf(181,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[25])).
% cnf(182,plain,(op_or),inference(split_conjunct,[status(thm)],[26])).
% cnf(197,plain,(cn3),inference(split_conjunct,[status(thm)],[31])).
% cnf(198,plain,(cn2),inference(split_conjunct,[status(thm)],[32])).
% cnf(199,plain,(cn1),inference(split_conjunct,[status(thm)],[33])).
% cnf(200,plain,(modus_ponens),inference(split_conjunct,[status(thm)],[34])).
% cnf(201,plain,(op_equiv),inference(split_conjunct,[status(thm)],[35])).
% fof(202, plain,((~(equivalence_1)|![X1]:![X2]:is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))&(?[X1]:?[X2]:~(is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))|equivalence_1)),inference(fof_nnf,[status(thm)],[36])).
% fof(203, plain,((~(equivalence_1)|![X3]:![X4]:is_a_theorem(implies(equiv(X3,X4),implies(X3,X4))))&(?[X5]:?[X6]:~(is_a_theorem(implies(equiv(X5,X6),implies(X5,X6))))|equivalence_1)),inference(variable_rename,[status(thm)],[202])).
% fof(204, plain,((~(equivalence_1)|![X3]:![X4]:is_a_theorem(implies(equiv(X3,X4),implies(X3,X4))))&(~(is_a_theorem(implies(equiv(esk49_0,esk50_0),implies(esk49_0,esk50_0))))|equivalence_1)),inference(skolemize,[status(esa)],[203])).
% fof(205, plain,![X3]:![X4]:((is_a_theorem(implies(equiv(X3,X4),implies(X3,X4)))|~(equivalence_1))&(~(is_a_theorem(implies(equiv(esk49_0,esk50_0),implies(esk49_0,esk50_0))))|equivalence_1)),inference(shift_quantors,[status(thm)],[204])).
% cnf(206,plain,(equivalence_1|~is_a_theorem(implies(equiv(esk49_0,esk50_0),implies(esk49_0,esk50_0)))),inference(split_conjunct,[status(thm)],[205])).
% cnf(208,negated_conjecture,(~equivalence_1),inference(split_conjunct,[status(thm)],[39])).
% cnf(213,plain,(~is_a_theorem(implies(equiv(esk49_0,esk50_0),implies(esk49_0,esk50_0)))),inference(sr,[status(thm)],[206,208,theory(equality)])).
% cnf(216,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[147,181,theory(equality)])).
% cnf(217,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[216,theory(equality)])).
% cnf(218,plain,(not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))),inference(spm,[status(thm)],[217,217,theory(equality)])).
% cnf(219,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(rw,[status(thm)],[180,200,theory(equality)])).
% cnf(220,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(implies(X2,X1))),inference(cn,[status(thm)],[219,theory(equality)])).
% cnf(221,plain,(is_a_theorem(implies(X1,implies(not(X1),X2)))|$false),inference(rw,[status(thm)],[55,198,theory(equality)])).
% cnf(222,plain,(is_a_theorem(implies(X1,implies(not(X1),X2)))),inference(cn,[status(thm)],[221,theory(equality)])).
% cnf(225,plain,(is_a_theorem(implies(implies(not(X1),X1),X1))|$false),inference(rw,[status(thm)],[49,197,theory(equality)])).
% cnf(226,plain,(is_a_theorem(implies(implies(not(X1),X1),X1))),inference(cn,[status(thm)],[225,theory(equality)])).
% cnf(229,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[43,217,theory(equality)])).
% cnf(230,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[229,182,theory(equality)])).
% cnf(231,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[230,theory(equality)])).
% cnf(232,plain,(is_a_theorem(X1)|~is_a_theorem(or(X2,X1))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[220,231,theory(equality)])).
% cnf(233,plain,(implies(implies(X1,X2),X3)=or(and(X1,not(X2)),X3)),inference(spm,[status(thm)],[231,217,theory(equality)])).
% cnf(234,plain,(is_a_theorem(implies(or(X1,X1),X1))),inference(rw,[status(thm)],[226,231,theory(equality)])).
% cnf(235,plain,(is_a_theorem(implies(X1,or(X1,X2)))),inference(rw,[status(thm)],[222,231,theory(equality)])).
% cnf(238,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[143,201,theory(equality)])).
% cnf(239,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[238,theory(equality)])).
% cnf(243,plain,(is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|$false),inference(rw,[status(thm)],[153,199,theory(equality)])).
% cnf(244,plain,(is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))),inference(cn,[status(thm)],[243,theory(equality)])).
% cnf(245,plain,(is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))|~is_a_theorem(implies(X3,X1))),inference(spm,[status(thm)],[220,244,theory(equality)])).
% cnf(246,plain,(is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X3),or(X1,X3))))),inference(spm,[status(thm)],[244,231,theory(equality)])).
% cnf(247,plain,(is_a_theorem(implies(implies(X1,not(X2)),implies(or(X2,X3),implies(X1,X3))))),inference(spm,[status(thm)],[244,231,theory(equality)])).
% cnf(251,plain,(is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X1,X3))))),inference(rw,[status(thm)],[246,231,theory(equality)])).
% cnf(261,plain,(not(equiv(X1,X2))=implies(implies(X1,X2),and(X2,not(X1)))),inference(spm,[status(thm)],[218,239,theory(equality)])).
% cnf(264,plain,(is_a_theorem(or(X1,or(not(X1),X2)))),inference(spm,[status(thm)],[235,231,theory(equality)])).
% cnf(270,plain,(is_a_theorem(X1)|~is_a_theorem(or(and(X2,not(X3)),X1))|~is_a_theorem(implies(X2,X3))),inference(spm,[status(thm)],[232,217,theory(equality)])).
% cnf(275,plain,(is_a_theorem(X1)|~is_a_theorem(or(and(or(X2,X2),not(X2)),X1))),inference(spm,[status(thm)],[270,234,theory(equality)])).
% cnf(290,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(or(X2,X2),X2),X1))),inference(rw,[status(thm)],[275,233,theory(equality)])).
% cnf(294,plain,(is_a_theorem(implies(implies(X1,X2),implies(or(X1,X1),X2)))),inference(spm,[status(thm)],[290,244,theory(equality)])).
% cnf(298,plain,(is_a_theorem(implies(or(X1,X1),X2))|~is_a_theorem(implies(X1,X2))),inference(spm,[status(thm)],[220,294,theory(equality)])).
% cnf(361,plain,(is_a_theorem(implies(implies(X1,X2),implies(not(X3),X2)))|~is_a_theorem(or(X3,X1))),inference(spm,[status(thm)],[245,231,theory(equality)])).
% cnf(362,plain,(is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4)))),inference(spm,[status(thm)],[245,244,theory(equality)])).
% cnf(363,plain,(is_a_theorem(implies(implies(implies(or(X1,X1),X2),X3),implies(implies(X1,X2),X3)))),inference(spm,[status(thm)],[245,294,theory(equality)])).
% cnf(369,plain,(is_a_theorem(implies(implies(or(X1,X2),X3),implies(X1,X3)))),inference(spm,[status(thm)],[245,235,theory(equality)])).
% cnf(370,plain,(is_a_theorem(implies(implies(X1,X2),or(X3,X2)))|~is_a_theorem(or(X3,X1))),inference(rw,[status(thm)],[361,231,theory(equality)])).
% cnf(380,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(or(X1,X3),X2))),inference(spm,[status(thm)],[220,369,theory(equality)])).
% cnf(381,plain,(is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(or(X1,X4),X2),X3)))),inference(spm,[status(thm)],[245,369,theory(equality)])).
% cnf(399,plain,(is_a_theorem(implies(and(X1,not(X2)),X3))|~is_a_theorem(implies(implies(implies(X1,X2),X4),X3))),inference(spm,[status(thm)],[380,233,theory(equality)])).
% cnf(400,plain,(is_a_theorem(implies(X1,or(or(X1,X2),X3)))),inference(spm,[status(thm)],[380,235,theory(equality)])).
% cnf(416,plain,(is_a_theorem(implies(implies(or(or(X1,X2),X3),X4),implies(X1,X4)))),inference(spm,[status(thm)],[245,400,theory(equality)])).
% cnf(453,plain,(is_a_theorem(implies(X1,implies(implies(X2,X3),or(X1,X3))))),inference(spm,[status(thm)],[380,251,theory(equality)])).
% cnf(461,plain,(is_a_theorem(implies(implies(X1,X2),or(X3,X2)))|~is_a_theorem(X3)),inference(spm,[status(thm)],[220,453,theory(equality)])).
% cnf(462,plain,(is_a_theorem(implies(implies(implies(implies(X1,X2),or(X3,X2)),X4),implies(X3,X4)))),inference(spm,[status(thm)],[245,453,theory(equality)])).
% cnf(527,plain,(is_a_theorem(implies(or(X1,X2),implies(or(not(X1),not(X1)),X2)))),inference(spm,[status(thm)],[290,247,theory(equality)])).
% cnf(550,plain,(is_a_theorem(implies(X1,implies(or(not(X1),not(X1)),X2)))),inference(spm,[status(thm)],[380,527,theory(equality)])).
% cnf(562,plain,(is_a_theorem(implies(implies(implies(or(not(X1),not(X1)),X2),X3),implies(X1,X3)))),inference(spm,[status(thm)],[245,550,theory(equality)])).
% cnf(633,plain,(is_a_theorem(implies(or(X1,X2),or(X3,X2)))|~is_a_theorem(X3)),inference(spm,[status(thm)],[461,231,theory(equality)])).
% cnf(892,plain,(is_a_theorem(implies(X1,or(X2,X3)))|~is_a_theorem(X2)),inference(spm,[status(thm)],[380,633,theory(equality)])).
% cnf(904,plain,(is_a_theorem(implies(implies(or(X1,X2),X3),implies(X4,X3)))|~is_a_theorem(X1)),inference(spm,[status(thm)],[245,892,theory(equality)])).
% cnf(1177,plain,(is_a_theorem(implies(implies(X1,X2),X3))|~is_a_theorem(implies(implies(or(X1,X1),X2),X3))),inference(spm,[status(thm)],[220,363,theory(equality)])).
% cnf(1236,plain,(is_a_theorem(implies(implies(or(X1,X2),X3),implies(implies(or(not(X1),X4),X2),X3)))),inference(spm,[status(thm)],[381,231,theory(equality)])).
% cnf(1299,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(implies(implies(X3,X4),or(X1,X4)),X2))),inference(spm,[status(thm)],[220,462,theory(equality)])).
% cnf(1437,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(implies(or(not(X1),not(X1)),X3),X2))),inference(spm,[status(thm)],[220,562,theory(equality)])).
% cnf(2158,plain,(is_a_theorem(implies(X1,implies(X2,or(X1,X3))))),inference(spm,[status(thm)],[1299,562,theory(equality)])).
% cnf(2171,plain,(is_a_theorem(implies(X1,or(implies(or(X2,X2),X2),X3)))),inference(spm,[status(thm)],[290,2158,theory(equality)])).
% cnf(2183,plain,(is_a_theorem(implies(implies(implies(X1,or(X2,X3)),X4),implies(X2,X4)))),inference(spm,[status(thm)],[245,2158,theory(equality)])).
% cnf(2189,plain,(is_a_theorem(implies(X1,or(X2,or(X1,X3))))),inference(spm,[status(thm)],[2158,231,theory(equality)])).
% cnf(2191,plain,(is_a_theorem(or(X1,implies(X2,or(not(X1),X3))))),inference(spm,[status(thm)],[2158,231,theory(equality)])).
% cnf(2207,plain,(is_a_theorem(implies(implies(or(implies(or(X1,X1),X1),X2),X3),implies(X4,X3)))),inference(spm,[status(thm)],[245,2171,theory(equality)])).
% cnf(2364,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(implies(X3,or(X1,X4)),X2))),inference(spm,[status(thm)],[220,2183,theory(equality)])).
% cnf(2506,plain,(is_a_theorem(implies(implies(or(X1,or(X2,X3)),X4),implies(X2,X4)))),inference(spm,[status(thm)],[245,2189,theory(equality)])).
% cnf(2644,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(or(X3,or(X1,X4)),X2))),inference(spm,[status(thm)],[220,2506,theory(equality)])).
% cnf(3027,plain,(is_a_theorem(implies(X1,implies(implies(or(X1,X2),X3),or(X4,X3))))),inference(spm,[status(thm)],[2644,251,theory(equality)])).
% cnf(3169,plain,(is_a_theorem(implies(implies(or(implies(or(X1,X1),X1),X2),X3),or(X4,X3)))),inference(spm,[status(thm)],[290,3027,theory(equality)])).
% cnf(3656,plain,(is_a_theorem(implies(implies(implies(or(X1,X1),X1),X2),implies(X3,X2)))),inference(spm,[status(thm)],[1177,2207,theory(equality)])).
% cnf(3716,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(implies(or(X3,X3),X3),X2))),inference(spm,[status(thm)],[220,3656,theory(equality)])).
% cnf(5370,plain,(is_a_theorem(implies(implies(or(X1,X2),X3),implies(implies(or(implies(or(X4,X4),X4),X5),X2),X3)))),inference(spm,[status(thm)],[245,3169,theory(equality)])).
% cnf(6830,plain,(is_a_theorem(implies(X1,implies(X2,X2)))),inference(spm,[status(thm)],[3716,369,theory(equality)])).
% cnf(6831,plain,(is_a_theorem(implies(X1,implies(X2,or(X2,X3))))),inference(spm,[status(thm)],[3716,416,theory(equality)])).
% cnf(6895,plain,(is_a_theorem(or(X1,implies(X2,X2)))),inference(spm,[status(thm)],[6830,231,theory(equality)])).
% cnf(7961,plain,(is_a_theorem(implies(implies(implies(X1,or(not(X2),X3)),X4),or(X2,X4)))),inference(spm,[status(thm)],[370,2191,theory(equality)])).
% cnf(7963,plain,(is_a_theorem(implies(implies(implies(X1,X1),X2),or(X3,X2)))),inference(spm,[status(thm)],[370,6895,theory(equality)])).
% cnf(7965,plain,(is_a_theorem(implies(implies(or(not(X1),X2),X3),or(X1,X3)))),inference(spm,[status(thm)],[370,264,theory(equality)])).
% cnf(8001,plain,(is_a_theorem(or(X1,X2))|~is_a_theorem(implies(implies(X3,X3),X2))),inference(spm,[status(thm)],[220,7963,theory(equality)])).
% cnf(8003,plain,(is_a_theorem(implies(implies(or(X1,X2),X3),implies(implies(implies(X4,X4),X2),X3)))),inference(spm,[status(thm)],[245,7963,theory(equality)])).
% cnf(8027,plain,(is_a_theorem(or(X1,X2))|~is_a_theorem(implies(or(not(X1),X3),X2))),inference(spm,[status(thm)],[220,7965,theory(equality)])).
% cnf(8101,plain,(is_a_theorem(or(X1,implies(X2,or(X2,X3))))),inference(spm,[status(thm)],[8027,6831,theory(equality)])).
% cnf(8216,plain,(is_a_theorem(implies(implies(implies(X1,or(X1,X2)),X3),or(X4,X3)))),inference(spm,[status(thm)],[370,8101,theory(equality)])).
% cnf(8249,plain,(is_a_theorem(implies(implies(X1,X2),X3))|~is_a_theorem(implies(implies(implies(X2,X4),implies(X1,X4)),X3))),inference(spm,[status(thm)],[220,362,theory(equality)])).
% cnf(10758,plain,(is_a_theorem(implies(and(X1,not(X2)),X3))|~is_a_theorem(implies(not(equiv(X1,X2)),X3))),inference(spm,[status(thm)],[399,261,theory(equality)])).
% cnf(10878,plain,(is_a_theorem(implies(and(X1,not(X1)),or(X2,X3)))),inference(spm,[status(thm)],[399,7963,theory(equality)])).
% cnf(10887,plain,(is_a_theorem(implies(and(X1,not(X2)),X3))|~is_a_theorem(or(equiv(X1,X2),X3))),inference(rw,[status(thm)],[10758,231,theory(equality)])).
% cnf(10960,plain,(is_a_theorem(implies(or(and(X1,not(X1)),and(X1,not(X1))),or(X2,X3)))),inference(spm,[status(thm)],[298,10878,theory(equality)])).
% cnf(10967,plain,(is_a_theorem(or(equiv(X1,X1),or(X2,X3)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[10960,233,theory(equality)]),261,theory(equality)]),231,theory(equality)])).
% cnf(10972,plain,(is_a_theorem(implies(implies(or(X1,X2),X3),or(equiv(X4,X4),X3)))),inference(spm,[status(thm)],[370,10967,theory(equality)])).
% cnf(11845,plain,(is_a_theorem(implies(X1,or(equiv(X2,X2),X3)))),inference(spm,[status(thm)],[1437,10972,theory(equality)])).
% cnf(11893,plain,(is_a_theorem(implies(implies(or(equiv(X1,X1),X2),X3),implies(X4,X3)))),inference(spm,[status(thm)],[245,11845,theory(equality)])).
% cnf(12140,plain,(is_a_theorem(implies(X1,equiv(X2,X2)))),inference(spm,[status(thm)],[290,11893,theory(equality)])).
% cnf(12177,plain,(is_a_theorem(or(X1,equiv(X2,X2)))),inference(spm,[status(thm)],[8027,12140,theory(equality)])).
% cnf(12211,plain,(is_a_theorem(implies(implies(equiv(X1,X1),X2),or(X3,X2)))),inference(spm,[status(thm)],[370,12177,theory(equality)])).
% cnf(12370,plain,(is_a_theorem(or(X1,X2))|~is_a_theorem(implies(equiv(X3,X3),X2))),inference(spm,[status(thm)],[220,12211,theory(equality)])).
% cnf(21149,plain,(is_a_theorem(or(X1,X2))|~is_a_theorem(implies(implies(X3,or(not(X1),X4)),X2))),inference(spm,[status(thm)],[220,7961,theory(equality)])).
% cnf(36068,plain,(is_a_theorem(implies(X1,implies(implies(implies(X2,X2),X3),X3)))),inference(spm,[status(thm)],[3716,8003,theory(equality)])).
% cnf(37089,plain,(is_a_theorem(or(X1,implies(implies(implies(X2,X2),X3),X3)))),inference(spm,[status(thm)],[12370,36068,theory(equality)])).
% cnf(37179,plain,(is_a_theorem(implies(implies(implies(implies(implies(X1,X1),X2),X2),X3),or(X4,X3)))),inference(spm,[status(thm)],[370,37089,theory(equality)])).
% cnf(69107,plain,(is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))|~is_a_theorem(X1)),inference(spm,[status(thm)],[1177,904,theory(equality)])).
% cnf(113477,plain,(is_a_theorem(implies(implies(X1,X2),implies(implies(or(not(X1),X3),X1),X2)))),inference(spm,[status(thm)],[1177,1236,theory(equality)])).
% cnf(879420,plain,(is_a_theorem(implies(implies(or(implies(or(X1,X1),X1),X2),X3),X3))),inference(spm,[status(thm)],[290,5370,theory(equality)])).
% cnf(879548,plain,(is_a_theorem(implies(implies(implies(or(X1,X1),X1),X2),X2))),inference(spm,[status(thm)],[1177,879420,theory(equality)])).
% cnf(1097936,plain,(is_a_theorem(implies(implies(X1,or(X2,X2)),implies(X1,X2)))),inference(spm,[status(thm)],[8249,879548,theory(equality)])).
% cnf(1099680,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,or(X2,X2)))),inference(spm,[status(thm)],[220,1097936,theory(equality)])).
% cnf(1099708,plain,(is_a_theorem(implies(X1,implies(X2,X1)))),inference(spm,[status(thm)],[2364,1097936,theory(equality)])).
% cnf(1099720,plain,(is_a_theorem(or(X1,implies(X2,not(X1))))),inference(spm,[status(thm)],[21149,1097936,theory(equality)])).
% cnf(1099906,plain,(is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3)))),inference(spm,[status(thm)],[245,1099708,theory(equality)])).
% cnf(1100097,plain,(is_a_theorem(implies(implies(implies(X1,not(X2)),X3),or(X2,X3)))),inference(spm,[status(thm)],[370,1099720,theory(equality)])).
% cnf(1101461,plain,(is_a_theorem(or(X1,implies(X2,implies(X3,X2))))),inference(spm,[status(thm)],[8001,1099906,theory(equality)])).
% cnf(1101891,plain,(is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),or(X4,X3)))),inference(spm,[status(thm)],[370,1101461,theory(equality)])).
% cnf(1114167,plain,(is_a_theorem(implies(implies(implies(X1,or(X1,X2)),X3),X3))),inference(spm,[status(thm)],[1099680,8216,theory(equality)])).
% cnf(1114224,plain,(is_a_theorem(implies(implies(implies(implies(implies(X1,X1),X2),X2),X3),X3))),inference(spm,[status(thm)],[1099680,37179,theory(equality)])).
% cnf(1117011,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,or(X2,X3)),X1))),inference(spm,[status(thm)],[220,1114167,theory(equality)])).
% cnf(1161109,plain,(is_a_theorem(or(X1,X2))|~is_a_theorem(implies(implies(X3,not(X1)),X2))),inference(spm,[status(thm)],[220,1100097,theory(equality)])).
% cnf(1237875,plain,(is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3))),inference(spm,[status(thm)],[1099680,1101891,theory(equality)])).
% cnf(1237983,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,implies(X3,X2)),X1))),inference(spm,[status(thm)],[220,1237875,theory(equality)])).
% cnf(1238023,plain,(is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X2))))),inference(spm,[status(thm)],[8249,1237875,theory(equality)])).
% cnf(1238161,plain,(is_a_theorem(implies(X1,implies(X2,X3)))|~is_a_theorem(implies(X1,X3))),inference(spm,[status(thm)],[220,1238023,theory(equality)])).
% cnf(1238318,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,or(X3,X2)),X1))),inference(spm,[status(thm)],[1237983,231,theory(equality)])).
% cnf(1245084,plain,(is_a_theorem(implies(implies(or(not(X1),X2),X1),or(X3,X1)))),inference(spm,[status(thm)],[1238318,113477,theory(equality)])).
% cnf(1303103,plain,(is_a_theorem(implies(implies(X1,implies(implies(X2,X2),X3)),implies(X1,X3)))),inference(spm,[status(thm)],[8249,1114224,theory(equality)])).
% cnf(1361597,plain,(is_a_theorem(implies(implies(implies(X1,X1),X2),implies(implies(X2,X3),X3)))),inference(spm,[status(thm)],[8249,1303103,theory(equality)])).
% cnf(1382735,plain,(is_a_theorem(or(X1,implies(implies(not(X1),X2),X2)))),inference(spm,[status(thm)],[1161109,1361597,theory(equality)])).
% cnf(1382787,plain,(is_a_theorem(or(X1,implies(or(X1,X2),X2)))),inference(rw,[status(thm)],[1382735,231,theory(equality)])).
% cnf(1383100,plain,(is_a_theorem(implies(implies(implies(or(X1,X2),X2),X3),or(X1,X3)))),inference(spm,[status(thm)],[370,1382787,theory(equality)])).
% cnf(1399420,plain,(is_a_theorem(implies(implies(implies(or(X1,X2),X2),X1),X1))),inference(spm,[status(thm)],[1099680,1383100,theory(equality)])).
% cnf(1399433,plain,(is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3))))),inference(spm,[status(thm)],[8249,1383100,theory(equality)])).
% cnf(1399534,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(or(X1,X2),X2),X1))),inference(spm,[status(thm)],[220,1399420,theory(equality)])).
% cnf(1399558,plain,(is_a_theorem(implies(and(or(X1,X2),not(X2)),X1))),inference(spm,[status(thm)],[399,1399420,theory(equality)])).
% cnf(1399665,plain,(is_a_theorem(implies(and(or(X1,X2),not(X2)),implies(X3,X1)))),inference(spm,[status(thm)],[1238161,1399558,theory(equality)])).
% cnf(1417712,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(or(implies(X1,X2),X2))),inference(spm,[status(thm)],[1399534,69107,theory(equality)])).
% cnf(1457824,plain,(is_a_theorem(or(X1,implies(X1,X2)))),inference(spm,[status(thm)],[1117011,1399433,theory(equality)])).
% cnf(1457892,plain,(is_a_theorem(implies(and(X1,not(X2)),implies(equiv(X1,X2),X3)))),inference(spm,[status(thm)],[10887,1457824,theory(equality)])).
% cnf(1457952,plain,(is_a_theorem(implies(implies(implies(X1,X2),X3),or(X1,X3)))),inference(spm,[status(thm)],[370,1457824,theory(equality)])).
% cnf(1459130,plain,(is_a_theorem(implies(implies(implies(X1,X2),X1),X1))),inference(spm,[status(thm)],[1099680,1457952,theory(equality)])).
% cnf(1459238,plain,(is_a_theorem(X1)|~is_a_theorem(implies(implies(X1,X2),X1))),inference(spm,[status(thm)],[220,1459130,theory(equality)])).
% cnf(1463640,plain,(is_a_theorem(or(not(X1),X1))),inference(spm,[status(thm)],[1459238,1245084,theory(equality)])).
% cnf(1465751,plain,(is_a_theorem(implies(implies(X1,X2),or(not(X1),X2)))),inference(spm,[status(thm)],[370,1463640,theory(equality)])).
% cnf(1471869,plain,(is_a_theorem(or(not(X1),X2))|~is_a_theorem(implies(X1,X2))),inference(spm,[status(thm)],[220,1465751,theory(equality)])).
% cnf(1581981,plain,(is_a_theorem(or(not(and(or(X1,X2),not(X2))),implies(X3,X1)))),inference(spm,[status(thm)],[1471869,1399665,theory(equality)])).
% cnf(1585019,plain,(is_a_theorem(or(implies(or(X1,X2),X2),implies(X3,X1)))),inference(rw,[status(thm)],[1581981,217,theory(equality)])).
% cnf(1592420,plain,(is_a_theorem(implies(or(X1,implies(X2,X1)),implies(X2,X1)))),inference(spm,[status(thm)],[1417712,1585019,theory(equality)])).
% cnf(1598330,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,implies(X1,X2)))),inference(spm,[status(thm)],[220,1592420,theory(equality)])).
% cnf(1649100,plain,(is_a_theorem(or(not(and(X1,not(X2))),implies(equiv(X1,X2),X3)))),inference(spm,[status(thm)],[1471869,1457892,theory(equality)])).
% cnf(1649134,plain,(is_a_theorem(or(implies(X1,X2),implies(equiv(X1,X2),X3)))),inference(rw,[status(thm)],[1649100,217,theory(equality)])).
% cnf(1649142,plain,(is_a_theorem(implies(equiv(X1,X2),implies(X1,X2)))),inference(spm,[status(thm)],[1598330,1649134,theory(equality)])).
% cnf(1649204,plain,($false),inference(rw,[status(thm)],[213,1649142,theory(equality)])).
% cnf(1649205,plain,($false),inference(cn,[status(thm)],[1649204,theory(equality)])).
% cnf(1649206,plain,($false),1649205,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 41830
% # ...of these trivial : 26232
% # ...subsumed : 5573
% # ...remaining for further processing: 10025
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 16
% # Backward-rewritten : 278
% # Generated clauses : 1046139
% # ...of the previous two non-trivial : 528606
% # Contextual simplify-reflections : 210
% # Paramodulations : 1046139
% # Factorizations : 0
% # Equation resolutions : 0
% # Current number of processed clauses: 9731
% # Positive orientable unit clauses: 8229
% # Positive unorientable unit clauses: 0
% # Negative unit clauses : 3
% # Non-unit-clauses : 1499
% # Current number of unprocessed clauses: 476652
% # ...number of literals in the above : 565234
% # Clause-clause subsumption calls (NU) : 169366
% # Rec. Clause-clause subsumption calls : 169366
% # Unit Clause-clause subsumption calls : 71675
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 3686165
% # Indexed BW rewrite successes : 270
% # Backwards rewriting index: 1521 leaves, 17.11+/-71.562 terms/leaf
% # Paramod-from index: 122 leaves, 68.28+/-194.083 terms/leaf
% # Paramod-into index: 1463 leaves, 17.33+/-72.400 terms/leaf
% # -------------------------------------------------
% # User time : 58.146 s
% # System time : 1.361 s
% # Total time : 59.507 s
% # Maximum resident set size: 0 pages
% PrfWatch: 78.96 CPU 81.03 WC
% FINAL PrfWatch: 78.96 CPU 81.03 WC
% SZS output end Solution for /tmp/SystemOnTPTP11992/LCL472+1.tptp
%
%------------------------------------------------------------------------------