%------------------------------------------------------------------------------
% File     : SRASS---0.1
% Problem  : LCL561+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s

% Computer : art09.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Wed Dec 29 14:08:00 EST 2010

% Result   : Theorem 270.89s
% Output   : Solution 282.73s
% 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/SystemOnTPTP18596/LCL561+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM       ... 
% not found
% Adding ~C to TBU       ... ~hilbert_equivalence_1:
% ---- Iteration 1 (0 axioms selected)
% Looking for TBU SAT   ... yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... equivalence_1:
%  CSA axiom equivalence_1 found
% Looking for CSA axiom ... s1_0_op_equiv: CSA axiom s1_0_op_equiv found
% Looking for CSA axiom ... hilbert_op_equiv: CSA axiom hilbert_op_equiv found
% ---- Iteration 2 (3 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... substitution_of_equivalents:
%  CSA axiom substitution_of_equivalents found
% Looking for CSA axiom ... equivalence_2:
%  CSA axiom equivalence_2 found
% Looking for CSA axiom ... equivalence_3:
%  CSA axiom equivalence_3 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_strict_equiv:
%  CSA axiom s1_0_op_strict_equiv found
% ---- Iteration 4 (9 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... s1_0_substitution_strict_equiv:
%  CSA axiom s1_0_substitution_strict_equiv found
% Looking for CSA axiom ... s1_0_adjunction:
%  CSA axiom s1_0_adjunction found
% Looking for CSA axiom ... s1_0_axiom_m1:
%  CSA axiom s1_0_axiom_m1 found
% ---- Iteration 5 (12 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not 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
% Looking for CSA axiom ... s1_0_axiom_m4:
%  CSA axiom s1_0_axiom_m4 found
% ---- Iteration 6 (15 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not 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_implies_and:
%  CSA axiom hilbert_op_implies_and found
% Looking for CSA axiom ... modus_ponens:
%  CSA axiom modus_ponens found
% ---- Iteration 7 (18 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... 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 8 (21 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% cn1:
%  CSA axiom cn1 found
% Looking for CSA axiom ... substitution_of_equivalents:s1_0_op_possibly:
%  CSA axiom s1_0_op_possibly found
% Looking for CSA axiom ... s1_0_modus_ponens_strict_implies:
%  CSA axiom s1_0_modus_ponens_strict_implies found
% ---- Iteration 9 (24 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:
% 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 10 (27 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:and_1:
%  CSA axiom and_1 found
% Looking for CSA axiom ... and_2: CSA axiom and_2 found
% Looking for CSA axiom ... and_3:
%  CSA axiom and_3 found
% ---- Iteration 11 (30 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:kn1:
%  CSA axiom kn1 found
% Looking for CSA axiom ... kn2:
%  CSA axiom kn2 found
% Looking for CSA axiom ... modus_tollens:
%  CSA axiom modus_tollens found
% ---- Iteration 12 (33 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents: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 13 (36 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:cn2:
%  CSA axiom cn2 found
% Looking for CSA axiom ... cn3:
%  CSA axiom cn3 found
% Looking for CSA axiom ... r1:
%  CSA axiom r1 found
% ---- Iteration 14 (39 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:
% r2:
%  CSA axiom r2 found
% Looking for CSA axiom ... r3:
%  CSA axiom r3 found
% Looking for CSA axiom ... r4:
%  CSA axiom r4 found
% ---- Iteration 15 (42 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents: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 16 (45 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:axiom_4:
%  CSA axiom axiom_4 found
% Looking for CSA axiom ... substitution_strict_equiv:
%  CSA axiom substitution_strict_equiv found
% Looking for CSA axiom ... axiom_s4:
%  CSA axiom axiom_s4 found
% ---- Iteration 17 (48 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:axiom_m1:
%  CSA axiom axiom_m1 found
% Looking for CSA axiom ... axiom_m2:
%  CSA axiom axiom_m2 found
% Looking for CSA axiom ... axiom_m3:
%  CSA axiom axiom_m3 found
% ---- Iteration 18 (51 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:axiom_m4:
%  CSA axiom axiom_m4 found
% Looking for CSA axiom ... axiom_m5:
%  CSA axiom axiom_m5 found
% Looking for CSA axiom ... kn3:
%  CSA axiom kn3 found
% ---- Iteration 19 (54 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% 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 ... adjunction:
%  CSA axiom adjunction found
% ---- Iteration 20 (57 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:
% axiom_B:
%  CSA axiom axiom_B found
% Looking for CSA axiom ... axiom_5:
%  CSA axiom axiom_5 found
% Looking for CSA axiom ... axiom_s1:
%  CSA axiom axiom_s1 found
% ---- Iteration 21 (60 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:op_strict_implies:
%  CSA axiom op_strict_implies found
% Looking for CSA axiom ... op_strict_equiv:
%  CSA axiom op_strict_equiv found
% Looking for CSA axiom ... op_implies_or:
%  CSA axiom op_implies_or found
% ---- Iteration 22 (63 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:axiom_s3:
%  CSA axiom axiom_s3 found
% Looking for CSA axiom ... axiom_s2:
%  CSA axiom axiom_s2 found
% Looking for CSA axiom ... axiom_m6:
%  CSA axiom axiom_m6 found
% ---- Iteration 23 (66 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:axiom_m7:
%  CSA axiom axiom_m7 found
% Looking for CSA axiom ... axiom_m8:
%  CSA axiom axiom_m8 found
% Looking for CSA axiom ... axiom_m9:
% axiom_m10:
%  CSA axiom axiom_m10 found
% ---- Iteration 24 (69 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... hilbert_op_or:
% substitution_of_equivalents:axiom_m9:
% op_possibly:
%  CSA axiom op_possibly found
% Looking for CSA axiom ... op_necessarily:
%  CSA axiom op_necessarily found
% Looking for CSA axiom ... modus_ponens_strict_implies:
%  CSA axiom modus_ponens_strict_implies found
% ---- Iteration 25 (72 axioms selected)
% Looking for TBU SAT   ... 
% no
% Looking for TBU UNS   ... 
% yes - theorem proved
% ---- Selection completed
% Selected axioms are   ... :modus_ponens_strict_implies:op_necessarily:op_possibly:axiom_m10:axiom_m8:axiom_m7:axiom_m6:axiom_s2:axiom_s3:op_implies_or:op_strict_equiv:op_strict_implies:axiom_s1:axiom_5:axiom_B:adjunction:op_and:op_or:kn3:axiom_m5:axiom_m4:axiom_m3:axiom_m2:axiom_m1:axiom_s4:substitution_strict_equiv:axiom_4:axiom_M:axiom_K:r5:r4:r3:r2:r1:cn3:cn2:or_3:or_2:or_1:modus_tollens:kn2:kn1:and_3:and_2:and_1:necessitation:op_equiv:op_implies_and:s1_0_modus_ponens_strict_implies:s1_0_op_possibly:cn1:implies_3:implies_2:implies_1:modus_ponens: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_substitution_strict_equiv:s1_0_op_strict_equiv:s1_0_op_strict_implies:s1_0_op_or:equivalence_3:equivalence_2:substitution_of_equivalents:hilbert_op_equiv:s1_0_op_equiv:equivalence_1 (72)
% Unselected axioms are ... :hilbert_op_or:substitution_of_equivalents:axiom_m9:s1_0_op_implies (4)
% SZS status THM for /tmp/SystemOnTPTP18596/LCL561+1.tptp
% Looking for THM       ... 
% found
% SZS output start Solution for /tmp/SystemOnTPTP18596/LCL561+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 32589
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% PrfWatch: 1.93 CPU 2.02 WC
% PrfWatch: 3.93 CPU 4.03 WC
% PrfWatch: 5.91 CPU 6.03 WC
% # Preprocessing time     : 0.022 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 7.90 CPU 8.04 WC
% PrfWatch: 9.90 CPU 10.04 WC
% # SZS output start CNFRefutation.
% fof(1, 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(11, 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(12, axiom,(op_strict_implies=>![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),file('/tmp/SRASS.s.p', op_strict_implies)).
% fof(16, 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(18, axiom,(op_or=>![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),file('/tmp/SRASS.s.p', op_or)).
% fof(20, axiom,(axiom_m5<=>![X1]:![X2]:![X5]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X5)),strict_implies(X1,X5)))),file('/tmp/SRASS.s.p', axiom_m5)).
% fof(21, axiom,(axiom_m4<=>![X1]:is_a_theorem(strict_implies(X1,and(X1,X1)))),file('/tmp/SRASS.s.p', axiom_m4)).
% fof(22, axiom,(axiom_m3<=>![X1]:![X2]:![X5]:is_a_theorem(strict_implies(and(and(X1,X2),X5),and(X1,and(X2,X5))))),file('/tmp/SRASS.s.p', axiom_m3)).
% fof(23, axiom,(axiom_m2<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),X1))),file('/tmp/SRASS.s.p', axiom_m2)).
% fof(24, axiom,(axiom_m1<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),file('/tmp/SRASS.s.p', axiom_m1)).
% fof(26, axiom,(substitution_strict_equiv<=>![X1]:![X2]:(is_a_theorem(strict_equiv(X1,X2))=>X1=X2)),file('/tmp/SRASS.s.p', substitution_strict_equiv)).
% fof(47, axiom,(op_equiv=>![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(48, axiom,(op_implies_and=>![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(49, axiom,modus_ponens_strict_implies,file('/tmp/SRASS.s.p', s1_0_modus_ponens_strict_implies)).
% fof(56, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(57, axiom,axiom_m5,file('/tmp/SRASS.s.p', s1_0_axiom_m5)).
% fof(58, axiom,axiom_m4,file('/tmp/SRASS.s.p', s1_0_axiom_m4)).
% fof(59, axiom,axiom_m3,file('/tmp/SRASS.s.p', s1_0_axiom_m3)).
% fof(60, axiom,axiom_m2,file('/tmp/SRASS.s.p', s1_0_axiom_m2)).
% fof(61, axiom,axiom_m1,file('/tmp/SRASS.s.p', s1_0_axiom_m1)).
% fof(62, axiom,adjunction,file('/tmp/SRASS.s.p', s1_0_adjunction)).
% fof(63, axiom,substitution_strict_equiv,file('/tmp/SRASS.s.p', s1_0_substitution_strict_equiv)).
% fof(64, axiom,op_strict_equiv,file('/tmp/SRASS.s.p', s1_0_op_strict_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(70, axiom,op_equiv,file('/tmp/SRASS.s.p', hilbert_op_equiv)).
% fof(72, axiom,(equivalence_1<=>![X1]:![X2]:is_a_theorem(implies(equiv(X1,X2),implies(X1,X2)))),file('/tmp/SRASS.s.p', equivalence_1)).
% fof(73, conjecture,equivalence_1,file('/tmp/SRASS.s.p', hilbert_equivalence_1)).
% fof(74, negated_conjecture,~(equivalence_1),inference(assume_negation,[status(cth)],[73])).
% fof(75, negated_conjecture,~(equivalence_1),inference(fof_simplification,[status(thm)],[74,theory(equality)])).
% fof(76, 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)],[1])).
% fof(77, 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)],[76])).
% fof(78, 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(esk1_0)&is_a_theorem(strict_implies(esk1_0,esk2_0)))&~(is_a_theorem(esk2_0)))|modus_ponens_strict_implies)),inference(skolemize,[status(esa)],[77])).
% fof(79, 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(esk1_0)&is_a_theorem(strict_implies(esk1_0,esk2_0)))&~(is_a_theorem(esk2_0)))|modus_ponens_strict_implies)),inference(shift_quantors,[status(thm)],[78])).
% fof(80, 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(esk1_0)|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(esk1_0,esk2_0))|modus_ponens_strict_implies))&(~(is_a_theorem(esk2_0))|modus_ponens_strict_implies))),inference(distribute,[status(thm)],[79])).
% cnf(84,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)],[80])).
% fof(133, plain,(~(op_strict_equiv)|![X1]:![X2]:strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))),inference(fof_nnf,[status(thm)],[11])).
% fof(134, plain,(~(op_strict_equiv)|![X3]:![X4]:strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))),inference(variable_rename,[status(thm)],[133])).
% fof(135, plain,![X3]:![X4]:(strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))|~(op_strict_equiv)),inference(shift_quantors,[status(thm)],[134])).
% cnf(136,plain,(strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv),inference(split_conjunct,[status(thm)],[135])).
% fof(137, plain,(~(op_strict_implies)|![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),inference(fof_nnf,[status(thm)],[12])).
% fof(138, plain,(~(op_strict_implies)|![X3]:![X4]:strict_implies(X3,X4)=necessarily(implies(X3,X4))),inference(variable_rename,[status(thm)],[137])).
% fof(139, plain,![X3]:![X4]:(strict_implies(X3,X4)=necessarily(implies(X3,X4))|~(op_strict_implies)),inference(shift_quantors,[status(thm)],[138])).
% cnf(140,plain,(strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies),inference(split_conjunct,[status(thm)],[139])).
% fof(159, 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)],[16])).
% fof(160, 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)],[159])).
% fof(161, plain,((~(adjunction)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4))))&(((is_a_theorem(esk18_0)&is_a_theorem(esk19_0))&~(is_a_theorem(and(esk18_0,esk19_0))))|adjunction)),inference(skolemize,[status(esa)],[160])).
% fof(162, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk18_0)&is_a_theorem(esk19_0))&~(is_a_theorem(and(esk18_0,esk19_0))))|adjunction)),inference(shift_quantors,[status(thm)],[161])).
% fof(163, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk18_0)|adjunction)&(is_a_theorem(esk19_0)|adjunction))&(~(is_a_theorem(and(esk18_0,esk19_0)))|adjunction))),inference(distribute,[status(thm)],[162])).
% cnf(167,plain,(is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(split_conjunct,[status(thm)],[163])).
% fof(172, plain,(~(op_or)|![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),inference(fof_nnf,[status(thm)],[18])).
% fof(173, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(variable_rename,[status(thm)],[172])).
% fof(174, plain,![X3]:![X4]:(or(X3,X4)=not(and(not(X3),not(X4)))|~(op_or)),inference(shift_quantors,[status(thm)],[173])).
% cnf(175,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[174])).
% fof(182, plain,((~(axiom_m5)|![X1]:![X2]:![X5]:is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X5)),strict_implies(X1,X5))))&(?[X1]:?[X2]:?[X5]:~(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X5)),strict_implies(X1,X5))))|axiom_m5)),inference(fof_nnf,[status(thm)],[20])).
% fof(183, plain,((~(axiom_m5)|![X6]:![X7]:![X8]:is_a_theorem(strict_implies(and(strict_implies(X6,X7),strict_implies(X7,X8)),strict_implies(X6,X8))))&(?[X9]:?[X10]:?[X11]:~(is_a_theorem(strict_implies(and(strict_implies(X9,X10),strict_implies(X10,X11)),strict_implies(X9,X11))))|axiom_m5)),inference(variable_rename,[status(thm)],[182])).
% fof(184, plain,((~(axiom_m5)|![X6]:![X7]:![X8]:is_a_theorem(strict_implies(and(strict_implies(X6,X7),strict_implies(X7,X8)),strict_implies(X6,X8))))&(~(is_a_theorem(strict_implies(and(strict_implies(esk23_0,esk24_0),strict_implies(esk24_0,esk25_0)),strict_implies(esk23_0,esk25_0))))|axiom_m5)),inference(skolemize,[status(esa)],[183])).
% fof(185, plain,![X6]:![X7]:![X8]:((is_a_theorem(strict_implies(and(strict_implies(X6,X7),strict_implies(X7,X8)),strict_implies(X6,X8)))|~(axiom_m5))&(~(is_a_theorem(strict_implies(and(strict_implies(esk23_0,esk24_0),strict_implies(esk24_0,esk25_0)),strict_implies(esk23_0,esk25_0))))|axiom_m5)),inference(shift_quantors,[status(thm)],[184])).
% cnf(187,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)],[185])).
% fof(188, 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)],[21])).
% fof(189, 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)],[188])).
% fof(190, plain,((~(axiom_m4)|![X2]:is_a_theorem(strict_implies(X2,and(X2,X2))))&(~(is_a_theorem(strict_implies(esk26_0,and(esk26_0,esk26_0))))|axiom_m4)),inference(skolemize,[status(esa)],[189])).
% fof(191, plain,![X2]:((is_a_theorem(strict_implies(X2,and(X2,X2)))|~(axiom_m4))&(~(is_a_theorem(strict_implies(esk26_0,and(esk26_0,esk26_0))))|axiom_m4)),inference(shift_quantors,[status(thm)],[190])).
% cnf(193,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4),inference(split_conjunct,[status(thm)],[191])).
% fof(194, plain,((~(axiom_m3)|![X1]:![X2]:![X5]:is_a_theorem(strict_implies(and(and(X1,X2),X5),and(X1,and(X2,X5)))))&(?[X1]:?[X2]:?[X5]:~(is_a_theorem(strict_implies(and(and(X1,X2),X5),and(X1,and(X2,X5)))))|axiom_m3)),inference(fof_nnf,[status(thm)],[22])).
% fof(195, plain,((~(axiom_m3)|![X6]:![X7]:![X8]:is_a_theorem(strict_implies(and(and(X6,X7),X8),and(X6,and(X7,X8)))))&(?[X9]:?[X10]:?[X11]:~(is_a_theorem(strict_implies(and(and(X9,X10),X11),and(X9,and(X10,X11)))))|axiom_m3)),inference(variable_rename,[status(thm)],[194])).
% fof(196, plain,((~(axiom_m3)|![X6]:![X7]:![X8]:is_a_theorem(strict_implies(and(and(X6,X7),X8),and(X6,and(X7,X8)))))&(~(is_a_theorem(strict_implies(and(and(esk27_0,esk28_0),esk29_0),and(esk27_0,and(esk28_0,esk29_0)))))|axiom_m3)),inference(skolemize,[status(esa)],[195])).
% fof(197, plain,![X6]:![X7]:![X8]:((is_a_theorem(strict_implies(and(and(X6,X7),X8),and(X6,and(X7,X8))))|~(axiom_m3))&(~(is_a_theorem(strict_implies(and(and(esk27_0,esk28_0),esk29_0),and(esk27_0,and(esk28_0,esk29_0)))))|axiom_m3)),inference(shift_quantors,[status(thm)],[196])).
% cnf(199,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|~axiom_m3),inference(split_conjunct,[status(thm)],[197])).
% fof(200, 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)],[23])).
% fof(201, 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)],[200])).
% fof(202, plain,((~(axiom_m2)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),X3)))&(~(is_a_theorem(strict_implies(and(esk30_0,esk31_0),esk30_0)))|axiom_m2)),inference(skolemize,[status(esa)],[201])).
% fof(203, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),X3))|~(axiom_m2))&(~(is_a_theorem(strict_implies(and(esk30_0,esk31_0),esk30_0)))|axiom_m2)),inference(shift_quantors,[status(thm)],[202])).
% cnf(205,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2),inference(split_conjunct,[status(thm)],[203])).
% fof(206, 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)],[24])).
% fof(207, 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)],[206])).
% fof(208, plain,((~(axiom_m1)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))))&(~(is_a_theorem(strict_implies(and(esk32_0,esk33_0),and(esk33_0,esk32_0))))|axiom_m1)),inference(skolemize,[status(esa)],[207])).
% fof(209, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),and(X4,X3)))|~(axiom_m1))&(~(is_a_theorem(strict_implies(and(esk32_0,esk33_0),and(esk33_0,esk32_0))))|axiom_m1)),inference(shift_quantors,[status(thm)],[208])).
% cnf(211,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1),inference(split_conjunct,[status(thm)],[209])).
% fof(218, 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)],[26])).
% fof(219, 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)],[218])).
% fof(220, plain,((~(substitution_strict_equiv)|![X3]:![X4]:(~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4))&((is_a_theorem(strict_equiv(esk35_0,esk36_0))&~(esk35_0=esk36_0))|substitution_strict_equiv)),inference(skolemize,[status(esa)],[219])).
% fof(221, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk35_0,esk36_0))&~(esk35_0=esk36_0))|substitution_strict_equiv)),inference(shift_quantors,[status(thm)],[220])).
% fof(222, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk35_0,esk36_0))|substitution_strict_equiv)&(~(esk35_0=esk36_0)|substitution_strict_equiv))),inference(distribute,[status(thm)],[221])).
% cnf(225,plain,(X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2))),inference(split_conjunct,[status(thm)],[222])).
% fof(348, plain,(~(op_equiv)|![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),inference(fof_nnf,[status(thm)],[47])).
% fof(349, plain,(~(op_equiv)|![X3]:![X4]:equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))),inference(variable_rename,[status(thm)],[348])).
% fof(350, plain,![X3]:![X4]:(equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))|~(op_equiv)),inference(shift_quantors,[status(thm)],[349])).
% cnf(351,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[350])).
% fof(352, plain,(~(op_implies_and)|![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),inference(fof_nnf,[status(thm)],[48])).
% fof(353, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(variable_rename,[status(thm)],[352])).
% fof(354, plain,![X3]:![X4]:(implies(X3,X4)=not(and(X3,not(X4)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[353])).
% cnf(355,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[354])).
% cnf(356,plain,(modus_ponens_strict_implies),inference(split_conjunct,[status(thm)],[49])).
% cnf(391,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[56])).
% cnf(392,plain,(axiom_m5),inference(split_conjunct,[status(thm)],[57])).
% cnf(393,plain,(axiom_m4),inference(split_conjunct,[status(thm)],[58])).
% cnf(394,plain,(axiom_m3),inference(split_conjunct,[status(thm)],[59])).
% cnf(395,plain,(axiom_m2),inference(split_conjunct,[status(thm)],[60])).
% cnf(396,plain,(axiom_m1),inference(split_conjunct,[status(thm)],[61])).
% cnf(397,plain,(adjunction),inference(split_conjunct,[status(thm)],[62])).
% cnf(398,plain,(substitution_strict_equiv),inference(split_conjunct,[status(thm)],[63])).
% cnf(399,plain,(op_strict_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(415,plain,(op_equiv),inference(split_conjunct,[status(thm)],[70])).
% fof(417, plain,((~(equivalence_1)|![X1]:![X2]:is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))&(?[X1]:?[X2]:~(is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))|equivalence_1)),inference(fof_nnf,[status(thm)],[72])).
% fof(418, plain,((~(equivalence_1)|![X3]:![X4]:is_a_theorem(implies(equiv(X3,X4),implies(X3,X4))))&(?[X5]:?[X6]:~(is_a_theorem(implies(equiv(X5,X6),implies(X5,X6))))|equivalence_1)),inference(variable_rename,[status(thm)],[417])).
% fof(419, plain,((~(equivalence_1)|![X3]:![X4]:is_a_theorem(implies(equiv(X3,X4),implies(X3,X4))))&(~(is_a_theorem(implies(equiv(esk90_0,esk91_0),implies(esk90_0,esk91_0))))|equivalence_1)),inference(skolemize,[status(esa)],[418])).
% fof(420, plain,![X3]:![X4]:((is_a_theorem(implies(equiv(X3,X4),implies(X3,X4)))|~(equivalence_1))&(~(is_a_theorem(implies(equiv(esk90_0,esk91_0),implies(esk90_0,esk91_0))))|equivalence_1)),inference(shift_quantors,[status(thm)],[419])).
% cnf(421,plain,(equivalence_1|~is_a_theorem(implies(equiv(esk90_0,esk91_0),implies(esk90_0,esk91_0)))),inference(split_conjunct,[status(thm)],[420])).
% cnf(423,negated_conjecture,(~equivalence_1),inference(split_conjunct,[status(thm)],[75])).
% cnf(435,plain,(X1=X2|$false|~is_a_theorem(strict_equiv(X1,X2))),inference(rw,[status(thm)],[225,398,theory(equality)])).
% cnf(436,plain,(X1=X2|~is_a_theorem(strict_equiv(X1,X2))),inference(cn,[status(thm)],[435,theory(equality)])).
% cnf(437,plain,(~is_a_theorem(implies(equiv(esk90_0,esk91_0),implies(esk90_0,esk91_0)))),inference(sr,[status(thm)],[421,423,theory(equality)])).
% cnf(442,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|$false),inference(rw,[status(thm)],[193,393,theory(equality)])).
% cnf(443,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))),inference(cn,[status(thm)],[442,theory(equality)])).
% cnf(444,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[205,395,theory(equality)])).
% cnf(445,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))),inference(cn,[status(thm)],[444,theory(equality)])).
% cnf(446,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(rw,[status(thm)],[84,356,theory(equality)])).
% cnf(447,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(cn,[status(thm)],[446,theory(equality)])).
% cnf(448,plain,(is_a_theorem(X1)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[447,445,theory(equality)])).
% cnf(450,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)|$false),inference(rw,[status(thm)],[140,400,theory(equality)])).
% cnf(451,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)),inference(cn,[status(thm)],[450,theory(equality)])).
% cnf(452,plain,(is_a_theorem(and(X1,X2))|$false|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(rw,[status(thm)],[167,397,theory(equality)])).
% cnf(453,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(cn,[status(thm)],[452,theory(equality)])).
% cnf(454,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[355,391,theory(equality)])).
% cnf(455,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[454,theory(equality)])).
% cnf(457,plain,(not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))),inference(spm,[status(thm)],[455,455,theory(equality)])).
% cnf(461,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[211,396,theory(equality)])).
% cnf(462,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[461,theory(equality)])).
% cnf(464,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[175,455,theory(equality)])).
% cnf(465,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[464,401,theory(equality)])).
% cnf(466,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[465,theory(equality)])).
% cnf(467,plain,(necessarily(or(X1,X2))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[451,466,theory(equality)])).
% cnf(468,plain,(implies(implies(X1,X2),X3)=or(and(X1,not(X2)),X3)),inference(spm,[status(thm)],[466,455,theory(equality)])).
% cnf(478,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)|$false),inference(rw,[status(thm)],[136,399,theory(equality)])).
% cnf(479,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)),inference(cn,[status(thm)],[478,theory(equality)])).
% cnf(480,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)],[453,479,theory(equality)])).
% cnf(487,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[351,415,theory(equality)])).
% cnf(488,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[487,theory(equality)])).
% cnf(491,plain,(is_a_theorem(strict_implies(equiv(X1,X2),and(implies(X2,X1),implies(X1,X2))))),inference(spm,[status(thm)],[462,488,theory(equality)])).
% cnf(498,plain,(~is_a_theorem(implies(and(implies(esk90_0,esk91_0),implies(esk91_0,esk90_0)),implies(esk90_0,esk91_0)))),inference(rw,[status(thm)],[437,488,theory(equality)])).
% cnf(502,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|$false),inference(rw,[status(thm)],[199,394,theory(equality)])).
% cnf(503,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))),inference(cn,[status(thm)],[502,theory(equality)])).
% cnf(504,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(and(and(X1,X2),X3))),inference(spm,[status(thm)],[447,503,theory(equality)])).
% cnf(509,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|$false),inference(rw,[status(thm)],[187,392,theory(equality)])).
% cnf(510,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))),inference(cn,[status(thm)],[509,theory(equality)])).
% cnf(511,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))),inference(spm,[status(thm)],[447,510,theory(equality)])).
% cnf(516,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_equiv(X1,X2))),inference(spm,[status(thm)],[448,479,theory(equality)])).
% cnf(555,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|~is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(spm,[status(thm)],[480,462,theory(equality)])).
% cnf(556,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(and(X1,X2),X3)))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))),inference(spm,[status(thm)],[480,503,theory(equality)])).
% cnf(559,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|~is_a_theorem(strict_implies(and(X1,X1),X1))),inference(spm,[status(thm)],[480,443,theory(equality)])).
% cnf(560,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[555,462,theory(equality)])).
% cnf(561,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[560,theory(equality)])).
% cnf(562,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|$false),inference(rw,[status(thm)],[559,445,theory(equality)])).
% cnf(563,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))),inference(cn,[status(thm)],[562,theory(equality)])).
% cnf(564,plain,(and(X1,X1)=X1),inference(spm,[status(thm)],[436,563,theory(equality)])).
% cnf(572,plain,(strict_implies(X1,X1)=strict_equiv(X1,X1)),inference(spm,[status(thm)],[479,564,theory(equality)])).
% cnf(575,plain,(not(not(X1))=implies(not(X1),X1)),inference(spm,[status(thm)],[455,564,theory(equality)])).
% cnf(585,plain,(is_a_theorem(strict_equiv(X1,X1))),inference(rw,[status(thm)],[563,564,theory(equality)])).
% cnf(591,plain,(not(not(X1))=or(X1,X1)),inference(rw,[status(thm)],[575,466,theory(equality)])).
% cnf(596,plain,(is_a_theorem(strict_implies(X1,X1))),inference(spm,[status(thm)],[516,585,theory(equality)])).
% cnf(607,plain,(not(implies(X1,X2))=implies(implies(X1,X2),and(X1,not(X2)))),inference(spm,[status(thm)],[457,564,theory(equality)])).
% cnf(633,plain,(and(X1,X2)=and(X2,X1)),inference(spm,[status(thm)],[436,561,theory(equality)])).
% cnf(651,plain,(is_a_theorem(strict_implies(and(X3,and(X1,X2)),and(X1,and(X2,X3))))),inference(spm,[status(thm)],[503,633,theory(equality)])).
% cnf(652,plain,(and(strict_implies(X2,X1),strict_implies(X1,X2))=strict_equiv(X1,X2)),inference(spm,[status(thm)],[479,633,theory(equality)])).
% cnf(656,plain,(not(and(not(X2),X1))=implies(X1,X2)),inference(spm,[status(thm)],[455,633,theory(equality)])).
% cnf(660,plain,(is_a_theorem(strict_implies(and(X2,X1),X1))),inference(spm,[status(thm)],[445,633,theory(equality)])).
% cnf(690,plain,(strict_equiv(X2,X1)=strict_equiv(X1,X2)),inference(rw,[status(thm)],[652,479,theory(equality)])).
% cnf(735,plain,(not(and(X1,or(X2,X2)))=implies(X1,not(X2))),inference(spm,[status(thm)],[455,591,theory(equality)])).
% cnf(813,plain,(implies(not(X2),X1)=implies(not(X1),X2)),inference(spm,[status(thm)],[455,656,theory(equality)])).
% cnf(817,plain,(not(and(or(X1,X1),X2))=implies(X2,not(X1))),inference(spm,[status(thm)],[656,591,theory(equality)])).
% cnf(829,plain,(or(X2,X1)=implies(not(X1),X2)),inference(rw,[status(thm)],[813,466,theory(equality)])).
% cnf(830,plain,(or(X2,X1)=or(X1,X2)),inference(rw,[status(thm)],[829,466,theory(equality)])).
% cnf(838,plain,(necessarily(or(X2,X1))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[467,830,theory(equality)])).
% cnf(850,plain,(strict_implies(not(X2),X1)=strict_implies(not(X1),X2)),inference(rw,[status(thm)],[838,467,theory(equality)])).
% cnf(1028,plain,(and(strict_implies(not(X2),X1),strict_implies(X2,not(X1)))=strict_equiv(not(X1),X2)),inference(spm,[status(thm)],[479,850,theory(equality)])).
% cnf(1031,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[447,850,theory(equality)])).
% cnf(1048,plain,(strict_implies(not(X1),and(not(X2),X3))=strict_implies(implies(X3,X2),X1)),inference(spm,[status(thm)],[850,656,theory(equality)])).
% cnf(1052,plain,(strict_implies(not(X1),not(X2))=strict_implies(or(X2,X2),X1)),inference(spm,[status(thm)],[850,591,theory(equality)])).
% cnf(1069,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)],[1031,455,theory(equality)])).
% cnf(1096,plain,(is_a_theorem(strict_implies(equiv(X1,X2),equiv(X2,X1)))),inference(spm,[status(thm)],[491,488,theory(equality)])).
% cnf(1348,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(X3)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[504,453,theory(equality)])).
% cnf(1475,plain,(is_a_theorem(strict_equiv(equiv(X1,X2),equiv(X2,X1)))|~is_a_theorem(strict_implies(equiv(X1,X2),equiv(X2,X1)))),inference(spm,[status(thm)],[480,1096,theory(equality)])).
% cnf(1486,plain,(is_a_theorem(strict_equiv(equiv(X1,X2),equiv(X2,X1)))|$false),inference(rw,[status(thm)],[1475,1096,theory(equality)])).
% cnf(1487,plain,(is_a_theorem(strict_equiv(equiv(X1,X2),equiv(X2,X1)))),inference(cn,[status(thm)],[1486,theory(equality)])).
% cnf(1577,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)],[511,453,theory(equality)])).
% cnf(1768,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)],[1069,466,theory(equality)])).
% cnf(2329,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)],[1348,479,theory(equality)])).
% cnf(2480,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)],[556,564,theory(equality)])).
% cnf(2496,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))|$false),inference(rw,[status(thm)],[2480,660,theory(equality)])).
% cnf(2497,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))),inference(cn,[status(thm)],[2496,theory(equality)])).
% cnf(2509,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X1,and(X1,X2))))),inference(rw,[status(thm)],[2497,690,theory(equality)])).
% cnf(2510,plain,(and(X1,X2)=and(X1,and(X1,X2))),inference(spm,[status(thm)],[436,2509,theory(equality)])).
% cnf(3995,plain,(is_a_theorem(strict_implies(and(X1,and(X3,X2)),and(X2,and(X3,X1))))),inference(spm,[status(thm)],[651,633,theory(equality)])).
% cnf(15150,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(not(X1),X2)),inference(rw,[status(thm)],[1028,633,theory(equality)])).
% cnf(16012,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)],[1768,1048,theory(equality)]),466,theory(equality)])).
% cnf(16844,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(spm,[status(thm)],[596,1052,theory(equality)])).
% cnf(16884,plain,(is_a_theorem(strict_implies(or(X1,X1),X1))),inference(spm,[status(thm)],[596,1052,theory(equality)])).
% cnf(17022,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|~is_a_theorem(strict_implies(X1,or(X1,X1)))),inference(spm,[status(thm)],[480,16884,theory(equality)])).
% cnf(17848,plain,(is_a_theorem(strict_implies(not(not(X1)),or(X1,X1)))),inference(rw,[status(thm)],[16844,850,theory(equality)])).
% cnf(32712,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,or(X2,X2)))),inference(spm,[status(thm)],[1577,16884,theory(equality)])).
% cnf(32758,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,and(X3,X2)))),inference(spm,[status(thm)],[1577,660,theory(equality)])).
% cnf(32789,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,not(not(X2))))),inference(spm,[status(thm)],[32712,591,theory(equality)])).
% cnf(32802,plain,(is_a_theorem(strict_implies(or(or(X1,X1),or(X1,X1)),X1))),inference(spm,[status(thm)],[32712,16884,theory(equality)])).
% cnf(33243,plain,(is_a_theorem(strict_implies(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[32802,591,theory(equality)]),850,theory(equality)])).
% cnf(33245,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)],[480,33243,theory(equality)])).
% cnf(33299,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[33245,850,theory(equality)]),17848,theory(equality)])).
% cnf(33300,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))),inference(cn,[status(thm)],[33299,theory(equality)])).
% cnf(33335,plain,(is_a_theorem(strict_equiv(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[33300,690,theory(equality)])).
% cnf(33336,plain,(not(X1)=not(or(X1,X1))),inference(spm,[status(thm)],[436,33335,theory(equality)])).
% cnf(33439,plain,(not(and(not(X1),X2))=implies(X2,or(X1,X1))),inference(spm,[status(thm)],[656,33336,theory(equality)])).
% cnf(33736,plain,(implies(X2,X1)=implies(X2,or(X1,X1))),inference(rw,[status(thm)],[33439,656,theory(equality)])).
% cnf(36321,plain,(is_a_theorem(strict_implies(or(and(X1,X2),and(X1,X2)),X2))),inference(spm,[status(thm)],[32758,16884,theory(equality)])).
% cnf(37240,plain,(is_a_theorem(strict_implies(or(and(X1,not(not(X2))),and(X1,not(not(X2)))),X2))),inference(spm,[status(thm)],[32789,36321,theory(equality)])).
% cnf(37276,plain,(is_a_theorem(strict_implies(not(implies(X1,not(X2))),X2))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[37240,468,theory(equality)]),607,theory(equality)])).
% cnf(37280,plain,(is_a_theorem(strict_implies(not(X2),implies(X1,not(X2))))),inference(rw,[status(thm)],[37276,850,theory(equality)])).
% cnf(37281,plain,(is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[447,37280,theory(equality)])).
% cnf(48041,plain,(necessarily(implies(X1,X2))=strict_implies(X1,or(X2,X2))),inference(spm,[status(thm)],[451,33736,theory(equality)])).
% cnf(48178,plain,(strict_implies(X1,X2)=strict_implies(X1,or(X2,X2))),inference(rw,[status(thm)],[48041,451,theory(equality)])).
% cnf(51614,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[17022,48178,theory(equality)]),596,theory(equality)])).
% cnf(51615,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))),inference(cn,[status(thm)],[51614,theory(equality)])).
% cnf(51767,plain,(X1=or(X1,X1)),inference(spm,[status(thm)],[436,51615,theory(equality)])).
% cnf(51938,plain,(not(and(X1,X2))=implies(X1,not(X2))),inference(rw,[status(thm)],[735,51767,theory(equality)])).
% cnf(51967,plain,(not(and(X1,X2))=implies(X2,not(X1))),inference(rw,[status(thm)],[817,51767,theory(equality)])).
% cnf(51969,plain,(not(not(X1))=X1),inference(rw,[status(thm)],[591,51767,theory(equality)])).
% cnf(52108,plain,(is_a_theorem(strict_implies(X1,implies(X2,X1)))),inference(spm,[status(thm)],[37280,51969,theory(equality)])).
% cnf(52222,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)),inference(spm,[status(thm)],[37281,51969,theory(equality)])).
% cnf(55298,plain,(is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X1,X3))),inference(spm,[status(thm)],[1577,52108,theory(equality)])).
% cnf(57233,plain,(not(implies(X1,not(X2)))=and(X1,X2)),inference(spm,[status(thm)],[51969,51938,theory(equality)])).
% cnf(57540,plain,(implies(X1,not(X2))=implies(X2,not(X1))),inference(rw,[status(thm)],[51967,51938,theory(equality)])).
% cnf(57552,plain,(necessarily(implies(X2,not(X1)))=strict_implies(X1,not(X2))),inference(spm,[status(thm)],[451,57540,theory(equality)])).
% cnf(57820,plain,(strict_implies(X2,not(X1))=strict_implies(X1,not(X2))),inference(rw,[status(thm)],[57552,451,theory(equality)])).
% cnf(66963,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)],[2329,572,theory(equality)])).
% cnf(66973,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)],[66963,2510,theory(equality)])).
% cnf(66974,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|$false|~is_a_theorem(X2)),inference(rw,[status(thm)],[66973,596,theory(equality)])).
% cnf(66975,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|~is_a_theorem(X2)),inference(cn,[status(thm)],[66974,theory(equality)])).
% cnf(77106,plain,(is_a_theorem(strict_implies(and(X1,X2),implies(X3,X1)))),inference(spm,[status(thm)],[55298,445,theory(equality)])).
% cnf(77134,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(and(X2,X3))),inference(spm,[status(thm)],[447,77106,theory(equality)])).
% cnf(78498,plain,(is_a_theorem(implies(X1,strict_implies(X2,X2)))|~is_a_theorem(X3)),inference(spm,[status(thm)],[77134,66975,theory(equality)])).
% cnf(79371,plain,(is_a_theorem(implies(X1,strict_implies(X2,X2)))),inference(spm,[status(thm)],[78498,1487,theory(equality)])).
% cnf(79579,plain,(is_a_theorem(or(X1,strict_implies(X2,X2)))),inference(spm,[status(thm)],[79371,466,theory(equality)])).
% cnf(79585,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(or(strict_implies(X2,X2),X3),X1))),inference(spm,[status(thm)],[16012,79579,theory(equality)])).
% cnf(80103,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)],[480,3995,theory(equality)])).
% cnf(80178,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))|$false),inference(rw,[status(thm)],[80103,3995,theory(equality)])).
% cnf(80179,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))),inference(cn,[status(thm)],[80178,theory(equality)])).
% cnf(99144,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(X1,not(X2))),inference(spm,[status(thm)],[479,57820,theory(equality)])).
% cnf(99736,plain,(strict_equiv(not(X1),X2)=strict_equiv(X1,not(X2))),inference(rw,[status(thm)],[99144,15150,theory(equality)])).
% cnf(100089,plain,(not(X1)=X2|~is_a_theorem(strict_equiv(X1,not(X2)))),inference(spm,[status(thm)],[436,99736,theory(equality)])).
% cnf(100257,plain,(not(X1)=implies(X2,not(X3))|~is_a_theorem(strict_equiv(X1,and(X2,X3)))),inference(spm,[status(thm)],[100089,57233,theory(equality)])).
% cnf(180963,plain,(not(X1)=implies(X2,not(X3))|~is_a_theorem(strict_equiv(X1,and(X3,X2)))),inference(spm,[status(thm)],[100257,633,theory(equality)])).
% cnf(193700,plain,(not(and(X1,and(X2,X3)))=implies(and(X2,X1),not(X3))),inference(spm,[status(thm)],[180963,80179,theory(equality)])).
% cnf(193716,plain,(implies(X1,implies(X2,not(X3)))=implies(and(X2,X1),not(X3))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[193700,51938,theory(equality)]),51938,theory(equality)])).
% cnf(194019,plain,(implies(and(X1,X2),X3)=implies(X2,implies(X1,X3))),inference(spm,[status(thm)],[193716,51969,theory(equality)])).
% cnf(286053,plain,(necessarily(implies(X2,implies(X1,X3)))=strict_implies(and(X1,X2),X3)),inference(spm,[status(thm)],[451,194019,theory(equality)])).
% cnf(286428,plain,(~is_a_theorem(implies(implies(esk91_0,esk90_0),implies(implies(esk90_0,esk91_0),implies(esk90_0,esk91_0))))),inference(rw,[status(thm)],[498,194019,theory(equality)])).
% cnf(286620,plain,(strict_implies(X2,implies(X1,X3))=strict_implies(and(X1,X2),X3)),inference(rw,[status(thm)],[286053,451,theory(equality)])).
% cnf(286719,plain,(~is_a_theorem(implies(implies(esk90_0,esk91_0),implies(esk90_0,esk91_0)))),inference(spm,[status(thm)],[286428,52222,theory(equality)])).
% cnf(289246,plain,(is_a_theorem(strict_implies(X2,implies(X1,X1)))),inference(rw,[status(thm)],[445,286620,theory(equality)])).
% cnf(289760,plain,(is_a_theorem(implies(X1,X1))),inference(spm,[status(thm)],[79585,289246,theory(equality)])).
% cnf(289927,plain,($false),inference(rw,[status(thm)],[286719,289760,theory(equality)])).
% cnf(289928,plain,($false),inference(cn,[status(thm)],[289927,theory(equality)])).
% cnf(289929,plain,($false),289928,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses                  : 14471
% # ...of these trivial                : 908
% # ...subsumed                        : 10854
% # ...remaining for further processing: 2709
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed                  : 51
% # Backward-rewritten                 : 1077
% # Generated clauses                  : 204004
% # ...of the previous two non-trivial : 165553
% # Contextual simplify-reflections    : 728
% # Paramodulations                    : 204004
% # Factorizations                     : 0
% # Equation resolutions               : 0
% # Current number of processed clauses: 1581
% #    Positive orientable unit clauses: 599
% #    Positive unorientable unit clauses: 34
% #    Negative unit clauses           : 4
% #    Non-unit-clauses                : 944
% # Current number of unprocessed clauses: 65843
% # ...number of literals in the above : 112614
% # Clause-clause subsumption calls (NU) : 152061
% # Rec. Clause-clause subsumption calls : 151080
% # Unit Clause-clause subsumption calls : 1127
% # Rewrite failures with RHS unbound  : 0
% # Indexed BW rewrite attempts        : 52761
% # Indexed BW rewrite successes       : 1938
% # Backwards rewriting index:  1114 leaves,   3.31+/-6.499 terms/leaf
% # Paramod-from index:          215 leaves,   3.64+/-9.170 terms/leaf
% # Paramod-into index:          986 leaves,   3.33+/-6.721 terms/leaf
% # -------------------------------------------------
% # User time              : 7.008 s
% # System time            : 0.255 s
% # Total time             : 7.263 s
% # Maximum resident set size: 0 pages
% PrfWatch: 11.45 CPU 11.63 WC
% FINAL PrfWatch: 11.45 CPU 11.63 WC
% SZS output end Solution for /tmp/SystemOnTPTP18596/LCL561+1.tptp
% 
%------------------------------------------------------------------------------