%------------------------------------------------------------------------------
% File     : SRASS---0.1
% Problem  : LCL551+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 : art01.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 13:58:38 EST 2010

% Result   : Theorem 0s
% Output   : Solution 0s
% 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/SystemOnTPTP5709/LCL551+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM       ... 
% not found
% Adding ~C to TBU       ... ~hilbert_modus_tollens:
% ---- Iteration 1 (0 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... modus_tollens:
%  CSA axiom modus_tollens found
% Looking for CSA axiom ... hilbert_op_implies_and: CSA axiom hilbert_op_implies_and found
% Looking for CSA axiom ... cn2:
%  CSA axiom cn2 found
% ---- Iteration 2 (3 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... cn3:
%  CSA axiom cn3 found
% Looking for CSA axiom ... kn3:
%  CSA axiom kn3 found
% Looking for CSA axiom ... s1_0_op_possibly:
%  CSA axiom s1_0_op_possibly found
% ---- Iteration 3 (6 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... s1_0_op_or:
%  CSA axiom s1_0_op_or found
% Looking for CSA axiom ... s1_0_op_strict_implies:
%  CSA axiom s1_0_op_strict_implies found
% Looking for CSA axiom ... s1_0_op_equiv:
%  CSA axiom s1_0_op_equiv found
% ---- Iteration 4 (9 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... s1_0_op_strict_equiv:
%  CSA axiom s1_0_op_strict_equiv found
% Looking for CSA axiom ... s1_0_modus_ponens_strict_implies:
%  CSA axiom s1_0_modus_ponens_strict_implies found
% Looking for CSA axiom ... s1_0_adjunction:
%  CSA axiom s1_0_adjunction found
% ---- Iteration 5 (12 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... s1_0_axiom_m1:
%  CSA axiom s1_0_axiom_m1 found
% Looking for CSA axiom ... s1_0_axiom_m2:
%  CSA axiom s1_0_axiom_m2 found
% Looking for CSA axiom ... s1_0_axiom_m3:
%  CSA axiom s1_0_axiom_m3 found
% ---- Iteration 6 (15 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... s1_0_axiom_m4:
%  CSA axiom s1_0_axiom_m4 found
% Looking for CSA axiom ... s1_0_axiom_m5:
%  CSA axiom s1_0_axiom_m5 found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% substitution_of_equivalents:
%  CSA axiom substitution_of_equivalents found
% ---- Iteration 7 (18 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% modus_ponens:
%  CSA axiom modus_ponens found
% Looking for CSA axiom ... implies_1:
%  CSA axiom implies_1 found
% Looking for CSA axiom ... implies_2:
%  CSA axiom implies_2 found
% ---- Iteration 8 (21 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% implies_3:
%  CSA axiom implies_3 found
% Looking for CSA axiom ... cn1:
%  CSA axiom cn1 found
% Looking for CSA axiom ... axiom_m6:
%  CSA axiom axiom_m6 found
% ---- Iteration 9 (24 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:axiom_m8: CSA axiom axiom_m8 found
% Looking for CSA axiom ... axiom_m9: CSA axiom axiom_m9 found
% Looking for CSA axiom ... s1_0_substitution_strict_equiv: CSA axiom s1_0_substitution_strict_equiv found
% ---- Iteration 10 (27 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:op_implies_and: CSA axiom op_implies_and found
% Looking for CSA axiom ... op_equiv: CSA axiom op_equiv found
% Looking for CSA axiom ... necessitation: CSA axiom necessitation found
% ---- Iteration 11 (30 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:modus_ponens_strict_implies: CSA axiom modus_ponens_strict_implies found
% Looking for CSA axiom ... adjunction: CSA axiom adjunction found
% Looking for CSA axiom ... axiom_s2: CSA axiom axiom_s2 found
% ---- Iteration 12 (33 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:axiom_m7: CSA axiom axiom_m7 found
% Looking for CSA axiom ... and_1: CSA axiom and_1 found
% Looking for CSA axiom ... and_2: CSA axiom and_2 found
% ---- Iteration 13 (36 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:and_3: CSA axiom and_3 found
% Looking for CSA axiom ... kn1: CSA axiom kn1 found
% Looking for CSA axiom ... kn2: CSA axiom kn2 found
% ---- Iteration 14 (39 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:op_implies_or: CSA axiom op_implies_or found
% Looking for CSA axiom ... axiom_m10: CSA axiom axiom_m10 found
% Looking for CSA axiom ... or_1: CSA axiom or_1 found
% ---- Iteration 15 (42 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:or_2: CSA axiom or_2 found
% Looking for CSA axiom ... or_3: CSA axiom or_3 found
% Looking for CSA axiom ... equivalence_1: CSA axiom equivalence_1 found
% ---- Iteration 16 (45 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:equivalence_2: CSA axiom equivalence_2 found
% Looking for CSA axiom ... equivalence_3: CSA axiom equivalence_3 found
% Looking for CSA axiom ... r1: CSA axiom r1 found
% ---- Iteration 17 (48 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:r2: CSA axiom r2 found
% Looking for CSA axiom ... r3: CSA axiom r3 found
% Looking for CSA axiom ... r4: CSA axiom r4 found
% ---- Iteration 18 (51 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:r5: CSA axiom r5 found
% Looking for CSA axiom ... axiom_K: CSA axiom axiom_K found
% Looking for CSA axiom ... axiom_M: CSA axiom axiom_M found
% ---- Iteration 19 (54 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:axiom_4: CSA axiom axiom_4 found
% Looking for CSA axiom ... axiom_s1: CSA axiom axiom_s1 found
% Looking for CSA axiom ... axiom_s3: CSA axiom axiom_s3 found
% ---- Iteration 20 (57 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:substitution_of_equivalents:substitution_strict_equiv: CSA axiom substitution_strict_equiv found
% Looking for CSA axiom ... axiom_s4: CSA axiom axiom_s4 found
% Looking for CSA axiom ... axiom_m1: CSA axiom axiom_m1 found
% ---- Iteration 21 (60 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:substitution_of_equivalents:axiom_m2: CSA axiom axiom_m2 found
% Looking for CSA axiom ... axiom_m3: CSA axiom axiom_m3 found
% Looking for CSA axiom ... axiom_m4: CSA axiom axiom_m4 found
% ---- Iteration 22 (63 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:substitution_of_equivalents:axiom_m5: CSA axiom axiom_m5 found
% Looking for CSA axiom ... op_possibly: CSA axiom op_possibly found
% Looking for CSA axiom ... op_necessarily: CSA axiom op_necessarily found
% ---- Iteration 23 (66 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:substitution_of_equivalents:op_or: CSA axiom op_or found
% Looking for CSA axiom ... op_and: CSA axiom op_and found
% Looking for CSA axiom ... axiom_B: CSA axiom axiom_B found
% ---- Iteration 24 (69 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:hilbert_op_equiv:substitution_of_equivalents:axiom_5: CSA axiom axiom_5 found
% Looking for CSA axiom ... op_strict_implies: CSA axiom op_strict_implies found
% Looking for CSA axiom ... op_strict_equiv: CSA axiom op_strict_equiv found
% ---- Iteration 25 (72 axioms selected)
% Looking for TBU SAT   ... no
% Looking for TBU UNS   ... yes - theorem proved
% ---- Selection completed
% Selected axioms are   ... :op_strict_equiv:op_strict_implies:axiom_5:axiom_B:op_and:op_or:op_necessarily:op_possibly:axiom_m5:axiom_m4:axiom_m3:axiom_m2:axiom_m1:axiom_s4:substitution_strict_equiv:axiom_s3:axiom_s1:axiom_4:axiom_M:axiom_K:r5:r4:r3:r2:r1:equivalence_3:equivalence_2:equivalence_1:or_3:or_2:or_1:axiom_m10:op_implies_or:kn2:kn1:and_3:and_2:and_1:axiom_m7:axiom_s2:adjunction:modus_ponens_strict_implies:necessitation:op_equiv:op_implies_and:s1_0_substitution_strict_equiv:axiom_m9:axiom_m8:axiom_m6:cn1:implies_3:implies_2:implies_1:modus_ponens:substitution_of_equivalents:s1_0_axiom_m5:s1_0_axiom_m4:s1_0_axiom_m3:s1_0_axiom_m2:s1_0_axiom_m1:s1_0_adjunction:s1_0_modus_ponens_strict_implies:s1_0_op_strict_equiv:s1_0_op_equiv:s1_0_op_strict_implies:s1_0_op_or:s1_0_op_possibly:kn3:cn3:cn2:hilbert_op_implies_and:modus_tollens (72)
% Unselected axioms are ... :hilbert_op_or:hilbert_op_equiv:substitution_of_equivalents:s1_0_op_implies (4)
% SZS status THM for /tmp/SystemOnTPTP5709/LCL551+1.tptp
% Looking for THM       ... found
% SZS output start Solution for /tmp/SystemOnTPTP5709/LCL551+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 22219
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% PrfWatch: 1.93 CPU 2.03 WC
% PrfWatch: 3.93 CPU 4.04 WC
% PrfWatch: 5.93 CPU 6.04 WC
% # Preprocessing time     : 0.022 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 7.93 CPU 8.05 WC
% PrfWatch: 9.93 CPU 10.06 WC
% # SZS output start CNFRefutation.
% fof(1, axiom,(op_strict_equiv=>![X1]:![X2]:strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))),file('/tmp/SRASS.s.p', op_strict_equiv)).
% fof(2, axiom,(op_strict_implies=>![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),file('/tmp/SRASS.s.p', op_strict_implies)).
% fof(6, axiom,(op_or=>![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),file('/tmp/SRASS.s.p', op_or)).
% fof(9, axiom,(axiom_m5<=>![X1]:![X2]:![X3]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))),file('/tmp/SRASS.s.p', axiom_m5)).
% fof(10, axiom,(axiom_m4<=>![X1]:is_a_theorem(strict_implies(X1,and(X1,X1)))),file('/tmp/SRASS.s.p', axiom_m4)).
% fof(11, axiom,(axiom_m3<=>![X1]:![X2]:![X3]:is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))),file('/tmp/SRASS.s.p', axiom_m3)).
% fof(12, axiom,(axiom_m2<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),X1))),file('/tmp/SRASS.s.p', axiom_m2)).
% fof(13, axiom,(axiom_m1<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),file('/tmp/SRASS.s.p', axiom_m1)).
% fof(15, axiom,(substitution_strict_equiv<=>![X1]:![X2]:(is_a_theorem(strict_equiv(X1,X2))=>X1=X2)),file('/tmp/SRASS.s.p', substitution_strict_equiv)).
% fof(41, axiom,(adjunction<=>![X1]:![X2]:((is_a_theorem(X1)&is_a_theorem(X2))=>is_a_theorem(and(X1,X2)))),file('/tmp/SRASS.s.p', adjunction)).
% fof(42, axiom,(modus_ponens_strict_implies<=>![X1]:![X2]:((is_a_theorem(X1)&is_a_theorem(strict_implies(X1,X2)))=>is_a_theorem(X2))),file('/tmp/SRASS.s.p', modus_ponens_strict_implies)).
% fof(44, axiom,(op_equiv=>![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(45, axiom,(op_implies_and=>![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(46, axiom,substitution_strict_equiv,file('/tmp/SRASS.s.p', s1_0_substitution_strict_equiv)).
% fof(56, axiom,axiom_m5,file('/tmp/SRASS.s.p', s1_0_axiom_m5)).
% fof(57, axiom,axiom_m4,file('/tmp/SRASS.s.p', s1_0_axiom_m4)).
% fof(58, axiom,axiom_m3,file('/tmp/SRASS.s.p', s1_0_axiom_m3)).
% fof(59, axiom,axiom_m2,file('/tmp/SRASS.s.p', s1_0_axiom_m2)).
% fof(60, axiom,axiom_m1,file('/tmp/SRASS.s.p', s1_0_axiom_m1)).
% fof(61, axiom,adjunction,file('/tmp/SRASS.s.p', s1_0_adjunction)).
% fof(62, axiom,modus_ponens_strict_implies,file('/tmp/SRASS.s.p', s1_0_modus_ponens_strict_implies)).
% fof(63, axiom,op_strict_equiv,file('/tmp/SRASS.s.p', s1_0_op_strict_equiv)).
% fof(64, axiom,op_equiv,file('/tmp/SRASS.s.p', s1_0_op_equiv)).
% fof(65, axiom,op_strict_implies,file('/tmp/SRASS.s.p', s1_0_op_strict_implies)).
% fof(66, axiom,op_or,file('/tmp/SRASS.s.p', s1_0_op_or)).
% fof(71, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(72, axiom,(modus_tollens<=>![X1]:![X2]:is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2)))),file('/tmp/SRASS.s.p', modus_tollens)).
% fof(73, conjecture,modus_tollens,file('/tmp/SRASS.s.p', hilbert_modus_tollens)).
% fof(74, negated_conjecture,~(modus_tollens),inference(assume_negation,[status(cth)],[73])).
% fof(75, negated_conjecture,~(modus_tollens),inference(fof_simplification,[status(thm)],[74,theory(equality)])).
% fof(76, plain,(~(op_strict_equiv)|![X1]:![X2]:strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))),inference(fof_nnf,[status(thm)],[1])).
% fof(77, plain,(~(op_strict_equiv)|![X3]:![X4]:strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))),inference(variable_rename,[status(thm)],[76])).
% fof(78, plain,![X3]:![X4]:(strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))|~(op_strict_equiv)),inference(shift_quantors,[status(thm)],[77])).
% cnf(79,plain,(strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv),inference(split_conjunct,[status(thm)],[78])).
% fof(80, plain,(~(op_strict_implies)|![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),inference(fof_nnf,[status(thm)],[2])).
% fof(81, plain,(~(op_strict_implies)|![X3]:![X4]:strict_implies(X3,X4)=necessarily(implies(X3,X4))),inference(variable_rename,[status(thm)],[80])).
% fof(82, plain,![X3]:![X4]:(strict_implies(X3,X4)=necessarily(implies(X3,X4))|~(op_strict_implies)),inference(shift_quantors,[status(thm)],[81])).
% cnf(83,plain,(strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies),inference(split_conjunct,[status(thm)],[82])).
% fof(100, plain,(~(op_or)|![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),inference(fof_nnf,[status(thm)],[6])).
% fof(101, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(variable_rename,[status(thm)],[100])).
% fof(102, plain,![X3]:![X4]:(or(X3,X4)=not(and(not(X3),not(X4)))|~(op_or)),inference(shift_quantors,[status(thm)],[101])).
% cnf(103,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[102])).
% fof(112, plain,((~(axiom_m5)|![X1]:![X2]:![X3]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))))&(?[X1]:?[X2]:?[X3]:~(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))))|axiom_m5)),inference(fof_nnf,[status(thm)],[9])).
% fof(113, plain,((~(axiom_m5)|![X4]:![X5]:![X6]:is_a_theorem(strict_implies(and(strict_implies(X4,X5),strict_implies(X5,X6)),strict_implies(X4,X6))))&(?[X7]:?[X8]:?[X9]:~(is_a_theorem(strict_implies(and(strict_implies(X7,X8),strict_implies(X8,X9)),strict_implies(X7,X9))))|axiom_m5)),inference(variable_rename,[status(thm)],[112])).
% fof(114, plain,((~(axiom_m5)|![X4]:![X5]:![X6]:is_a_theorem(strict_implies(and(strict_implies(X4,X5),strict_implies(X5,X6)),strict_implies(X4,X6))))&(~(is_a_theorem(strict_implies(and(strict_implies(esk3_0,esk4_0),strict_implies(esk4_0,esk5_0)),strict_implies(esk3_0,esk5_0))))|axiom_m5)),inference(skolemize,[status(esa)],[113])).
% fof(115, plain,![X4]:![X5]:![X6]:((is_a_theorem(strict_implies(and(strict_implies(X4,X5),strict_implies(X5,X6)),strict_implies(X4,X6)))|~(axiom_m5))&(~(is_a_theorem(strict_implies(and(strict_implies(esk3_0,esk4_0),strict_implies(esk4_0,esk5_0)),strict_implies(esk3_0,esk5_0))))|axiom_m5)),inference(shift_quantors,[status(thm)],[114])).
% cnf(117,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_m5),inference(split_conjunct,[status(thm)],[115])).
% fof(118, plain,((~(axiom_m4)|![X1]:is_a_theorem(strict_implies(X1,and(X1,X1))))&(?[X1]:~(is_a_theorem(strict_implies(X1,and(X1,X1))))|axiom_m4)),inference(fof_nnf,[status(thm)],[10])).
% fof(119, plain,((~(axiom_m4)|![X2]:is_a_theorem(strict_implies(X2,and(X2,X2))))&(?[X3]:~(is_a_theorem(strict_implies(X3,and(X3,X3))))|axiom_m4)),inference(variable_rename,[status(thm)],[118])).
% fof(120, plain,((~(axiom_m4)|![X2]:is_a_theorem(strict_implies(X2,and(X2,X2))))&(~(is_a_theorem(strict_implies(esk6_0,and(esk6_0,esk6_0))))|axiom_m4)),inference(skolemize,[status(esa)],[119])).
% fof(121, plain,![X2]:((is_a_theorem(strict_implies(X2,and(X2,X2)))|~(axiom_m4))&(~(is_a_theorem(strict_implies(esk6_0,and(esk6_0,esk6_0))))|axiom_m4)),inference(shift_quantors,[status(thm)],[120])).
% cnf(123,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4),inference(split_conjunct,[status(thm)],[121])).
% fof(124, plain,((~(axiom_m3)|![X1]:![X2]:![X3]:is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))))&(?[X1]:?[X2]:?[X3]:~(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))))|axiom_m3)),inference(fof_nnf,[status(thm)],[11])).
% fof(125, plain,((~(axiom_m3)|![X4]:![X5]:![X6]:is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X4,and(X5,X6)))))&(?[X7]:?[X8]:?[X9]:~(is_a_theorem(strict_implies(and(and(X7,X8),X9),and(X7,and(X8,X9)))))|axiom_m3)),inference(variable_rename,[status(thm)],[124])).
% fof(126, plain,((~(axiom_m3)|![X4]:![X5]:![X6]:is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X4,and(X5,X6)))))&(~(is_a_theorem(strict_implies(and(and(esk7_0,esk8_0),esk9_0),and(esk7_0,and(esk8_0,esk9_0)))))|axiom_m3)),inference(skolemize,[status(esa)],[125])).
% fof(127, plain,![X4]:![X5]:![X6]:((is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X4,and(X5,X6))))|~(axiom_m3))&(~(is_a_theorem(strict_implies(and(and(esk7_0,esk8_0),esk9_0),and(esk7_0,and(esk8_0,esk9_0)))))|axiom_m3)),inference(shift_quantors,[status(thm)],[126])).
% cnf(129,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|~axiom_m3),inference(split_conjunct,[status(thm)],[127])).
% fof(130, plain,((~(axiom_m2)|![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),X1)))&(?[X1]:?[X2]:~(is_a_theorem(strict_implies(and(X1,X2),X1)))|axiom_m2)),inference(fof_nnf,[status(thm)],[12])).
% fof(131, plain,((~(axiom_m2)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),X3)))&(?[X5]:?[X6]:~(is_a_theorem(strict_implies(and(X5,X6),X5)))|axiom_m2)),inference(variable_rename,[status(thm)],[130])).
% fof(132, plain,((~(axiom_m2)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),X3)))&(~(is_a_theorem(strict_implies(and(esk10_0,esk11_0),esk10_0)))|axiom_m2)),inference(skolemize,[status(esa)],[131])).
% fof(133, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),X3))|~(axiom_m2))&(~(is_a_theorem(strict_implies(and(esk10_0,esk11_0),esk10_0)))|axiom_m2)),inference(shift_quantors,[status(thm)],[132])).
% cnf(135,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2),inference(split_conjunct,[status(thm)],[133])).
% fof(136, plain,((~(axiom_m1)|![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))))&(?[X1]:?[X2]:~(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))))|axiom_m1)),inference(fof_nnf,[status(thm)],[13])).
% fof(137, plain,((~(axiom_m1)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))))&(?[X5]:?[X6]:~(is_a_theorem(strict_implies(and(X5,X6),and(X6,X5))))|axiom_m1)),inference(variable_rename,[status(thm)],[136])).
% fof(138, plain,((~(axiom_m1)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))))&(~(is_a_theorem(strict_implies(and(esk12_0,esk13_0),and(esk13_0,esk12_0))))|axiom_m1)),inference(skolemize,[status(esa)],[137])).
% fof(139, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),and(X4,X3)))|~(axiom_m1))&(~(is_a_theorem(strict_implies(and(esk12_0,esk13_0),and(esk13_0,esk12_0))))|axiom_m1)),inference(shift_quantors,[status(thm)],[138])).
% cnf(141,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1),inference(split_conjunct,[status(thm)],[139])).
% fof(148, plain,((~(substitution_strict_equiv)|![X1]:![X2]:(~(is_a_theorem(strict_equiv(X1,X2)))|X1=X2))&(?[X1]:?[X2]:(is_a_theorem(strict_equiv(X1,X2))&~(X1=X2))|substitution_strict_equiv)),inference(fof_nnf,[status(thm)],[15])).
% fof(149, plain,((~(substitution_strict_equiv)|![X3]:![X4]:(~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4))&(?[X5]:?[X6]:(is_a_theorem(strict_equiv(X5,X6))&~(X5=X6))|substitution_strict_equiv)),inference(variable_rename,[status(thm)],[148])).
% fof(150, plain,((~(substitution_strict_equiv)|![X3]:![X4]:(~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4))&((is_a_theorem(strict_equiv(esk15_0,esk16_0))&~(esk15_0=esk16_0))|substitution_strict_equiv)),inference(skolemize,[status(esa)],[149])).
% fof(151, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk15_0,esk16_0))&~(esk15_0=esk16_0))|substitution_strict_equiv)),inference(shift_quantors,[status(thm)],[150])).
% fof(152, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk15_0,esk16_0))|substitution_strict_equiv)&(~(esk15_0=esk16_0)|substitution_strict_equiv))),inference(distribute,[status(thm)],[151])).
% cnf(155,plain,(X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2))),inference(split_conjunct,[status(thm)],[152])).
% fof(304, plain,((~(adjunction)|![X1]:![X2]:((~(is_a_theorem(X1))|~(is_a_theorem(X2)))|is_a_theorem(and(X1,X2))))&(?[X1]:?[X2]:((is_a_theorem(X1)&is_a_theorem(X2))&~(is_a_theorem(and(X1,X2))))|adjunction)),inference(fof_nnf,[status(thm)],[41])).
% fof(305, plain,((~(adjunction)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4))))&(?[X5]:?[X6]:((is_a_theorem(X5)&is_a_theorem(X6))&~(is_a_theorem(and(X5,X6))))|adjunction)),inference(variable_rename,[status(thm)],[304])).
% fof(306, plain,((~(adjunction)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4))))&(((is_a_theorem(esk64_0)&is_a_theorem(esk65_0))&~(is_a_theorem(and(esk64_0,esk65_0))))|adjunction)),inference(skolemize,[status(esa)],[305])).
% fof(307, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk64_0)&is_a_theorem(esk65_0))&~(is_a_theorem(and(esk64_0,esk65_0))))|adjunction)),inference(shift_quantors,[status(thm)],[306])).
% fof(308, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk64_0)|adjunction)&(is_a_theorem(esk65_0)|adjunction))&(~(is_a_theorem(and(esk64_0,esk65_0)))|adjunction))),inference(distribute,[status(thm)],[307])).
% cnf(312,plain,(is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(split_conjunct,[status(thm)],[308])).
% fof(313, plain,((~(modus_ponens_strict_implies)|![X1]:![X2]:((~(is_a_theorem(X1))|~(is_a_theorem(strict_implies(X1,X2))))|is_a_theorem(X2)))&(?[X1]:?[X2]:((is_a_theorem(X1)&is_a_theorem(strict_implies(X1,X2)))&~(is_a_theorem(X2)))|modus_ponens_strict_implies)),inference(fof_nnf,[status(thm)],[42])).
% fof(314, plain,((~(modus_ponens_strict_implies)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(strict_implies(X3,X4))))|is_a_theorem(X4)))&(?[X5]:?[X6]:((is_a_theorem(X5)&is_a_theorem(strict_implies(X5,X6)))&~(is_a_theorem(X6)))|modus_ponens_strict_implies)),inference(variable_rename,[status(thm)],[313])).
% fof(315, plain,((~(modus_ponens_strict_implies)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(strict_implies(X3,X4))))|is_a_theorem(X4)))&(((is_a_theorem(esk66_0)&is_a_theorem(strict_implies(esk66_0,esk67_0)))&~(is_a_theorem(esk67_0)))|modus_ponens_strict_implies)),inference(skolemize,[status(esa)],[314])).
% fof(316, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(strict_implies(X3,X4))))|is_a_theorem(X4))|~(modus_ponens_strict_implies))&(((is_a_theorem(esk66_0)&is_a_theorem(strict_implies(esk66_0,esk67_0)))&~(is_a_theorem(esk67_0)))|modus_ponens_strict_implies)),inference(shift_quantors,[status(thm)],[315])).
% fof(317, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(strict_implies(X3,X4))))|is_a_theorem(X4))|~(modus_ponens_strict_implies))&(((is_a_theorem(esk66_0)|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(esk66_0,esk67_0))|modus_ponens_strict_implies))&(~(is_a_theorem(esk67_0))|modus_ponens_strict_implies))),inference(distribute,[status(thm)],[316])).
% cnf(321,plain,(is_a_theorem(X1)|~modus_ponens_strict_implies|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(X2)),inference(split_conjunct,[status(thm)],[317])).
% fof(330, plain,(~(op_equiv)|![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),inference(fof_nnf,[status(thm)],[44])).
% fof(331, plain,(~(op_equiv)|![X3]:![X4]:equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))),inference(variable_rename,[status(thm)],[330])).
% fof(332, plain,![X3]:![X4]:(equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))|~(op_equiv)),inference(shift_quantors,[status(thm)],[331])).
% cnf(333,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[332])).
% fof(334, plain,(~(op_implies_and)|![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),inference(fof_nnf,[status(thm)],[45])).
% fof(335, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(variable_rename,[status(thm)],[334])).
% fof(336, plain,![X3]:![X4]:(implies(X3,X4)=not(and(X3,not(X4)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[335])).
% cnf(337,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[336])).
% cnf(338,plain,(substitution_strict_equiv),inference(split_conjunct,[status(thm)],[46])).
% cnf(391,plain,(axiom_m5),inference(split_conjunct,[status(thm)],[56])).
% cnf(392,plain,(axiom_m4),inference(split_conjunct,[status(thm)],[57])).
% cnf(393,plain,(axiom_m3),inference(split_conjunct,[status(thm)],[58])).
% cnf(394,plain,(axiom_m2),inference(split_conjunct,[status(thm)],[59])).
% cnf(395,plain,(axiom_m1),inference(split_conjunct,[status(thm)],[60])).
% cnf(396,plain,(adjunction),inference(split_conjunct,[status(thm)],[61])).
% cnf(397,plain,(modus_ponens_strict_implies),inference(split_conjunct,[status(thm)],[62])).
% cnf(398,plain,(op_strict_equiv),inference(split_conjunct,[status(thm)],[63])).
% cnf(399,plain,(op_equiv),inference(split_conjunct,[status(thm)],[64])).
% cnf(400,plain,(op_strict_implies),inference(split_conjunct,[status(thm)],[65])).
% cnf(401,plain,(op_or),inference(split_conjunct,[status(thm)],[66])).
% cnf(421,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[71])).
% fof(422, plain,((~(modus_tollens)|![X1]:![X2]:is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))))&(?[X1]:?[X2]:~(is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))))|modus_tollens)),inference(fof_nnf,[status(thm)],[72])).
% fof(423, plain,((~(modus_tollens)|![X3]:![X4]:is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4))))&(?[X5]:?[X6]:~(is_a_theorem(implies(implies(not(X6),not(X5)),implies(X5,X6))))|modus_tollens)),inference(variable_rename,[status(thm)],[422])).
% fof(424, plain,((~(modus_tollens)|![X3]:![X4]:is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4))))&(~(is_a_theorem(implies(implies(not(esk92_0),not(esk91_0)),implies(esk91_0,esk92_0))))|modus_tollens)),inference(skolemize,[status(esa)],[423])).
% fof(425, plain,![X3]:![X4]:((is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4)))|~(modus_tollens))&(~(is_a_theorem(implies(implies(not(esk92_0),not(esk91_0)),implies(esk91_0,esk92_0))))|modus_tollens)),inference(shift_quantors,[status(thm)],[424])).
% cnf(426,plain,(modus_tollens|~is_a_theorem(implies(implies(not(esk92_0),not(esk91_0)),implies(esk91_0,esk92_0)))),inference(split_conjunct,[status(thm)],[425])).
% cnf(428,negated_conjecture,(~modus_tollens),inference(split_conjunct,[status(thm)],[75])).
% cnf(439,plain,(X1=X2|$false|~is_a_theorem(strict_equiv(X1,X2))),inference(rw,[status(thm)],[155,338,theory(equality)])).
% cnf(440,plain,(X1=X2|~is_a_theorem(strict_equiv(X1,X2))),inference(cn,[status(thm)],[439,theory(equality)])).
% cnf(445,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|$false),inference(rw,[status(thm)],[123,392,theory(equality)])).
% cnf(446,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))),inference(cn,[status(thm)],[445,theory(equality)])).
% cnf(447,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[135,394,theory(equality)])).
% cnf(448,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))),inference(cn,[status(thm)],[447,theory(equality)])).
% cnf(449,plain,(~is_a_theorem(implies(implies(not(esk92_0),not(esk91_0)),implies(esk91_0,esk92_0)))),inference(sr,[status(thm)],[426,428,theory(equality)])).
% cnf(450,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)|$false),inference(rw,[status(thm)],[83,400,theory(equality)])).
% cnf(451,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)),inference(cn,[status(thm)],[450,theory(equality)])).
% cnf(452,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(rw,[status(thm)],[321,397,theory(equality)])).
% cnf(453,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(cn,[status(thm)],[452,theory(equality)])).
% cnf(454,plain,(is_a_theorem(X1)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[453,448,theory(equality)])).
% cnf(456,plain,(is_a_theorem(and(X1,X2))|$false|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(rw,[status(thm)],[312,396,theory(equality)])).
% cnf(457,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(cn,[status(thm)],[456,theory(equality)])).
% cnf(458,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[337,421,theory(equality)])).
% cnf(459,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[458,theory(equality)])).
% cnf(461,plain,(not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))),inference(spm,[status(thm)],[459,459,theory(equality)])).
% cnf(465,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[141,395,theory(equality)])).
% cnf(466,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[465,theory(equality)])).
% cnf(468,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[103,459,theory(equality)])).
% cnf(469,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[468,401,theory(equality)])).
% cnf(470,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[469,theory(equality)])).
% cnf(471,plain,(necessarily(or(X1,X2))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[451,470,theory(equality)])).
% cnf(473,plain,(implies(implies(X1,X2),X3)=or(and(X1,not(X2)),X3)),inference(spm,[status(thm)],[470,459,theory(equality)])).
% cnf(476,plain,(~is_a_theorem(implies(or(esk92_0,not(esk91_0)),implies(esk91_0,esk92_0)))),inference(rw,[status(thm)],[449,470,theory(equality)])).
% cnf(482,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)|$false),inference(rw,[status(thm)],[79,398,theory(equality)])).
% cnf(483,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)),inference(cn,[status(thm)],[482,theory(equality)])).
% cnf(484,plain,(is_a_theorem(strict_equiv(X1,X2))|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(strict_implies(X1,X2))),inference(spm,[status(thm)],[457,483,theory(equality)])).
% cnf(492,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[333,399,theory(equality)])).
% cnf(493,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[492,theory(equality)])).
% cnf(496,plain,(is_a_theorem(strict_implies(equiv(X1,X2),and(implies(X2,X1),implies(X1,X2))))),inference(spm,[status(thm)],[466,493,theory(equality)])).
% cnf(506,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|$false),inference(rw,[status(thm)],[129,393,theory(equality)])).
% cnf(507,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))),inference(cn,[status(thm)],[506,theory(equality)])).
% cnf(508,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(and(and(X1,X2),X3))),inference(spm,[status(thm)],[453,507,theory(equality)])).
% cnf(513,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|$false),inference(rw,[status(thm)],[117,391,theory(equality)])).
% cnf(514,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))),inference(cn,[status(thm)],[513,theory(equality)])).
% cnf(515,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))),inference(spm,[status(thm)],[453,514,theory(equality)])).
% cnf(520,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_equiv(X1,X2))),inference(spm,[status(thm)],[454,483,theory(equality)])).
% cnf(559,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|~is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(spm,[status(thm)],[484,466,theory(equality)])).
% cnf(560,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(and(X1,X2),X3)))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))),inference(spm,[status(thm)],[484,507,theory(equality)])).
% cnf(563,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|~is_a_theorem(strict_implies(and(X1,X1),X1))),inference(spm,[status(thm)],[484,446,theory(equality)])).
% cnf(564,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[559,466,theory(equality)])).
% cnf(565,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[564,theory(equality)])).
% cnf(566,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|$false),inference(rw,[status(thm)],[563,448,theory(equality)])).
% cnf(567,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))),inference(cn,[status(thm)],[566,theory(equality)])).
% cnf(568,plain,(and(X1,X1)=X1),inference(spm,[status(thm)],[440,567,theory(equality)])).
% cnf(576,plain,(strict_implies(X1,X1)=strict_equiv(X1,X1)),inference(spm,[status(thm)],[483,568,theory(equality)])).
% cnf(578,plain,(not(not(X1))=implies(not(X1),X1)),inference(spm,[status(thm)],[459,568,theory(equality)])).
% cnf(589,plain,(is_a_theorem(strict_equiv(X1,X1))),inference(rw,[status(thm)],[567,568,theory(equality)])).
% cnf(595,plain,(not(not(X1))=or(X1,X1)),inference(rw,[status(thm)],[578,470,theory(equality)])).
% cnf(607,plain,(not(implies(X1,X2))=implies(implies(X1,X2),and(X1,not(X2)))),inference(spm,[status(thm)],[461,568,theory(equality)])).
% cnf(611,plain,(is_a_theorem(strict_implies(X1,X1))),inference(spm,[status(thm)],[520,589,theory(equality)])).
% cnf(637,plain,(and(X1,X2)=and(X2,X1)),inference(spm,[status(thm)],[440,565,theory(equality)])).
% cnf(667,plain,(is_a_theorem(strict_implies(and(X3,and(X1,X2)),and(X1,and(X2,X3))))),inference(spm,[status(thm)],[507,637,theory(equality)])).
% cnf(668,plain,(and(strict_implies(X2,X1),strict_implies(X1,X2))=strict_equiv(X1,X2)),inference(spm,[status(thm)],[483,637,theory(equality)])).
% cnf(670,plain,(not(and(not(X2),X1))=implies(X1,X2)),inference(spm,[status(thm)],[459,637,theory(equality)])).
% cnf(677,plain,(is_a_theorem(strict_implies(and(X2,X1),X1))),inference(spm,[status(thm)],[448,637,theory(equality)])).
% cnf(708,plain,(strict_equiv(X2,X1)=strict_equiv(X1,X2)),inference(rw,[status(thm)],[668,483,theory(equality)])).
% cnf(753,plain,(not(and(X1,or(X2,X2)))=implies(X1,not(X2))),inference(spm,[status(thm)],[459,595,theory(equality)])).
% cnf(815,plain,(implies(not(X2),X1)=implies(not(X1),X2)),inference(spm,[status(thm)],[459,670,theory(equality)])).
% cnf(818,plain,(not(and(or(X1,X1),X2))=implies(X2,not(X1))),inference(spm,[status(thm)],[670,595,theory(equality)])).
% cnf(831,plain,(or(X2,X1)=implies(not(X1),X2)),inference(rw,[status(thm)],[815,470,theory(equality)])).
% cnf(832,plain,(or(X2,X1)=or(X1,X2)),inference(rw,[status(thm)],[831,470,theory(equality)])).
% cnf(842,plain,(necessarily(or(X2,X1))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[471,832,theory(equality)])).
% cnf(854,plain,(strict_implies(not(X2),X1)=strict_implies(not(X1),X2)),inference(rw,[status(thm)],[842,471,theory(equality)])).
% cnf(1032,plain,(and(strict_implies(not(X2),X1),strict_implies(X2,not(X1)))=strict_equiv(not(X1),X2)),inference(spm,[status(thm)],[483,854,theory(equality)])).
% cnf(1035,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[453,854,theory(equality)])).
% cnf(1052,plain,(strict_implies(not(X1),not(X2))=strict_implies(or(X2,X2),X1)),inference(spm,[status(thm)],[854,595,theory(equality)])).
% cnf(1055,plain,(strict_implies(not(X1),and(not(X2),X3))=strict_implies(implies(X3,X2),X1)),inference(spm,[status(thm)],[854,670,theory(equality)])).
% cnf(1074,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),and(X2,not(X3))))|~is_a_theorem(implies(X2,X3))),inference(spm,[status(thm)],[1035,459,theory(equality)])).
% cnf(1131,plain,(is_a_theorem(strict_implies(equiv(X1,X2),equiv(X2,X1)))),inference(spm,[status(thm)],[496,493,theory(equality)])).
% cnf(1354,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(X3)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[508,457,theory(equality)])).
% cnf(1555,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X3,X2))|~is_a_theorem(strict_implies(X1,X3))),inference(spm,[status(thm)],[515,457,theory(equality)])).
% cnf(1765,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),and(not(X2),not(X3))))|~is_a_theorem(or(X2,X3))),inference(spm,[status(thm)],[1074,470,theory(equality)])).
% cnf(1802,plain,(implies(not(X1),not(X2))=implies(or(X2,X2),X1)),inference(spm,[status(thm)],[670,753,theory(equality)])).
% cnf(1820,plain,(or(X1,not(X2))=implies(or(X2,X2),X1)),inference(rw,[status(thm)],[1802,470,theory(equality)])).
% cnf(2321,plain,(is_a_theorem(and(strict_implies(X1,X2),and(strict_implies(X2,X1),X3)))|~is_a_theorem(strict_equiv(X1,X2))|~is_a_theorem(X3)),inference(spm,[status(thm)],[1354,483,theory(equality)])).
% cnf(2478,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))|~is_a_theorem(strict_implies(and(X1,and(X1,X2)),and(X1,X2)))),inference(spm,[status(thm)],[560,568,theory(equality)])).
% cnf(2494,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))|$false),inference(rw,[status(thm)],[2478,677,theory(equality)])).
% cnf(2495,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))),inference(cn,[status(thm)],[2494,theory(equality)])).
% cnf(2507,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X1,and(X1,X2))))),inference(rw,[status(thm)],[2495,708,theory(equality)])).
% cnf(2508,plain,(and(X1,X2)=and(X1,and(X1,X2))),inference(spm,[status(thm)],[440,2507,theory(equality)])).
% cnf(4314,plain,(is_a_theorem(strict_implies(and(X1,and(X3,X2)),and(X2,and(X3,X1))))),inference(spm,[status(thm)],[667,637,theory(equality)])).
% cnf(5283,plain,(~is_a_theorem(implies(implies(or(esk91_0,esk91_0),esk92_0),implies(esk91_0,esk92_0)))),inference(rw,[status(thm)],[476,1820,theory(equality)])).
% cnf(15149,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(not(X1),X2)),inference(rw,[status(thm)],[1032,637,theory(equality)])).
% cnf(15945,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(spm,[status(thm)],[611,1052,theory(equality)])).
% cnf(15985,plain,(is_a_theorem(strict_implies(or(X1,X1),X1))),inference(spm,[status(thm)],[611,1052,theory(equality)])).
% cnf(16123,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|~is_a_theorem(strict_implies(X1,or(X1,X1)))),inference(spm,[status(thm)],[484,15985,theory(equality)])).
% cnf(16695,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(or(X3,X2),X1))|~is_a_theorem(or(X2,X3))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[1765,1055,theory(equality)]),470,theory(equality)])).
% cnf(17600,plain,(is_a_theorem(strict_implies(not(not(X1)),or(X1,X1)))),inference(rw,[status(thm)],[15945,854,theory(equality)])).
% cnf(31344,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,or(X2,X2)))),inference(spm,[status(thm)],[1555,15985,theory(equality)])).
% cnf(31385,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,and(X3,X2)))),inference(spm,[status(thm)],[1555,677,theory(equality)])).
% cnf(31423,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,not(not(X2))))),inference(spm,[status(thm)],[31344,595,theory(equality)])).
% cnf(31436,plain,(is_a_theorem(strict_implies(or(or(X1,X1),or(X1,X1)),X1))),inference(spm,[status(thm)],[31344,15985,theory(equality)])).
% cnf(32244,plain,(is_a_theorem(strict_implies(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[31436,595,theory(equality)]),854,theory(equality)])).
% cnf(32246,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|~is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(spm,[status(thm)],[484,32244,theory(equality)])).
% cnf(32300,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[32246,854,theory(equality)]),17600,theory(equality)])).
% cnf(32301,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))),inference(cn,[status(thm)],[32300,theory(equality)])).
% cnf(32336,plain,(is_a_theorem(strict_equiv(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[32301,708,theory(equality)])).
% cnf(32337,plain,(not(X1)=not(or(X1,X1))),inference(spm,[status(thm)],[440,32336,theory(equality)])).
% cnf(32441,plain,(not(and(not(X1),X2))=implies(X2,or(X1,X1))),inference(spm,[status(thm)],[670,32337,theory(equality)])).
% cnf(32728,plain,(implies(X2,X1)=implies(X2,or(X1,X1))),inference(rw,[status(thm)],[32441,670,theory(equality)])).
% cnf(35179,plain,(is_a_theorem(strict_implies(or(and(X1,X2),and(X1,X2)),X2))),inference(spm,[status(thm)],[31385,15985,theory(equality)])).
% cnf(36293,plain,(is_a_theorem(strict_implies(or(and(X1,not(not(X2))),and(X1,not(not(X2)))),X2))),inference(spm,[status(thm)],[31423,35179,theory(equality)])).
% cnf(36329,plain,(is_a_theorem(strict_implies(not(implies(X1,not(X2))),X2))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[36293,473,theory(equality)]),607,theory(equality)])).
% cnf(36333,plain,(is_a_theorem(strict_implies(not(X2),implies(X1,not(X2))))),inference(rw,[status(thm)],[36329,854,theory(equality)])).
% cnf(46505,plain,(necessarily(implies(X1,X2))=strict_implies(X1,or(X2,X2))),inference(spm,[status(thm)],[451,32728,theory(equality)])).
% cnf(46640,plain,(strict_implies(X1,X2)=strict_implies(X1,or(X2,X2))),inference(rw,[status(thm)],[46505,451,theory(equality)])).
% cnf(48389,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[16123,46640,theory(equality)]),611,theory(equality)])).
% cnf(48390,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))),inference(cn,[status(thm)],[48389,theory(equality)])).
% cnf(48539,plain,(X1=or(X1,X1)),inference(spm,[status(thm)],[440,48390,theory(equality)])).
% cnf(48697,plain,(not(and(X1,X2))=implies(X1,not(X2))),inference(rw,[status(thm)],[753,48539,theory(equality)])).
% cnf(48727,plain,(not(and(X1,X2))=implies(X2,not(X1))),inference(rw,[status(thm)],[818,48539,theory(equality)])).
% cnf(48729,plain,(not(not(X1))=X1),inference(rw,[status(thm)],[595,48539,theory(equality)])).
% cnf(48738,plain,(~is_a_theorem(implies(implies(esk91_0,esk92_0),implies(esk91_0,esk92_0)))),inference(rw,[status(thm)],[5283,48539,theory(equality)])).
% cnf(48866,plain,(is_a_theorem(strict_implies(X1,implies(X2,X1)))),inference(spm,[status(thm)],[36333,48729,theory(equality)])).
% cnf(51877,plain,(is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X1,X3))),inference(spm,[status(thm)],[1555,48866,theory(equality)])).
% cnf(52802,plain,(not(implies(X1,not(X2)))=and(X1,X2)),inference(spm,[status(thm)],[48729,48697,theory(equality)])).
% cnf(53137,plain,(implies(X1,not(X2))=implies(X2,not(X1))),inference(rw,[status(thm)],[48727,48697,theory(equality)])).
% cnf(53149,plain,(necessarily(implies(X2,not(X1)))=strict_implies(X1,not(X2))),inference(spm,[status(thm)],[451,53137,theory(equality)])).
% cnf(53401,plain,(strict_implies(X2,not(X1))=strict_implies(X1,not(X2))),inference(rw,[status(thm)],[53149,451,theory(equality)])).
% cnf(59793,plain,(is_a_theorem(and(strict_implies(X1,X1),and(strict_implies(X1,X1),X2)))|~is_a_theorem(strict_implies(X1,X1))|~is_a_theorem(X2)),inference(spm,[status(thm)],[2321,576,theory(equality)])).
% cnf(59802,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|~is_a_theorem(strict_implies(X1,X1))|~is_a_theorem(X2)),inference(rw,[status(thm)],[59793,2508,theory(equality)])).
% cnf(59803,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|$false|~is_a_theorem(X2)),inference(rw,[status(thm)],[59802,611,theory(equality)])).
% cnf(59804,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|~is_a_theorem(X2)),inference(cn,[status(thm)],[59803,theory(equality)])).
% cnf(73533,plain,(is_a_theorem(strict_implies(and(X1,X2),implies(X3,X1)))),inference(spm,[status(thm)],[51877,448,theory(equality)])).
% cnf(73567,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(and(X2,X3))),inference(spm,[status(thm)],[453,73533,theory(equality)])).
% cnf(74887,plain,(is_a_theorem(implies(X1,strict_implies(X2,X2)))|~is_a_theorem(X3)),inference(spm,[status(thm)],[73567,59804,theory(equality)])).
% cnf(76040,plain,(is_a_theorem(implies(X1,strict_implies(X2,X2)))),inference(spm,[status(thm)],[74887,1131,theory(equality)])).
% cnf(76195,plain,(is_a_theorem(or(X1,strict_implies(X2,X2)))),inference(spm,[status(thm)],[76040,470,theory(equality)])).
% cnf(76204,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(or(strict_implies(X2,X2),X3),X1))),inference(spm,[status(thm)],[16695,76195,theory(equality)])).
% cnf(77875,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(X3,and(X2,X1))))),inference(spm,[status(thm)],[484,4314,theory(equality)])).
% cnf(77950,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))|$false),inference(rw,[status(thm)],[77875,4314,theory(equality)])).
% cnf(77951,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))),inference(cn,[status(thm)],[77950,theory(equality)])).
% cnf(97139,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(X1,not(X2))),inference(spm,[status(thm)],[483,53401,theory(equality)])).
% cnf(97733,plain,(strict_equiv(not(X1),X2)=strict_equiv(X1,not(X2))),inference(rw,[status(thm)],[97139,15149,theory(equality)])).
% cnf(98027,plain,(not(X1)=X2|~is_a_theorem(strict_equiv(X1,not(X2)))),inference(spm,[status(thm)],[440,97733,theory(equality)])).
% cnf(98196,plain,(not(X1)=implies(X2,not(X3))|~is_a_theorem(strict_equiv(X1,and(X2,X3)))),inference(spm,[status(thm)],[98027,52802,theory(equality)])).
% cnf(185512,plain,(not(X1)=implies(X2,not(X3))|~is_a_theorem(strict_equiv(X1,and(X3,X2)))),inference(spm,[status(thm)],[98196,637,theory(equality)])).
% cnf(189239,plain,(not(and(X1,and(X2,X3)))=implies(and(X2,X1),not(X3))),inference(spm,[status(thm)],[185512,77951,theory(equality)])).
% cnf(189256,plain,(implies(X1,implies(X2,not(X3)))=implies(and(X2,X1),not(X3))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[189239,48697,theory(equality)]),48697,theory(equality)])).
% cnf(189556,plain,(implies(and(X1,X2),X3)=implies(X2,implies(X1,X3))),inference(spm,[status(thm)],[189256,48729,theory(equality)])).
% cnf(286987,plain,(necessarily(implies(X2,implies(X1,X3)))=strict_implies(and(X1,X2),X3)),inference(spm,[status(thm)],[451,189556,theory(equality)])).
% cnf(287561,plain,(strict_implies(X2,implies(X1,X3))=strict_implies(and(X1,X2),X3)),inference(rw,[status(thm)],[286987,451,theory(equality)])).
% cnf(290107,plain,(is_a_theorem(strict_implies(X2,implies(X1,X1)))),inference(rw,[status(thm)],[448,287561,theory(equality)])).
% cnf(290627,plain,(is_a_theorem(implies(X1,X1))),inference(spm,[status(thm)],[76204,290107,theory(equality)])).
% cnf(290798,plain,($false),inference(rw,[status(thm)],[48738,290627,theory(equality)])).
% cnf(290799,plain,($false),inference(cn,[status(thm)],[290798,theory(equality)])).
% cnf(290800,plain,($false),290799,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses                  : 14437
% # ...of these trivial                : 878
% # ...subsumed                        : 10845
% # ...remaining for further processing: 2714
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed                  : 56
% # Backward-rewritten                 : 1059
% # Generated clauses                  : 204249
% # ...of the previous two non-trivial : 165252
% # Contextual simplify-reflections    : 732
% # Paramodulations                    : 204249
% # Factorizations                     : 0
% # Equation resolutions               : 0
% # Current number of processed clauses: 1599
% #    Positive orientable unit clauses: 605
% #    Positive unorientable unit clauses: 34
% #    Negative unit clauses           : 3
% #    Non-unit-clauses                : 957
% # Current number of unprocessed clauses: 67606
% # ...number of literals in the above : 115621
% # Clause-clause subsumption calls (NU) : 163058
% # Rec. Clause-clause subsumption calls : 161933
% # Unit Clause-clause subsumption calls : 1177
% # Rewrite failures with RHS unbound  : 0
% # Indexed BW rewrite attempts        : 53429
% # Indexed BW rewrite successes       : 1882
% # Backwards rewriting index:  1134 leaves,   3.30+/-6.469 terms/leaf
% # Paramod-from index:          219 leaves,   3.60+/-9.098 terms/leaf
% # Paramod-into index:         1004 leaves,   3.32+/-6.690 terms/leaf
% # -------------------------------------------------
% # User time              : 7.074 s
% # System time            : 0.263 s
% # Total time             : 7.337 s
% # Maximum resident set size: 0 pages
% PrfWatch: 11.58 CPU 11.73 WC
% FINAL PrfWatch: 11.58 CPU 11.73 WC
% SZS output end Solution for /tmp/SystemOnTPTP5709/LCL551+1.tptp
% 
%------------------------------------------------------------------------------