TSTP Solution File: LCL558+1 by SRASS---0.1
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%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : LCL558+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Wed Dec 29 14:02:28 EST 2010
% Result : Theorem 284.32s
% Output : Solution 296.47s
% 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/SystemOnTPTP25880/LCL558+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% not found
% Adding ~C to TBU ... ~hilbert_or_1:
% ---- Iteration 1 (0 axioms selected)
% Looking for TBU SAT ... yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... 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 2 (3 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... r1:
% CSA axiom r1 found
% Looking for CSA axiom ... r2:
% CSA axiom r2 found
% Looking for CSA axiom ... r3:
% CSA axiom r3 found
% ---- Iteration 3 (6 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... r4:
% CSA axiom r4 found
% Looking for CSA axiom ... r5:
% CSA axiom r5 found
% Looking for CSA axiom ... s1_0_op_possibly:
% CSA axiom s1_0_op_possibly found
% ---- Iteration 4 (9 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... s1_0_op_or:
% CSA axiom s1_0_op_or found
% Looking for CSA axiom ... s1_0_op_strict_implies:
% CSA axiom s1_0_op_strict_implies found
% Looking for CSA axiom ... s1_0_op_equiv: CSA axiom s1_0_op_equiv found
% ---- Iteration 5 (12 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 6 (15 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 7 (18 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 ... hilbert_op_equiv:
% substitution_of_equivalents:
% CSA axiom substitution_of_equivalents found
% ---- Iteration 8 (21 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% modus_ponens:
% CSA axiom modus_ponens found
% Looking for CSA axiom ... implies_1:
% CSA axiom implies_1 found
% Looking for CSA axiom ... implies_2:
% CSA axiom implies_2 found
% ---- Iteration 9 (24 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% implies_3: CSA axiom implies_3 found
% Looking for CSA axiom ... cn1:
% CSA axiom cn1 found
% Looking for CSA axiom ... op_or:
% CSA axiom op_or found
% ---- Iteration 10 (27 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% op_and:
% CSA axiom op_and found
% Looking for CSA axiom ... s1_0_op_strict_equiv:
% CSA axiom s1_0_op_strict_equiv found
% Looking for CSA axiom ... s1_0_modus_ponens_strict_implies:
% CSA axiom s1_0_modus_ponens_strict_implies found
% ---- Iteration 11 (30 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% op_implies_and:
% CSA axiom op_implies_and found
% Looking for CSA axiom ... necessitation:
% CSA axiom necessitation found
% Looking for CSA axiom ... adjunction:
% CSA axiom adjunction found
% ---- Iteration 12 (33 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% 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 13 (36 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% kn1:
% CSA axiom kn1 found
% Looking for CSA axiom ... kn2:
% CSA axiom kn2 found
% Looking for CSA axiom ... op_implies_or:
% CSA axiom op_implies_or found
% ---- Iteration 14 (39 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% modus_tollens:
% CSA axiom modus_tollens found
% Looking for CSA axiom ... equivalence_1:
% CSA axiom equivalence_1 found
% Looking for CSA axiom ... equivalence_2:
% CSA axiom equivalence_2 found
% ---- Iteration 15 (42 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% equivalence_3:
% CSA axiom equivalence_3 found
% Looking for CSA axiom ... cn2:
% CSA axiom cn2 found
% Looking for CSA axiom ... cn3:
% CSA axiom cn3 found
% ---- Iteration 16 (45 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% 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 17 (48 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ... not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% substitution_of_equivalents:
% modus_ponens_strict_implies:
% CSA axiom modus_ponens_strict_implies found
% Looking for CSA axiom ... kn3:
% CSA axiom kn3 found
% Looking for CSA axiom ... axiom_s1:
% CSA axiom axiom_s1 found
% ---- Iteration 18 (51 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% substitution_of_equivalents:axiom_s4:
% CSA axiom axiom_s4 found
% Looking for CSA axiom ... axiom_m1:
% CSA axiom axiom_m1 found
% Looking for CSA axiom ... axiom_m2:
% CSA axiom axiom_m2 found
% ---- Iteration 19 (54 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% substitution_of_equivalents: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 20 (57 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% substitution_of_equivalents:
% op_possibly:
% CSA axiom op_possibly found
% Looking for CSA axiom ... op_necessarily:
% CSA axiom op_necessarily found
% Looking for CSA axiom ... op_equiv:
% CSA axiom op_equiv found
% ---- Iteration 21 (60 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% substitution_of_equivalents:axiom_B:
% CSA axiom axiom_B found
% Looking for CSA axiom ... axiom_5:
% CSA axiom axiom_5 found
% Looking for CSA axiom ... op_strict_implies:
% CSA axiom op_strict_implies found
% ---- Iteration 22 (63 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% substitution_of_equivalents:axiom_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:
% hilbert_op_equiv:
% 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:
% CSA axiom axiom_m9 found
% ---- Iteration 24 (69 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... hilbert_op_or:
% hilbert_op_equiv:
% substitution_of_equivalents:axiom_m10:
% CSA axiom axiom_m10 found
% Looking for CSA axiom ... substitution_strict_equiv:
% CSA axiom substitution_strict_equiv found
% Looking for CSA axiom ... op_strict_equiv:
% CSA axiom op_strict_equiv found
% ---- Iteration 25 (72 axioms selected)
% Looking for TBU SAT ...
% no
% Looking for TBU UNS ...
% yes - theorem proved
% ---- Selection completed
% Selected axioms are ... :op_strict_equiv:substitution_strict_equiv:axiom_m10:axiom_m9:axiom_m8:axiom_m7:axiom_m6:axiom_s2:axiom_s3:op_strict_implies:axiom_5:axiom_B:op_equiv:op_necessarily:op_possibly:axiom_m5:axiom_m4:axiom_m3:axiom_m2:axiom_m1:axiom_s4:axiom_s1:kn3:modus_ponens_strict_implies:axiom_4:axiom_M:axiom_K:cn3:cn2:equivalence_3:equivalence_2:equivalence_1:modus_tollens:op_implies_or:kn2:kn1:and_3:and_2:and_1:adjunction:necessitation:op_implies_and:s1_0_modus_ponens_strict_implies:s1_0_op_strict_equiv:op_and:op_or:cn1:implies_3:implies_2:implies_1:modus_ponens:substitution_of_equivalents: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_equiv:s1_0_op_strict_implies:s1_0_op_or:s1_0_op_possibly:r5:r4:r3:r2:r1:or_3:or_2:or_1 (72)
% Unselected axioms are ... :hilbert_op_or:hilbert_op_equiv:substitution_of_equivalents:s1_0_op_implies (4)
% SZS status THM for /tmp/SystemOnTPTP25880/LCL558+1.tptp
% Looking for THM ...
% found
% SZS output start Solution for /tmp/SystemOnTPTP25880/LCL558+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 9681
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.01 WC
% PrfWatch: 1.93 CPU 2.02 WC
% PrfWatch: 3.93 CPU 4.02 WC
% PrfWatch: 5.92 CPU 6.03 WC
% # Preprocessing time : 0.024 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 7.90 CPU 8.03 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,(substitution_strict_equiv<=>![X1]:![X2]:(is_a_theorem(strict_equiv(X1,X2))=>X1=X2)),file('/tmp/SRASS.s.p', substitution_strict_equiv)).
% fof(10, axiom,(op_strict_implies=>![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),file('/tmp/SRASS.s.p', op_strict_implies)).
% fof(13, axiom,(op_equiv=>![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),file('/tmp/SRASS.s.p', op_equiv)).
% fof(16, 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(17, axiom,(axiom_m4<=>![X1]:is_a_theorem(strict_implies(X1,and(X1,X1)))),file('/tmp/SRASS.s.p', axiom_m4)).
% fof(18, 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(19, axiom,(axiom_m2<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),X1))),file('/tmp/SRASS.s.p', axiom_m2)).
% fof(20, axiom,(axiom_m1<=>![X1]:![X2]:is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),file('/tmp/SRASS.s.p', axiom_m1)).
% fof(24, 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(38, axiom,(and_2<=>![X1]:![X2]:is_a_theorem(implies(and(X1,X2),X2))),file('/tmp/SRASS.s.p', and_2)).
% fof(40, axiom,(adjunction<=>![X1]:![X2]:((is_a_theorem(X1)&is_a_theorem(X2))=>is_a_theorem(and(X1,X2)))),file('/tmp/SRASS.s.p', adjunction)).
% fof(42, axiom,(op_implies_and=>![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),file('/tmp/SRASS.s.p', op_implies_and)).
% fof(43, axiom,modus_ponens_strict_implies,file('/tmp/SRASS.s.p', s1_0_modus_ponens_strict_implies)).
% fof(44, axiom,op_strict_equiv,file('/tmp/SRASS.s.p', s1_0_op_strict_equiv)).
% fof(46, axiom,(op_or=>![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),file('/tmp/SRASS.s.p', op_or)).
% fof(53, axiom,op_implies_and,file('/tmp/SRASS.s.p', hilbert_op_implies_and)).
% fof(54, axiom,axiom_m5,file('/tmp/SRASS.s.p', s1_0_axiom_m5)).
% fof(55, axiom,axiom_m4,file('/tmp/SRASS.s.p', s1_0_axiom_m4)).
% fof(56, axiom,axiom_m3,file('/tmp/SRASS.s.p', s1_0_axiom_m3)).
% fof(57, axiom,axiom_m2,file('/tmp/SRASS.s.p', s1_0_axiom_m2)).
% fof(58, axiom,axiom_m1,file('/tmp/SRASS.s.p', s1_0_axiom_m1)).
% fof(59, axiom,adjunction,file('/tmp/SRASS.s.p', s1_0_adjunction)).
% fof(60, axiom,substitution_strict_equiv,file('/tmp/SRASS.s.p', s1_0_substitution_strict_equiv)).
% fof(61, axiom,op_equiv,file('/tmp/SRASS.s.p', s1_0_op_equiv)).
% fof(62, axiom,op_strict_implies,file('/tmp/SRASS.s.p', s1_0_op_strict_implies)).
% fof(63, axiom,op_or,file('/tmp/SRASS.s.p', s1_0_op_or)).
% fof(72, axiom,(or_1<=>![X1]:![X2]:is_a_theorem(implies(X1,or(X1,X2)))),file('/tmp/SRASS.s.p', or_1)).
% fof(73, conjecture,or_1,file('/tmp/SRASS.s.p', hilbert_or_1)).
% fof(74, negated_conjecture,~(or_1),inference(assume_negation,[status(cth)],[73])).
% fof(75, negated_conjecture,~(or_1),inference(fof_simplification,[status(thm)],[74,theory(equality)])).
% fof(76, plain,(~(op_strict_equiv)|![X1]:![X2]:strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))),inference(fof_nnf,[status(thm)],[1])).
% fof(77, plain,(~(op_strict_equiv)|![X3]:![X4]:strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))),inference(variable_rename,[status(thm)],[76])).
% fof(78, plain,![X3]:![X4]:(strict_equiv(X3,X4)=and(strict_implies(X3,X4),strict_implies(X4,X3))|~(op_strict_equiv)),inference(shift_quantors,[status(thm)],[77])).
% cnf(79,plain,(strict_equiv(X1,X2)=and(strict_implies(X1,X2),strict_implies(X2,X1))|~op_strict_equiv),inference(split_conjunct,[status(thm)],[78])).
% fof(80, plain,((~(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)],[2])).
% fof(81, 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)],[80])).
% fof(82, plain,((~(substitution_strict_equiv)|![X3]:![X4]:(~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4))&((is_a_theorem(strict_equiv(esk1_0,esk2_0))&~(esk1_0=esk2_0))|substitution_strict_equiv)),inference(skolemize,[status(esa)],[81])).
% fof(83, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk1_0,esk2_0))&~(esk1_0=esk2_0))|substitution_strict_equiv)),inference(shift_quantors,[status(thm)],[82])).
% fof(84, plain,![X3]:![X4]:(((~(is_a_theorem(strict_equiv(X3,X4)))|X3=X4)|~(substitution_strict_equiv))&((is_a_theorem(strict_equiv(esk1_0,esk2_0))|substitution_strict_equiv)&(~(esk1_0=esk2_0)|substitution_strict_equiv))),inference(distribute,[status(thm)],[83])).
% cnf(87,plain,(X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2))),inference(split_conjunct,[status(thm)],[84])).
% fof(130, plain,(~(op_strict_implies)|![X1]:![X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))),inference(fof_nnf,[status(thm)],[10])).
% fof(131, plain,(~(op_strict_implies)|![X3]:![X4]:strict_implies(X3,X4)=necessarily(implies(X3,X4))),inference(variable_rename,[status(thm)],[130])).
% fof(132, plain,![X3]:![X4]:(strict_implies(X3,X4)=necessarily(implies(X3,X4))|~(op_strict_implies)),inference(shift_quantors,[status(thm)],[131])).
% cnf(133,plain,(strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies),inference(split_conjunct,[status(thm)],[132])).
% fof(146, plain,(~(op_equiv)|![X1]:![X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))),inference(fof_nnf,[status(thm)],[13])).
% fof(147, plain,(~(op_equiv)|![X3]:![X4]:equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))),inference(variable_rename,[status(thm)],[146])).
% fof(148, plain,![X3]:![X4]:(equiv(X3,X4)=and(implies(X3,X4),implies(X4,X3))|~(op_equiv)),inference(shift_quantors,[status(thm)],[147])).
% cnf(149,plain,(equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv),inference(split_conjunct,[status(thm)],[148])).
% fof(158, 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)],[16])).
% fof(159, 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)],[158])).
% fof(160, 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(esk16_0,esk17_0),strict_implies(esk17_0,esk18_0)),strict_implies(esk16_0,esk18_0))))|axiom_m5)),inference(skolemize,[status(esa)],[159])).
% fof(161, 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(esk16_0,esk17_0),strict_implies(esk17_0,esk18_0)),strict_implies(esk16_0,esk18_0))))|axiom_m5)),inference(shift_quantors,[status(thm)],[160])).
% cnf(163,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)],[161])).
% fof(164, 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)],[17])).
% fof(165, 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)],[164])).
% fof(166, plain,((~(axiom_m4)|![X2]:is_a_theorem(strict_implies(X2,and(X2,X2))))&(~(is_a_theorem(strict_implies(esk19_0,and(esk19_0,esk19_0))))|axiom_m4)),inference(skolemize,[status(esa)],[165])).
% fof(167, plain,![X2]:((is_a_theorem(strict_implies(X2,and(X2,X2)))|~(axiom_m4))&(~(is_a_theorem(strict_implies(esk19_0,and(esk19_0,esk19_0))))|axiom_m4)),inference(shift_quantors,[status(thm)],[166])).
% cnf(169,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4),inference(split_conjunct,[status(thm)],[167])).
% fof(170, 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)],[18])).
% fof(171, 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)],[170])).
% fof(172, 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(esk20_0,esk21_0),esk22_0),and(esk20_0,and(esk21_0,esk22_0)))))|axiom_m3)),inference(skolemize,[status(esa)],[171])).
% fof(173, 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(esk20_0,esk21_0),esk22_0),and(esk20_0,and(esk21_0,esk22_0)))))|axiom_m3)),inference(shift_quantors,[status(thm)],[172])).
% cnf(175,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|~axiom_m3),inference(split_conjunct,[status(thm)],[173])).
% fof(176, 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)],[19])).
% fof(177, 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)],[176])).
% fof(178, plain,((~(axiom_m2)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),X3)))&(~(is_a_theorem(strict_implies(and(esk23_0,esk24_0),esk23_0)))|axiom_m2)),inference(skolemize,[status(esa)],[177])).
% fof(179, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),X3))|~(axiom_m2))&(~(is_a_theorem(strict_implies(and(esk23_0,esk24_0),esk23_0)))|axiom_m2)),inference(shift_quantors,[status(thm)],[178])).
% cnf(181,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2),inference(split_conjunct,[status(thm)],[179])).
% fof(182, 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)],[20])).
% fof(183, 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)],[182])).
% fof(184, plain,((~(axiom_m1)|![X3]:![X4]:is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))))&(~(is_a_theorem(strict_implies(and(esk25_0,esk26_0),and(esk26_0,esk25_0))))|axiom_m1)),inference(skolemize,[status(esa)],[183])).
% fof(185, plain,![X3]:![X4]:((is_a_theorem(strict_implies(and(X3,X4),and(X4,X3)))|~(axiom_m1))&(~(is_a_theorem(strict_implies(and(esk25_0,esk26_0),and(esk26_0,esk25_0))))|axiom_m1)),inference(shift_quantors,[status(thm)],[184])).
% cnf(187,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1),inference(split_conjunct,[status(thm)],[185])).
% fof(206, 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)],[24])).
% fof(207, 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)],[206])).
% fof(208, 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(esk34_0)&is_a_theorem(strict_implies(esk34_0,esk35_0)))&~(is_a_theorem(esk35_0)))|modus_ponens_strict_implies)),inference(skolemize,[status(esa)],[207])).
% fof(209, 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(esk34_0)&is_a_theorem(strict_implies(esk34_0,esk35_0)))&~(is_a_theorem(esk35_0)))|modus_ponens_strict_implies)),inference(shift_quantors,[status(thm)],[208])).
% fof(210, 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(esk34_0)|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(esk34_0,esk35_0))|modus_ponens_strict_implies))&(~(is_a_theorem(esk35_0))|modus_ponens_strict_implies))),inference(distribute,[status(thm)],[209])).
% cnf(214,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)],[210])).
% fof(291, 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)],[38])).
% fof(292, 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)],[291])).
% fof(293, plain,((~(and_2)|![X3]:![X4]:is_a_theorem(implies(and(X3,X4),X4)))&(~(is_a_theorem(implies(and(esk56_0,esk57_0),esk57_0)))|and_2)),inference(skolemize,[status(esa)],[292])).
% fof(294, plain,![X3]:![X4]:((is_a_theorem(implies(and(X3,X4),X4))|~(and_2))&(~(is_a_theorem(implies(and(esk56_0,esk57_0),esk57_0)))|and_2)),inference(shift_quantors,[status(thm)],[293])).
% cnf(295,plain,(and_2|~is_a_theorem(implies(and(esk56_0,esk57_0),esk57_0))),inference(split_conjunct,[status(thm)],[294])).
% cnf(296,plain,(is_a_theorem(implies(and(X1,X2),X2))|~and_2),inference(split_conjunct,[status(thm)],[294])).
% fof(303, 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)],[40])).
% fof(304, 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)],[303])).
% fof(305, plain,((~(adjunction)|![X3]:![X4]:((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4))))&(((is_a_theorem(esk60_0)&is_a_theorem(esk61_0))&~(is_a_theorem(and(esk60_0,esk61_0))))|adjunction)),inference(skolemize,[status(esa)],[304])).
% fof(306, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk60_0)&is_a_theorem(esk61_0))&~(is_a_theorem(and(esk60_0,esk61_0))))|adjunction)),inference(shift_quantors,[status(thm)],[305])).
% fof(307, plain,![X3]:![X4]:((((~(is_a_theorem(X3))|~(is_a_theorem(X4)))|is_a_theorem(and(X3,X4)))|~(adjunction))&(((is_a_theorem(esk60_0)|adjunction)&(is_a_theorem(esk61_0)|adjunction))&(~(is_a_theorem(and(esk60_0,esk61_0)))|adjunction))),inference(distribute,[status(thm)],[306])).
% cnf(311,plain,(is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(split_conjunct,[status(thm)],[307])).
% fof(320, plain,(~(op_implies_and)|![X1]:![X2]:implies(X1,X2)=not(and(X1,not(X2)))),inference(fof_nnf,[status(thm)],[42])).
% fof(321, plain,(~(op_implies_and)|![X3]:![X4]:implies(X3,X4)=not(and(X3,not(X4)))),inference(variable_rename,[status(thm)],[320])).
% fof(322, plain,![X3]:![X4]:(implies(X3,X4)=not(and(X3,not(X4)))|~(op_implies_and)),inference(shift_quantors,[status(thm)],[321])).
% cnf(323,plain,(implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and),inference(split_conjunct,[status(thm)],[322])).
% cnf(324,plain,(modus_ponens_strict_implies),inference(split_conjunct,[status(thm)],[43])).
% cnf(325,plain,(op_strict_equiv),inference(split_conjunct,[status(thm)],[44])).
% fof(330, plain,(~(op_or)|![X1]:![X2]:or(X1,X2)=not(and(not(X1),not(X2)))),inference(fof_nnf,[status(thm)],[46])).
% fof(331, plain,(~(op_or)|![X3]:![X4]:or(X3,X4)=not(and(not(X3),not(X4)))),inference(variable_rename,[status(thm)],[330])).
% fof(332, plain,![X3]:![X4]:(or(X3,X4)=not(and(not(X3),not(X4)))|~(op_or)),inference(shift_quantors,[status(thm)],[331])).
% cnf(333,plain,(or(X1,X2)=not(and(not(X1),not(X2)))|~op_or),inference(split_conjunct,[status(thm)],[332])).
% cnf(368,plain,(op_implies_and),inference(split_conjunct,[status(thm)],[53])).
% cnf(369,plain,(axiom_m5),inference(split_conjunct,[status(thm)],[54])).
% cnf(370,plain,(axiom_m4),inference(split_conjunct,[status(thm)],[55])).
% cnf(371,plain,(axiom_m3),inference(split_conjunct,[status(thm)],[56])).
% cnf(372,plain,(axiom_m2),inference(split_conjunct,[status(thm)],[57])).
% cnf(373,plain,(axiom_m1),inference(split_conjunct,[status(thm)],[58])).
% cnf(374,plain,(adjunction),inference(split_conjunct,[status(thm)],[59])).
% cnf(375,plain,(substitution_strict_equiv),inference(split_conjunct,[status(thm)],[60])).
% cnf(376,plain,(op_equiv),inference(split_conjunct,[status(thm)],[61])).
% cnf(377,plain,(op_strict_implies),inference(split_conjunct,[status(thm)],[62])).
% cnf(378,plain,(op_or),inference(split_conjunct,[status(thm)],[63])).
% fof(422, plain,((~(or_1)|![X1]:![X2]:is_a_theorem(implies(X1,or(X1,X2))))&(?[X1]:?[X2]:~(is_a_theorem(implies(X1,or(X1,X2))))|or_1)),inference(fof_nnf,[status(thm)],[72])).
% fof(423, plain,((~(or_1)|![X3]:![X4]:is_a_theorem(implies(X3,or(X3,X4))))&(?[X5]:?[X6]:~(is_a_theorem(implies(X5,or(X5,X6))))|or_1)),inference(variable_rename,[status(thm)],[422])).
% fof(424, plain,((~(or_1)|![X3]:![X4]:is_a_theorem(implies(X3,or(X3,X4))))&(~(is_a_theorem(implies(esk91_0,or(esk91_0,esk92_0))))|or_1)),inference(skolemize,[status(esa)],[423])).
% fof(425, plain,![X3]:![X4]:((is_a_theorem(implies(X3,or(X3,X4)))|~(or_1))&(~(is_a_theorem(implies(esk91_0,or(esk91_0,esk92_0))))|or_1)),inference(shift_quantors,[status(thm)],[424])).
% cnf(426,plain,(or_1|~is_a_theorem(implies(esk91_0,or(esk91_0,esk92_0)))),inference(split_conjunct,[status(thm)],[425])).
% cnf(428,negated_conjecture,(~or_1),inference(split_conjunct,[status(thm)],[75])).
% cnf(435,plain,(~is_a_theorem(implies(esk91_0,or(esk91_0,esk92_0)))),inference(sr,[status(thm)],[426,428,theory(equality)])).
% cnf(440,plain,(X1=X2|$false|~is_a_theorem(strict_equiv(X1,X2))),inference(rw,[status(thm)],[87,375,theory(equality)])).
% cnf(441,plain,(X1=X2|~is_a_theorem(strict_equiv(X1,X2))),inference(cn,[status(thm)],[440,theory(equality)])).
% cnf(446,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))|$false),inference(rw,[status(thm)],[169,370,theory(equality)])).
% cnf(447,plain,(is_a_theorem(strict_implies(X1,and(X1,X1)))),inference(cn,[status(thm)],[446,theory(equality)])).
% cnf(448,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))|$false),inference(rw,[status(thm)],[181,372,theory(equality)])).
% cnf(449,plain,(is_a_theorem(strict_implies(and(X1,X2),X1))),inference(cn,[status(thm)],[448,theory(equality)])).
% cnf(450,plain,(is_a_theorem(X1)|$false|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(rw,[status(thm)],[214,324,theory(equality)])).
% cnf(451,plain,(is_a_theorem(X1)|~is_a_theorem(X2)|~is_a_theorem(strict_implies(X2,X1))),inference(cn,[status(thm)],[450,theory(equality)])).
% cnf(452,plain,(is_a_theorem(X1)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[451,449,theory(equality)])).
% cnf(454,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)|$false),inference(rw,[status(thm)],[133,377,theory(equality)])).
% cnf(455,plain,(necessarily(implies(X1,X2))=strict_implies(X1,X2)),inference(cn,[status(thm)],[454,theory(equality)])).
% cnf(456,plain,(is_a_theorem(and(X1,X2))|$false|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(rw,[status(thm)],[311,374,theory(equality)])).
% cnf(457,plain,(is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)),inference(cn,[status(thm)],[456,theory(equality)])).
% cnf(458,plain,(not(and(X1,not(X2)))=implies(X1,X2)|$false),inference(rw,[status(thm)],[323,368,theory(equality)])).
% cnf(459,plain,(not(and(X1,not(X2)))=implies(X1,X2)),inference(cn,[status(thm)],[458,theory(equality)])).
% cnf(461,plain,(not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))),inference(spm,[status(thm)],[459,459,theory(equality)])).
% cnf(465,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[187,373,theory(equality)])).
% cnf(466,plain,(is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[465,theory(equality)])).
% cnf(468,plain,(implies(not(X1),X2)=or(X1,X2)|~op_or),inference(rw,[status(thm)],[333,459,theory(equality)])).
% cnf(469,plain,(implies(not(X1),X2)=or(X1,X2)|$false),inference(rw,[status(thm)],[468,378,theory(equality)])).
% cnf(470,plain,(implies(not(X1),X2)=or(X1,X2)),inference(cn,[status(thm)],[469,theory(equality)])).
% cnf(471,plain,(necessarily(or(X1,X2))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[455,470,theory(equality)])).
% cnf(473,plain,(implies(implies(X1,X2),X3)=or(and(X1,not(X2)),X3)),inference(spm,[status(thm)],[470,459,theory(equality)])).
% cnf(481,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)|$false),inference(rw,[status(thm)],[79,325,theory(equality)])).
% cnf(482,plain,(and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2)),inference(cn,[status(thm)],[481,theory(equality)])).
% cnf(483,plain,(is_a_theorem(strict_equiv(X1,X2))|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(strict_implies(X1,X2))),inference(spm,[status(thm)],[457,482,theory(equality)])).
% cnf(491,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)|$false),inference(rw,[status(thm)],[149,376,theory(equality)])).
% cnf(492,plain,(and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)),inference(cn,[status(thm)],[491,theory(equality)])).
% cnf(506,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|$false),inference(rw,[status(thm)],[175,371,theory(equality)])).
% cnf(507,plain,(is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))),inference(cn,[status(thm)],[506,theory(equality)])).
% cnf(508,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(and(and(X1,X2),X3))),inference(spm,[status(thm)],[451,507,theory(equality)])).
% cnf(513,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|$false),inference(rw,[status(thm)],[163,369,theory(equality)])).
% cnf(514,plain,(is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))),inference(cn,[status(thm)],[513,theory(equality)])).
% cnf(515,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))),inference(spm,[status(thm)],[451,514,theory(equality)])).
% cnf(520,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_equiv(X1,X2))),inference(spm,[status(thm)],[452,482,theory(equality)])).
% cnf(559,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|~is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))),inference(spm,[status(thm)],[483,466,theory(equality)])).
% cnf(560,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(and(X1,X2),X3)))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))),inference(spm,[status(thm)],[483,507,theory(equality)])).
% cnf(563,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|~is_a_theorem(strict_implies(and(X1,X1),X1))),inference(spm,[status(thm)],[483,447,theory(equality)])).
% cnf(564,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))|$false),inference(rw,[status(thm)],[559,466,theory(equality)])).
% cnf(565,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1)))),inference(cn,[status(thm)],[564,theory(equality)])).
% cnf(566,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))|$false),inference(rw,[status(thm)],[563,449,theory(equality)])).
% cnf(567,plain,(is_a_theorem(strict_equiv(and(X1,X1),X1))),inference(cn,[status(thm)],[566,theory(equality)])).
% cnf(568,plain,(and(X1,X1)=X1),inference(spm,[status(thm)],[441,567,theory(equality)])).
% cnf(576,plain,(strict_implies(X1,X1)=strict_equiv(X1,X1)),inference(spm,[status(thm)],[482,568,theory(equality)])).
% cnf(578,plain,(not(not(X1))=implies(not(X1),X1)),inference(spm,[status(thm)],[459,568,theory(equality)])).
% cnf(589,plain,(is_a_theorem(strict_equiv(X1,X1))),inference(rw,[status(thm)],[567,568,theory(equality)])).
% cnf(595,plain,(not(not(X1))=or(X1,X1)),inference(rw,[status(thm)],[578,470,theory(equality)])).
% cnf(607,plain,(not(implies(X1,X2))=implies(implies(X1,X2),and(X1,not(X2)))),inference(spm,[status(thm)],[461,568,theory(equality)])).
% cnf(611,plain,(is_a_theorem(strict_implies(X1,X1))),inference(spm,[status(thm)],[520,589,theory(equality)])).
% cnf(637,plain,(and(X1,X2)=and(X2,X1)),inference(spm,[status(thm)],[441,565,theory(equality)])).
% cnf(667,plain,(is_a_theorem(strict_implies(and(X3,and(X1,X2)),and(X1,and(X2,X3))))),inference(spm,[status(thm)],[507,637,theory(equality)])).
% cnf(668,plain,(and(strict_implies(X2,X1),strict_implies(X1,X2))=strict_equiv(X1,X2)),inference(spm,[status(thm)],[482,637,theory(equality)])).
% cnf(671,plain,(not(and(not(X2),X1))=implies(X1,X2)),inference(spm,[status(thm)],[459,637,theory(equality)])).
% cnf(677,plain,(is_a_theorem(strict_implies(and(X2,X1),X1))),inference(spm,[status(thm)],[449,637,theory(equality)])).
% cnf(707,plain,(and_2|~is_a_theorem(implies(and(esk57_0,esk56_0),esk57_0))),inference(rw,[status(thm)],[295,637,theory(equality)])).
% cnf(708,plain,(strict_equiv(X2,X1)=strict_equiv(X1,X2)),inference(rw,[status(thm)],[668,482,theory(equality)])).
% cnf(753,plain,(not(and(X1,or(X2,X2)))=implies(X1,not(X2))),inference(spm,[status(thm)],[459,595,theory(equality)])).
% cnf(777,plain,(is_a_theorem(strict_implies(equiv(X1,X2),implies(X2,X1)))),inference(spm,[status(thm)],[677,492,theory(equality)])).
% cnf(816,plain,(implies(not(X2),X1)=implies(not(X1),X2)),inference(spm,[status(thm)],[459,671,theory(equality)])).
% cnf(818,plain,(not(and(or(X1,X1),X2))=implies(X2,not(X1))),inference(spm,[status(thm)],[671,595,theory(equality)])).
% cnf(832,plain,(or(X2,X1)=implies(not(X1),X2)),inference(rw,[status(thm)],[816,470,theory(equality)])).
% cnf(833,plain,(or(X2,X1)=or(X1,X2)),inference(rw,[status(thm)],[832,470,theory(equality)])).
% cnf(842,plain,(necessarily(or(X2,X1))=strict_implies(not(X1),X2)),inference(spm,[status(thm)],[471,833,theory(equality)])).
% cnf(854,plain,(strict_implies(not(X2),X1)=strict_implies(not(X1),X2)),inference(rw,[status(thm)],[842,471,theory(equality)])).
% cnf(1032,plain,(and(strict_implies(not(X2),X1),strict_implies(X2,not(X1)))=strict_equiv(not(X1),X2)),inference(spm,[status(thm)],[482,854,theory(equality)])).
% cnf(1035,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),X2))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[451,854,theory(equality)])).
% cnf(1052,plain,(strict_implies(not(X1),not(X2))=strict_implies(or(X2,X2),X1)),inference(spm,[status(thm)],[854,595,theory(equality)])).
% cnf(1055,plain,(strict_implies(not(X1),and(not(X2),X3))=strict_implies(implies(X3,X2),X1)),inference(spm,[status(thm)],[854,671,theory(equality)])).
% cnf(1075,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),and(X2,not(X3))))|~is_a_theorem(implies(X2,X3))),inference(spm,[status(thm)],[1035,459,theory(equality)])).
% cnf(1103,plain,(is_a_theorem(strict_implies(equiv(X1,not(X2)),or(X2,X1)))),inference(spm,[status(thm)],[777,470,theory(equality)])).
% cnf(1354,plain,(is_a_theorem(and(X1,and(X2,X3)))|~is_a_theorem(X3)|~is_a_theorem(and(X1,X2))),inference(spm,[status(thm)],[508,457,theory(equality)])).
% cnf(1555,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X3,X2))|~is_a_theorem(strict_implies(X1,X3))),inference(spm,[status(thm)],[515,457,theory(equality)])).
% cnf(1765,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(not(X1),and(not(X2),not(X3))))|~is_a_theorem(or(X2,X3))),inference(spm,[status(thm)],[1075,470,theory(equality)])).
% cnf(2321,plain,(is_a_theorem(and(strict_implies(X1,X2),and(strict_implies(X2,X1),X3)))|~is_a_theorem(strict_equiv(X1,X2))|~is_a_theorem(X3)),inference(spm,[status(thm)],[1354,482,theory(equality)])).
% cnf(2478,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))|~is_a_theorem(strict_implies(and(X1,and(X1,X2)),and(X1,X2)))),inference(spm,[status(thm)],[560,568,theory(equality)])).
% cnf(2494,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))|$false),inference(rw,[status(thm)],[2478,677,theory(equality)])).
% cnf(2495,plain,(is_a_theorem(strict_equiv(and(X1,and(X1,X2)),and(X1,X2)))),inference(cn,[status(thm)],[2494,theory(equality)])).
% cnf(2507,plain,(is_a_theorem(strict_equiv(and(X1,X2),and(X1,and(X1,X2))))),inference(rw,[status(thm)],[2495,708,theory(equality)])).
% cnf(2508,plain,(and(X1,X2)=and(X1,and(X1,X2))),inference(spm,[status(thm)],[441,2507,theory(equality)])).
% cnf(4314,plain,(is_a_theorem(strict_implies(and(X1,and(X3,X2)),and(X2,and(X3,X1))))),inference(spm,[status(thm)],[667,637,theory(equality)])).
% cnf(15151,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(not(X1),X2)),inference(rw,[status(thm)],[1032,637,theory(equality)])).
% cnf(15947,plain,(is_a_theorem(strict_implies(not(or(X1,X1)),not(X1)))),inference(spm,[status(thm)],[611,1052,theory(equality)])).
% cnf(15987,plain,(is_a_theorem(strict_implies(or(X1,X1),X1))),inference(spm,[status(thm)],[611,1052,theory(equality)])).
% cnf(16125,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|~is_a_theorem(strict_implies(X1,or(X1,X1)))),inference(spm,[status(thm)],[483,15987,theory(equality)])).
% cnf(16697,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(or(X3,X2),X1))|~is_a_theorem(or(X2,X3))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[1765,1055,theory(equality)]),470,theory(equality)])).
% cnf(17592,plain,(is_a_theorem(strict_implies(not(not(X1)),or(X1,X1)))),inference(rw,[status(thm)],[15947,854,theory(equality)])).
% cnf(31325,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,or(X2,X2)))),inference(spm,[status(thm)],[1555,15987,theory(equality)])).
% cnf(31377,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,and(X3,X2)))),inference(spm,[status(thm)],[1555,677,theory(equality)])).
% cnf(31415,plain,(is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(strict_implies(X1,not(not(X2))))),inference(spm,[status(thm)],[31325,595,theory(equality)])).
% cnf(31424,plain,(is_a_theorem(strict_implies(or(or(X1,X1),or(X1,X1)),X1))),inference(spm,[status(thm)],[31325,15987,theory(equality)])).
% cnf(32236,plain,(is_a_theorem(strict_implies(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[31424,595,theory(equality)]),854,theory(equality)])).
% cnf(32238,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)],[483,32236,theory(equality)])).
% cnf(32292,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[32238,854,theory(equality)]),17592,theory(equality)])).
% cnf(32293,plain,(is_a_theorem(strict_equiv(not(or(X1,X1)),not(X1)))),inference(cn,[status(thm)],[32292,theory(equality)])).
% cnf(32328,plain,(is_a_theorem(strict_equiv(not(X1),not(or(X1,X1))))),inference(rw,[status(thm)],[32293,708,theory(equality)])).
% cnf(32329,plain,(not(X1)=not(or(X1,X1))),inference(spm,[status(thm)],[441,32328,theory(equality)])).
% cnf(32433,plain,(not(and(not(X1),X2))=implies(X2,or(X1,X1))),inference(spm,[status(thm)],[671,32329,theory(equality)])).
% cnf(32720,plain,(implies(X2,X1)=implies(X2,or(X1,X1))),inference(rw,[status(thm)],[32433,671,theory(equality)])).
% cnf(35168,plain,(is_a_theorem(strict_implies(or(and(X1,X2),and(X1,X2)),X2))),inference(spm,[status(thm)],[31377,15987,theory(equality)])).
% cnf(36283,plain,(is_a_theorem(strict_implies(or(and(X1,not(not(X2))),and(X1,not(not(X2)))),X2))),inference(spm,[status(thm)],[31415,35168,theory(equality)])).
% cnf(36319,plain,(is_a_theorem(strict_implies(not(implies(X1,not(X2))),X2))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[36283,473,theory(equality)]),607,theory(equality)])).
% cnf(36325,plain,(is_a_theorem(strict_implies(not(X2),implies(X1,not(X2))))),inference(rw,[status(thm)],[36319,854,theory(equality)])).
% cnf(36326,plain,(is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(not(X2))),inference(spm,[status(thm)],[451,36325,theory(equality)])).
% cnf(46497,plain,(necessarily(implies(X1,X2))=strict_implies(X1,or(X2,X2))),inference(spm,[status(thm)],[455,32720,theory(equality)])).
% cnf(46632,plain,(strict_implies(X1,X2)=strict_implies(X1,or(X2,X2))),inference(rw,[status(thm)],[46497,455,theory(equality)])).
% cnf(48381,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[16125,46632,theory(equality)]),611,theory(equality)])).
% cnf(48382,plain,(is_a_theorem(strict_equiv(X1,or(X1,X1)))),inference(cn,[status(thm)],[48381,theory(equality)])).
% cnf(48531,plain,(X1=or(X1,X1)),inference(spm,[status(thm)],[441,48382,theory(equality)])).
% cnf(48758,plain,(not(and(X1,X2))=implies(X1,not(X2))),inference(rw,[status(thm)],[753,48531,theory(equality)])).
% cnf(48788,plain,(not(and(X1,X2))=implies(X2,not(X1))),inference(rw,[status(thm)],[818,48531,theory(equality)])).
% cnf(48790,plain,(not(not(X1))=X1),inference(rw,[status(thm)],[595,48531,theory(equality)])).
% cnf(48927,plain,(is_a_theorem(strict_implies(X1,implies(X2,X1)))),inference(spm,[status(thm)],[36325,48790,theory(equality)])).
% cnf(49036,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)),inference(spm,[status(thm)],[36326,48790,theory(equality)])).
% cnf(51884,plain,(is_a_theorem(strict_implies(X1,implies(X2,X3)))|~is_a_theorem(strict_implies(X1,X3))),inference(spm,[status(thm)],[1555,48927,theory(equality)])).
% cnf(52811,plain,(not(implies(X1,not(X2)))=and(X1,X2)),inference(spm,[status(thm)],[48790,48758,theory(equality)])).
% cnf(53146,plain,(implies(X1,not(X2))=implies(X2,not(X1))),inference(rw,[status(thm)],[48788,48758,theory(equality)])).
% cnf(53158,plain,(necessarily(implies(X2,not(X1)))=strict_implies(X1,not(X2))),inference(spm,[status(thm)],[455,53146,theory(equality)])).
% cnf(53410,plain,(strict_implies(X2,not(X1))=strict_implies(X1,not(X2))),inference(rw,[status(thm)],[53158,455,theory(equality)])).
% cnf(59802,plain,(is_a_theorem(and(strict_implies(X1,X1),and(strict_implies(X1,X1),X2)))|~is_a_theorem(strict_implies(X1,X1))|~is_a_theorem(X2)),inference(spm,[status(thm)],[2321,576,theory(equality)])).
% cnf(59811,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)],[59802,2508,theory(equality)])).
% cnf(59812,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|$false|~is_a_theorem(X2)),inference(rw,[status(thm)],[59811,611,theory(equality)])).
% cnf(59813,plain,(is_a_theorem(and(strict_implies(X1,X1),X2))|~is_a_theorem(X2)),inference(cn,[status(thm)],[59812,theory(equality)])).
% cnf(73542,plain,(is_a_theorem(strict_implies(and(X1,X2),implies(X3,X1)))),inference(spm,[status(thm)],[51884,449,theory(equality)])).
% cnf(73576,plain,(is_a_theorem(implies(X1,X2))|~is_a_theorem(and(X2,X3))),inference(spm,[status(thm)],[451,73542,theory(equality)])).
% cnf(74896,plain,(is_a_theorem(implies(X1,strict_implies(X2,X2)))|~is_a_theorem(X3)),inference(spm,[status(thm)],[73576,59813,theory(equality)])).
% cnf(76049,plain,(is_a_theorem(implies(X1,strict_implies(X2,X2)))),inference(spm,[status(thm)],[74896,1103,theory(equality)])).
% cnf(76204,plain,(is_a_theorem(or(X1,strict_implies(X2,X2)))),inference(spm,[status(thm)],[76049,470,theory(equality)])).
% cnf(76213,plain,(is_a_theorem(X1)|~is_a_theorem(strict_implies(or(strict_implies(X2,X2),X3),X1))),inference(spm,[status(thm)],[16697,76204,theory(equality)])).
% cnf(77884,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))|~is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(X3,and(X2,X1))))),inference(spm,[status(thm)],[483,4314,theory(equality)])).
% cnf(77959,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))|$false),inference(rw,[status(thm)],[77884,4314,theory(equality)])).
% cnf(77960,plain,(is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(X3,and(X2,X1))))),inference(cn,[status(thm)],[77959,theory(equality)])).
% cnf(97148,plain,(and(strict_implies(X2,not(X1)),strict_implies(not(X2),X1))=strict_equiv(X1,not(X2))),inference(spm,[status(thm)],[482,53410,theory(equality)])).
% cnf(97742,plain,(strict_equiv(not(X1),X2)=strict_equiv(X1,not(X2))),inference(rw,[status(thm)],[97148,15151,theory(equality)])).
% cnf(98037,plain,(not(X1)=X2|~is_a_theorem(strict_equiv(X1,not(X2)))),inference(spm,[status(thm)],[441,97742,theory(equality)])).
% cnf(98200,plain,(not(X1)=implies(X2,not(X3))|~is_a_theorem(strict_equiv(X1,and(X2,X3)))),inference(spm,[status(thm)],[98037,52811,theory(equality)])).
% cnf(186256,plain,(not(X1)=implies(X2,not(X3))|~is_a_theorem(strict_equiv(X1,and(X3,X2)))),inference(spm,[status(thm)],[98200,637,theory(equality)])).
% cnf(189954,plain,(not(and(X1,and(X2,X3)))=implies(and(X2,X1),not(X3))),inference(spm,[status(thm)],[186256,77960,theory(equality)])).
% cnf(189971,plain,(implies(X1,implies(X2,not(X3)))=implies(and(X2,X1),not(X3))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[189954,48758,theory(equality)]),48758,theory(equality)])).
% cnf(190272,plain,(implies(and(X1,X2),X3)=implies(X2,implies(X1,X3))),inference(spm,[status(thm)],[189971,48790,theory(equality)])).
% cnf(287801,plain,(necessarily(implies(X2,implies(X1,X3)))=strict_implies(and(X1,X2),X3)),inference(spm,[status(thm)],[455,190272,theory(equality)])).
% cnf(288169,plain,(is_a_theorem(implies(X2,implies(X1,X2)))|~and_2),inference(rw,[status(thm)],[296,190272,theory(equality)])).
% cnf(288180,plain,(and_2|~is_a_theorem(implies(esk56_0,implies(esk57_0,esk57_0)))),inference(rw,[status(thm)],[707,190272,theory(equality)])).
% cnf(288375,plain,(strict_implies(X2,implies(X1,X3))=strict_implies(and(X1,X2),X3)),inference(rw,[status(thm)],[287801,455,theory(equality)])).
% cnf(288460,plain,(and_2|~is_a_theorem(implies(esk57_0,esk57_0))),inference(spm,[status(thm)],[288180,49036,theory(equality)])).
% cnf(290921,plain,(is_a_theorem(strict_implies(X2,implies(X1,X1)))),inference(rw,[status(thm)],[449,288375,theory(equality)])).
% cnf(291441,plain,(is_a_theorem(implies(X1,X1))),inference(spm,[status(thm)],[76213,290921,theory(equality)])).
% cnf(291622,plain,(and_2|$false),inference(rw,[status(thm)],[288460,291441,theory(equality)])).
% cnf(291623,plain,(and_2),inference(cn,[status(thm)],[291622,theory(equality)])).
% cnf(291681,plain,(is_a_theorem(implies(X1,implies(X2,X1)))|$false),inference(rw,[status(thm)],[288169,291623,theory(equality)])).
% cnf(291682,plain,(is_a_theorem(implies(X1,implies(X2,X1)))),inference(cn,[status(thm)],[291681,theory(equality)])).
% cnf(291795,plain,(is_a_theorem(implies(X1,or(X2,X1)))),inference(spm,[status(thm)],[291682,470,theory(equality)])).
% cnf(293982,plain,(is_a_theorem(implies(X1,or(X1,X2)))),inference(spm,[status(thm)],[291795,833,theory(equality)])).
% cnf(294207,plain,($false),inference(rw,[status(thm)],[435,293982,theory(equality)])).
% cnf(294208,plain,($false),inference(cn,[status(thm)],[294207,theory(equality)])).
% cnf(294209,plain,($false),294208,['proof']).
% # SZS output end CNFRefutation
% PrfWatch: 11.69 CPU 12.04 WC
% # Processed clauses : 14570
% # ...of these trivial : 977
% # ...subsumed : 10851
% # ...remaining for further processing: 2742
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 56
% # Backward-rewritten : 1090
% # Generated clauses : 205664
% # ...of the previous two non-trivial : 165023
% # Contextual simplify-reflections : 732
% # Paramodulations : 205664
% # Factorizations : 0
% # Equation resolutions : 0
% # Current number of processed clauses: 1596
% # Positive orientable unit clauses: 631
% # Positive unorientable unit clauses: 34
% # Negative unit clauses : 4
% # Non-unit-clauses : 927
% # Current number of unprocessed clauses: 67551
% # ...number of literals in the above : 115848
% # Clause-clause subsumption calls (NU) : 150088
% # Rec. Clause-clause subsumption calls : 148440
% # Unit Clause-clause subsumption calls : 4816
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 54190
% # Indexed BW rewrite successes : 1900
% # Backwards rewriting index: 1084 leaves, 3.43+/-6.654 terms/leaf
% # Paramod-from index: 232 leaves, 3.51+/-9.042 terms/leaf
% # Paramod-into index: 956 leaves, 3.46+/-6.914 terms/leaf
% # -------------------------------------------------
% # User time : 7.201 s
% # System time : 0.267 s
% # Total time : 7.468 s
% # Maximum resident set size: 0 pages
% PrfWatch: 11.71 CPU 12.22 WC
% FINAL PrfWatch: 11.71 CPU 12.22 WC
% SZS output end Solution for /tmp/SystemOnTPTP25880/LCL558+1.tptp
%
%------------------------------------------------------------------------------