TSTP Solution File: HWV003-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HWV003-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 19:01:06 EDT 2022
% Result : Unsatisfiable 103.23s 103.53s
% Output : Refutation 103.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : HWV003-1 : TPTP v8.1.0. Released v1.1.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 22:29:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 103.23/103.53 ============================== Prover9 ===============================
% 103.23/103.53 Prover9 (32) version 2009-11A, November 2009.
% 103.23/103.53 Process 26662 was started by sandbox2 on n020.cluster.edu,
% 103.23/103.53 Thu Jun 16 22:29:19 2022
% 103.23/103.53 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26509_n020.cluster.edu".
% 103.23/103.53 ============================== end of head ===========================
% 103.23/103.53
% 103.23/103.53 ============================== INPUT =================================
% 103.23/103.53
% 103.23/103.53 % Reading from file /tmp/Prover9_26509_n020.cluster.edu
% 103.23/103.53
% 103.23/103.53 set(prolog_style_variables).
% 103.23/103.53 set(auto2).
% 103.23/103.53 % set(auto2) -> set(auto).
% 103.23/103.53 % set(auto) -> set(auto_inference).
% 103.23/103.53 % set(auto) -> set(auto_setup).
% 103.23/103.53 % set(auto_setup) -> set(predicate_elim).
% 103.23/103.53 % set(auto_setup) -> assign(eq_defs, unfold).
% 103.23/103.53 % set(auto) -> set(auto_limits).
% 103.23/103.53 % set(auto_limits) -> assign(max_weight, "100.000").
% 103.23/103.53 % set(auto_limits) -> assign(sos_limit, 20000).
% 103.23/103.53 % set(auto) -> set(auto_denials).
% 103.23/103.53 % set(auto) -> set(auto_process).
% 103.23/103.53 % set(auto2) -> assign(new_constants, 1).
% 103.23/103.53 % set(auto2) -> assign(fold_denial_max, 3).
% 103.23/103.53 % set(auto2) -> assign(max_weight, "200.000").
% 103.23/103.53 % set(auto2) -> assign(max_hours, 1).
% 103.23/103.53 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 103.23/103.53 % set(auto2) -> assign(max_seconds, 0).
% 103.23/103.53 % set(auto2) -> assign(max_minutes, 5).
% 103.23/103.53 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 103.23/103.53 % set(auto2) -> set(sort_initial_sos).
% 103.23/103.53 % set(auto2) -> assign(sos_limit, -1).
% 103.23/103.53 % set(auto2) -> assign(lrs_ticks, 3000).
% 103.23/103.53 % set(auto2) -> assign(max_megs, 400).
% 103.23/103.53 % set(auto2) -> assign(stats, some).
% 103.23/103.53 % set(auto2) -> clear(echo_input).
% 103.23/103.53 % set(auto2) -> set(quiet).
% 103.23/103.53 % set(auto2) -> clear(print_initial_clauses).
% 103.23/103.53 % set(auto2) -> clear(print_given).
% 103.23/103.53 assign(lrs_ticks,-1).
% 103.23/103.53 assign(sos_limit,10000).
% 103.23/103.53 assign(order,kbo).
% 103.23/103.53 set(lex_order_vars).
% 103.23/103.53 clear(print_given).
% 103.23/103.53
% 103.23/103.53 % formulas(sos). % not echoed (47 formulas)
% 103.23/103.53
% 103.23/103.53 ============================== end of input ==========================
% 103.23/103.53
% 103.23/103.53 % From the command line: assign(max_seconds, 300).
% 103.23/103.53
% 103.23/103.53 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 103.23/103.53
% 103.23/103.53 % Formulas that are not ordinary clauses:
% 103.23/103.53
% 103.23/103.53 ============================== end of process non-clausal formulas ===
% 103.23/103.53
% 103.23/103.53 ============================== PROCESS INITIAL CLAUSES ===============
% 103.23/103.53
% 103.23/103.53 ============================== PREDICATE ELIMINATION =================
% 103.23/103.53
% 103.23/103.53 ============================== end predicate elimination =============
% 103.23/103.53
% 103.23/103.53 Auto_denials:
% 103.23/103.53 % copying label prove_circuit to answer in negative clause
% 103.23/103.53
% 103.23/103.53 Term ordering decisions:
% 103.23/103.53
% 103.23/103.53 % Assigning unary symbol not kb_weight 0 and highest precedence (22).
% 103.23/103.53 Function symbol KB weights: n0=1. n1=1. a11=1. a15=1. a14=1. a=1. a12=1. a13=1. a16=1. a17=1. b=1. c1=1. carryin=1. s1=1. and=1. or=1. xor=1. carryout=1. sum=1. not=0.
% 103.23/103.53
% 103.23/103.53 ============================== end of process initial clauses ========
% 103.23/103.53
% 103.23/103.53 ============================== CLAUSES FOR SEARCH ====================
% 103.23/103.53
% 103.23/103.53 ============================== end of clauses for search =============
% 103.23/103.53
% 103.23/103.53 ============================== SEARCH ================================
% 103.23/103.53
% 103.23/103.53 % Starting search at 0.02 seconds.
% 103.23/103.53
% 103.23/103.53 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 65 (0.00 of 0.58 sec).
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=26.000, iters=4043
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=25.000, iters=3446
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=24.000, iters=3359
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=23.000, iters=3334
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=22.000, iters=3417
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=21.000, iters=3336
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=20.000, iters=3392
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=19.000, iters=3365
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=18.000, iters=3388
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=17.000, iters=3333
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=16.000, iters=5776
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=15.000, iters=4862
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=14.000, iters=4360
% 103.23/103.53
% 103.23/103.53 Low Water (keep): wt=13.000, iters=4250
% 103.23/103.53
% 103.23/103.53 Low Water (displace): id=8757, wt=51.000
% 103.23/103.53
% 103.23/103.53 Low Water (displace): id=5455, wt=50.000
% 103.23/103.53
% 103.23/103.53 Low Water (displace): id=17282, wt=13.000
% 103.23/103.53
% 103.23/103.53 Low Water (displace): id=17413, wt=12.000
% 103.23/103.53
% 103.23/103.53 Low Water (displace): id=17879, wt=11.000
% 103.23/103.53
% 103.23/103.53 Low Water (displace): id=18966, wt=10.000
% 103.23/103.53
% 103.23/103.53 ============================== PROOF =================================
% 103.23/103.53 % SZS status Unsatisfiable
% 103.23/103.53 % SZS output start Refutation
% 103.23/103.53
% 103.23/103.53 % Proof 1 at 99.87 (+ 2.67) seconds: prove_circuit.
% 103.23/103.53 % Length of proof is 510.
% 103.23/103.53 % Level of proof is 33.
% 103.23/103.53 % Maximum clause weight is 37.000.
% 103.23/103.53 % Given clauses 6518.
% 103.23/103.53
% 103.23/103.53 1 circuit(s1,c1) # label(the_output_circuit) # label(negated_conjecture). [assumption].
% 103.23/103.53 2 not(n0) = n1 # label(not_definition1) # label(axiom). [assumption].
% 103.23/103.53 3 not(n1) = n0 # label(not_definition2) # label(axiom). [assumption].
% 103.23/103.53 4 and(A,n0) = n0 # label(and_definition1) # label(axiom). [assumption].
% 103.23/103.53 5 and(A,n1) = A # label(and_definition2) # label(axiom). [assumption].
% 103.23/103.53 6 or(A,n0) = A # label(or_definition1) # label(axiom). [assumption].
% 103.23/103.53 7 or(A,n1) = n1 # label(or_definition2) # label(axiom). [assumption].
% 103.23/103.53 8 not(not(A)) = A # label(not_involution) # label(axiom). [assumption].
% 103.23/103.53 9 and(A,A) = A # label(and_idempotency) # label(axiom). [assumption].
% 103.23/103.53 10 or(A,A) = A # label(or_idempotency) # label(axiom). [assumption].
% 103.23/103.53 11 and(A,not(A)) = n0 # label(and_not_evaluation1) # label(axiom). [assumption].
% 103.23/103.53 12 or(A,not(A)) = n1 # label(or_not_evaluation1) # label(axiom). [assumption].
% 103.23/103.53 13 a11 = not(and(a,b)) # label(circuit1) # label(negated_conjecture). [assumption].
% 103.23/103.53 14 not(and(a,b)) = a11. [copy(13),flip(a)].
% 103.23/103.53 15 a12 = not(and(a11,a)) # label(circuit2) # label(negated_conjecture). [assumption].
% 103.23/103.53 16 not(and(a11,a)) = a12. [copy(15),flip(a)].
% 103.23/103.53 17 a13 = not(and(a11,b)) # label(circuit3) # label(negated_conjecture). [assumption].
% 103.23/103.53 18 not(and(a11,b)) = a13. [copy(17),flip(a)].
% 103.23/103.53 19 a14 = not(and(a12,a13)) # label(circuit4) # label(negated_conjecture). [assumption].
% 103.23/103.53 20 not(and(a12,a13)) = a14. [copy(19),flip(a)].
% 103.23/103.53 21 a15 = not(and(a14,carryin)) # label(circuit5) # label(negated_conjecture). [assumption].
% 103.23/103.53 22 not(and(a14,carryin)) = a15. [copy(21),flip(a)].
% 103.23/103.53 23 a16 = not(and(a14,a15)) # label(circuit6) # label(negated_conjecture). [assumption].
% 103.23/103.53 24 not(and(a14,a15)) = a16. [copy(23),flip(a)].
% 103.23/103.53 25 a17 = not(and(a15,carryin)) # label(circuit7) # label(negated_conjecture). [assumption].
% 103.23/103.53 26 not(and(a15,carryin)) = a17. [copy(25),flip(a)].
% 103.23/103.53 27 s1 = not(and(a16,a17)) # label(circuit8) # label(negated_conjecture). [assumption].
% 103.23/103.53 28 not(and(a16,a17)) = s1. [copy(27),flip(a)].
% 103.23/103.53 29 c1 = not(and(a11,a15)) # label(circuit9) # label(negated_conjecture). [assumption].
% 103.23/103.53 30 not(and(a11,a15)) = c1. [copy(29),flip(a)].
% 103.23/103.53 31 and(A,B) = and(B,A) # label(and_symmetry) # label(negated_conjecture). [assumption].
% 103.23/103.53 32 or(A,B) = or(B,A) # label(or_symmetry) # label(negated_conjecture). [assumption].
% 103.23/103.53 33 or(and(A,B),B) = B # label(and_or_subsumption1) # label(axiom). [assumption].
% 103.23/103.53 34 or(A,and(A,B)) = A. [copy(33),rewrite([32(2)]),rewrite([31(1)])].
% 103.23/103.53 42 and(and(A,B),B) = and(A,B) # label(and_evaluation1) # label(axiom). [assumption].
% 103.23/103.53 43 and(A,and(A,B)) = and(A,B). [copy(42),rewrite([31(2)]),rewrite([31(1),31(3)])].
% 103.23/103.53 44 or(or(A,B),B) = or(A,B) # label(or_evaluation1) # label(axiom). [assumption].
% 103.23/103.53 45 or(A,or(A,B)) = or(A,B). [copy(44),rewrite([32(2)]),rewrite([32(1),32(3)])].
% 103.23/103.53 46 not(and(A,B)) = or(not(A),not(B)) # label(demorgan1) # label(axiom). [assumption].
% 103.23/103.53 47 not(or(A,B)) = and(not(A),not(B)) # label(demorgan2) # label(axiom). [assumption].
% 103.23/103.53 51 or(and(A,not(B)),B) = or(A,B) # label(karnaugh1) # label(axiom). [assumption].
% 103.23/103.53 52 or(A,and(B,not(A))) = or(A,B). [copy(51),rewrite([32(3)]),rewrite([32(4)])].
% 103.23/103.53 53 sum(A,B,C) = xor(xor(A,B),C) # label(sum_definition) # label(negated_conjecture). [assumption].
% 103.23/103.53 54 and(and(A,B),C) = and(and(A,C),B) # label(and_commutativity) # label(negated_conjecture). [assumption].
% 103.23/103.53 55 and(A,and(B,C)) = and(C,and(A,B)). [copy(54),rewrite([31(2),31(4)]),rewrite([31(3)])].
% 103.23/103.53 56 or(or(A,B),C) = or(or(A,C),B) # label(or_commutativity) # label(negated_conjecture). [assumption].
% 103.23/103.53 57 or(A,or(B,C)) = or(C,or(A,B)). [copy(56),rewrite([32(2),32(4)]),rewrite([32(3)])].
% 103.23/103.53 58 or(or(and(A,B),C),B) = or(C,B) # label(and_or_subsumption3) # label(axiom). [assumption].
% 103.23/103.53 59 or(A,or(B,and(A,C))) = or(A,B). [copy(58),rewrite([32(2),32(3),32(4)]),rewrite([31(1)])].
% 103.23/103.53 62 and(or(A,B),C) = or(and(A,C),and(B,C)) # label(and_or_simplification) # label(negated_conjecture). [assumption].
% 103.23/103.53 63 or(and(A,B),and(B,C)) = and(B,or(A,C)). [copy(62),rewrite([31(2)]),flip(a),rewrite([31(2)])].
% 103.23/103.53 64 xor(A,B) = or(and(A,not(B)),and(B,not(A))) # label(xor_definition) # label(axiom). [assumption].
% 103.23/103.53 65 carryout(A,B,C) = or(and(A,or(B,C)),and(not(A),and(B,C))) # label(carryout_definition) # label(negated_conjecture). [assumption].
% 103.23/103.53 66 carryout(A,B,C) = or(and(A,or(B,C)),and(B,and(C,not(A)))). [copy(65),rewrite([55(6),31(5),55(6,R),31(5)])].
% 103.23/103.53 69 -circuit(sum(a,b,carryin),carryout(a,b,carryin)) # label(prove_circuit) # label(negated_conjecture) # answer(prove_circuit). [assumption].
% 103.23/103.53 70 -circuit(or(and(carryin,and(or(a,not(b)),or(b,not(a)))),and(not(carryin),or(and(a,not(b)),and(b,not(a))))),or(and(a,or(b,carryin)),and(b,and(carryin,not(a))))) # answer(prove_circuit). [copy(69),rewrite([53(4),64(3),64(11),31(12),47(23),46(18),8(18),32(17),46(22),8(22),32(21),31(22),32(24),66(28)])].
% 103.23/103.53 71 or(not(a15),not(a14)) = a16. [back_rewrite(24),rewrite([31(3),46(4)])].
% 103.23/103.53 72 or(not(a11),not(a15)) = c1. [back_rewrite(30),rewrite([46(4)])].
% 103.23/103.53 73 or(not(a16),not(a17)) = s1. [back_rewrite(28),rewrite([46(4)])].
% 103.23/103.53 74 or(not(a15),not(carryin)) = a17. [back_rewrite(26),rewrite([46(4)])].
% 103.23/103.53 75 or(not(a14),not(carryin)) = a15. [back_rewrite(22),rewrite([46(4)])].
% 103.23/103.53 76 or(not(a12),not(a13)) = a14. [back_rewrite(20),rewrite([46(4)])].
% 103.23/103.53 77 or(not(a11),not(b)) = a13. [back_rewrite(18),rewrite([46(4)])].
% 103.23/103.53 78 or(not(a11),not(a)) = a12. [back_rewrite(16),rewrite([46(4)])].
% 103.23/103.53 79 or(not(a),not(b)) = a11. [back_rewrite(14),rewrite([46(4)])].
% 103.23/103.53 83 or(n0,not(A)) = not(A). [para(3(a,1),46(a,2,1)),rewrite([31(2),5(2)]),flip(a)].
% 103.23/103.53 85 or(not(A),or(not(B),and(A,B))) = n1. [para(46(a,1),12(a,1,2)),rewrite([57(5),32(4),57(5,R),32(4)])].
% 103.23/103.53 87 and(n1,not(A)) = not(A). [para(2(a,1),47(a,2,1)),rewrite([32(2),6(2)]),flip(a)].
% 103.23/103.53 90 or(A,or(B,not(A))) = n1. [para(47(a,1),12(a,1,2)),rewrite([32(5),57(5),32(4),57(5,R),32(4),52(4)])].
% 103.23/103.53 93 or(not(A),and(A,B)) = or(B,not(A)). [para(8(a,1),52(a,1,2,2)),rewrite([31(2),32(5)])].
% 103.23/103.53 95 or(and(A,B),and(C,or(not(A),not(B)))) = or(C,and(A,B)). [para(46(a,1),52(a,1,2,2)),rewrite([32(8)])].
% 103.23/103.53 97 or(or(A,B),and(C,and(not(A),not(B)))) = or(A,or(B,C)). [para(47(a,1),52(a,1,2,2)),rewrite([32(8),57(8),32(7),57(8,R),32(7)])].
% 103.23/103.53 98 and(A,and(B,not(A))) = n0. [para(11(a,1),55(a,2,2)),rewrite([31(2),4(5)])].
% 103.23/103.53 99 or(A,or(B,and(C,not(A)))) = or(A,or(C,B)). [para(52(a,1),57(a,2,2)),rewrite([32(3),57(6),32(5),57(6,R),32(5)])].
% 103.23/103.53 103 and(n0,or(A,B)) = n0. [para(4(a,1),63(a,1,1)),rewrite([31(3),4(3),10(3),32(3)]),flip(a)].
% 103.23/103.53 104 or(n0,and(A,B)) = and(A,B). [para(4(a,1),63(a,1,2)),rewrite([32(3),6(5),31(4)])].
% 103.23/103.53 105 and(n1,or(A,B)) = or(A,B). [para(5(a,1),63(a,1,1)),rewrite([31(2),5(2)]),flip(a)].
% 103.23/103.53 106 or(A,and(B,A)) = A. [para(5(a,1),63(a,1,2)),rewrite([32(2),7(4),5(4)])].
% 103.23/103.53 107 and(A,or(A,B)) = A. [para(9(a,1),63(a,1,1)),rewrite([34(2)]),flip(a)].
% 103.23/103.53 108 and(A,or(B,A)) = A. [para(9(a,1),63(a,1,2)),rewrite([32(2),106(2)]),flip(a)].
% 103.23/103.53 109 and(not(A),or(A,B)) = and(B,not(A)). [para(11(a,1),63(a,1,1)),rewrite([31(3),104(4)]),flip(a)].
% 103.23/103.53 110 and(A,or(B,not(A))) = and(B,A). [para(11(a,1),63(a,1,2)),rewrite([32(3),104(3)]),flip(a)].
% 103.23/103.53 111 or(and(A,B),and(A,C)) = and(A,or(B,C)). [para(31(a,1),63(a,1,1))].
% 103.23/103.53 112 and(and(A,B),or(A,C)) = and(A,B). [para(43(a,1),63(a,1,1)),rewrite([31(3),55(3),31(2),55(3,R),31(2),111(4),34(2)]),flip(a)].
% 103.23/103.53 113 and(A,or(B,and(A,C))) = and(A,or(B,C)). [para(43(a,1),63(a,1,2)),rewrite([63(3)]),flip(a)].
% 103.23/103.53 115 or(and(A,B),and(C,A)) = and(A,or(C,B)). [para(63(a,1),52(a,2)),rewrite([46(4),95(7)])].
% 103.23/103.53 116 and(and(A,B),or(C,D)) = and(A,and(B,or(C,D))). [para(55(a,1),63(a,1,1)),rewrite([31(3),31(4),55(4),31(3),55(4,R),31(3),111(5),63(3),31(4)]),flip(a)].
% 103.23/103.53 117 or(and(A,B),or(and(B,C),and(A,and(B,D)))) = and(B,or(A,C)). [para(63(a,1),59(a,2)),rewrite([31(4),55(4),31(3),55(4,R),31(3)])].
% 103.23/103.53 120 and(A,and(B,or(A,C))) = and(A,B). [back_rewrite(112),rewrite([116(3)])].
% 103.23/103.53 122 or(a16,not(a15)) = a16. [para(71(a,1),45(a,1,2)),rewrite([32(4),71(9)])].
% 103.23/103.53 123 and(a15,a14) = not(a16). [para(71(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 125 or(c1,not(a11)) = c1. [para(72(a,1),45(a,1,2)),rewrite([32(4),72(9)])].
% 103.23/103.53 126 and(a11,a15) = not(c1). [para(72(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 128 or(s1,not(a16)) = s1. [para(73(a,1),45(a,1,2)),rewrite([32(4),73(9)])].
% 103.23/103.53 129 and(a16,a17) = not(s1). [para(73(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 131 or(a17,not(a15)) = a17. [para(74(a,1),45(a,1,2)),rewrite([32(4),74(9)])].
% 103.23/103.53 132 and(a15,carryin) = not(a17). [para(74(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 133 or(not(a15),or(not(carryin),and(A,not(a15)))) = a17. [para(74(a,1),59(a,2)),rewrite([31(7)])].
% 103.23/103.53 134 or(a15,not(a14)) = a15. [para(75(a,1),45(a,1,2)),rewrite([32(4),75(9)])].
% 103.23/103.53 135 and(a14,carryin) = not(a15). [para(75(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 136 or(not(a14),or(not(carryin),and(A,not(a14)))) = a15. [para(75(a,1),59(a,2)),rewrite([31(7)])].
% 103.23/103.53 137 or(a14,not(a12)) = a14. [para(76(a,1),45(a,1,2)),rewrite([32(4),76(9)])].
% 103.23/103.53 138 and(a12,a13) = not(a14). [para(76(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 140 or(a13,not(a11)) = a13. [para(77(a,1),45(a,1,2)),rewrite([32(4),77(9)])].
% 103.23/103.53 141 and(a11,b) = not(a13). [para(77(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 143 or(a12,not(a11)) = a12. [para(78(a,1),45(a,1,2)),rewrite([32(4),78(9)])].
% 103.23/103.53 144 and(a11,a) = not(a12). [para(78(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 146 or(a11,not(a)) = a11. [para(79(a,1),45(a,1,2)),rewrite([32(4),79(9)])].
% 103.23/103.53 147 and(a,b) = not(a11). [para(79(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.53 156 or(not(a16),and(A,a15)) = and(a15,or(A,a14)). [para(123(a,1),63(a,1,2)),rewrite([32(5)])].
% 103.23/103.53 159 or(n0,or(not(A),not(B))) = or(not(A),not(B)). [para(46(a,1),83(a,1,2)),rewrite([46(7)])].
% 103.23/103.53 160 or(a11,not(c1)) = a11. [para(126(a,1),34(a,1,2))].
% 103.23/103.53 165 or(a16,not(s1)) = a16. [para(129(a,1),34(a,1,2))].
% 103.23/103.53 166 or(not(s1),and(A,a17)) = and(a17,or(A,a16)). [para(129(a,1),63(a,1,1)),rewrite([31(4),32(8)])].
% 103.23/103.53 167 or(not(s1),and(A,a16)) = and(a16,or(A,a17)). [para(129(a,1),63(a,1,2)),rewrite([32(5)])].
% 103.23/103.53 170 or(A,or(not(A),not(B))) = n1. [para(8(a,1),85(a,1,1)),rewrite([31(3),93(4)])].
% 103.23/103.54 171 or(or(not(A),not(B)),or(not(C),and(A,and(B,C)))) = n1. [para(46(a,1),85(a,1,1)),rewrite([31(6),55(6),31(5),55(6,R),31(5)])].
% 103.23/103.54 177 or(not(a11),or(not(a15),not(c1))) = n1. [para(126(a,1),85(a,1,2,2))].
% 103.23/103.54 183 and(a14,not(a15)) = not(a15). [para(134(a,1),47(a,1,1)),rewrite([8(7),31(6)]),flip(a)].
% 103.23/103.54 187 or(not(a15),and(A,carryin)) = and(carryin,or(A,a14)). [para(135(a,1),63(a,1,1)),rewrite([31(4),32(8)])].
% 103.23/103.54 189 or(a17,not(a14)) = n1. [para(135(a,1),85(a,1,2,2)),rewrite([32(7),74(7),32(4)])].
% 103.23/103.54 191 or(a14,and(not(a14),not(a12))) = a14. [para(137(a,1),52(a,2)),rewrite([31(6)])].
% 103.23/103.54 201 or(a12,not(a14)) = a12. [para(138(a,1),34(a,1,2))].
% 103.23/103.54 202 or(not(a14),and(A,a13)) = and(a13,or(A,a12)). [para(138(a,1),63(a,1,1)),rewrite([31(4),32(8)])].
% 103.23/103.54 203 or(not(a14),and(A,a12)) = and(a12,or(A,a13)). [para(138(a,1),63(a,1,2)),rewrite([32(5)])].
% 103.23/103.54 206 or(a11,not(a13)) = a11. [para(141(a,1),34(a,1,2))].
% 103.23/103.54 220 or(a,not(a11)) = a. [para(147(a,1),34(a,1,2))].
% 103.23/103.54 223 or(a13,not(a)) = n1. [para(147(a,1),85(a,1,2,2)),rewrite([32(7),77(7),32(4)])].
% 103.23/103.54 229 or(a14,a16) = n1. [para(71(a,1),90(a,1,2))].
% 103.23/103.54 230 or(a15,c1) = n1. [para(72(a,1),90(a,1,2))].
% 103.23/103.54 232 or(a17,carryin) = n1. [para(74(a,1),90(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 233 or(a15,carryin) = n1. [para(75(a,1),90(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 235 or(a13,b) = n1. [para(77(a,1),90(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 236 or(a,a12) = n1. [para(78(a,1),90(a,1,2))].
% 103.23/103.54 237 or(a11,b) = n1. [para(79(a,1),90(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 238 or(a15,a16) = n1. [para(122(a,1),90(a,1,2))].
% 103.23/103.54 239 or(a11,c1) = n1. [para(125(a,1),90(a,1,2))].
% 103.23/103.54 240 or(a16,s1) = n1. [para(128(a,1),90(a,1,2))].
% 103.23/103.54 241 or(a15,a17) = n1. [para(131(a,1),90(a,1,2))].
% 103.23/103.54 243 or(a14,a12) = n1. [para(137(a,1),90(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 244 or(a11,a13) = n1. [para(140(a,1),90(a,1,2))].
% 103.23/103.54 245 or(a11,a12) = n1. [para(143(a,1),90(a,1,2))].
% 103.23/103.54 246 or(a11,a) = n1. [para(146(a,1),90(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 251 and(not(a15),not(c1)) = n0. [para(230(a,1),47(a,1,1)),rewrite([3(2)]),flip(a)].
% 103.23/103.54 276 or(not(A),and(B,A)) = or(B,not(A)). [para(93(a,1),32(a,1)),rewrite([31(3),32(5)]),flip(a)].
% 103.23/103.54 280 or(and(A,not(B)),and(B,and(A,C))) = and(A,or(C,not(B))). [para(93(a,1),63(a,2,2)),rewrite([31(2),55(4,R),31(3)])].
% 103.23/103.54 285 or(not(a14),not(a16)) = a15. [para(134(a,1),93(a,2)),rewrite([31(5),123(5)])].
% 103.23/103.54 286 or(carryin,not(a14)) = a16. [para(135(a,1),93(a,1,2)),rewrite([32(5),71(5)]),flip(a)].
% 103.23/103.54 289 or(not(a11),not(a12)) = a. [para(144(a,1),93(a,1,2)),rewrite([220(9)])].
% 103.23/103.54 291 or(b,not(a)) = a12. [para(147(a,1),93(a,1,2)),rewrite([32(5),78(5)]),flip(a)].
% 103.23/103.54 293 -circuit(or(and(a12,and(carryin,or(a,not(b)))),and(not(carryin),or(and(a,not(b)),and(b,not(a))))),or(and(a,or(b,carryin)),and(b,and(carryin,not(a))))) # answer(prove_circuit). [back_rewrite(70),rewrite([291(9),31(7),55(8,R),31(7)])].
% 103.23/103.54 303 and(not(a16),not(s1)) = n0. [para(240(a,1),47(a,1,1)),rewrite([3(2)]),flip(a)].
% 103.23/103.54 308 or(and(A,or(B,C)),and(D,or(and(not(B),not(C)),not(A)))) = or(D,and(A,or(B,C))). [para(47(a,1),95(a,1,2,2,1)),rewrite([31(2),31(11)])].
% 103.23/103.54 313 and(not(a15),not(a17)) = n0. [para(241(a,1),47(a,1,1)),rewrite([3(2)]),flip(a)].
% 103.23/103.54 317 and(not(a14),not(a12)) = n0. [para(243(a,1),47(a,1,1)),rewrite([3(2)]),flip(a)].
% 103.23/103.54 319 or(n0,a14) = a14. [back_rewrite(191),rewrite([317(6),32(3)])].
% 103.23/103.54 322 or(or(A,not(B)),and(B,and(C,not(A)))) = or(A,or(C,not(B))). [para(8(a,1),97(a,1,2,2,1)),rewrite([32(2),55(5,R),31(4),57(9),32(8),57(9,R),32(8)])].
% 103.23/103.54 353 and(not(a11),not(a)) = n0. [para(246(a,1),47(a,1,1)),rewrite([3(2)]),flip(a)].
% 103.23/103.54 364 or(A,and(B,or(C,not(A)))) = or(A,B). [para(34(a,1),99(a,2,2)),rewrite([111(4)])].
% 103.23/103.54 378 or(or(A,B),and(not(A),and(not(B),or(C,and(D,not(B)))))) = or(A,or(B,or(C,D))). [para(99(a,1),97(a,2,2)),rewrite([55(8),55(8),32(10)])].
% 103.23/103.54 381 and(n1,a14) = a14. [para(319(a,1),52(a,2)),rewrite([2(4),31(4),104(5)])].
% 103.23/103.54 422 and(c1,not(a11)) = not(a11). [para(160(a,1),47(a,1,1)),rewrite([8(7),31(6)]),flip(a)].
% 103.23/103.54 431 or(n0,a16) = a16. [para(165(a,1),52(a,2)),rewrite([31(6),303(6),32(3)])].
% 103.23/103.54 432 and(n1,a16) = a16. [para(431(a,1),52(a,2)),rewrite([2(4),31(4),104(5)])].
% 103.23/103.54 435 and(n0,c1) = n0. [para(72(a,1),103(a,1,2))].
% 103.23/103.54 437 and(n0,a17) = n0. [para(74(a,1),103(a,1,2))].
% 103.23/103.54 448 and(n1,a17) = a17. [para(74(a,1),105(a,1,2)),rewrite([74(8)])].
% 103.23/103.54 449 and(n1,a13) = a13. [para(77(a,1),105(a,1,2)),rewrite([77(8)])].
% 103.23/103.54 450 and(n1,a12) = a12. [para(78(a,1),105(a,1,2)),rewrite([78(8)])].
% 103.23/103.54 453 or(a15,not(c1)) = a15. [para(126(a,1),106(a,1,2))].
% 103.23/103.54 461 or(n0,c1) = c1. [para(435(a,1),106(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 463 or(n0,a17) = a17. [para(437(a,1),106(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 468 or(A,and(B,or(A,C))) = and(or(A,C),or(A,B)). [para(107(a,1),63(a,1,1)),rewrite([31(2)])].
% 103.23/103.54 470 and(a15,not(a14)) = not(a14). [para(75(a,1),107(a,1,2)),rewrite([31(4)])].
% 103.23/103.54 474 and(a11,not(a)) = not(a). [para(79(a,1),107(a,1,2)),rewrite([31(4)])].
% 103.23/103.54 475 and(n1,a) = a. [para(236(a,1),107(a,1,2)),rewrite([31(3)])].
% 103.23/103.54 479 and(c1,not(a15)) = not(a15). [para(72(a,1),108(a,1,2)),rewrite([31(4)])].
% 103.23/103.54 482 and(a15,not(carryin)) = not(carryin). [para(75(a,1),108(a,1,2)),rewrite([31(4)])].
% 103.23/103.54 486 and(a11,not(b)) = not(b). [para(79(a,1),108(a,1,2)),rewrite([31(4)])].
% 103.23/103.54 487 and(n1,carryin) = carryin. [para(232(a,1),108(a,1,2)),rewrite([31(3)])].
% 103.23/103.54 488 and(n1,b) = b. [para(235(a,1),108(a,1,2)),rewrite([31(3)])].
% 103.23/103.54 495 or(n0,carryin) = carryin. [para(487(a,1),104(a,1,2)),rewrite([487(6)])].
% 103.23/103.54 496 and(not(A),or(B,A)) = and(B,not(A)). [para(109(a,1),31(a,1)),rewrite([32(3),31(5)]),flip(a)].
% 103.23/103.54 499 and(not(A),or(B,and(A,C))) = and(B,not(A)). [para(59(a,1),109(a,1,2)),rewrite([109(3),31(6)]),flip(a)].
% 103.23/103.54 500 or(and(A,not(B)),and(C,or(A,B))) = and(or(A,B),or(C,not(B))). [para(109(a,1),63(a,1,1)),rewrite([32(3),31(4),32(6),32(8)])].
% 103.23/103.54 501 or(and(A,not(B)),and(C,not(B))) = and(not(B),or(A,or(B,C))). [para(109(a,1),63(a,1,2))].
% 103.23/103.54 503 and(a15,a16) = not(a14). [para(71(a,1),109(a,1,2)),rewrite([8(3),8(8),31(7),470(7)])].
% 103.23/103.54 504 and(a11,not(a15)) = and(a11,c1). [para(72(a,1),109(a,1,2)),rewrite([8(3),8(8),31(7)]),flip(a)].
% 103.23/103.54 506 and(a15,a17) = not(carryin). [para(74(a,1),109(a,1,2)),rewrite([8(3),8(8),31(7),482(7)])].
% 103.23/103.54 507 and(a14,not(carryin)) = not(a16). [para(75(a,1),109(a,1,2)),rewrite([8(3),31(3),123(3),8(7),31(6)]),flip(a)].
% 103.23/103.54 509 and(a11,a13) = not(b). [para(77(a,1),109(a,1,2)),rewrite([8(3),8(8),31(7),486(7)])].
% 103.23/103.54 510 and(a11,a12) = not(a). [para(78(a,1),109(a,1,2)),rewrite([8(3),8(8),31(7),474(7)])].
% 103.23/103.54 511 and(a,not(b)) = not(a12). [para(79(a,1),109(a,1,2)),rewrite([8(3),31(3),144(3),8(7),31(6)]),flip(a)].
% 103.23/103.54 513 and(carryin,not(a15)) = not(a15). [para(233(a,1),109(a,1,2)),rewrite([31(4),87(4)]),flip(a)].
% 103.23/103.54 516 and(b,not(a11)) = not(a11). [para(237(a,1),109(a,1,2)),rewrite([31(4),87(4)]),flip(a)].
% 103.23/103.54 518 and(not(A),or(B,and(C,not(A)))) = and(or(C,B),not(A)). [para(99(a,1),109(a,1,2)),rewrite([109(4),31(8)]),flip(a)].
% 103.23/103.54 521 -circuit(or(and(a12,and(carryin,or(a,not(b)))),and(not(carryin),or(not(a12),and(b,not(a))))),or(and(a,or(b,carryin)),and(b,and(carryin,not(a))))) # answer(prove_circuit). [back_rewrite(293),rewrite([511(14)])].
% 103.23/103.54 522 or(or(A,B),and(not(A),and(or(C,D),not(B)))) = or(A,or(B,or(C,D))). [back_rewrite(378),rewrite([518(7),32(3)])].
% 103.23/103.54 524 or(n0,b) = b. [para(488(a,1),104(a,1,2)),rewrite([488(6)])].
% 103.23/103.54 531 and(a14,a16) = not(a15). [para(71(a,1),110(a,1,2)),rewrite([31(7),183(7)])].
% 103.23/103.54 532 and(a15,not(a11)) = and(a15,c1). [para(72(a,1),110(a,1,2)),rewrite([31(7)]),flip(a)].
% 103.23/103.54 534 and(a17,carryin) = not(a15). [para(74(a,1),110(a,1,2)),rewrite([31(3),31(7),513(7)])].
% 103.23/103.54 535 and(carryin,not(a14)) = not(a17). [para(75(a,1),110(a,1,2)),rewrite([31(3),132(3),31(6)]),flip(a)].
% 103.23/103.54 537 and(a13,b) = not(a11). [para(77(a,1),110(a,1,2)),rewrite([31(3),31(7),516(7)])].
% 103.23/103.54 539 and(b,not(a)) = not(a13). [para(79(a,1),110(a,1,2)),rewrite([31(3),141(3),31(6)]),flip(a)].
% 103.23/103.54 541 and(or(A,B),or(B,not(A))) = B. [para(108(a,1),110(a,2)),rewrite([47(3),52(5)])].
% 103.23/103.54 543 -circuit(or(not(a16),and(a12,and(carryin,or(a,not(b))))),or(and(a,or(b,carryin)),and(b,and(carryin,not(a))))) # answer(prove_circuit). [back_rewrite(521),rewrite([539(16),76(15),31(12),507(12),32(11)])].
% 103.23/103.54 547 or(and(A,and(B,C)),and(C,D)) = and(C,or(D,and(A,B))). [para(55(a,2),111(a,1,1)),rewrite([32(6)])].
% 103.23/103.54 552 and(a14,a17) = a14. [para(189(a,1),110(a,1,2)),rewrite([31(3),381(3),31(4)]),flip(a)].
% 103.23/103.54 556 or(a14,a17) = a17. [para(552(a,1),106(a,1,2)),rewrite([32(3)])].
% 103.23/103.54 557 and(A,and(B,or(C,and(A,D)))) = and(A,and(B,or(C,D))). [para(113(a,1),55(a,2,2)),rewrite([31(3),55(7,R),31(6)])].
% 103.23/103.54 558 or(and(A,or(B,C)),and(D,or(B,and(A,C)))) = and(or(B,and(A,C)),or(A,D)). [para(113(a,1),63(a,1,1)),rewrite([31(5)])].
% 103.23/103.54 569 or(or(A,B),not(C)) = or(A,or(B,not(C))). [para(113(a,1),93(a,1,2)),rewrite([93(4),32(7),57(7,R),32(6),93(6)])].
% 103.23/103.54 570 or(and(A,B),and(or(C,B),or(C,A))) = or(C,and(A,B)). [para(113(a,1),106(a,1,2)),rewrite([32(5),57(5),32(4),468(4)])].
% 103.23/103.54 599 and(a,not(a13)) = n0. [para(223(a,1),47(a,1,1)),rewrite([3(2),8(6),31(5)]),flip(a)].
% 103.23/103.54 603 and(a,a13) = a. [para(223(a,1),110(a,1,2)),rewrite([31(3),475(3),31(4)]),flip(a)].
% 103.23/103.54 604 or(not(a),not(a13)) = not(a). [para(603(a,1),46(a,1,1)),flip(a)].
% 103.23/103.54 609 and(or(A,B),or(A,C)) = or(A,and(C,B)). [para(115(a,1),59(a,1,2)),rewrite([468(3)])].
% 103.23/103.54 613 or(and(A,not(B)),and(C,or(B,A))) = and(or(B,A),or(C,not(B))). [para(109(a,1),115(a,1,2)),rewrite([31(2),32(5),32(8)])].
% 103.23/103.54 614 or(and(A,B),and(or(B,C),or(A,C))) = or(C,and(A,B)). [back_rewrite(570),rewrite([32(2),32(3)])].
% 103.23/103.54 615 or(A,and(B,or(A,C))) = or(A,and(B,C)). [back_rewrite(468),rewrite([609(6)])].
% 103.23/103.54 623 and(a16,carryin) = carryin. [para(286(a,1),107(a,1,2)),rewrite([31(3)])].
% 103.23/103.54 624 and(not(a14),not(carryin)) = and(a16,not(carryin)). [para(286(a,1),109(a,1,2)),rewrite([31(4)]),flip(a)].
% 103.23/103.54 632 or(a12,b) = a12. [para(291(a,1),45(a,1,2)),rewrite([32(3),291(7)])].
% 103.23/103.54 635 and(a12,b) = b. [para(291(a,1),107(a,1,2)),rewrite([31(3)])].
% 103.23/103.54 636 and(not(a),not(b)) = and(a12,not(b)). [para(291(a,1),109(a,1,2)),rewrite([31(4)]),flip(a)].
% 103.23/103.54 638 and(A,and(not(A),or(B,C))) = n0. [para(11(a,1),116(a,1,1)),rewrite([103(3)]),flip(a)].
% 103.23/103.54 639 or(and(A,and(B,or(C,D))),and(E,or(C,D))) = and(or(C,D),or(E,and(A,B))). [para(116(a,1),63(a,1,1)),rewrite([31(5),32(9)])].
% 103.23/103.54 641 and(a15,and(a14,or(A,B))) = and(not(a16),or(A,B)). [para(123(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 642 and(and(A,B),not(C)) = and(A,and(B,not(C))). [para(83(a,1),116(a,1,2)),rewrite([83(6)])].
% 103.23/103.54 643 and(a11,and(a15,or(A,B))) = and(not(c1),or(A,B)). [para(126(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 644 and(a16,and(a17,or(A,B))) = and(not(s1),or(A,B)). [para(129(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 646 and(a14,and(carryin,or(A,B))) = and(not(a15),or(A,B)). [para(135(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 647 and(a12,and(a13,or(A,B))) = and(not(a14),or(A,B)). [para(138(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 648 and(a11,and(b,or(A,B))) = and(not(a13),or(A,B)). [para(141(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 650 and(a11,and(a,or(A,B))) = and(not(a12),or(A,B)). [para(144(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 651 and(a,and(b,or(A,B))) = and(not(a11),or(A,B)). [para(147(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 653 or(and(A,B),and(C,and(D,or(not(A),not(B))))) = or(and(C,D),and(A,B)). [para(116(a,1),95(a,1,2))].
% 103.23/103.54 668 and(n1,and(or(A,B),or(C,D))) = and(or(A,B),or(C,D)). [para(105(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 687 and(a,and(a13,or(A,B))) = and(a,or(A,B)). [para(603(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 694 and(b,not(a12)) = n0. [para(632(a,1),109(a,1,2)),rewrite([31(4),11(4)]),flip(a)].
% 103.23/103.54 696 and(b,or(A,a12)) = b. [para(635(a,1),63(a,1,1)),rewrite([31(3),106(4),32(4)]),flip(a)].
% 103.23/103.54 698 and(a12,and(b,or(A,B))) = and(b,or(A,B)). [para(635(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 708 or(and(A,a16),or(and(B,a16),and(A,not(s1)))) = and(a16,or(A,B)). [para(129(a,1),117(a,1,2,2,2)),rewrite([31(4)])].
% 103.23/103.54 711 or(not(a15),or(and(A,carryin),and(B,not(a15)))) = and(carryin,or(A,a14)). [para(135(a,1),117(a,1,1)),rewrite([31(4),31(7),55(8,R),31(7),135(7),32(12)])].
% 103.23/103.54 714 or(and(A,a12),or(and(B,a12),and(A,not(a14)))) = and(a12,or(A,B)). [para(138(a,1),117(a,1,2,2,2)),rewrite([31(4)])].
% 103.23/103.54 740 or(and(A,not(B)),or(and(C,not(B)),and(A,and(D,not(B))))) = and(not(B),or(A,or(B,C))). [para(109(a,1),117(a,1,2,1)),rewrite([31(6)])].
% 103.23/103.54 741 and(not(A),or(B,or(A,C))) = and(not(A),or(B,C)). [para(109(a,1),117(a,1,2,2,2)),rewrite([31(4),740(9)])].
% 103.23/103.54 749 or(and(A,a16),or(and(B,a16),and(A,carryin))) = and(a16,or(A,B)). [para(623(a,1),117(a,1,2,2,2)),rewrite([31(4)])].
% 103.23/103.54 754 or(and(A,not(B)),and(C,not(B))) = and(not(B),or(A,C)). [back_rewrite(501),rewrite([741(9)])].
% 103.23/103.54 824 or(not(a17),not(carryin)) = a15. [para(534(a,1),46(a,1,1)),rewrite([8(3)]),flip(a)].
% 103.23/103.54 833 and(a13,or(A,not(a11))) = and(a13,or(A,b)). [para(537(a,1),113(a,1,2,2))].
% 103.23/103.54 852 and(not(a13),or(A,a)) = and(A,not(a13)). [para(599(a,1),63(a,1,1)),rewrite([31(4),104(5),32(7)]),flip(a)].
% 103.23/103.54 861 or(a12,not(b)) = n1. [para(694(a,1),46(a,1,1)),rewrite([2(2),8(6),32(5)]),flip(a)].
% 103.23/103.54 866 or(a17,and(A,not(a15))) = a17. [para(133(a,1),57(a,1)),rewrite([74(9),32(6)]),flip(a)].
% 103.23/103.54 870 or(a15,and(A,not(a14))) = a15. [para(136(a,1),57(a,1)),rewrite([75(9),32(6)]),flip(a)].
% 103.23/103.54 907 or(c1,not(a15)) = c1. [para(251(a,1),52(a,1,2)),rewrite([32(3),461(3)]),flip(a)].
% 103.23/103.54 981 and(a15,or(a11,a14)) = or(not(a16),not(c1)). [para(126(a,1),156(a,1,2)),flip(a)].
% 103.23/103.54 996 and(not(a14),or(A,not(a12))) = and(A,not(a14)). [para(317(a,1),63(a,1,2)),rewrite([32(5),104(5)]),flip(a)].
% 103.23/103.54 1011 and(not(a11),or(A,not(a))) = and(A,not(a11)). [para(353(a,1),63(a,1,2)),rewrite([32(5),104(5)]),flip(a)].
% 103.23/103.54 1014 or(not(a11),and(A,c1)) = and(c1,or(A,not(a11))). [para(422(a,1),63(a,1,2)),rewrite([32(5)])].
% 103.23/103.54 1080 or(a14,not(s1)) = a17. [para(229(a,1),166(a,2,2)),rewrite([552(5),32(4),31(7),448(7)])].
% 103.23/103.54 1081 or(not(carryin),not(s1)) = a17. [para(238(a,1),166(a,2,2)),rewrite([506(5),32(5),31(8),448(8)])].
% 103.23/103.54 1088 and(s1,not(a14)) = not(a17). [para(1080(a,1),47(a,1,1)),rewrite([8(7),31(6)]),flip(a)].
% 103.23/103.54 1091 and(not(a14),not(s1)) = and(a17,not(a14)). [para(1080(a,1),109(a,1,2)),rewrite([31(4),31(9)]),flip(a)].
% 103.23/103.54 1092 and(a17,s1) = and(a14,s1). [para(1080(a,1),110(a,1,2)),rewrite([31(3)])].
% 103.23/103.54 1110 or(not(a14),not(s1)) = a16. [para(241(a,1),167(a,2,2)),rewrite([503(5),32(5),31(8),432(8)])].
% 103.23/103.54 1136 or(b,not(a12)) = or(a,b). [para(511(a,1),52(a,1,2)),rewrite([32(7)])].
% 103.23/103.54 1190 or(a15,or(a17,not(A))) = n1. [para(313(a,1),171(a,1,2,2,2)),rewrite([8(4),8(6),4(6),32(6),463(6),32(5),57(5)])].
% 103.23/103.54 1204 or(a14,not(carryin)) = a17. [para(535(a,1),46(a,1,1)),rewrite([8(3),8(6),32(5)]),flip(a)].
% 103.23/103.54 1213 and(a17,not(a14)) = and(a16,not(carryin)). [para(1204(a,1),109(a,1,2)),rewrite([31(4),31(9),624(9)])].
% 103.23/103.54 1214 and(not(a14),not(s1)) = and(a16,not(carryin)). [back_rewrite(1091),rewrite([1213(9)])].
% 103.23/103.54 1224 or(a,not(b)) = a13. [para(539(a,1),46(a,1,1)),rewrite([8(3),8(6),32(5)]),flip(a)].
% 103.23/103.54 1225 or(a,not(a13)) = or(a,b). [para(539(a,1),52(a,1,2))].
% 103.23/103.54 1231 -circuit(or(not(a16),and(a12,and(a13,carryin))),or(and(a,or(b,carryin)),and(b,and(carryin,not(a))))) # answer(prove_circuit). [back_rewrite(543),rewrite([1224(8),31(6)])].
% 103.23/103.54 1235 and(a13,not(a)) = and(a12,not(b)). [para(1224(a,1),109(a,1,2)),rewrite([31(4),31(9),636(9)])].
% 103.23/103.54 1244 and(a11,and(a15,c1)) = n0. [para(177(a,1),47(a,1,1)),rewrite([3(2),8(4),47(8),8(5),8(6)]),flip(a)].
% 103.23/103.54 1249 -circuit(s1,or(and(a,or(b,carryin)),and(b,and(carryin,not(a))))) # answer(prove_circuit). [para(55(a,1),1231(a,1,2)),rewrite([138(6),535(6),73(5)])].
% 103.23/103.54 1290 and(carryin,s1) = not(a17). [para(1081(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.54 1295 and(s1,not(carryin)) = and(a14,s1). [para(1081(a,1),110(a,1,2)),rewrite([31(3),1092(3),31(7)]),flip(a)].
% 103.23/103.54 1298 or(s1,not(carryin)) = a15. [para(1290(a,1),93(a,1,2)),rewrite([32(5),824(5)]),flip(a)].
% 103.23/103.54 1305 or(a15,s1) = a15. [para(1298(a,1),45(a,1,2)),rewrite([32(3),1298(7)])].
% 103.23/103.54 1308 and(a15,s1) = s1. [para(1298(a,1),107(a,1,2)),rewrite([31(3)])].
% 103.23/103.54 1363 and(a14,s1) = not(a16). [para(1110(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.54 1367 and(a14,not(s1)) = not(a15). [para(1110(a,1),109(a,1,2)),rewrite([8(3),531(3),8(7),31(6)]),flip(a)].
% 103.23/103.54 1368 and(a16,s1) = not(a17). [para(1110(a,1),110(a,1,2)),rewrite([31(3),31(7),1088(7)])].
% 103.23/103.54 1376 and(s1,not(carryin)) = not(a16). [back_rewrite(1295),rewrite([1363(7)])].
% 103.23/103.54 1386 or(s1,not(a14)) = a15. [para(1363(a,1),93(a,1,2)),rewrite([285(5)]),flip(a)].
% 103.23/103.54 1431 and(a16,not(carryin)) = and(a15,not(s1)). [para(1386(a,1),109(a,1,2)),rewrite([31(4),1214(9)]),flip(a)].
% 103.23/103.54 1433 and(a17,not(a14)) = and(a15,not(s1)). [back_rewrite(1213),rewrite([1431(8)])].
% 103.23/103.54 1475 and(c1,or(a15,not(a11))) = not(a11). [para(1244(a,1),93(a,1,2)),rewrite([32(4),83(4),32(8),1014(8)]),flip(a)].
% 103.23/103.54 1532 or(a,not(a14)) = a13. [para(236(a,1),202(a,2,2)),rewrite([603(5),32(4),31(7),449(7)])].
% 103.23/103.54 1536 or(not(a14),not(b)) = a13. [para(245(a,1),202(a,2,2)),rewrite([509(5),31(8),449(8)])].
% 103.23/103.54 1540 and(a14,not(a)) = not(a13). [para(1532(a,1),47(a,1,1)),rewrite([8(7),31(6)]),flip(a)].
% 103.23/103.54 1542 and(not(a14),not(a)) = and(a12,not(b)). [para(1532(a,1),109(a,1,2)),rewrite([31(4),1235(4)]),flip(a)].
% 103.23/103.54 1543 and(a14,a13) = and(a14,a). [para(1532(a,1),110(a,1,2)),rewrite([31(6)])].
% 103.23/103.54 1554 or(not(a14),not(a)) = a12. [para(244(a,1),203(a,2,2)),rewrite([510(5),31(8),450(8)])].
% 103.23/103.54 1568 and(a14,b) = not(a13). [para(1536(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.54 1570 and(a14,not(b)) = and(a14,a). [para(1536(a,1),109(a,1,2)),rewrite([8(3),1543(3),8(8),31(7)]),flip(a)].
% 103.23/103.54 1571 and(b,not(a14)) = not(a11). [para(1536(a,1),110(a,1,2)),rewrite([31(3),537(3),31(6)]),flip(a)].
% 103.23/103.54 1581 or(not(a14),not(a13)) = or(b,not(a14)). [para(1568(a,1),93(a,1,2))].
% 103.23/103.54 1586 or(a,b) = or(a14,a). [para(1540(a,1),52(a,1,2)),rewrite([1225(4),32(6)])].
% 103.23/103.54 1589 or(b,not(a14)) = a12. [para(1540(a,1),93(a,1,2)),rewrite([1581(5),32(9),1554(9)])].
% 103.23/103.54 1592 or(a,not(a13)) = or(a14,a). [back_rewrite(1225),rewrite([1586(7)])].
% 103.23/103.54 1593 or(b,not(a12)) = or(a14,a). [back_rewrite(1136),rewrite([1586(7)])].
% 103.23/103.54 1597 and(a14,a) = not(a12). [para(1589(a,1),47(a,1,1)),rewrite([8(7),31(6),1570(6)]),flip(a)].
% 103.23/103.54 1599 and(not(a14),not(b)) = and(a12,not(b)). [para(1589(a,1),109(a,1,2)),rewrite([31(4)]),flip(a)].
% 103.23/103.54 1600 and(a14,a12) = not(a13). [para(1589(a,1),110(a,1,2)),rewrite([31(6),1568(6)])].
% 103.23/103.54 1601 and(a14,not(b)) = not(a12). [back_rewrite(1570),rewrite([1597(7)])].
% 103.23/103.54 1648 or(a14,not(b)) = a11. [para(1571(a,1),46(a,1,1)),rewrite([8(3),8(6),32(5)]),flip(a)].
% 103.23/103.54 1649 or(a14,not(a11)) = or(a14,b). [para(1571(a,1),52(a,1,2))].
% 103.23/103.54 1652 and(a14,not(a11)) = n0. [para(1571(a,1),98(a,1,2))].
% 103.23/103.54 1656 or(a11,a14) = a11. [para(1648(a,1),45(a,1,2)),rewrite([32(3),1648(7)])].
% 103.23/103.54 1660 and(a12,not(b)) = and(a11,not(a14)). [para(1648(a,1),109(a,1,2)),rewrite([31(4),31(9),1599(9)]),flip(a)].
% 103.23/103.54 1661 or(not(a16),not(c1)) = not(c1). [back_rewrite(981),rewrite([1656(4),31(3),126(3)]),flip(a)].
% 103.23/103.54 1664 and(not(a14),not(a)) = and(a11,not(a14)). [back_rewrite(1542),rewrite([1660(9)])].
% 103.23/103.54 1686 and(a14,or(A,not(a11))) = and(A,a14). [para(1652(a,1),63(a,1,2)),rewrite([32(4),104(4)]),flip(a)].
% 103.23/103.54 1701 or(a14,b) = or(a14,a). [para(1601(a,1),52(a,1,2)),rewrite([1593(4),32(6)]),flip(a)].
% 103.23/103.54 1705 or(a14,not(a11)) = or(a14,a). [back_rewrite(1649),rewrite([1701(7)])].
% 103.23/103.54 1831 or(not(a15),not(c1)) = or(a11,not(a15)). [para(532(a,1),46(a,1,1)),rewrite([46(4),8(10),32(9)])].
% 103.23/103.54 1902 or(a17,and(a11,c1)) = a17. [para(504(a,1),866(a,1,2))].
% 103.23/103.54 1907 and(a11,and(a17,c1)) = and(a11,c1). [para(1902(a,1),108(a,1,2)),rewrite([31(5),55(5,R),31(4)])].
% 103.23/103.54 1908 and(a11,and(c1,not(a17))) = n0. [para(1902(a,1),109(a,1,2)),rewrite([31(4),11(4),31(7),55(7),31(6),55(7,R),31(6)]),flip(a)].
% 103.23/103.54 1912 or(a15,not(a11)) = a15. [para(1571(a,1),870(a,1,2))].
% 103.23/103.54 1915 and(a15,c1) = not(a11). [back_rewrite(1475),rewrite([1912(5),31(3)])].
% 103.23/103.54 1932 and(a11,c1) = not(a15). [para(1912(a,1),47(a,1,1)),rewrite([8(7),31(6),504(6)]),flip(a)].
% 103.23/103.54 1933 and(a11,and(a17,c1)) = not(a15). [back_rewrite(1907),rewrite([1932(8)])].
% 103.23/103.54 1942 or(a11,not(a15)) = a11. [para(1915(a,1),46(a,1,1)),rewrite([8(3),1831(6)]),flip(a)].
% 103.23/103.54 1947 or(not(a15),not(c1)) = a11. [back_rewrite(1831),rewrite([1942(9)])].
% 103.23/103.54 2323 or(a15,or(not(A),a17)) = n1. [para(32(a,1),1190(a,1,2))].
% 103.23/103.54 2468 and(A,or(not(A),not(B))) = and(A,not(B)). [para(11(a,1),280(a,1,2,2)),rewrite([4(4),32(4),104(4)]),flip(a)].
% 103.23/103.54 2486 and(a14,or(a17,not(A))) = a14. [para(552(a,1),280(a,1,2,2)),rewrite([32(6),63(6),12(3),31(3),381(3)]),flip(a)].
% 103.23/103.54 2490 or(and(A,b),and(a12,not(A))) = and(a12,or(b,not(A))). [para(635(a,1),280(a,1,2,2)),rewrite([32(6)])].
% 103.23/103.54 2590 and(a12,or(a14,a)) = b. [para(1593(a,1),110(a,1,2)),rewrite([31(8),635(8)])].
% 103.23/103.54 2610 and(a16,c1) = c1. [para(1661(a,1),47(a,1,1)),rewrite([8(3),8(4),8(5)]),flip(a)].
% 103.23/103.54 2613 and(c1,not(a16)) = n0. [para(1661(a,1),110(a,1,2)),rewrite([11(4),31(5)]),flip(a)].
% 103.23/103.54 2614 or(a16,not(c1)) = n1. [para(1661(a,1),170(a,1,2))].
% 103.23/103.54 2617 and(c1,or(A,a16)) = c1. [para(2610(a,1),63(a,1,1)),rewrite([31(3),106(4),32(4)]),flip(a)].
% 103.23/103.54 2619 and(a16,and(c1,or(A,B))) = and(c1,or(A,B)). [para(2610(a,1),116(a,1,1)),flip(a)].
% 103.23/103.54 2677 or(not(a15),or(not(a17),not(c1))) = or(a11,or(not(a17),not(c1))). [para(1933(a,1),276(a,1,2)),rewrite([46(4),32(8),46(13)])].
% 103.23/103.54 2774 or(and(A,or(B,C)),and(D,and(or(B,C),or(and(not(B),not(C)),not(A))))) = and(or(B,C),or(A,D)). [para(115(a,1),308(a,2)),rewrite([31(4),116(10)])].
% 103.23/103.54 2775 or(and(A,or(B,C)),and(D,and(E,or(and(not(B),not(C)),not(A))))) = or(and(D,E),and(A,or(B,C))). [para(116(a,1),308(a,1,2))].
% 103.23/103.54 2805 or(and(A,or(B,C)),and(D,or(B,C))) = and(or(B,C),or(D,A)). [back_rewrite(2774),rewrite([2775(11)])].
% 103.23/103.54 3084 or(a17,or(not(A),not(a15))) = or(n0,or(a17,not(A))). [para(313(a,1),322(a,1,2,2)),rewrite([4(5),32(5),32(10)]),flip(a)].
% 103.23/103.54 3149 or(n0,or(a17,not(a11))) = or(a17,c1). [para(1908(a,1),322(a,1,2)),rewrite([32(6),125(11)])].
% 103.23/103.54 3657 or(a15,and(A,c1)) = or(A,a15). [para(72(a,1),364(a,1,2,2)),rewrite([32(6)])].
% 103.23/103.54 3662 or(a13,and(A,a14)) = or(A,a13). [para(76(a,1),364(a,1,2,2)),rewrite([32(6)])].
% 103.23/103.54 3672 or(a12,and(A,a14)) = or(A,a12). [para(137(a,1),364(a,1,2,2)),rewrite([32(6)])].
% 103.23/103.54 3708 or(a12,and(A,not(a14))) = a12. [para(201(a,1),364(a,2)),rewrite([996(7)])].
% 103.23/103.54 3709 or(a13,and(A,a11)) = or(A,a13). [para(206(a,1),364(a,1,2,2)),rewrite([32(6)])].
% 103.23/103.54 3781 or(a11,and(A,a14)) = a11. [para(1656(a,1),364(a,2)),rewrite([1686(6)])].
% 103.23/103.54 3966 or(a11,not(a16)) = a11. [para(123(a,1),3781(a,1,2))].
% 103.23/103.54 3969 and(a16,not(a11)) = not(a11). [para(3966(a,1),47(a,1,1)),rewrite([8(7),31(6)]),flip(a)].
% 103.23/103.54 4302 or(a12,not(a17)) = a12. [para(535(a,1),3708(a,1,2))].
% 103.23/103.54 4307 and(a17,not(a12)) = not(a12). [para(4302(a,1),47(a,1,1)),rewrite([8(7),31(6)]),flip(a)].
% 103.23/103.54 4566 and(or(A,and(B,C)),or(not(B),and(not(A),not(C)))) = and(A,not(B)). [para(499(a,1),110(a,2)),rewrite([47(6),46(6),615(9)])].
% 103.23/103.54 4592 or(and(A,not(B)),and(B,C)) = and(or(A,B),or(C,not(B))). [para(500(a,1),52(a,2)),rewrite([46(7),8(7),32(6),31(7),55(7),31(6),55(7,R),31(6),541(6),31(3)])].
% 103.23/103.54 5048 or(or(A,B),and(C,D)) = or(A,or(B,and(C,D))). [para(104(a,1),522(a,1,1)),rewrite([2(3),46(5),668(8),95(7),57(7),32(6),57(7,R),32(6),57(8,R),32(7),57(7,R),32(6),104(6)])].
% 103.23/103.54 6051 or(and(A,B),and(or(C,B),or(A,D))) = and(or(C,B),or(A,D)). [para(541(a,1),117(a,1,2,2,2)),rewrite([31(4),57(7),2805(6),32(3)])].
% 103.23/103.54 6064 or(n0,or(a17,not(A))) = or(not(A),a17). [para(2323(a,1),541(a,1,1)),rewrite([32(7),57(7),32(6),3084(7),105(7)])].
% 103.23/103.54 6112 or(a17,not(a11)) = or(a17,c1). [back_rewrite(3149),rewrite([6064(6),32(4)])].
% 103.23/103.54 6646 and(not(a11),not(a17)) = and(c1,not(a17)). [para(6112(a,1),109(a,1,2)),rewrite([109(6)]),flip(a)].
% 103.23/103.54 6652 and(a14,or(a17,c1)) = a14. [para(6112(a,1),2486(a,1,2))].
% 103.23/103.54 6692 or(and(A,B),and(C,or(A,D))) = and(or(A,D),or(C,and(A,B))). [para(120(a,1),547(a,1,1)),rewrite([31(3)])].
% 103.23/103.54 6890 and(or(A,B),or(C,or(D,and(A,C)))) = and(or(C,D),or(A,B)). [back_rewrite(6051),rewrite([32(2),6692(5),5048(4),32(6)])].
% 103.23/103.54 6931 and(or(A,B),or(C,B)) = or(B,and(C,A)). [back_rewrite(614),rewrite([6692(5),5048(4),6890(5)])].
% 103.23/103.54 7053 or(and(A,or(B,C)),and(B,and(D,not(A)))) = and(or(B,and(A,C)),or(A,D)). [para(558(a,1),52(a,2)),rewrite([46(8),47(8),31(11),55(11),31(10),55(11,R),31(10),4566(10),55(5,R),31(4)])].
% 103.23/103.54 7276 or(c1,and(A,or(B,c1))) = or(c1,and(A,B)). [para(2617(a,1),558(a,1,1)),rewrite([31(4),2610(4),31(8),2610(8),32(9),6931(10)])].
% 103.23/103.54 7362 -circuit(s1,and(or(a,carryin),or(b,and(a,carryin)))) # answer(prove_circuit). [back_rewrite(1249),rewrite([7053(13),31(10)])].
% 103.23/103.54 7714 or(a11,or(not(A),not(c1))) = or(a11,not(A)). [para(160(a,1),569(a,1,1)),rewrite([32(8)]),flip(a)].
% 103.23/103.54 7730 or(a15,or(not(A),not(c1))) = or(a15,not(A)). [para(453(a,1),569(a,1,1)),rewrite([32(8)]),flip(a)].
% 103.23/103.54 7742 or(a,or(not(A),not(b))) = or(a13,not(A)). [para(1224(a,1),569(a,1,1)),rewrite([32(8)]),flip(a)].
% 103.23/103.54 7863 or(not(a15),or(not(a17),not(c1))) = or(a11,not(a17)). [back_rewrite(2677),rewrite([7714(15)])].
% 103.23/103.54 8411 and(or(A,a12),or(b,not(A))) = or(b,and(a12,not(A))). [para(696(a,1),613(a,1,2)),rewrite([32(5)]),flip(a)].
% 103.23/103.54 8514 or(a17,and(a14,c1)) = a17. [para(6652(a,1),615(a,1,2)),rewrite([32(3),556(3)]),flip(a)].
% 103.23/103.54 8527 and(a14,and(a17,c1)) = and(a14,c1). [para(8514(a,1),108(a,1,2)),rewrite([31(5),55(5,R),31(4)])].
% 103.23/103.54 8607 and(A,and(not(A),s1)) = n0. [para(73(a,1),638(a,1,2,2))].
% 103.23/103.54 8666 and(A,or(B,and(not(A),s1))) = and(B,A). [para(8607(a,1),63(a,1,2)),rewrite([32(3),104(3)]),flip(a)].
% 103.23/103.54 8702 or(and(A,and(B,or(C,D))),and(E,and(F,or(C,D)))) = and(or(C,D),or(and(E,F),and(A,B))). [para(116(a,1),639(a,1,2))].
% 103.23/103.54 8929 and(a15,and(a14,c1)) = n0. [para(72(a,1),641(a,1,2,2)),rewrite([72(12),31(9),2613(9)])].
% 103.23/103.54 8931 and(a12,not(a16)) = and(a15,not(a13)). [para(78(a,1),641(a,1,2,2)),rewrite([1600(4),78(11),31(8)]),flip(a)].
% 103.23/103.54 8945 and(not(a),not(a16)) = and(a15,not(a13)). [para(604(a,1),641(a,1,2,2)),rewrite([1540(5),604(11),31(9)]),flip(a)].
% 103.23/103.54 8967 or(not(a14),not(c1)) = a15. [para(8929(a,1),276(a,1,2)),rewrite([46(4),32(7),159(7),46(10),7730(12),134(9)])].
% 103.23/103.54 8972 and(a14,c1) = not(a15). [para(8967(a,1),47(a,1,1)),rewrite([8(5),8(6)]),flip(a)].
% 103.23/103.54 8973 and(a14,not(c1)) = not(a16). [para(8967(a,1),109(a,1,2)),rewrite([8(3),31(3),123(3),8(7),31(6)]),flip(a)].
% 103.23/103.54 8974 and(c1,not(a14)) = not(a11). [para(8967(a,1),110(a,1,2)),rewrite([31(3),1915(3),31(6)]),flip(a)].
% 103.23/103.54 8981 and(a14,and(a17,c1)) = not(a15). [back_rewrite(8527),rewrite([8972(8)])].
% 103.23/103.54 8984 or(c1,not(a14)) = a16. [para(8972(a,1),93(a,1,2)),rewrite([32(5),71(5)]),flip(a)].
% 103.23/103.54 8996 or(c1,and(A,not(a14))) = and(a16,or(A,c1)). [para(8984(a,1),609(a,1,1)),rewrite([32(3)]),flip(a)].
% 103.23/103.54 9087 and(s1,and(not(A),not(carryin))) = and(not(A),not(a16)). [para(1376(a,1),642(a,1,1)),rewrite([31(4),31(9)]),flip(a)].
% 103.23/103.54 9215 or(c1,not(a16)) = or(a14,c1). [para(8973(a,1),52(a,1,2)),rewrite([32(7)])].
% 103.23/103.54 9231 or(a14,c1) = or(a14,a). [para(8974(a,1),52(a,1,2)),rewrite([1705(4)]),flip(a)].
% 103.23/103.54 9242 or(c1,not(a16)) = or(a14,a). [back_rewrite(9215),rewrite([9231(7)])].
% 103.23/103.54 9244 and(c1,or(a14,a)) = c1. [para(9231(a,1),108(a,1,2))].
% 103.23/103.54 9253 and(s1,not(c1)) = and(a11,s1). [para(73(a,1),643(a,1,2,2)),rewrite([1308(4),73(10),31(7)]),flip(a)].
% 103.23/103.54 9254 and(a17,not(c1)) = and(a11,not(carryin)). [para(74(a,1),643(a,1,2,2)),rewrite([506(4),74(11),31(8)]),flip(a)].
% 103.23/103.54 9259 and(carryin,not(c1)) = and(a11,not(a17)). [para(495(a,1),643(a,1,2,2)),rewrite([132(4),495(9),31(8)]),flip(a)].
% 103.23/103.54 9260 and(a11,and(a15,b)) = and(b,not(c1)). [para(524(a,1),643(a,1,2,2)),rewrite([524(10),31(9)])].
% 103.23/103.54 9294 or(c1,and(A,or(a14,a))) = and(or(a14,a),or(A,c1)). [para(9244(a,1),63(a,1,1)),rewrite([31(5),32(11)])].
% 103.23/103.54 9296 and(a16,or(a14,a)) = c1. [para(9244(a,1),110(a,2)),rewrite([47(8),1664(9),8996(9),239(7),31(6),432(6),31(5)])].
% 103.23/103.54 9305 and(or(a14,a),or(A,c1)) = and(or(a14,a),or(A,a16)). [para(9296(a,1),63(a,1,1)),rewrite([31(5),9294(6),32(11)])].
% 103.23/103.54 9318 or(not(a14),and(a17,c1)) = a16. [para(8981(a,1),93(a,1,2)),rewrite([32(5),71(5),32(7)]),flip(a)].
% 103.23/103.54 9330 and(or(a14,a),or(A,a16)) = or(c1,and(A,not(a16))). [para(9242(a,1),609(a,1,1)),rewrite([32(5),9305(6)])].
% 103.23/103.54 9337 and(a16,and(a17,c1)) = and(c1,not(s1)). [para(72(a,1),644(a,1,2,2)),rewrite([72(12),31(9)])].
% 103.23/103.54 9367 or(c1,and(a11,s1)) = or(c1,s1). [para(9253(a,1),52(a,1,2))].
% 103.23/103.54 9372 and(a11,and(c1,s1)) = n0. [para(9253(a,1),98(a,1,2)),rewrite([55(5,R),31(4)])].
% 103.23/103.54 9388 or(not(a11),and(c1,s1)) = not(a11). [para(9372(a,1),93(a,1,2)),rewrite([32(4),83(4),32(8)]),flip(a)].
% 103.23/103.54 9396 and(c1,not(s1)) = and(a17,c1). [para(9318(a,1),108(a,1,2)),rewrite([31(5),9337(5)])].
% 103.23/103.54 9402 and(a16,and(a17,c1)) = and(a17,c1). [back_rewrite(9337),rewrite([9396(9)])].
% 103.23/103.54 9403 or(not(a17),not(c1)) = or(s1,not(c1)). [para(9396(a,1),46(a,1,1)),rewrite([46(4),8(10),32(9)])].
% 103.23/103.54 9404 or(s1,and(a17,c1)) = or(c1,s1). [para(9396(a,1),52(a,1,2)),rewrite([32(8)])].
% 103.23/103.54 9422 or(a11,not(a17)) = or(a11,s1). [back_rewrite(7863),rewrite([9403(7),57(7,R),32(6),1947(6),32(3)]),flip(a)].
% 103.23/103.54 9464 and(s1,not(a11)) = and(c1,not(a17)). [para(9422(a,1),109(a,1,2)),rewrite([109(6),31(9),6646(9)])].
% 103.23/103.54 9506 and(a14,and(c1,carryin)) = not(a15). [para(72(a,1),646(a,1,2,2)),rewrite([31(4),72(12),31(9),479(9)])].
% 103.23/103.54 9533 and(or(A,B),or(and(C,carryin),and(D,not(a15)))) = and(carryin,and(or(A,B),or(C,and(D,a14)))). [para(646(a,1),547(a,1,1,2)),rewrite([31(9),8702(10),116(15)])].
% 103.23/103.54 9541 or(not(a14),and(c1,carryin)) = a16. [para(9506(a,1),93(a,1,2)),rewrite([32(5),71(5),32(7)]),flip(a)].
% 103.23/103.54 9542 and(carryin,or(a14,a)) = and(c1,carryin). [para(9506(a,1),106(a,1,2)),rewrite([32(6),187(6),32(4),9231(4)])].
% 103.23/103.54 9554 and(a16,and(c1,carryin)) = and(c1,carryin). [para(9541(a,1),108(a,1,2)),rewrite([31(5)])].
% 103.23/103.54 9588 and(a12,and(a13,c1)) = not(a11). [para(72(a,1),647(a,1,2,2)),rewrite([72(12),31(9),8974(9)])].
% 103.23/103.54 9637 or(not(a12),and(a13,c1)) = a. [para(9588(a,1),93(a,1,2)),rewrite([32(5),289(5),32(7)]),flip(a)].
% 103.23/103.54 9681 and(b,not(c1)) = and(a15,not(a13)). [para(75(a,1),648(a,1,2,2)),rewrite([31(4),9260(5),75(11),31(8)])].
% 103.23/103.54 9726 and(a,and(a13,c1)) = and(a13,c1). [para(9637(a,1),108(a,1,2)),rewrite([31(5)])].
% 103.23/103.54 9848 and(a11,and(a,a17)) = not(a12). [para(74(a,1),650(a,1,2,2)),rewrite([74(12),31(9),4307(9)])].
% 103.23/103.54 9884 or(not(a11),and(a,a17)) = a. [para(9848(a,1),93(a,1,2)),rewrite([289(5),32(7)]),flip(a)].
% 103.23/103.54 9898 and(not(a11),or(not(a),not(a17))) = and(a,not(a17)). [para(9884(a,1),496(a,1,2)),rewrite([46(4),31(7),2468(7),46(10)]),flip(a)].
% 103.23/103.54 9925 and(a,and(a16,b)) = not(a11). [para(71(a,1),651(a,1,2,2)),rewrite([31(4),71(12),31(9),3969(9)])].
% 103.23/103.54 9962 or(not(a),and(a16,b)) = a12. [para(9925(a,1),93(a,1,2)),rewrite([32(5),78(5),32(7)]),flip(a)].
% 103.23/103.54 9967 or(not(a11),or(not(a16),not(b))) = or(a13,not(a16)). [para(9925(a,1),276(a,1,2)),rewrite([46(4),32(8),46(13),7742(15)])].
% 103.23/103.54 9990 or(a16,not(a)) = or(a12,a16). [para(9962(a,1),59(a,1,2)),rewrite([32(3)]),flip(a)].
% 103.23/103.54 9992 and(a12,and(a16,b)) = and(a16,b). [para(9962(a,1),108(a,1,2)),rewrite([31(5)])].
% 103.23/103.54 10093 or(and(A,B),and(C,not(A))) = and(or(A,C),or(B,not(A))). [para(107(a,1),653(a,1,2,2)),rewrite([4592(8),32(5)])].
% 103.23/103.54 10183 or(b,and(a12,not(A))) = and(a12,or(b,not(A))). [back_rewrite(2490),rewrite([10093(6),8411(6)])].
% 103.23/103.54 10850 or(a12,and(a15,not(s1))) = a12. [para(1433(a,1),3708(a,1,2))].
% 103.23/103.54 10860 or(a12,s1) = or(a15,a12). [para(10850(a,1),99(a,1,2)),rewrite([32(3),57(8),32(7),1305(7),32(6)])].
% 103.23/103.54 10882 and(not(a12),not(s1)) = and(not(a15),not(a12)). [para(10860(a,1),47(a,1,1)),rewrite([47(4)]),flip(a)].
% 103.23/103.54 11533 and(a13,c1) = and(a,c1). [para(72(a,1),687(a,1,2,2)),rewrite([9726(5),72(9)])].
% 103.23/103.54 11560 or(not(a12),and(a,c1)) = a. [back_rewrite(9637),rewrite([11533(5)])].
% 103.23/103.54 11570 or(a13,not(c1)) = or(a,not(c1)). [para(11533(a,1),276(a,1,2)),rewrite([276(6)]),flip(a)].
% 103.23/103.54 11921 or(a15,a13) = or(a15,a). [para(11533(a,1),3657(a,1,2)),rewrite([3657(5),32(3),32(6)]),flip(a)].
% 103.23/103.54 12031 and(b,or(a12,a16)) = b. [para(9990(a,1),698(a,1,2,2)),rewrite([120(7),635(3),9990(6)]),flip(a)].
% 103.23/103.54 12040 or(c1,and(a15,not(a13))) = or(b,and(a16,not(a12))). [para(12031(a,1),613(a,1,2)),rewrite([32(6),1593(13),31(13),9330(13),8931(11)]),flip(a)].
% 103.23/103.54 12077 or(a13,not(a16)) = or(a15,a). [para(123(a,1),3662(a,1,2)),rewrite([11921(7)])].
% 103.23/103.54 12085 or(not(a11),or(not(a16),not(b))) = or(a15,a). [back_rewrite(9967),rewrite([12077(12)])].
% 103.23/103.54 12087 and(not(a15),not(a)) = and(a16,not(a13)). [para(12077(a,1),47(a,1,1)),rewrite([47(4),8(10),31(9)])].
% 103.23/103.54 12479 or(not(a15),and(a16,b)) = c1. [para(1701(a,1),708(a,2,2)),rewrite([531(3),31(5),1367(9),32(8),45(9),9296(11)])].
% 103.23/103.54 12590 or(and(a,c1),and(a16,not(a12))) = and(a,a16). [para(11560(a,1),708(a,2,2)),rewrite([31(4),31(9),55(9,R),31(8),2610(8),10882(12),57(14,R),32(13),754(13),122(9),31(7),31(11)])].
% 103.23/103.54 12601 and(b,c1) = and(a16,b). [para(12479(a,1),108(a,1,2)),rewrite([31(5),55(5),31(4),2610(4)])].
% 103.23/103.54 12602 and(a15,and(a16,b)) = not(a11). [para(12479(a,1),109(a,1,2)),rewrite([8(3),1915(3),8(8),31(7)]),flip(a)].
% 103.23/103.54 12619 or(c1,and(a16,b)) = c1. [para(12601(a,1),106(a,1,2))].
% 103.23/103.54 12629 or(a15,and(a16,b)) = or(a15,b). [para(12601(a,1),3657(a,1,2)),rewrite([32(8)])].
% 103.23/103.54 12636 and(a16,or(b,c1)) = c1. [para(12619(a,1),113(a,1,2)),rewrite([2610(3),32(5)]),flip(a)].
% 103.23/103.54 12641 and(or(b,c1),or(A,a16)) = or(c1,and(A,b)). [para(12636(a,1),63(a,1,1)),rewrite([31(5),7276(6),32(9)]),flip(a)].
% 103.23/103.54 12643 and(a16,or(c1,and(A,b))) = c1. [para(12636(a,1),120(a,2)),rewrite([32(6),12641(7)])].
% 103.23/103.54 12658 or(a15,or(not(a16),not(b))) = or(a15,a). [para(12602(a,1),276(a,1,2)),rewrite([46(4),32(8),12085(8),46(8)]),flip(a)].
% 103.23/103.54 12675 or(a12,not(a16)) = or(a15,a12). [para(123(a,1),3672(a,1,2))].
% 103.23/103.54 12796 and(not(a15),not(a12)) = and(a16,not(a12)). [para(12675(a,1),47(a,1,1)),rewrite([47(4),8(10),31(9)])].
% 103.23/103.54 12816 or(and(A,carryin),and(B,not(a15))) = and(carryin,or(A,and(B,a14))). [para(711(a,1),108(a,1,2)),rewrite([31(11),116(11),9533(10),609(8),31(6),55(6,R),9(5),43(7)]),flip(a)].
% 103.23/103.54 12999 or(not(a13),and(a12,c1)) = b. [para(9231(a,1),714(a,2,2)),rewrite([1600(3),31(5),11(9),32(7),104(7),2590(11)])].
% 103.23/103.54 13036 and(a16,b) = and(a12,c1). [para(12999(a,1),108(a,1,2)),rewrite([31(5),55(5,R),31(4),12601(4),9992(5)])].
% 103.23/103.54 13048 or(a15,b) = or(a15,a12). [back_rewrite(12629),rewrite([13036(4),3657(5),32(3)]),flip(a)].
% 103.23/103.54 13069 or(not(a16),not(b)) = or(not(a12),not(c1)). [para(13036(a,1),46(a,1,1)),rewrite([46(4)]),flip(a)].
% 103.23/103.54 13073 or(b,and(a12,c1)) = b. [para(13036(a,1),106(a,1,2))].
% 103.23/103.54 13084 or(a15,not(a12)) = or(a15,a). [back_rewrite(12658),rewrite([13069(6),7730(7)])].
% 103.23/103.54 13105 and(not(a15),not(b)) = and(a16,not(a12)). [para(13048(a,1),47(a,1,1)),rewrite([47(4),12796(5)]),flip(a)].
% 103.23/103.54 13107 and(b,not(a15)) = and(a12,not(a15)). [para(13048(a,1),109(a,1,2)),rewrite([109(6)]),flip(a)].
% 103.23/103.54 13129 and(a12,or(b,c1)) = b. [para(13073(a,1),113(a,1,2)),rewrite([635(3)]),flip(a)].
% 103.23/103.54 13136 and(or(b,c1),or(A,a12)) = or(b,and(A,c1)). [para(13129(a,1),63(a,1,1)),rewrite([31(5),615(6),32(9)]),flip(a)].
% 103.23/103.54 13277 and(a16,not(a13)) = and(a12,not(a15)). [para(13084(a,1),47(a,1,1)),rewrite([47(4),12087(5),8(9),31(8)])].
% 103.23/103.54 13279 and(a16,not(a12)) = and(a,not(a15)). [para(13084(a,1),109(a,1,2)),rewrite([109(6),31(9),12796(9)]),flip(a)].
% 103.23/103.54 13310 and(not(a15),not(b)) = and(a,not(a15)). [back_rewrite(13105),rewrite([13279(9)])].
% 103.23/103.54 13317 and(a,c1) = and(a,a16). [back_rewrite(12590),rewrite([13279(7),111(8),907(5)])].
% 103.23/103.54 13321 or(c1,and(a15,not(a13))) = or(b,and(a,not(a15))). [back_rewrite(12040),rewrite([13279(11)])].
% 103.23/103.54 13705 and(not(a11),or(A,not(a17))) = and(not(a11),or(A,s1)). [para(9422(a,1),741(a,1,2,2)),rewrite([741(7)]),flip(a)].
% 103.23/103.54 13741 and(c1,not(a17)) = and(a,not(a17)). [back_rewrite(9898),rewrite([13705(8),32(6),1011(7),9464(4)])].
% 103.23/103.54 13750 and(s1,not(a11)) = and(a,not(a17)). [back_rewrite(9464),rewrite([13741(8)])].
% 103.23/103.54 13812 or(a,not(c1)) = or(a15,a). [para(11921(a,1),3709(a,2)),rewrite([31(4),126(4),11570(4)])].
% 103.23/103.54 13815 or(a13,not(c1)) = or(a15,a). [back_rewrite(11570),rewrite([13812(8)])].
% 103.23/103.54 13836 and(not(a13),not(c1)) = and(a15,not(a13)). [para(13815(a,1),109(a,1,2)),rewrite([852(6),31(9)]),flip(a)].
% 103.23/103.54 13928 or(and(a,a16),and(c1,carryin)) = c1. [para(1592(a,1),749(a,2,2)),rewrite([31(7),13277(7),32(11),12816(11),31(8),1600(8),1592(8),9542(8),9296(12)])].
% 103.23/103.54 15278 or(carryin,not(a11)) = or(c1,not(a17)). [para(9254(a,1),46(a,1,1)),rewrite([46(5),8(5),32(4),8(9),32(8)])].
% 103.23/103.54 15284 or(c1,and(a11,not(a17))) = or(c1,carryin). [para(9259(a,1),52(a,1,2))].
% 103.23/103.54 15299 and(a16,or(c1,s1)) = or(c1,carryin). [para(9367(a,1),708(a,2,2)),rewrite([31(3),2610(3),31(6),55(6,R),31(5),1368(5),9396(9),4592(9),615(10),31(7),496(7),15284(6)]),flip(a)].
% 103.23/103.54 15343 and(c1,s1) = and(a,not(a17)). [para(9388(a,1),108(a,1,2)),rewrite([31(6),55(6),31(5),422(5),13750(4)]),flip(a)].
% 103.23/103.54 15352 or(c1,and(a,not(a17))) = c1. [para(15343(a,1),34(a,1,2))].
% 103.23/103.54 15365 and(a,or(c1,not(a17))) = and(a,a16). [para(15352(a,1),113(a,1,2)),rewrite([13317(3)]),flip(a)].
% 103.23/103.54 15379 or(c1,not(a17)) = or(c1,carryin). [para(9404(a,1),708(a,2,2)),rewrite([31(3),1368(3),31(7),9402(7),11(9),32(7),104(7),93(6),15299(9)])].
% 103.23/103.54 15384 and(a,or(c1,carryin)) = and(a,a16). [back_rewrite(15365),rewrite([15379(5)])].
% 103.23/103.54 15386 or(carryin,not(a11)) = or(c1,carryin). [back_rewrite(15278),rewrite([15379(8)])].
% 103.23/103.54 15486 or(and(A,a16),and(c1,carryin)) = and(a16,or(A,and(c1,carryin))). [para(9554(a,1),63(a,1,2))].
% 103.23/103.54 15488 and(a16,or(a,and(c1,carryin))) = c1. [back_rewrite(13928),rewrite([15486(7)])].
% 103.23/103.54 15489 or(b,and(a,not(a15))) = or(b,c1). [para(9681(a,1),52(a,1,2)),rewrite([13321(6),32(9)])].
% 103.23/103.54 15494 or(c1,and(a15,not(a13))) = or(b,c1). [back_rewrite(13321),rewrite([15489(12)])].
% 103.23/103.54 15714 and(a13,or(c1,carryin)) = and(a13,or(b,carryin)). [para(15386(a,1),833(a,1,2)),rewrite([32(9)])].
% 103.23/103.54 16127 and(a16,or(c1,not(a13))) = c1. [para(141(a,1),12643(a,1,2,2))].
% 103.23/103.54 16136 and(or(c1,not(a13)),or(A,a16)) = or(c1,and(A,not(a13))). [para(16127(a,1),63(a,1,1)),rewrite([31(6),615(7),32(11)]),flip(a)].
% 103.23/103.54 16141 or(c1,not(a13)) = or(b,c1). [para(16127(a,1),613(a,1,2)),rewrite([13836(5),32(6),15494(6),2614(11),31(9),105(9)]),flip(a)].
% 103.23/103.54 16143 or(c1,and(A,not(a13))) = or(c1,and(A,b)). [back_rewrite(16136),rewrite([16141(4),12641(6)]),flip(a)].
% 103.23/103.54 16145 or(c1,and(a15,b)) = or(b,c1). [back_rewrite(15494),rewrite([16143(6)])].
% 103.23/103.54 16224 and(a12,or(b,not(a15))) = b. [para(13107(a,1),34(a,1,2)),rewrite([10183(6)])].
% 103.23/103.54 16233 and(or(b,not(a15)),or(A,a12)) = or(b,and(A,not(a15))). [para(16224(a,1),63(a,1,1)),rewrite([31(6),615(7),32(11)]),flip(a)].
% 103.23/103.54 16237 or(b,not(a15)) = or(b,c1). [para(16224(a,1),613(a,1,2)),rewrite([13310(5),32(6),15489(6),861(11),31(9),105(9)]),flip(a)].
% 103.23/103.54 16238 or(b,and(A,not(a15))) = or(b,and(A,c1)). [back_rewrite(16233),rewrite([16237(4),13136(6)]),flip(a)].
% 103.23/103.54 16239 or(b,and(a,a16)) = or(b,c1). [back_rewrite(15489),rewrite([16238(6),13317(4)])].
% 103.23/103.54 16832 and(a,or(b,carryin)) = and(a,a16). [para(15384(a,1),687(a,2)),rewrite([15714(6),687(7)])].
% 103.23/103.54 16860 and(c1,or(a,carryin)) = c1. [para(15488(a,1),557(a,1,2)),rewrite([9(3),55(8,R),31(7),2619(8)]),flip(a)].
% 103.23/103.54 17149 or(b,and(a,carryin)) = or(b,c1). [para(16832(a,1),615(a,1,2)),rewrite([16239(5)]),flip(a)].
% 103.23/103.54 17151 -circuit(s1,and(or(a,carryin),or(b,c1))) # answer(prove_circuit). [back_rewrite(7362),rewrite([17149(9)])].
% 103.23/103.54 28604 and(or(a,carryin),or(b,c1)) = c1. [para(16860(a,1),8666(a,2)),rewrite([47(8),31(11),9087(11),8945(9),16143(9),16145(8)])].
% 103.23/103.54 28609 -circuit(s1,c1) # answer(prove_circuit). [back_rewrite(17151),rewrite([28604(8)])].
% 103.23/103.54 28610 $F # answer(prove_circuit). [resolve(28609,a,1,a)].
% 103.23/103.54
% 103.23/103.54 % SZS output end Refutation
% 103.23/103.54 ============================== end of proof ==========================
% 103.23/103.54
% 103.23/103.54 ============================== STATISTICS ============================
% 103.23/103.54
% 103.23/103.54 Given=6518. Generated=4709344. Kept=28580. proofs=1.
% 103.23/103.54 Usable=5878. Sos=9998. Demods=15786. Limbo=5, Disabled=12745. Hints=0.
% 103.23/103.54 Megabytes=20.89.
% 103.23/103.54 User_CPU=99.88, System_CPU=2.67, Wall_clock=103.
% 103.23/103.54
% 103.23/103.54 ============================== end of statistics =====================
% 103.23/103.54
% 103.23/103.54 ============================== end of search =========================
% 103.23/103.54
% 103.23/103.54 THEOREM PROVED
% 103.23/103.54 % SZS status Unsatisfiable
% 103.23/103.54
% 103.23/103.54 Exiting with 1 proof.
% 103.23/103.54
% 103.23/103.54 Process 26662 exit (max_proofs) Thu Jun 16 22:31:02 2022
% 103.23/103.54 Prover9 interrupted
%------------------------------------------------------------------------------