%------------------------------------------------------------------------------
% File     : SRASS---0.1
% Problem  : LCL556+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 : art06.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 14:00:26 EST 2010

% Result   : Theorem 277.19s
% Output   : Solution 289.28s
% 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/SystemOnTPTP3231/LCL556+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM       ... 
% not found
% Adding ~C to TBU       ... ~hilbert_and_2:
% ---- Iteration 1 (0 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... and_2: CSA axiom and_2 found
% Looking for CSA axiom ... s1_0_op_equiv:
%  CSA axiom s1_0_op_equiv found
% Looking for CSA axiom ... s1_0_adjunction: CSA axiom s1_0_adjunction found
% ---- Iteration 2 (3 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 3 (6 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_implies_and:
%  CSA axiom hilbert_op_implies_and found
% ---- Iteration 4 (9 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% and_1:
%  CSA axiom and_1 found
% Looking for CSA axiom ... and_3:
%  CSA axiom and_3 found
% Looking for CSA axiom ... kn1:
%  CSA axiom kn1 found
% ---- Iteration 5 (12 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% kn2:
%  CSA axiom kn2 found
% Looking for CSA axiom ... adjunction:
%  CSA axiom adjunction found
% Looking for CSA axiom ... s1_0_op_possibly:
%  CSA axiom s1_0_op_possibly found
% ---- Iteration 6 (15 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% 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_strict_equiv: CSA axiom s1_0_op_strict_equiv found
% ---- Iteration 7 (18 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% s1_0_modus_ponens_strict_implies:
%  CSA axiom s1_0_modus_ponens_strict_implies found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:
%  CSA axiom substitution_of_equivalents found
% Looking for CSA axiom ... modus_ponens:
%  CSA axiom modus_ponens found
% ---- Iteration 8 (21 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% implies_1:
%  CSA axiom implies_1 found
% Looking for CSA axiom ... implies_2:
%  CSA axiom implies_2 found
% Looking for CSA axiom ... implies_3:
%  CSA axiom implies_3 found
% ---- Iteration 9 (24 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% cn1:
%  CSA axiom cn1 found
% Looking for CSA axiom ... axiom_s1:
%  CSA axiom axiom_s1 found
% Looking for CSA axiom ... kn3:
%  CSA axiom kn3 found
% ---- Iteration 10 (27 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% s1_0_substitution_strict_equiv: CSA axiom s1_0_substitution_strict_equiv found
% Looking for CSA axiom ... axiom_m1:
%  CSA axiom axiom_m1 found
% Looking for CSA axiom ... axiom_m2:
%  CSA axiom axiom_m2 found
% ---- Iteration 11 (30 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% axiom_m3:
%  CSA axiom axiom_m3 found
% Looking for CSA axiom ... axiom_m4:
%  CSA axiom axiom_m4 found
% Looking for CSA axiom ... axiom_m5:
%  CSA axiom axiom_m5 found
% ---- Iteration 12 (33 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% necessitation:
%  CSA axiom necessitation found
% Looking for CSA axiom ... modus_ponens_strict_implies:
%  CSA axiom modus_ponens_strict_implies found
% Looking for CSA axiom ... modus_tollens:
%  CSA axiom modus_tollens found
% ---- Iteration 13 (36 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% or_1:
%  CSA axiom or_1 found
% Looking for CSA axiom ... or_2:
%  CSA axiom or_2 found
% Looking for CSA axiom ... or_3:
%  CSA axiom or_3 found
% ---- Iteration 14 (39 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% equivalence_1:
%  CSA axiom equivalence_1 found
% Looking for CSA axiom ... equivalence_2:
%  CSA axiom equivalence_2 found
% Looking for CSA axiom ... equivalence_3:
%  CSA axiom equivalence_3 found
% ---- Iteration 15 (42 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% cn2:
%  CSA axiom cn2 found
% Looking for CSA axiom ... cn3:
%  CSA axiom cn3 found
% Looking for CSA axiom ... r1:
%  CSA axiom r1 found
% ---- Iteration 16 (45 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% r2:
%  CSA axiom r2 found
% Looking for CSA axiom ... r3:
%  CSA axiom r3 found
% Looking for CSA axiom ... r4:
%  CSA axiom r4 found
% ---- Iteration 17 (48 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% r5:
%  CSA axiom r5 found
% Looking for CSA axiom ... op_implies_and:
%  CSA axiom op_implies_and found
% Looking for CSA axiom ... op_equiv:
%  CSA axiom op_equiv found
% ---- Iteration 18 (51 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% axiom_K:
%  CSA axiom axiom_K found
% Looking for CSA axiom ... axiom_M:
%  CSA axiom axiom_M found
% Looking for CSA axiom ... axiom_4:
%  CSA axiom axiom_4 found
% ---- Iteration 19 (54 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% axiom_B:
%  CSA axiom axiom_B found
% Looking for CSA axiom ... axiom_5:
%  CSA axiom axiom_5 found
% Looking for CSA axiom ... axiom_s2:
%  CSA axiom axiom_s2 found
% ---- Iteration 20 (57 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% axiom_m7:
%  CSA axiom axiom_m7 found
% Looking for CSA axiom ... substitution_of_equivalents:substitution_strict_equiv:
%  CSA axiom substitution_strict_equiv found
% Looking for CSA axiom ... axiom_s4:
%  CSA axiom axiom_s4 found
% ---- Iteration 21 (60 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% substitution_of_equivalents:axiom_m6:
%  CSA axiom axiom_m6 found
% Looking for CSA axiom ... axiom_m8:
%  CSA axiom axiom_m8 found
% Looking for CSA axiom ... axiom_m9:
%  CSA axiom axiom_m9 found
% ---- Iteration 22 (63 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% substitution_of_equivalents:op_possibly:
%  CSA axiom op_possibly found
% Looking for CSA axiom ... op_necessarily:
%  CSA axiom op_necessarily found
% Looking for CSA axiom ... op_or:
%  CSA axiom op_or found
% ---- Iteration 23 (66 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_equiv:
% hilbert_op_or:
% substitution_of_equivalents:op_and:
%  CSA axiom op_and 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 24 (69 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:op_and:op_or:op_necessarily:op_possibly:axiom_m9:axiom_m8:axiom_m6:axiom_s4:substitution_strict_equiv:axiom_m7:axiom_s2:axiom_5:axiom_B:axiom_4:axiom_M:axiom_K:op_equiv:op_implies_and:r5:r4:r3:r2:r1:cn3:cn2:equivalence_3:equivalence_2:equivalence_1:or_3:or_2:or_1:modus_tollens:modus_ponens_strict_implies:necessitation:axiom_m5:axiom_m4:axiom_m3:axiom_m2:axiom_m1:s1_0_substitution_strict_equiv:kn3:axiom_s1:cn1:implies_3:implies_2:implies_1:modus_ponens:substitution_of_equivalents:s1_0_modus_ponens_strict_implies:s1_0_op_strict_equiv:s1_0_op_strict_implies:s1_0_op_or:s1_0_op_possibly:adjunction:kn2:kn1:and_3:and_1:hilbert_op_implies_and: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_op_equiv:and_2 (69)
% Unselected axioms are ... :hilbert_op_equiv:hilbert_op_or:substitution_of_equivalents:op_implies_or:axiom_s3:axiom_m10:s1_0_op_implies (7)
% SZS status THM for /tmp/SystemOnTPTP3231/LCL556+1.tptp
% Looking for THM       ... 
% found
% SZS output start Solution for /tmp/SystemOnTPTP3231/LCL556+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 18944
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% PrfWatch: 1.92 CPU 2.02 WC
% PrfWatch: 3.91 CPU 4.03 WC
% PrfWatch: 5.91 CPU 6.03 WC
% # Preprocessing time     : 0.021 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 7.91 CPU 8.04 WC
% PrfWatch: 9.90 CPU 10.04 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(4, axiom,(op_or=>![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),file('/tmp/SRASS.s.p', op_or)).
% fof(11, axiom,(substitution_strict_equiv<=>![X1]:![X2]:(is_a_theorem(strict_equiv(X1,X2))=>X1=X2)),file('/tmp/SRASS.s.p', substitution_strict_equiv)).
% fof(19, axiom,(op_equiv=>![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(20, axiom,(op_implies_and=>![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(35, 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(37, axiom,(axiom_m5<=>![X1]:![X2]:![X6]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X6)),strict_implies(X1,X6)))),file('/tmp/SRASS.s.p', axiom_m5)).
% fof(38, axiom,(axiom_m4<=>![X1]:is_a_theorem(strict_implies(X1,and(X1,X1)))),file('/tmp/SRASS.s.p', axiom_m4)).
% fof(39, axiom,(axiom_m3<=>![X1]:![X2]:![X6]:is_a_theorem(strict_implies(and(and(X1,X2),X6),and(X1,and(X2,X6))))),file('/tmp/SRASS.s.p', axiom_m3)).
% fof(40, axiom,(axiom_m2<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),X1))),file('/tmp/SRASS.s.p', axiom_m2)).
% fof(41, axiom,(axiom_m1<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),file('/tmp/SRASS.s.p', axiom_m1)).
% fof(42, axiom,substitution_strict_equiv,file('/tmp/SRASS.s.p', s1_0_substitution_strict_equiv)).
% fof(51, axiom,modus_ponens_strict_implies,file('/tmp/SRASS.s.p', s1_0_modus_ponens_strict_implies)).
% fof(52, axiom,op_strict_equiv,file('/tmp/SRASS.s.p', s1_0_op_strict_equiv)).
% fof(53, axiom,op_strict_implies,file('/tmp/SRASS.s.p', s1_0_op_strict_implies)).
% fof(54, axiom,op_or,file('/tmp/SRASS.s.p', s1_0_op_or)).
% fof(56, 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(61, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(62, axiom,axiom_m5,file('/tmp/SRASS.s.p', s1_0_axiom_m5)).
% fof(63, axiom,axiom_m4,file('/tmp/SRASS.s.p', s1_0_axiom_m4)).
% fof(64, axiom,axiom_m3,file('/tmp/SRASS.s.p', s1_0_axiom_m3)).
% fof(65, axiom,axiom_m2,file('/tmp/SRASS.s.p', s1_0_axiom_m2)).
% fof(66, axiom,axiom_m1,file('/tmp/SRASS.s.p', s1_0_axiom_m1)).
% fof(67, axiom,adjunction,file('/tmp/SRASS.s.p', s1_0_adjunction)).
% fof(68, axiom,op_equiv,file('/tmp/SRASS.s.p', s1_0_op_equiv)).
% fof(69, axiom,(and_2<=>![X1]:![X2]:is_a_theorem(implies(and(X1,X2),X2))),file('/tmp/SRASS.s.p', and_2)).
% fof(70, conjecture,and_2,file('/tmp/SRASS.s.p', hilbert_and_2)).
% fof(71, negated_conjecture,~(and_2),inference(assume_negation,[status(cth)],[70])).
% fof(72, negated_conjecture,~(and_2),inference(fof_simplification,[status(thm)],[71,theory(equality)])).
% fof(73, 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(74, plain,(~(op_strict_equiv)|![X3]:![X4]:strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))),inference(variable_rename,[status(thm)],[73])).
% fof(75, plain,![X3]:![X4]:(strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))|~(op_strict_equiv)),inference(shift_quantors,[status(thm)],[74])).
% cnf(76,plain,(strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv),inference(split_conjunct,[status(thm)],[75])).
% fof(77, plain,(~(op_strict_implies)|![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),inference(fof_nnf,[status(thm)],[2])).
% fof(78, plain,(~(op_strict_implies)|![X3]:![X4]:strict_implies(X3,X4)=necessarily(implies(X3,X4))),inference(variable_rename,[status(thm)],[77])).
% fof(79, plain,![X3]:![X4]:(strict_implies(X3,X4)=necessarily(implies(X3,X4))|~(op_strict_implies)),inference(shift_quantors,[status(thm)],[78])).
% cnf(80,plain,(strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies),inference(split_conjunct,[status(thm)],[79])).
% fof(85, plain,(~(op_or)|![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),inference(fof_nnf,[status(thm)],[4])).
% fof(86, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(variable_rename,[status(thm)],[85])).
% fof(87, plain,![X3]:![X4]:(or(X3,X4)=not(and(not(X3),not(X4)))|~(op_or)),inference(shift_quantors,[status(thm)],[86])).
% cnf(88,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[87])).
% fof(121, 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)],[11])).
% fof(122, 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)],[121])).
% fof(123, plain,((~(substitution_strict_equiv)|![X3]:![X4]:(~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4))&((is_a_theorem(strict_equiv(esk6_0,esk7_0))&~(esk6_0=esk7_0))|substitution_strict_equiv)),inference(skolemize,[status(esa)],[122])).
% fof(124, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk6_0,esk7_0))&~(esk6_0=esk7_0))|substitution_strict_equiv)),inference(shift_quantors,[status(thm)],[123])).
% fof(125, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk6_0,esk7_0))|substitution_strict_equiv)&(~(esk6_0=esk7_0)|substitution_strict_equiv))),inference(distribute,[status(thm)],[124])).
% cnf(128,plain,(X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2))),inference(split_conjunct,[status(thm)],[125])).
% fof(171, plain,(~(op_equiv)|![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),inference(fof_nnf,[status(thm)],[19])).
% fof(172, plain,(~(op_equiv)|![X3]:![X4]:equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))),inference(variable_rename,[status(thm)],[171])).
% fof(173, plain,![X3]:![X4]:(equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))|~(op_equiv)),inference(shift_quantors,[status(thm)],[172])).
% cnf(174,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[173])).
% fof(175, plain,(~(op_implies_and)|![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),inference(fof_nnf,[status(thm)],[20])).
% fof(176, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(variable_rename,[status(thm)],[175])).
% fof(177, plain,![X3]:![X4]:(implies(X3,X4)=not(and(X3,not(X4)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[176])).
% cnf(178,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[177])).
% fof(263, 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)],[35])).
% fof(264, 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)],[263])).
% fof(265, 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(esk47_0)&is_a_theorem(strict_implies(esk47_0,esk48_0)))&~(is_a_theorem(esk48_0)))|modus_ponens_strict_implies)),inference(skolemize,[status(esa)],[264])).
% fof(266, 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(esk47_0)&is_a_theorem(strict_implies(esk47_0,esk48_0)))&~(is_a_theorem(esk48_0)))|modus_ponens_strict_implies)),inference(shift_quantors,[status(thm)],[265])).
% fof(267, 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(esk47_0)|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(esk47_0,esk48_0))|modus_ponens_strict_implies))&(~(is_a_theorem(esk48_0))|modus_ponens_strict_implies))),inference(distribute,[status(thm)],[266])).
% cnf(271,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)],[267])).
% fof(280, plain,((~(axiom_m5)|![X1]:![X2]:![X6]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X6)),strict_implies(X1,X6))))&(?[X1]:?[X2]:?[X6]:~(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X6)),strict_implies(X1,X6))))|axiom_m5)),inference(fof_nnf,[status(thm)],[37])).
% fof(281, plain,((~(axiom_m5)|![X7]:![X8]:![X9]:is_a_theorem(strict_implies(and(strict_implies(X7,X8),strict_implies(X8,X9)),strict_implies(X7,X9))))&(?[X10]:?[X11]:?[X12]:~(is_a_theorem(strict_implies(and(strict_implies(X10,X11),strict_implies(X11,X12)),strict_implies(X10,X12))))|axiom_m5)),inference(variable_rename,[status(thm)],[280])).
% fof(282, plain,((~(axiom_m5)|![X7]:![X8]:![X9]:is_a_theorem(strict_implies(and(strict_implies(X7,X8),strict_implies(X8,X9)),strict_implies(X7,X9))))&(~(is_a_theorem(strict_implies(and(strict_implies(esk50_0,esk51_0),strict_implies(esk51_0,esk52_0)),strict_implies(esk50_0,esk52_0))))|axiom_m5)),inference(skolemize,[status(esa)],[281])).
% fof(283, plain,![X7]:![X8]:![X9]:((is_a_theorem(strict_implies(and(strict_implies(X7,X8),strict_implies(X8,X9)),strict_implies(X7,X9)))|~(axiom_m5))&(~(is_a_theorem(strict_implies(and(strict_implies(esk50_0,esk51_0),strict_implies(esk51_0,esk52_0)),strict_implies(esk50_0,esk52_0))))|axiom_m5)),inference(shift_quantors,[status(thm)],[282])).
% cnf(285,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)],[283])).
% fof(286, 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)],[38])).
% fof(287, 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)],[286])).
% fof(288, plain,((~(axiom_m4)|![X2]:is_a_theorem(strict_implies(X2,and(X2,X2))))&(~(is_a_theorem(strict_implies(esk53_0,and(esk53_0,esk53_0))))|axiom_m4)),inference(skolemize,[status(esa)],[287])).
% fof(289, plain,![X2]:((is_a_theorem(strict_implies(X2,and(X2,X2)))|~(axiom_m4))&(~(is_a_theorem(strict_implies(esk53_0,and(esk53_0,esk53_0))))|axiom_m4)),inference(shift_quantors,[status(thm)],[288])).
% cnf(291,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4),inference(split_conjunct,[status(thm)],[289])).
% fof(292, plain,((~(axiom_m3)|![X1]:![X2]:![X6]:is_a_theorem(strict_implies(and(and(X1,X2),X6),and(X1,and(X2,X6)))))&(?[X1]:?[X2]:?[X6]:~(is_a_theorem(strict_implies(and(and(X1,X2),X6),and(X1,and(X2,X6)))))|axiom_m3)),inference(fof_nnf,[status(thm)],[39])).
% fof(293, plain,((~(axiom_m3)|![X7]:![X8]:![X9]:is_a_theorem(strict_implies(and(and(X7,X8),X9),and(X7,and(X8,X9)))))&(?[X10]:?[X11]:?[X12]:~(is_a_theorem(strict_implies(and(and(X10,X11),X12),and(X10,and(X11,X12)))))|axiom_m3)),inference(variable_rename,[status(thm)],[292])).
% fof(294, plain,((~(axiom_m3)|![X7]:![X8]:![X9]:is_a_theorem(strict_implies(and(and(X7,X8),X9),and(X7,and(X8,X9)))))&(~(is_a_theorem(strict_implies(and(and(esk54_0,esk55_0),esk56_0),and(esk54_0,and(esk55_0,esk56_0)))))|axiom_m3)),inference(skolemize,[status(esa)],[293])).
% fof(295, plain,![X7]:![X8]:![X9]:((is_a_theorem(strict_implies(and(and(X7,X8),X9),and(X7,and(X8,X9))))|~(axiom_m3))&(~(is_a_theorem(strict_implies(and(and(esk54_0,esk55_0),esk56_0),and(esk54_0,and(esk55_0,esk56_0)))))|axiom_m3)),inference(shift_quantors,[status(thm)],[294])).
% cnf(297,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|~axiom_m3),inference(split_conjunct,[status(thm)],[295])).
% fof(298, 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)],[40])).
% fof(299, 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)],[298])).
% fof(300, plain,((~(axiom_m2)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),X3)))&(~(is_a_theorem(strict_implies(and(esk57_0,esk58_0),esk57_0)))|axiom_m2)),inference(skolemize,[status(esa)],[299])).
% fof(301, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),X3))|~(axiom_m2))&(~(is_a_theorem(strict_implies(and(esk57_0,esk58_0),esk57_0)))|axiom_m2)),inference(shift_quantors,[status(thm)],[300])).
% cnf(303,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2),inference(split_conjunct,[status(thm)],[301])).
% fof(304, 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)],[41])).
% fof(305, 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)],[304])).
% fof(306, plain,((~(axiom_m1)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))))&(~(is_a_theorem(strict_implies(and(esk59_0,esk60_0),and(esk60_0,esk59_0))))|axiom_m1)),inference(skolemize,[status(esa)],[305])).
% fof(307, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),and(X4,X3)))|~(axiom_m1))&(~(is_a_theorem(strict_implies(and(esk59_0,esk60_0),and(esk60_0,esk59_0))))|axiom_m1)),inference(shift_quantors,[status(thm)],[306])).
% cnf(309,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1),inference(split_conjunct,[status(thm)],[307])).
% cnf(310,plain,(substitution_strict_equiv),inference(split_conjunct,[status(thm)],[42])).
% cnf(357,plain,(modus_ponens_strict_implies),inference(split_conjunct,[status(thm)],[51])).
% cnf(358,plain,(op_strict_equiv),inference(split_conjunct,[status(thm)],[52])).
% cnf(359,plain,(op_strict_implies),inference(split_conjunct,[status(thm)],[53])).
% cnf(360,plain,(op_or),inference(split_conjunct,[status(thm)],[54])).
% fof(362, 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)],[56])).
% fof(363, 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)],[362])).
% fof(364, plain,((~(adjunction)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4))))&(((is_a_theorem(esk79_0)&is_a_theorem(esk80_0))&~(is_a_theorem(and(esk79_0,esk80_0))))|adjunction)),inference(skolemize,[status(esa)],[363])).
% fof(365, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk79_0)&is_a_theorem(esk80_0))&~(is_a_theorem(and(esk79_0,esk80_0))))|adjunction)),inference(shift_quantors,[status(thm)],[364])).
% fof(366, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk79_0)|adjunction)&(is_a_theorem(esk80_0)|adjunction))&(~(is_a_theorem(and(esk79_0,esk80_0)))|adjunction))),inference(distribute,[status(thm)],[365])).
% cnf(370,plain,(is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(split_conjunct,[status(thm)],[366])).
% cnf(395,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[61])).
% cnf(396,plain,(axiom_m5),inference(split_conjunct,[status(thm)],[62])).
% cnf(397,plain,(axiom_m4),inference(split_conjunct,[status(thm)],[63])).
% cnf(398,plain,(axiom_m3),inference(split_conjunct,[status(thm)],[64])).
% cnf(399,plain,(axiom_m2),inference(split_conjunct,[status(thm)],[65])).
% cnf(400,plain,(axiom_m1),inference(split_conjunct,[status(thm)],[66])).
% cnf(401,plain,(adjunction),inference(split_conjunct,[status(thm)],[67])).
% cnf(402,plain,(op_equiv),inference(split_conjunct,[status(thm)],[68])).
% fof(403, plain,((~(and_2)|![X1]:![X2]:is_a_theorem(implies(and(X1,X2),X2)))&(?[X1]:?[X2]:~(is_a_theorem(implies(and(X1,X2),X2)))|and_2)),inference(fof_nnf,[status(thm)],[69])).
% fof(404, plain,((~(and_2)|![X3]:![X4]:is_a_theorem(implies(and(X3,X4),X4)))&(?[X5]:?[X6]:~(is_a_theorem(implies(and(X5,X6),X6)))|and_2)),inference(variable_rename,[status(thm)],[403])).
% fof(405, plain,((~(and_2)|![X3]:![X4]:is_a_theorem(implies(and(X3,X4),X4)))&(~(is_a_theorem(implies(and(esk88_0,esk89_0),esk89_0)))|and_2)),inference(skolemize,[status(esa)],[404])).
% fof(406, plain,![X3]:![X4]:((is_a_theorem(implies(and(X3,X4),X4))|~(and_2))&(~(is_a_theorem(implies(and(esk88_0,esk89_0),esk89_0)))|and_2)),inference(shift_quantors,[status(thm)],[405])).
% cnf(407,plain,(and_2|~is_a_theorem(implies(and(esk88_0,esk89_0),esk89_0))),inference(split_conjunct,[status(thm)],[406])).
% cnf(409,negated_conjecture,(~and_2),inference(split_conjunct,[status(thm)],[72])).
% cnf(416,plain,(~is_a_theorem(implies(and(esk88_0,esk89_0),esk89_0))),inference(sr,[status(thm)],[407,409,theory(equality)])).
% cnf(421,plain,(X1=X2|$false|~is_a_theorem(strict_equiv(X1,X2))),inference(rw,[status(thm)],[128,310,theory(equality)])).
% cnf(422,plain,(X1=X2|~is_a_theorem(strict_equiv(X1,X2))),inference(cn,[status(thm)],[421,theory(equality)])).
% cnf(427,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|$false),inference(rw,[status(thm)],[291,397,theory(equality)])).
% cnf(428,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))),inference(cn,[status(thm)],[427,theory(equality)])).
% cnf(429,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)|$false),inference(rw,[status(thm)],[80,359,theory(equality)])).
% cnf(430,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)),inference(cn,[status(thm)],[429,theory(equality)])).
% cnf(431,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[303,399,theory(equality)])).
% cnf(432,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))),inference(cn,[status(thm)],[431,theory(equality)])).
% cnf(433,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(rw,[status(thm)],[271,357,theory(equality)])).
% cnf(434,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(cn,[status(thm)],[433,theory(equality)])).
% cnf(435,plain,(is_a_theorem(X1)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[434,432,theory(equality)])).
% cnf(437,plain,(is_a_theorem(and(X1,X2))|$false|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(rw,[status(thm)],[370,401,theory(equality)])).
% cnf(438,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(cn,[status(thm)],[437,theory(equality)])).
% cnf(439,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[178,395,theory(equality)])).
% cnf(440,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[439,theory(equality)])).
% cnf(442,plain,(not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))),inference(spm,[status(thm)],[440,440,theory(equality)])).
% cnf(446,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[309,400,theory(equality)])).
% cnf(447,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[446,theory(equality)])).
% cnf(449,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[88,440,theory(equality)])).
% cnf(450,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[449,360,theory(equality)])).
% cnf(451,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[450,theory(equality)])).
% cnf(452,plain,(necessarily(or(X1,X2))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[430,451,theory(equality)])).
% cnf(454,plain,(implies(implies(X1,X2),X3)=or(and(X1,not(X2)),X3)),inference(spm,[status(thm)],[451,440,theory(equality)])).
% cnf(463,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)|$false),inference(rw,[status(thm)],[76,358,theory(equality)])).
% cnf(464,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)),inference(cn,[status(thm)],[463,theory(equality)])).
% cnf(465,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)],[438,464,theory(equality)])).
% cnf(472,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[174,402,theory(equality)])).
% cnf(473,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[472,theory(equality)])).
% cnf(476,plain,(is_a_theorem(strict_implies(equiv(X1,X2),and(implies(X2,X1),implies(X1,X2))))),inference(spm,[status(thm)],[447,473,theory(equality)])).
% cnf(487,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|$false),inference(rw,[status(thm)],[297,398,theory(equality)])).
% cnf(488,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))),inference(cn,[status(thm)],[487,theory(equality)])).
% cnf(489,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(and(and(X1,X2),X3))),inference(spm,[status(thm)],[434,488,theory(equality)])).
% cnf(494,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|$false),inference(rw,[status(thm)],[285,396,theory(equality)])).
% cnf(495,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))),inference(cn,[status(thm)],[494,theory(equality)])).
% cnf(496,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))),inference(spm,[status(thm)],[434,495,theory(equality)])).
% cnf(501,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_equiv(X1,X2))),inference(spm,[status(thm)],[435,464,theory(equality)])).
% cnf(540,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|~is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(spm,[status(thm)],[465,447,theory(equality)])).
% cnf(541,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(and(X1,X2),X3)))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))),inference(spm,[status(thm)],[465,488,theory(equality)])).
% cnf(544,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|~is_a_theorem(strict_implies(and(X1,X1),X1))),inference(spm,[status(thm)],[465,428,theory(equality)])).
% cnf(545,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[540,447,theory(equality)])).
% cnf(546,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[545,theory(equality)])).
% cnf(547,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|$false),inference(rw,[status(thm)],[544,432,theory(equality)])).
% cnf(548,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))),inference(cn,[status(thm)],[547,theory(equality)])).
% cnf(549,plain,(and(X1,X1)=X1),inference(spm,[status(thm)],[422,548,theory(equality)])).
% cnf(557,plain,(strict_implies(X1,X1)=strict_equiv(X1,X1)),inference(spm,[status(thm)],[464,549,theory(equality)])).
% cnf(559,plain,(not(not(X1))=implies(not(X1),X1)),inference(spm,[status(thm)],[440,549,theory(equality)])).
% cnf(570,plain,(is_a_theorem(strict_equiv(X1,X1))),inference(rw,[status(thm)],[548,549,theory(equality)])).
% cnf(576,plain,(not(not(X1))=or(X1,X1)),inference(rw,[status(thm)],[559,451,theory(equality)])).
% cnf(581,plain,(is_a_theorem(strict_implies(X1,X1))),inference(spm,[status(thm)],[501,570,theory(equality)])).
% cnf(600,plain,(not(implies(X1,X2))=implies(implies(X1,X2),and(X1,not(X2)))),inference(spm,[status(thm)],[442,549,theory(equality)])).
% cnf(618,plain,(and(X1,X2)=and(X2,X1)),inference(spm,[status(thm)],[422,546,theory(equality)])).
% cnf(636,plain,(is_a_theorem(strict_implies(and(X3,and(X1,X2)),and(X1,and(X2,X3))))),inference(spm,[status(thm)],[488,618,theory(equality)])).
% cnf(637,plain,(and(strict_implies(X2,X1),strict_implies(X1,X2))=strict_equiv(X1,X2)),inference(spm,[status(thm)],[464,618,theory(equality)])).
% cnf(639,plain,(not(and(not(X2),X1))=implies(X1,X2)),inference(spm,[status(thm)],[440,618,theory(equality)])).
% cnf(644,plain,(is_a_theorem(strict_implies(and(X2,X1),X1))),inference(spm,[status(thm)],[432,618,theory(equality)])).
% cnf(674,plain,(~is_a_theorem(implies(and(esk89_0,esk88_0),esk89_0))),inference(rw,[status(thm)],[416,618,theory(equality)])).
% cnf(675,plain,(strict_equiv(X2,X1)=strict_equiv(X1,X2)),inference(rw,[status(thm)],[637,464,theory(equality)])).
% cnf(721,plain,(not(and(X1,or(X2,X2)))=implies(X1,not(X2))),inference(spm,[status(thm)],[440,576,theory(equality)])).
% cnf(793,plain,(implies(not(X2),X1)=implies(not(X1),X2)),inference(spm,[status(thm)],[440,639,theory(equality)])).
% cnf(795,plain,(not(and(or(X1,X1),X2))=implies(X2,not(X1))),inference(spm,[status(thm)],[639,576,theory(equality)])).
% cnf(809,plain,(or(X2,X1)=implies(not(X1),X2)),inference(rw,[status(thm)],[793,451,theory(equality)])).
% cnf(810,plain,(or(X2,X1)=or(X1,X2)),inference(rw,[status(thm)],[809,451,theory(equality)])).
% cnf(819,plain,(necessarily(or(X2,X1))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[452,810,theory(equality)])).
% cnf(831,plain,(strict_implies(not(X2),X1)=strict_implies(not(X1),X2)),inference(rw,[status(thm)],[819,452,theory(equality)])).
% cnf(1044,plain,(and(strict_implies(not(X2),X1),strict_implies(X2,not(X1)))=strict_equiv(not(X1),X2)),inference(spm,[status(thm)],[464,831,theory(equality)])).
% cnf(1047,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[434,831,theory(equality)])).
% cnf(1064,plain,(strict_implies(not(X1),not(X2))=strict_implies(or(X2,X2),X1)),inference(spm,[status(thm)],[831,576,theory(equality)])).
% cnf(1067,plain,(strict_implies(not(X1),and(not(X2),X3))=strict_implies(implies(X3,X2),X1)),inference(spm,[status(thm)],[831,639,theory(equality)])).
% cnf(1087,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)],[1047,440,theory(equality)])).
% cnf(1152,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(X3)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[489,438,theory(equality)])).
% cnf(1162,plain,(is_a_theorem(strict_implies(equiv(X1,X2),equiv(X2,X1)))),inference(spm,[status(thm)],[476,473,theory(equality)])).
% cnf(1576,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)],[496,438,theory(equality)])).
% cnf(1790,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)],[1087,451,theory(equality)])).
% cnf(2445,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)],[1152,464,theory(equality)])).
% cnf(2526,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)],[541,549,theory(equality)])).
% cnf(2542,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))|$false),inference(rw,[status(thm)],[2526,644,theory(equality)])).
% cnf(2543,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))),inference(cn,[status(thm)],[2542,theory(equality)])).
% cnf(2555,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X1,and(X1,X2))))),inference(rw,[status(thm)],[2543,675,theory(equality)])).
% cnf(2556,plain,(and(X1,X2)=and(X1,and(X1,X2))),inference(spm,[status(thm)],[422,2555,theory(equality)])).
% cnf(4131,plain,(is_a_theorem(strict_implies(and(X1,and(X3,X2)),and(X2,and(X3,X1))))),inference(spm,[status(thm)],[636,618,theory(equality)])).
% cnf(16940,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(not(X1),X2)),inference(rw,[status(thm)],[1044,618,theory(equality)])).
% cnf(17804,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(spm,[status(thm)],[581,1064,theory(equality)])).
% cnf(17844,plain,(is_a_theorem(strict_implies(or(X1,X1),X1))),inference(spm,[status(thm)],[581,1064,theory(equality)])).
% cnf(17992,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|~is_a_theorem(strict_implies(X1,or(X1,X1)))),inference(spm,[status(thm)],[465,17844,theory(equality)])).
% cnf(18591,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)],[1790,1067,theory(equality)]),451,theory(equality)])).
% cnf(34332,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,or(X2,X2)))),inference(spm,[status(thm)],[1576,17844,theory(equality)])).
% cnf(34374,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,and(X3,X2)))),inference(spm,[status(thm)],[1576,644,theory(equality)])).
% cnf(34414,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,not(not(X2))))),inference(spm,[status(thm)],[34332,576,theory(equality)])).
% cnf(34427,plain,(is_a_theorem(strict_implies(or(or(X1,X1),or(X1,X1)),X1))),inference(spm,[status(thm)],[34332,17844,theory(equality)])).
% cnf(35276,plain,(is_a_theorem(strict_implies(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[34427,1064,theory(equality)])).
% cnf(35278,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)],[465,35276,theory(equality)])).
% cnf(35337,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|$false),inference(rw,[status(thm)],[35278,17804,theory(equality)])).
% cnf(35338,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))),inference(cn,[status(thm)],[35337,theory(equality)])).
% cnf(35375,plain,(is_a_theorem(strict_equiv(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[35338,675,theory(equality)])).
% cnf(35376,plain,(not(X1)=not(or(X1,X1))),inference(spm,[status(thm)],[422,35375,theory(equality)])).
% cnf(35479,plain,(not(and(not(X1),X2))=implies(X2,or(X1,X1))),inference(spm,[status(thm)],[639,35376,theory(equality)])).
% cnf(35781,plain,(implies(X2,X1)=implies(X2,or(X1,X1))),inference(rw,[status(thm)],[35479,639,theory(equality)])).
% cnf(38766,plain,(is_a_theorem(strict_implies(or(and(X1,X2),and(X1,X2)),X2))),inference(spm,[status(thm)],[34374,17844,theory(equality)])).
% cnf(39705,plain,(is_a_theorem(strict_implies(or(and(X1,not(not(X2))),and(X1,not(not(X2)))),X2))),inference(spm,[status(thm)],[34414,38766,theory(equality)])).
% cnf(39745,plain,(is_a_theorem(strict_implies(not(implies(X1,not(X2))),X2))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[39705,454,theory(equality)]),600,theory(equality)])).
% cnf(39753,plain,(is_a_theorem(strict_implies(not(X2),implies(X1,not(X2))))),inference(rw,[status(thm)],[39745,831,theory(equality)])).
% cnf(39754,plain,(is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[434,39753,theory(equality)])).
% cnf(51002,plain,(necessarily(implies(X1,X2))=strict_implies(X1,or(X2,X2))),inference(spm,[status(thm)],[430,35781,theory(equality)])).
% cnf(51140,plain,(strict_implies(X1,X2)=strict_implies(X1,or(X2,X2))),inference(rw,[status(thm)],[51002,430,theory(equality)])).
% cnf(54968,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[17992,51140,theory(equality)]),581,theory(equality)])).
% cnf(54969,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))),inference(cn,[status(thm)],[54968,theory(equality)])).
% cnf(55120,plain,(X1=or(X1,X1)),inference(spm,[status(thm)],[422,54969,theory(equality)])).
% cnf(55292,plain,(not(and(X1,X2))=implies(X1,not(X2))),inference(rw,[status(thm)],[721,55120,theory(equality)])).
% cnf(55327,plain,(not(and(X1,X2))=implies(X2,not(X1))),inference(rw,[status(thm)],[795,55120,theory(equality)])).
% cnf(55329,plain,(not(not(X1))=X1),inference(rw,[status(thm)],[576,55120,theory(equality)])).
% cnf(55474,plain,(is_a_theorem(strict_implies(X1,implies(X2,X1)))),inference(spm,[status(thm)],[39753,55329,theory(equality)])).
% cnf(55581,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)),inference(spm,[status(thm)],[39754,55329,theory(equality)])).
% cnf(58708,plain,(is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X1,X3))),inference(spm,[status(thm)],[1576,55474,theory(equality)])).
% cnf(59678,plain,(not(implies(X1,not(X2)))=and(X1,X2)),inference(spm,[status(thm)],[55329,55292,theory(equality)])).
% cnf(60017,plain,(implies(X1,not(X2))=implies(X2,not(X1))),inference(rw,[status(thm)],[55327,55292,theory(equality)])).
% cnf(60030,plain,(necessarily(implies(X2,not(X1)))=strict_implies(X1,not(X2))),inference(spm,[status(thm)],[430,60017,theory(equality)])).
% cnf(60282,plain,(strict_implies(X2,not(X1))=strict_implies(X1,not(X2))),inference(rw,[status(thm)],[60030,430,theory(equality)])).
% cnf(67283,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)],[2445,557,theory(equality)])).
% cnf(67293,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)],[67283,2556,theory(equality)])).
% cnf(67294,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|$false|~is_a_theorem(X2)),inference(rw,[status(thm)],[67293,581,theory(equality)])).
% cnf(67295,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|~is_a_theorem(X2)),inference(cn,[status(thm)],[67294,theory(equality)])).
% cnf(77564,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(X3,and(X2,X1))))),inference(spm,[status(thm)],[465,4131,theory(equality)])).
% cnf(77635,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))|$false),inference(rw,[status(thm)],[77564,4131,theory(equality)])).
% cnf(77636,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))),inference(cn,[status(thm)],[77635,theory(equality)])).
% cnf(79773,plain,(is_a_theorem(strict_implies(and(X1,X2),implies(X3,X1)))),inference(spm,[status(thm)],[58708,432,theory(equality)])).
% cnf(79807,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(and(X2,X3))),inference(spm,[status(thm)],[434,79773,theory(equality)])).
% cnf(81024,plain,(is_a_theorem(implies(X1,strict_implies(X2,X2)))|~is_a_theorem(X3)),inference(spm,[status(thm)],[79807,67295,theory(equality)])).
% cnf(81527,plain,(is_a_theorem(implies(X1,strict_implies(X2,X2)))),inference(spm,[status(thm)],[81024,1162,theory(equality)])).
% cnf(81698,plain,(is_a_theorem(or(X1,strict_implies(X2,X2)))),inference(spm,[status(thm)],[81527,451,theory(equality)])).
% cnf(81704,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(or(strict_implies(X2,X2),X3),X1))),inference(spm,[status(thm)],[18591,81698,theory(equality)])).
% cnf(99640,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(X1,not(X2))),inference(spm,[status(thm)],[464,60282,theory(equality)])).
% cnf(100222,plain,(strict_equiv(not(X1),X2)=strict_equiv(X1,not(X2))),inference(rw,[status(thm)],[99640,16940,theory(equality)])).
% cnf(101115,plain,(not(X1)=X2|~is_a_theorem(strict_equiv(X1,not(X2)))),inference(spm,[status(thm)],[422,100222,theory(equality)])).
% cnf(101271,plain,(not(X1)=implies(X2,not(X3))|~is_a_theorem(strict_equiv(X1,and(X2,X3)))),inference(spm,[status(thm)],[101115,59678,theory(equality)])).
% cnf(168352,plain,(not(X1)=implies(X2,not(X3))|~is_a_theorem(strict_equiv(X1,and(X3,X2)))),inference(spm,[status(thm)],[101271,618,theory(equality)])).
% cnf(184136,plain,(not(and(X1,and(X2,X3)))=implies(and(X2,X1),not(X3))),inference(spm,[status(thm)],[168352,77636,theory(equality)])).
% cnf(184152,plain,(implies(X1,implies(X2,not(X3)))=implies(and(X2,X1),not(X3))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[184136,55292,theory(equality)]),55292,theory(equality)])).
% cnf(184453,plain,(implies(and(X1,X2),X3)=implies(X2,implies(X1,X3))),inference(spm,[status(thm)],[184152,55329,theory(equality)])).
% cnf(281160,plain,(necessarily(implies(X2,implies(X1,X3)))=strict_implies(and(X1,X2),X3)),inference(spm,[status(thm)],[430,184453,theory(equality)])).
% cnf(281536,plain,(~is_a_theorem(implies(esk88_0,implies(esk89_0,esk89_0)))),inference(rw,[status(thm)],[674,184453,theory(equality)])).
% cnf(281729,plain,(strict_implies(X2,implies(X1,X3))=strict_implies(and(X1,X2),X3)),inference(rw,[status(thm)],[281160,430,theory(equality)])).
% cnf(281811,plain,(~is_a_theorem(implies(esk89_0,esk89_0))),inference(spm,[status(thm)],[281536,55581,theory(equality)])).
% cnf(284906,plain,(is_a_theorem(strict_implies(X2,implies(X1,X1)))),inference(rw,[status(thm)],[432,281729,theory(equality)])).
% cnf(285427,plain,(is_a_theorem(implies(X1,X1))),inference(spm,[status(thm)],[81704,284906,theory(equality)])).
% cnf(285607,plain,($false),inference(rw,[status(thm)],[281811,285427,theory(equality)])).
% cnf(285608,plain,($false),inference(cn,[status(thm)],[285607,theory(equality)])).
% cnf(285609,plain,($false),285608,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses                  : 14668
% # ...of these trivial                : 907
% # ...subsumed                        : 11065
% # ...remaining for further processing: 2696
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed                  : 54
% # Backward-rewritten                 : 1049
% # Generated clauses                  : 199879
% # ...of the previous two non-trivial : 162964
% # Contextual simplify-reflections    : 733
% # Paramodulations                    : 199879
% # Factorizations                     : 0
% # Equation resolutions               : 0
% # Current number of processed clauses: 1593
% #    Positive orientable unit clauses: 592
% #    Positive unorientable unit clauses: 34
% #    Negative unit clauses           : 3
% #    Non-unit-clauses                : 964
% # Current number of unprocessed clauses: 65217
% # ...number of literals in the above : 112193
% # Clause-clause subsumption calls (NU) : 143648
% # Rec. Clause-clause subsumption calls : 142739
% # Unit Clause-clause subsumption calls : 1028
% # Rewrite failures with RHS unbound  : 0
% # Indexed BW rewrite attempts        : 47115
% # Indexed BW rewrite successes       : 1942
% # Backwards rewriting index:  1133 leaves,   3.31+/-6.575 terms/leaf
% # Paramod-from index:          215 leaves,   3.61+/-9.178 terms/leaf
% # Paramod-into index:         1002 leaves,   3.33+/-6.813 terms/leaf
% # -------------------------------------------------
% # User time              : 6.970 s
% # System time            : 0.256 s
% # Total time             : 7.226 s
% # Maximum resident set size: 0 pages
% PrfWatch: 11.38 CPU 11.76 WC
% FINAL PrfWatch: 11.38 CPU 11.76 WC
% SZS output end Solution for /tmp/SystemOnTPTP3231/LCL556+1.tptp
% 
%------------------------------------------------------------------------------