TSTP Solution File: HWV002-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : HWV002-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n012.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 19:10:28 EDT 2022
% Result : Unsatisfiable 136.41s 136.61s
% Output : Refutation 136.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 46
% Syntax : Number of clauses : 1079 (1077 unt; 0 nHn; 748 RR)
% Number of literals : 1082 (1069 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 39 ( 39 usr; 35 con; 0-2 aty)
% Number of variables : 404 ( 40 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(xor_definition1,axiom,
xor(n0,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition1) ).
cnf(xor_definition3,axiom,
xor(X,X) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition3) ).
cnf(xor_simplification1,axiom,
xor(X,xor(X,Y)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_simplification1) ).
cnf(and_definition1,axiom,
and(n0,X) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition1) ).
cnf(and_definition3,axiom,
and(n1,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition3) ).
cnf(and_simplification1,axiom,
and(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_simplification1) ).
cnf(and_simplification2,axiom,
and(X,and(X,Y)) = and(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_simplification2) ).
cnf(and_xor_simplification,axiom,
and(X,xor(Y,Z)) = xor(and(X,Y),and(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_xor_simplification) ).
cnf(not_to_xor,axiom,
not(X) = xor(n1,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_to_xor) ).
cnf(or_to_xor,axiom,
or(X,Y) = xor(and(X,Y),xor(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_to_xor) ).
cnf(xor_commutativity,negated_conjecture,
xor(X,xor(Y,Z)) = xor(Y,xor(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(and_commutativity,negated_conjecture,
and(X,and(Y,Z)) = and(Y,and(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).
cnf(constructor1,negated_conjecture,
o1 = n13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor1) ).
cnf(constructor2,negated_conjecture,
o2 = n17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor2) ).
cnf(constructor3,negated_conjecture,
o3 = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor3) ).
cnf(constructor4,negated_conjecture,
a1 = and(inv1,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor4) ).
cnf(constructor5,negated_conjecture,
n2 = and(inv1,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor5) ).
cnf(constructor6,negated_conjecture,
n3 = or(a1,n24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor6) ).
cnf(constructor7,negated_conjecture,
n4 = or(n15,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor7) ).
cnf(constructor8,negated_conjecture,
n5 = or(n4,n21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor8) ).
cnf(constructor9,negated_conjecture,
n6 = and(i1,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor9) ).
cnf(constructor10,negated_conjecture,
n7 = and(n6,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor10) ).
cnf(constructor11,negated_conjecture,
n8 = or(a1,n10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor11) ).
cnf(constructor12,negated_conjecture,
n9 = or(n8,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor12) ).
cnf(constructor13,negated_conjecture,
n10 = or(n24,n7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor13) ).
cnf(constructor14,negated_conjecture,
n11 = or(a1,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor14) ).
cnf(constructor15,negated_conjecture,
n12 = or(n11,n16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor15) ).
cnf(constructor16,negated_conjecture,
n13 = or(n12,n21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor16) ).
cnf(constructor17,negated_conjecture,
n14 = and(i2,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor17) ).
cnf(constructor18,negated_conjecture,
n15 = and(inv2,n6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor18) ).
cnf(constructor19,negated_conjecture,
n16 = and(n14,inv2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor19) ).
cnf(constructor20,negated_conjecture,
n17 = or(n18,n21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor20) ).
cnf(constructor21,negated_conjecture,
n18 = or(n19,n25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor21) ).
cnf(constructor22,negated_conjecture,
n19 = and(n23,inv2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor22) ).
cnf(constructor23,negated_conjecture,
n20 = or(n22,n14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor23) ).
cnf(constructor24,negated_conjecture,
n21 = and(inv1,inv2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor24) ).
cnf(constructor25,negated_conjecture,
n22 = or(n23,n6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor25) ).
cnf(constructor26,negated_conjecture,
n23 = and(i1,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor26) ).
cnf(constructor27,negated_conjecture,
n24 = and(i1,inv1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor27) ).
cnf(constructor28,negated_conjecture,
n25 = or(n2,n24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor28) ).
cnf(constructor29,negated_conjecture,
inv1 = not(n20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor29) ).
cnf(constructor30,negated_conjecture,
inv2 = not(n9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor30) ).
cnf(output1,negated_conjecture,
circuit(o1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',output1) ).
cnf(44,plain,
circuit(n13),
inference('REWRITE',[status(thm)],[output1,constructor1,theory(equality)]) ).
cnf(output2,negated_conjecture,
circuit(o2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',output2) ).
cnf(46,plain,
circuit(n17),
inference('REWRITE',[status(thm)],[output2,constructor2,theory(equality)]) ).
cnf(output3,negated_conjecture,
circuit(o3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',output3) ).
cnf(48,plain,
circuit(n5),
inference('REWRITE',[status(thm)],[output3,constructor3,theory(equality)]) ).
cnf(prove_inversion,negated_conjecture,
( ~ circuit(not(i1))
| ~ circuit(not(i2))
| ~ circuit(not(i3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inversion) ).
cnf(50,plain,
not(n0) = n1,
inference('PARAMODULATE',[status(thm)],[xor_definition1,not_to_xor,theory(equality)]) ).
cnf(52,plain,
not(not(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[not_to_xor,xor_simplification1,theory(equality)]),not_to_xor,theory(equality)]) ).
cnf(54,plain,
and(n23,n19) = n19,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor22,theory(equality)]) ).
cnf(55,plain,
and(inv2,n19) = n19,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor22,theory(equality)]) ).
cnf(56,plain,
and(inv2,n15) = n15,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor18,theory(equality)]) ).
cnf(57,plain,
and(n6,n15) = n15,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor18,theory(equality)]) ).
cnf(58,plain,
and(n14,n16) = n16,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor19,theory(equality)]) ).
cnf(59,plain,
and(inv2,n16) = n16,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor19,theory(equality)]) ).
cnf(60,plain,
and(inv1,n21) = n21,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor24,theory(equality)]) ).
cnf(61,plain,
and(inv2,n21) = n21,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor24,theory(equality)]) ).
cnf(62,plain,
and(i1,n6) = n6,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor9,theory(equality)]) ).
cnf(63,plain,
and(i2,n6) = n6,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor9,theory(equality)]) ).
cnf(64,plain,
and(i1,n23) = n23,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor26,theory(equality)]) ).
cnf(65,plain,
and(i3,n23) = n23,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor26,theory(equality)]) ).
cnf(66,plain,
and(i1,n24) = n24,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor27,theory(equality)]) ).
cnf(67,plain,
and(inv1,n24) = n24,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor27,theory(equality)]) ).
cnf(68,plain,
and(n6,n7) = n7,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor10,theory(equality)]) ).
cnf(69,plain,
and(i3,n7) = n7,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor10,theory(equality)]) ).
cnf(70,plain,
and(inv1,n2) = n2,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor5,theory(equality)]) ).
cnf(71,plain,
and(i3,n2) = n2,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor5,theory(equality)]) ).
cnf(72,plain,
and(i2,n14) = n14,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor17,theory(equality)]) ).
cnf(73,plain,
and(i3,n14) = n14,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor17,theory(equality)]) ).
cnf(74,plain,
and(inv1,a1) = a1,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor4,theory(equality)]) ).
cnf(75,plain,
and(i2,a1) = a1,
inference('PARAMODULATE',[status(thm)],[and_simplification2,constructor4,theory(equality)]) ).
cnf(76,plain,
or(X,Y) = or(Y,X),
inference('PARAMODULATE',[status(thm)],[or_to_xor,or_to_xor,theory(equality)]) ).
cnf(93,plain,
xor(and(X,Y),or(X,Y)) = xor(X,Y),
inference('PARAMODULATE',[status(thm)],[xor_simplification1,or_to_xor,theory(equality)]) ).
cnf(94,plain,
xor(xor(X,Y),or(X,Y)) = and(X,Y),
inference('PARAMODULATE',[status(thm)],[xor_simplification1,or_to_xor,theory(equality)]) ).
cnf(95,plain,
or(X,xor(X,Y)) = xor(and(X,xor(X,Y)),Y),
inference('PARAMODULATE',[status(thm)],[or_to_xor,xor_simplification1,theory(equality)]) ).
cnf(96,plain,
or(X,and(X,Y)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[or_to_xor,and_simplification2,theory(equality)]),xor_simplification1,theory(equality)]) ).
cnf(97,plain,
or(and(X,Y),X) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[or_to_xor,and_simplification2,theory(equality)]),xor_simplification1,theory(equality)]) ).
cnf(98,plain,
or(and(X,Y),xor(X,Y)) = xor(and(and(X,Y),xor(X,Y)),or(X,Y)),
inference('PARAMODULATE',[status(thm)],[or_to_xor,or_to_xor,theory(equality)]) ).
cnf(99,plain,
not(xor(X,Y)) = xor(X,not(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[not_to_xor,xor_commutativity,theory(equality)]),not_to_xor,theory(equality)]) ).
cnf(103,plain,
xor(X,xor(Y,xor(Z,U))) = xor(xor(Y,U),xor(X,Z)),
inference('PARAMODULATE',[status(thm)],[xor_commutativity,xor_commutativity,theory(equality)]) ).
cnf(104,plain,
xor(X,or(Y,Z)) = xor(xor(X,Z),xor(and(Y,Z),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[xor_commutativity,or_to_xor,theory(equality)]),103,theory(equality)]) ).
cnf(107,plain,
and(X,n19) = and(n23,and(X,inv2)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor22,theory(equality)]) ).
cnf(108,plain,
and(X,n15) = and(n6,and(X,inv2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor18,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(109,plain,
and(X,n16) = and(n14,and(X,inv2)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor19,theory(equality)]) ).
cnf(110,plain,
and(X,n21) = and(inv2,and(inv1,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor24,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(111,plain,
and(X,n6) = and(i2,and(i1,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor9,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(112,plain,
and(X,n23) = and(i3,and(i1,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor26,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(113,plain,
and(X,n24) = and(inv1,and(i1,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor27,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(114,plain,
and(X,n7) = and(n6,and(X,i3)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor10,theory(equality)]) ).
cnf(115,plain,
and(X,n2) = and(inv1,and(X,i3)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor5,theory(equality)]) ).
cnf(116,plain,
and(X,n14) = and(i3,and(i2,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor17,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(117,plain,
and(X,a1) = and(inv1,and(i2,X)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,constructor4,theory(equality)]) ).
cnf(118,plain,
and(X,and(Y,Z)) = and(and(Y,Z),and(X,Y)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,and_simplification2,theory(equality)]) ).
cnf(121,plain,
and(and(X,Y),and(Z,U)) = and(Z,and(X,and(U,Y))),
inference('PARAMODULATE',[status(thm)],[and_commutativity,and_commutativity,theory(equality)]) ).
cnf(127,plain,
and(n14,xor(inv2,X)) = xor(n16,and(X,n14)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,constructor19,theory(equality)]) ).
cnf(130,plain,
and(inv2,xor(inv1,X)) = xor(n21,and(X,inv2)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,constructor24,theory(equality)]) ).
cnf(131,plain,
and(i1,xor(i2,X)) = xor(n6,and(i1,X)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,constructor9,theory(equality)]) ).
cnf(133,plain,
and(i1,xor(i3,X)) = xor(n23,and(i1,X)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,constructor26,theory(equality)]) ).
cnf(135,plain,
and(i1,xor(inv1,X)) = xor(n24,and(i1,X)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,constructor27,theory(equality)]) ).
cnf(138,plain,
and(i3,xor(n6,X)) = xor(n7,and(X,i3)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,constructor10,theory(equality)]) ).
cnf(142,plain,
and(i3,xor(i2,X)) = xor(n14,and(X,i3)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,constructor17,theory(equality)]) ).
cnf(144,plain,
and(i2,xor(inv1,X)) = xor(a1,and(i2,X)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,constructor4,theory(equality)]) ).
cnf(145,plain,
and(X,not(Y)) = xor(X,and(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_xor_simplification,and_definition3,theory(equality)]),not_to_xor,theory(equality)]) ).
cnf(146,plain,
xor(X,or(Y,Z)) = xor(xor(X,Z),and(Y,not(Z))),
inference('REWRITE',[status(thm)],[104,145,theory(equality)]) ).
cnf(147,plain,
and(X,xor(X,Y)) = and(X,not(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_xor_simplification,and_simplification1,theory(equality)]),145,theory(equality)]) ).
cnf(148,plain,
or(X,xor(X,Y)) = xor(and(X,not(Y)),Y),
inference('REWRITE',[status(thm)],[95,147,theory(equality)]) ).
cnf(151,plain,
and(and(X,Y),xor(X,Z)) = and(and(X,Y),not(Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_xor_simplification,and_simplification2,theory(equality)]),145,theory(equality)]) ).
cnf(152,plain,
or(and(X,Y),xor(X,Y)) = xor(and(and(X,Y),not(Y)),or(X,Y)),
inference('REWRITE',[status(thm)],[98,151,theory(equality)]) ).
cnf(163,plain,
and(n19,and(X,inv2)) = and(X,n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,55,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(175,plain,
and(n6,and(X,n15)) = and(X,n15),
inference('PARAMODULATE',[status(thm)],[and_commutativity,57,theory(equality)]) ).
cnf(180,plain,
and(n16,and(X,n14)) = and(X,n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,58,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(190,plain,
and(n21,and(inv1,X)) = and(X,n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,60,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(195,plain,
and(n21,and(X,inv2)) = and(X,n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,61,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(200,plain,
and(n6,and(i1,X)) = and(X,n6),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,62,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(205,plain,
and(n6,and(i2,X)) = and(X,n6),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,63,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(210,plain,
and(n23,and(i1,X)) = and(X,n23),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,64,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(215,plain,
and(n23,and(X,i3)) = and(X,n23),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,65,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(220,plain,
and(n24,and(i1,X)) = and(X,n24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,66,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(235,plain,
and(n7,and(X,i3)) = and(X,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,69,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(240,plain,
and(n2,and(inv1,X)) = and(X,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,70,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(245,plain,
and(n2,and(X,i3)) = and(X,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,71,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(250,plain,
and(n14,and(i2,X)) = and(X,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,72,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(255,plain,
and(n14,and(X,i3)) = and(X,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,73,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(266,plain,
and(i2,and(X,a1)) = and(X,a1),
inference('PARAMODULATE',[status(thm)],[and_commutativity,75,theory(equality)]) ).
cnf(267,plain,
and(i2,xor(a1,X)) = and(i2,xor(inv1,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_xor_simplification,75,theory(equality)]),144,theory(equality)]) ).
cnf(268,plain,
and(i2,xor(a1,X)) = xor(a1,and(i2,X)),
inference('REWRITE',[status(thm)],[144,267,theory(equality)]) ).
cnf(270,plain,
not(inv1) = n20,
inference('PARAMODULATE',[status(thm)],[52,constructor29,theory(equality)]) ).
cnf(271,plain,
not(inv2) = n9,
inference('PARAMODULATE',[status(thm)],[52,constructor30,theory(equality)]) ).
cnf(273,plain,
n20 = or(n14,n22),
inference('PARAMODULATE',[status(thm)],[constructor23,76,theory(equality)]) ).
cnf(277,plain,
n22 = or(n6,n23),
inference('PARAMODULATE',[status(thm)],[constructor25,76,theory(equality)]) ).
cnf(279,plain,
n13 = or(n21,n12),
inference('PARAMODULATE',[status(thm)],[constructor16,76,theory(equality)]) ).
cnf(280,plain,
n17 = or(n21,n18),
inference('PARAMODULATE',[status(thm)],[constructor20,76,theory(equality)]) ).
cnf(283,plain,
n4 = or(n3,n15),
inference('PARAMODULATE',[status(thm)],[constructor7,76,theory(equality)]) ).
cnf(284,plain,
n9 = or(n2,n8),
inference('PARAMODULATE',[status(thm)],[constructor12,76,theory(equality)]) ).
cnf(341,plain,
not(xor(inv1,X)) = xor(X,n20),
inference('PARAMODULATE',[status(thm)],[99,270,theory(equality)]) ).
cnf(343,plain,
or(X,not(Y)) = not(xor(X,or(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[or_to_xor,99,theory(equality)]),146,99,theory(equality)]) ).
cnf(344,plain,
and(n6,n19) = and(n23,n15),
inference('PARAMODULATE',[status(thm)],[107,constructor18,theory(equality)]) ).
cnf(345,plain,
and(n14,n19) = and(n23,n16),
inference('PARAMODULATE',[status(thm)],[107,constructor19,theory(equality)]) ).
cnf(346,plain,
and(inv1,n19) = and(n23,n21),
inference('PARAMODULATE',[status(thm)],[107,constructor24,theory(equality)]) ).
cnf(347,plain,
and(n15,n19) = and(n23,n15),
inference('PARAMODULATE',[status(thm)],[107,56,theory(equality)]) ).
cnf(348,plain,
and(n6,n19) = and(n15,n19),
inference('REWRITE',[status(thm)],[344,347,theory(equality)]) ).
cnf(349,plain,
and(n16,n19) = and(n14,n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[107,59,theory(equality)]),345,theory(equality)]) ).
cnf(350,plain,
and(n21,n19) = and(inv1,n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[107,61,theory(equality)]),346,theory(equality)]) ).
cnf(383,plain,
and(n21,and(X,n19)) = and(X,and(inv1,n19)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,350,theory(equality)]) ).
cnf(389,plain,
and(n14,n15) = and(n6,n16),
inference('PARAMODULATE',[status(thm)],[108,constructor19,theory(equality)]) ).
cnf(390,plain,
and(inv1,n15) = and(n6,n21),
inference('PARAMODULATE',[status(thm)],[108,constructor24,theory(equality)]) ).
cnf(391,plain,
and(n16,n15) = and(n14,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[108,59,theory(equality)]),389,theory(equality)]) ).
cnf(392,plain,
and(n21,n15) = and(inv1,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[108,61,theory(equality)]),390,theory(equality)]) ).
cnf(422,plain,
and(inv1,n16) = and(n14,n21),
inference('PARAMODULATE',[status(thm)],[109,constructor24,theory(equality)]) ).
cnf(423,plain,
and(n21,n16) = and(inv1,n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[109,61,theory(equality)]),422,theory(equality)]) ).
cnf(425,plain,
or(n14,and(X,n16)) = n14,
inference('PARAMODULATE',[status(thm)],[96,109,theory(equality)]) ).
cnf(427,plain,
and(and(X,inv2),and(Y,n14)) = and(X,and(Y,n16)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,109,theory(equality)]),121,theory(equality)]) ).
cnf(436,plain,
and(n21,and(X,n16)) = and(X,and(inv1,n16)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,423,theory(equality)]) ).
cnf(441,plain,
and(i2,n21) = and(inv2,a1),
inference('PARAMODULATE',[status(thm)],[110,constructor4,theory(equality)]) ).
cnf(442,plain,
and(i3,n21) = and(inv2,n2),
inference('PARAMODULATE',[status(thm)],[110,constructor5,theory(equality)]) ).
cnf(443,plain,
and(i1,n21) = and(inv2,n24),
inference('PARAMODULATE',[status(thm)],[110,constructor27,theory(equality)]) ).
cnf(444,plain,
and(n24,n21) = and(i1,n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,67,theory(equality)]),443,theory(equality)]) ).
cnf(445,plain,
and(n2,n21) = and(inv2,n2),
inference('PARAMODULATE',[status(thm)],[110,70,theory(equality)]) ).
cnf(446,plain,
and(a1,n21) = and(inv2,a1),
inference('PARAMODULATE',[status(thm)],[110,74,theory(equality)]) ).
cnf(448,plain,
or(inv2,and(X,n21)) = inv2,
inference('PARAMODULATE',[status(thm)],[96,110,theory(equality)]) ).
cnf(450,plain,
and(and(inv1,X),and(Y,inv2)) = and(Y,and(X,n21)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,110,theory(equality)]) ).
cnf(456,plain,
or(n21,and(inv2,a1)) = n21,
inference('PARAMODULATE',[status(thm)],[96,441,theory(equality)]) ).
cnf(463,plain,
or(i3,and(inv2,n2)) = i3,
inference('PARAMODULATE',[status(thm)],[96,442,theory(equality)]) ).
cnf(465,plain,
or(n21,and(inv2,n2)) = n21,
inference('PARAMODULATE',[status(thm)],[96,442,theory(equality)]) ).
cnf(468,plain,
and(n21,and(X,i3)) = and(X,and(inv2,n2)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,442,theory(equality)]) ).
cnf(471,plain,
or(n24,and(i1,n21)) = n24,
inference('PARAMODULATE',[status(thm)],[96,443,theory(equality)]) ).
cnf(472,plain,
and(n24,n15) = and(inv1,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[108,443,theory(equality)]),390,200,theory(equality)]) ).
cnf(488,plain,
and(n21,and(X,a1)) = and(X,and(inv2,a1)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,446,theory(equality)]) ).
cnf(499,plain,
or(n24,and(inv1,n15)) = n24,
inference('PARAMODULATE',[status(thm)],[96,472,theory(equality)]) ).
cnf(501,plain,
and(n24,and(X,n15)) = and(X,and(inv1,n15)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,472,theory(equality)]) ).
cnf(510,plain,
n7 = and(i2,n23),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[111,constructor26,theory(equality)]),constructor10,theory(equality)]) ).
cnf(511,plain,
and(inv1,n6) = and(i2,n24),
inference('PARAMODULATE',[status(thm)],[111,constructor27,theory(equality)]) ).
cnf(512,plain,
and(n23,n6) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[111,64,theory(equality)]),510,theory(equality)]) ).
cnf(513,plain,
and(n24,n6) = and(i2,n24),
inference('PARAMODULATE',[status(thm)],[111,66,theory(equality)]) ).
cnf(515,plain,
or(i2,and(X,n6)) = i2,
inference('PARAMODULATE',[status(thm)],[96,111,theory(equality)]) ).
cnf(516,plain,
and(and(i1,X),and(Y,i2)) = and(Y,and(X,n6)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,111,theory(equality)]) ).
cnf(521,plain,
and(i2,n7) = n7,
inference('PARAMODULATE',[status(thm)],[and_simplification2,510,theory(equality)]) ).
cnf(524,plain,
and(n23,n7) = n7,
inference('PARAMODULATE',[status(thm)],[and_simplification2,510,theory(equality)]) ).
cnf(526,plain,
and(n23,and(i2,X)) = and(X,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,510,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(528,plain,
and(n23,xor(i2,X)) = xor(n7,and(X,n23)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,510,theory(equality)]) ).
cnf(529,plain,
n22 = xor(n7,xor(n23,n6)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[or_to_xor,512,theory(equality)]),constructor25,theory(equality)]) ).
cnf(531,plain,
and(n6,and(X,n23)) = and(X,n7),
inference('PARAMODULATE',[status(thm)],[and_commutativity,512,theory(equality)]) ).
cnf(539,plain,
and(n7,xor(n23,X)) = and(n7,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_xor_simplification,524,theory(equality)]),145,theory(equality)]) ).
cnf(545,plain,
and(n24,a1) = and(i2,n24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_simplification2,511,theory(equality)]),117,theory(equality)]) ).
cnf(546,plain,
and(inv1,n6) = and(n24,a1),
inference('REWRITE',[status(thm)],[511,545,theory(equality)]) ).
cnf(547,plain,
and(n24,n6) = and(n24,a1),
inference('REWRITE',[status(thm)],[513,545,theory(equality)]) ).
cnf(553,plain,
and(n6,and(n24,a1)) = and(n24,a1),
inference('PARAMODULATE',[status(thm)],[and_simplification2,546,theory(equality)]) ).
cnf(556,plain,
and(n6,and(inv1,X)) = and(X,and(n24,a1)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,546,theory(equality)]) ).
cnf(561,plain,
and(n6,and(X,n24)) = and(X,and(n24,a1)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,547,theory(equality)]) ).
cnf(562,plain,
and(n6,a1) = and(n24,a1),
inference('REWRITE',[status(thm)],[553,74,556,561,theory(equality)]) ).
cnf(578,plain,
and(n6,and(X,a1)) = and(X,and(n24,a1)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,562,theory(equality)]) ).
cnf(583,plain,
and(inv1,n23) = and(i3,n24),
inference('PARAMODULATE',[status(thm)],[112,constructor27,theory(equality)]) ).
cnf(586,plain,
or(i3,and(X,n23)) = i3,
inference('PARAMODULATE',[status(thm)],[96,112,theory(equality)]) ).
cnf(587,plain,
and(and(i1,X),and(Y,i3)) = and(Y,and(X,n23)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,112,theory(equality)]) ).
cnf(591,plain,
or(n24,and(inv1,n23)) = n24,
inference('PARAMODULATE',[status(thm)],[96,583,theory(equality)]) ).
cnf(607,plain,
and(and(i1,X),n21) = and(n24,and(X,inv2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,113,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(609,plain,
and(and(i1,X),and(Y,inv1)) = and(Y,and(X,n24)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,113,theory(equality)]) ).
cnf(619,plain,
and(i3,n15) = and(inv2,n7),
inference('PARAMODULATE',[status(thm)],[108,114,theory(equality)]) ).
cnf(620,plain,
and(inv1,n7) = and(n6,n2),
inference('PARAMODULATE',[status(thm)],[114,constructor5,theory(equality)]) ).
cnf(621,plain,
n7 = and(n6,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[114,constructor17,theory(equality)]),521,theory(equality)]) ).
cnf(623,plain,
and(n2,n7) = and(n6,n2),
inference('PARAMODULATE',[status(thm)],[114,71,theory(equality)]) ).
cnf(624,plain,
and(n14,n7) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[114,73,theory(equality)]),621,theory(equality)]) ).
cnf(626,plain,
or(n6,and(X,n7)) = n6,
inference('PARAMODULATE',[status(thm)],[96,114,theory(equality)]) ).
cnf(629,plain,
and(n21,n7) = and(n2,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[114,442,theory(equality)]),108,theory(equality)]) ).
cnf(630,plain,
and(n24,n7) = and(n6,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[114,583,theory(equality)]),620,531,theory(equality)]) ).
cnf(653,plain,
and(n15,n7) = and(i3,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_simplification2,619,theory(equality)]),235,theory(equality)]) ).
cnf(654,plain,
and(n7,n16) = and(n14,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[109,619,theory(equality)]),255,theory(equality)]) ).
cnf(714,plain,
and(inv1,n23) = and(i1,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,115,theory(equality)]),583,theory(equality)]) ).
cnf(715,plain,
and(i1,n2) = and(i3,n24),
inference('REWRITE',[status(thm)],[583,714,theory(equality)]) ).
cnf(718,plain,
or(n24,and(i1,n2)) = n24,
inference('REWRITE',[status(thm)],[591,714,theory(equality)]) ).
cnf(724,plain,
and(n2,i2) = and(inv1,n14),
inference('PARAMODULATE',[status(thm)],[115,constructor17,theory(equality)]) ).
cnf(726,plain,
and(n23,n2) = and(i1,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[115,65,theory(equality)]),714,theory(equality)]) ).
cnf(727,plain,
and(n14,n2) = and(inv1,n14),
inference('PARAMODULATE',[status(thm)],[115,73,theory(equality)]) ).
cnf(731,plain,
and(and(X,i3),and(Y,inv1)) = and(Y,and(X,n2)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,115,theory(equality)]) ).
cnf(732,plain,
and(and(X,i3),and(Y,inv1)) = and(X,and(Y,n2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,115,theory(equality)]),121,theory(equality)]) ).
cnf(736,plain,
or(n23,and(i1,n2)) = n23,
inference('PARAMODULATE',[status(thm)],[96,714,theory(equality)]) ).
cnf(737,plain,
or(i3,and(i1,n2)) = i3,
inference('PARAMODULATE',[status(thm)],[586,714,theory(equality)]) ).
cnf(739,plain,
and(n24,n2) = and(i1,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_simplification2,714,theory(equality)]),113,theory(equality)]) ).
cnf(746,plain,
or(n2,and(inv1,n14)) = n2,
inference('PARAMODULATE',[status(thm)],[96,724,theory(equality)]) ).
cnf(766,plain,
n7 = and(i1,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[112,116,theory(equality)]),510,theory(equality)]) ).
cnf(767,plain,
and(inv1,n14) = and(i3,a1),
inference('PARAMODULATE',[status(thm)],[116,constructor4,theory(equality)]) ).
cnf(768,plain,
and(n2,i2) = and(i3,a1),
inference('REWRITE',[status(thm)],[724,767,theory(equality)]) ).
cnf(770,plain,
and(n14,n2) = and(i3,a1),
inference('REWRITE',[status(thm)],[727,767,theory(equality)]) ).
cnf(772,plain,
or(n2,and(i3,a1)) = n2,
inference('REWRITE',[status(thm)],[746,767,theory(equality)]) ).
cnf(780,plain,
and(a1,n14) = and(i3,a1),
inference('PARAMODULATE',[status(thm)],[116,75,theory(equality)]) ).
cnf(783,plain,
and(n23,n14) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[116,510,theory(equality)]),69,theory(equality)]) ).
cnf(786,plain,
and(n24,n14) = and(a1,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[116,545,theory(equality)]),114,578,theory(equality)]) ).
cnf(787,plain,
and(and(i2,X),and(Y,i3)) = and(Y,and(X,n14)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,116,theory(equality)]) ).
cnf(790,plain,
and(n24,n14) = and(n6,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,766,theory(equality)]),620,theory(equality)]) ).
cnf(791,plain,
and(inv1,n7) = and(n24,n14),
inference('REWRITE',[status(thm)],[620,790,theory(equality)]) ).
cnf(792,plain,
and(n2,n7) = and(n24,n14),
inference('REWRITE',[status(thm)],[623,790,theory(equality)]) ).
cnf(793,plain,
and(n24,n7) = and(n24,n14),
inference('REWRITE',[status(thm)],[630,790,theory(equality)]) ).
cnf(813,plain,
and(n23,and(X,n14)) = and(X,n7),
inference('PARAMODULATE',[status(thm)],[and_commutativity,783,theory(equality)]) ).
cnf(820,plain,
and(inv1,n16) = and(inv2,and(i3,a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,767,theory(equality)]),422,theory(equality)]) ).
cnf(825,plain,
and(a1,n2) = and(i3,a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_simplification2,768,theory(equality)]),245,theory(equality)]) ).
cnf(831,plain,
or(n6,and(n24,n14)) = n6,
inference('PARAMODULATE',[status(thm)],[626,791,theory(equality)]) ).
cnf(852,plain,
and(n2,and(X,a1)) = and(X,and(i3,a1)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,825,theory(equality)]) ).
cnf(857,plain,
and(n24,a1) = and(i1,a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,117,theory(equality)]),545,theory(equality)]) ).
cnf(858,plain,
and(i1,a1) = and(i2,n24),
inference('REWRITE',[status(thm)],[545,857,theory(equality)]) ).
cnf(859,plain,
and(inv1,n6) = and(i1,a1),
inference('REWRITE',[status(thm)],[546,857,theory(equality)]) ).
cnf(860,plain,
and(n24,n6) = and(i1,a1),
inference('REWRITE',[status(thm)],[547,857,theory(equality)]) ).
cnf(864,plain,
and(n6,and(inv1,X)) = and(X,and(i1,a1)),
inference('REWRITE',[status(thm)],[556,857,theory(equality)]) ).
cnf(867,plain,
and(n6,a1) = and(i1,a1),
inference('REWRITE',[status(thm)],[562,857,theory(equality)]) ).
cnf(874,plain,
and(n6,and(X,a1)) = and(X,and(i1,a1)),
inference('REWRITE',[status(thm)],[578,857,theory(equality)]) ).
cnf(878,plain,
and(n23,a1) = and(n24,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[117,510,theory(equality)]),791,theory(equality)]) ).
cnf(879,plain,
and(n23,a1) = and(a1,n7),
inference('REWRITE',[status(thm)],[786,878,theory(equality)]) ).
cnf(880,plain,
and(n23,a1) = and(n6,n2),
inference('REWRITE',[status(thm)],[790,878,theory(equality)]) ).
cnf(881,plain,
and(inv1,n7) = and(n23,a1),
inference('REWRITE',[status(thm)],[791,878,theory(equality)]) ).
cnf(882,plain,
and(n2,n7) = and(n23,a1),
inference('REWRITE',[status(thm)],[792,878,theory(equality)]) ).
cnf(883,plain,
and(n24,n7) = and(n23,a1),
inference('REWRITE',[status(thm)],[793,878,theory(equality)]) ).
cnf(894,plain,
or(n6,and(n23,a1)) = n6,
inference('REWRITE',[status(thm)],[831,878,theory(equality)]) ).
cnf(906,plain,
and(n21,and(i2,X)) = and(inv2,and(X,a1)),
inference('PARAMODULATE',[status(thm)],[110,117,theory(equality)]) ).
cnf(912,plain,
or(n24,and(i1,a1)) = n24,
inference('PARAMODULATE',[status(thm)],[96,857,theory(equality)]) ).
cnf(914,plain,
and(n24,and(X,a1)) = and(X,and(i1,a1)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,857,theory(equality)]) ).
cnf(918,plain,
and(inv1,n15) = and(inv2,and(i1,a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,859,theory(equality)]),390,theory(equality)]) ).
cnf(923,plain,
or(n24,and(n23,a1)) = n24,
inference('PARAMODULATE',[status(thm)],[96,878,theory(equality)]) ).
cnf(930,plain,
xor(n7,n22) = xor(n23,n6),
inference('PARAMODULATE',[status(thm)],[xor_simplification1,529,theory(equality)]) ).
cnf(931,plain,
xor(n6,xor(n23,n22)) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[xor_simplification1,529,theory(equality)]),xor_commutativity,theory(equality)]) ).
cnf(953,plain,
and(n23,n9) = xor(n23,n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor22,theory(equality)]),271,theory(equality)]) ).
cnf(955,plain,
and(inv2,not(n23)) = xor(n19,inv2),
inference('PARAMODULATE',[status(thm)],[145,constructor22,theory(equality)]) ).
cnf(963,plain,
and(n23,not(n19)) = and(n23,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,54,theory(equality)]),953,theory(equality)]) ).
cnf(968,plain,
and(n23,not(i1)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,64,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(970,plain,
and(n23,not(i3)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,65,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(972,plain,
and(inv2,not(n19)) = and(inv2,not(n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,55,theory(equality)]),955,theory(equality)]) ).
cnf(973,plain,
and(inv2,not(n19)) = xor(n19,inv2),
inference('REWRITE',[status(thm)],[955,972,theory(equality)]) ).
cnf(979,plain,
and(n19,n9) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,55,theory(equality)]),xor_definition3,271,theory(equality)]) ).
cnf(980,plain,
and(inv2,not(n6)) = xor(n15,inv2),
inference('PARAMODULATE',[status(thm)],[145,constructor18,theory(equality)]) ).
cnf(987,plain,
and(n6,n9) = xor(n6,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor18,theory(equality)]),271,theory(equality)]) ).
cnf(989,plain,
and(n14,n9) = xor(n16,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor19,theory(equality)]),271,theory(equality)]) ).
cnf(993,plain,
and(inv1,n9) = xor(n21,inv1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor24,theory(equality)]),271,theory(equality)]) ).
cnf(997,plain,
and(inv2,not(n15)) = and(inv2,not(n6)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,56,theory(equality)]),980,theory(equality)]) ).
cnf(998,plain,
and(inv2,not(n15)) = xor(n15,inv2),
inference('REWRITE',[status(thm)],[980,997,theory(equality)]) ).
cnf(1004,plain,
and(n15,n9) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,56,theory(equality)]),xor_definition3,271,theory(equality)]) ).
cnf(1006,plain,
and(n16,n9) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,59,theory(equality)]),xor_definition3,271,theory(equality)]) ).
cnf(1009,plain,
and(n21,n9) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,61,theory(equality)]),xor_definition3,271,theory(equality)]) ).
cnf(1011,plain,
and(n14,not(n16)) = and(n14,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,58,theory(equality)]),989,theory(equality)]) ).
cnf(1016,plain,
and(n14,not(i2)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,72,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(1018,plain,
and(n14,not(i3)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,73,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(1020,plain,
and(n6,not(n7)) = xor(n7,n6),
inference('PARAMODULATE',[status(thm)],[145,68,theory(equality)]) ).
cnf(1022,plain,
and(n7,not(n6)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,68,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(1024,plain,
and(i3,not(n7)) = xor(n7,i3),
inference('PARAMODULATE',[status(thm)],[145,69,theory(equality)]) ).
cnf(1036,plain,
and(i1,n20) = xor(n24,i1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor27,theory(equality)]),270,theory(equality)]) ).
cnf(1039,plain,
and(inv1,not(i1)) = xor(inv1,n24),
inference('PARAMODULATE',[status(thm)],[145,constructor27,theory(equality)]) ).
cnf(1042,plain,
and(i1,not(n24)) = and(i1,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,66,theory(equality)]),1036,theory(equality)]) ).
cnf(1043,plain,
and(n24,not(i1)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,66,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(1044,plain,
and(n6,not(i3)) = and(n6,not(n7)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor10,theory(equality)]),1020,theory(equality)]) ).
cnf(1045,plain,
and(n6,not(i3)) = xor(n7,n6),
inference('REWRITE',[status(thm)],[1020,1044,theory(equality)]) ).
cnf(1046,plain,
and(i3,not(n6)) = and(i3,not(n7)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor10,theory(equality)]),1024,theory(equality)]) ).
cnf(1049,plain,
and(n6,not(n15)) = and(n6,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,57,theory(equality)]),987,theory(equality)]) ).
cnf(1052,plain,
and(n6,not(i2)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,63,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(1054,plain,
and(inv1,not(n21)) = and(inv1,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,60,theory(equality)]),993,theory(equality)]) ).
cnf(1055,plain,
and(n21,n20) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,60,theory(equality)]),xor_definition3,270,theory(equality)]) ).
cnf(1056,plain,
and(inv1,not(n24)) = and(inv1,not(i1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,67,theory(equality)]),1039,theory(equality)]) ).
cnf(1057,plain,
and(n24,n20) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,67,theory(equality)]),xor_definition3,270,theory(equality)]) ).
cnf(1059,plain,
and(inv1,not(i3)) = xor(n2,inv1),
inference('PARAMODULATE',[status(thm)],[145,constructor5,theory(equality)]) ).
cnf(1060,plain,
and(i3,n20) = xor(n2,i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor5,theory(equality)]),270,theory(equality)]) ).
cnf(1067,plain,
and(i3,not(n2)) = and(i3,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,71,theory(equality)]),1060,theory(equality)]) ).
cnf(1068,plain,
and(n2,not(i3)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,71,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(1070,plain,
and(inv1,not(n2)) = and(inv1,not(i3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,70,theory(equality)]),1059,theory(equality)]) ).
cnf(1071,plain,
and(n2,n20) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,70,theory(equality)]),xor_definition3,270,theory(equality)]) ).
cnf(1072,plain,
and(inv1,not(i2)) = xor(inv1,a1),
inference('PARAMODULATE',[status(thm)],[145,constructor4,theory(equality)]) ).
cnf(1073,plain,
and(i2,n20) = xor(a1,i2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,constructor4,theory(equality)]),270,theory(equality)]) ).
cnf(1082,plain,
and(a1,not(i2)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,75,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(1083,plain,
and(inv1,not(a1)) = and(inv1,not(i2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,74,theory(equality)]),1072,theory(equality)]) ).
cnf(1084,plain,
and(inv1,not(a1)) = xor(inv1,a1),
inference('REWRITE',[status(thm)],[1072,1083,theory(equality)]) ).
cnf(1085,plain,
and(a1,n20) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,74,theory(equality)]),xor_definition3,270,theory(equality)]) ).
cnf(1086,plain,
and(X,not(X)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,and_simplification1,theory(equality)]),xor_definition3,theory(equality)]) ).
cnf(1088,plain,
and(n23,not(i2)) = xor(n7,n23),
inference('PARAMODULATE',[status(thm)],[145,510,theory(equality)]) ).
cnf(1090,plain,
and(n23,not(n6)) = and(n23,not(i2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,512,theory(equality)]),1088,theory(equality)]) ).
cnf(1093,plain,
and(n14,not(n6)) = xor(n14,n7),
inference('PARAMODULATE',[status(thm)],[145,621,theory(equality)]) ).
cnf(1094,plain,
and(n14,not(n7)) = and(n14,not(n6)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,624,theory(equality)]),1093,theory(equality)]) ).
cnf(1097,plain,
and(n14,not(i1)) = and(n14,not(n6)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,766,theory(equality)]),1093,theory(equality)]) ).
cnf(1099,plain,
and(n14,not(n7)) = and(n14,not(i1)),
inference('REWRITE',[status(thm)],[1094,1097,theory(equality)]) ).
cnf(1102,plain,
and(n23,not(n7)) = and(n23,not(i2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,524,theory(equality)]),1088,theory(equality)]) ).
cnf(1111,plain,
and(n16,not(n23)) = and(not(n19),n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,345,theory(equality)]),109,973,127,theory(equality)]) ).
cnf(1117,plain,
and(n23,not(n2)) = and(n20,n23),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,726,theory(equality)]),112,and_commutativity,1060,133,theory(equality)]) ).
cnf(1121,plain,
and(n19,not(n16)) = and(n19,not(n14)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,349,theory(equality)]),145,theory(equality)]) ).
cnf(1127,plain,
and(n14,not(n2)) = and(n20,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,770,theory(equality)]),116,1073,142,theory(equality)]) ).
cnf(1130,plain,
and(n14,not(a1)) = and(n20,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,780,theory(equality)]),116,1073,142,theory(equality)]) ).
cnf(1132,plain,
and(n16,not(n6)) = and(not(n15),n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,389,theory(equality)]),109,998,127,theory(equality)]) ).
cnf(1133,plain,
and(n15,not(n16)) = and(n15,not(n14)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,391,theory(equality)]),145,theory(equality)]) ).
cnf(1138,plain,
and(n7,not(n2)) = and(n20,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,882,theory(equality)]),526,1073,528,theory(equality)]) ).
cnf(1142,plain,
and(n24,not(n6)) = and(not(a1),n24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,860,theory(equality)]),113,and_commutativity,1084,135,theory(equality)]) ).
cnf(1143,plain,
and(n6,not(n24)) = and(n20,n6),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,860,theory(equality)]),111,and_commutativity,1073,131,theory(equality)]) ).
cnf(1144,plain,
and(n15,not(n21)) = and(n15,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,392,theory(equality)]),270,145,theory(equality)]) ).
cnf(1146,plain,
and(n21,not(i2)) = and(not(a1),n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,441,theory(equality)]),110,1084,130,theory(equality)]) ).
cnf(1147,plain,
and(i3,not(n21)) = xor(i3,and(inv2,n2)),
inference('PARAMODULATE',[status(thm)],[145,442,theory(equality)]) ).
cnf(1148,plain,
and(n24,not(n21)) = and(n9,n24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,444,theory(equality)]),113,and_commutativity,993,135,theory(equality)]) ).
cnf(1150,plain,
and(n2,not(n21)) = and(n2,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,445,theory(equality)]),271,145,theory(equality)]) ).
cnf(1151,plain,
and(n21,not(n2)) = and(not(i3),n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,445,theory(equality)]),110,1059,130,theory(equality)]) ).
cnf(1152,plain,
and(a1,not(n21)) = and(a1,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,446,theory(equality)]),271,145,theory(equality)]) ).
cnf(1153,plain,
and(a1,not(n24)) = and(a1,not(i1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,857,theory(equality)]),145,theory(equality)]) ).
cnf(1154,plain,
and(i3,not(n24)) = xor(i3,and(i1,n2)),
inference('PARAMODULATE',[status(thm)],[145,715,theory(equality)]) ).
cnf(1156,plain,
and(i2,not(n2)) = xor(i2,and(i3,a1)),
inference('PARAMODULATE',[status(thm)],[145,768,theory(equality)]) ).
cnf(1161,plain,
and(n24,not(n14)) = xor(n24,and(n23,a1)),
inference('PARAMODULATE',[status(thm)],[145,878,theory(equality)]) ).
cnf(1168,plain,
and(n7,not(n15)) = and(n9,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,653,theory(equality)]),114,and_commutativity,987,138,theory(equality)]) ).
cnf(1169,plain,
and(n24,not(n7)) = and(n24,not(n14)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,883,theory(equality)]),1161,theory(equality)]) ).
cnf(1170,plain,
and(n7,not(n24)) = and(n20,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,883,theory(equality)]),526,1073,528,theory(equality)]) ).
cnf(1171,plain,
and(n6,not(a1)) = and(n20,n6),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,867,theory(equality)]),111,and_commutativity,1073,131,theory(equality)]) ).
cnf(1173,plain,
and(n6,not(n2)) = xor(n6,and(n23,a1)),
inference('PARAMODULATE',[status(thm)],[145,880,theory(equality)]) ).
cnf(1178,plain,
and(n24,not(n2)) = and(not(i3),n24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,739,theory(equality)]),113,and_commutativity,1059,135,theory(equality)]) ).
cnf(1179,plain,
and(n2,not(n24)) = and(n2,not(i1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,739,theory(equality)]),145,theory(equality)]) ).
cnf(1180,plain,
and(i2,not(n24)) = xor(i2,and(i1,a1)),
inference('PARAMODULATE',[status(thm)],[145,858,theory(equality)]) ).
cnf(1182,plain,
and(a1,not(n2)) = and(a1,not(i3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,825,theory(equality)]),145,theory(equality)]) ).
cnf(1184,plain,
and(inv2,not(and(inv1,X))) = xor(inv2,and(X,n21)),
inference('PARAMODULATE',[status(thm)],[145,110,theory(equality)]) ).
cnf(1186,plain,
and(a1,not(n7)) = and(a1,not(n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,879,theory(equality)]),145,theory(equality)]) ).
cnf(1192,plain,
and(i2,not(and(i1,X))) = xor(i2,and(X,n6)),
inference('PARAMODULATE',[status(thm)],[145,111,theory(equality)]) ).
cnf(1196,plain,
and(X,not(and(X,Y))) = and(X,not(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,and_simplification2,theory(equality)]),145,theory(equality)]) ).
cnf(1199,plain,
and(and(X,Y),not(X)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,and_simplification2,theory(equality)]),and_definition1,xor_definition3,and_xor_simplification,theory(equality)]) ).
cnf(1200,plain,
or(and(X,Y),xor(X,Y)) = or(X,Y),
inference('REWRITE',[status(thm)],[152,xor_definition1,1199,theory(equality)]) ).
cnf(1201,plain,
xor(X,and(Y,not(Z))) = xor(and(Y,Z),xor(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[xor_commutativity,145,theory(equality)]),xor_commutativity,theory(equality)]) ).
cnf(1202,plain,
or(X,Y) = or(Y,xor(X,Y)),
inference('REWRITE',[status(thm)],[or_to_xor,148,1201,theory(equality)]) ).
cnf(1203,plain,
or(X,Y) = xor(and(Y,not(X)),X),
inference('REWRITE',[status(thm)],[148,1202,theory(equality)]) ).
cnf(1225,plain,
not(or(X,Y)) = and(not(X),not(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[99,145,theory(equality)]),1203,theory(equality)]) ).
cnf(1228,plain,
or(xor(X,Y),X) = or(X,Y),
inference('PARAMODULATE',[status(thm)],[1202,xor_simplification1,theory(equality)]) ).
cnf(1253,plain,
and(n9,not(n19)) = n9,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,979,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1254,plain,
and(n9,and(X,n19)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,979,theory(equality)]),and_definition1,and_commutativity,theory(equality)]) ).
cnf(1257,plain,
and(n9,not(n15)) = n9,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1004,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1262,plain,
and(n9,and(X,n16)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1006,theory(equality)]),and_definition1,and_commutativity,theory(equality)]) ).
cnf(1265,plain,
and(n9,not(n21)) = n9,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1009,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1266,plain,
and(n9,and(X,n21)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1009,theory(equality)]),and_definition1,and_commutativity,theory(equality)]) ).
cnf(1269,plain,
and(n20,not(n21)) = n20,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1055,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1274,plain,
and(n20,not(n24)) = n20,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1057,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1279,plain,
and(n20,not(n2)) = n20,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1071,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1283,plain,
and(n20,not(a1)) = n20,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1085,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1298,plain,
and(not(i1),not(n23)) = not(i1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,968,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1302,plain,
and(not(i3),not(n23)) = not(i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,970,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1320,plain,
and(not(i2),not(n14)) = not(i2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1016,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1324,plain,
and(not(i3),not(n14)) = not(i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1018,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1328,plain,
and(not(n6),not(n7)) = not(n6),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1022,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1329,plain,
and(not(n6),and(X,n7)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1022,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(1343,plain,
and(not(i1),not(n24)) = not(i1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1043,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1351,plain,
and(not(i2),not(n6)) = not(i2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1052,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1358,plain,
and(not(i3),not(n2)) = not(i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1068,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1362,plain,
and(i2,not(and(inv1,not(a1)))) = i2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[xor_simplification1,1073,theory(equality)]),1084,341,268,theory(equality)]) ).
cnf(1365,plain,
and(not(i2),not(a1)) = not(i2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1082,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1366,plain,
and(not(i2),and(X,a1)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1082,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(1372,plain,
and(not(X),xor(X,Y)) = and(Y,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_xor_simplification,1086,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1391,plain,
and(not(n19),and(n9,X)) = and(n9,X),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1253,theory(equality)]) ).
cnf(1397,plain,
and(not(n15),and(n9,X)) = and(n9,X),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1257,theory(equality)]) ).
cnf(1407,plain,
and(not(n21),and(n9,X)) = and(n9,X),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1265,theory(equality)]) ).
cnf(1412,plain,
and(not(n21),and(X,n20)) = and(X,n20),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1269,theory(equality)]) ).
cnf(1418,plain,
and(not(n24),and(X,n20)) = and(X,n20),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1274,theory(equality)]) ).
cnf(1423,plain,
and(not(n2),and(X,n20)) = and(X,n20),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1279,theory(equality)]) ).
cnf(1428,plain,
and(not(a1),and(X,n20)) = and(X,n20),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1283,theory(equality)]) ).
cnf(1475,plain,
and(not(n15),and(X,n6)) = and(X,and(n6,n9)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1049,theory(equality)]) ).
cnf(1547,plain,
and(not(X),not(and(X,Y))) = not(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1199,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(1638,plain,
or(and(X,not(Y)),xor(X,Y)) = xor(X,Y),
inference('PARAMODULATE',[status(thm)],[97,147,theory(equality)]) ).
cnf(1640,plain,
n0 = and(n7,not(n22)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[147,930,theory(equality)]),1022,539,theory(equality)]) ).
cnf(1654,plain,
and(X,not(Y)) = xor(Y,or(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,147,theory(equality)]),146,1372,theory(equality)]) ).
cnf(1655,plain,
or(X,not(Y)) = not(and(Y,not(X))),
inference('REWRITE',[status(thm)],[343,1654,theory(equality)]) ).
cnf(1670,plain,
and(n19,not(and(X,inv2))) = and(n19,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,163,theory(equality)]),145,theory(equality)]) ).
cnf(1678,plain,
and(n15,and(i1,a1)) = and(inv1,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[175,392,theory(equality)]),864,theory(equality)]) ).
cnf(1684,plain,
n16 = and(n16,i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[180,73,theory(equality)]),58,theory(equality)]) ).
cnf(1686,plain,
and(n14,n15) = and(i1,n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[180,766,theory(equality)]),654,theory(equality)]) ).
cnf(1687,plain,
and(n14,n15) = and(n14,n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[180,783,theory(equality)]),345,654,theory(equality)]) ).
cnf(1688,plain,
and(n14,n15) = and(n23,n16),
inference('REWRITE',[status(thm)],[345,1687,theory(equality)]) ).
cnf(1689,plain,
and(n16,n19) = and(n14,n15),
inference('REWRITE',[status(thm)],[349,1687,theory(equality)]) ).
cnf(1695,plain,
and(n16,and(i3,a1)) = and(inv1,n16),
inference('PARAMODULATE',[status(thm)],[180,767,theory(equality)]) ).
cnf(1697,plain,
and(inv1,n16) = and(a1,n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[180,780,theory(equality)]),1695,theory(equality)]) ).
cnf(1704,plain,
and(n21,and(X,n16)) = and(X,and(a1,n16)),
inference('REWRITE',[status(thm)],[436,1697,theory(equality)]) ).
cnf(1708,plain,
and(a1,n16) = and(inv2,and(i3,a1)),
inference('REWRITE',[status(thm)],[820,1697,theory(equality)]) ).
cnf(1729,plain,
and(i3,xor(n16,X)) = xor(n16,and(X,i3)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,1684,theory(equality)]) ).
cnf(1733,plain,
and(i3,n15) = and(n14,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_simplification2,1688,theory(equality)]),653,813,theory(equality)]) ).
cnf(1734,plain,
and(i3,n15) = and(n6,n16),
inference('REWRITE',[status(thm)],[389,1733,theory(equality)]) ).
cnf(1735,plain,
and(n16,n15) = and(i3,n15),
inference('REWRITE',[status(thm)],[391,1733,theory(equality)]) ).
cnf(1741,plain,
and(n7,n16) = and(i3,n15),
inference('REWRITE',[status(thm)],[654,1733,theory(equality)]) ).
cnf(1747,plain,
and(i3,n15) = and(i1,n16),
inference('REWRITE',[status(thm)],[1686,1733,theory(equality)]) ).
cnf(1748,plain,
and(i3,n15) = and(n14,n19),
inference('REWRITE',[status(thm)],[1687,1733,theory(equality)]) ).
cnf(1749,plain,
and(i3,n15) = and(n23,n16),
inference('REWRITE',[status(thm)],[1688,1733,theory(equality)]) ).
cnf(1750,plain,
and(n16,n19) = and(i3,n15),
inference('REWRITE',[status(thm)],[1689,1733,theory(equality)]) ).
cnf(1764,plain,
or(n14,and(i3,n15)) = n14,
inference('PARAMODULATE',[status(thm)],[425,1734,theory(equality)]) ).
cnf(1767,plain,
and(not(n15),n16) = and(i3,xor(n16,n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1734,theory(equality)]),1729,1132,theory(equality)]) ).
cnf(1771,plain,
and(n15,not(n14)) = and(n15,not(i3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1735,theory(equality)]),145,1133,theory(equality)]) ).
cnf(1772,plain,
and(n15,not(n16)) = and(n15,not(i3)),
inference('REWRITE',[status(thm)],[1133,1771,theory(equality)]) ).
cnf(1777,plain,
and(n15,n19) = and(i3,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_simplification2,1749,theory(equality)]),347,215,theory(equality)]) ).
cnf(1778,plain,
and(i3,n15) = and(n23,n15),
inference('REWRITE',[status(thm)],[347,1777,theory(equality)]) ).
cnf(1779,plain,
and(n6,n19) = and(i3,n15),
inference('REWRITE',[status(thm)],[348,1777,theory(equality)]) ).
cnf(1789,plain,
and(not(n19),n16) = and(not(n15),n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1749,theory(equality)]),1767,1729,1111,theory(equality)]) ).
cnf(1790,plain,
and(n16,not(n23)) = and(not(n15),n16),
inference('REWRITE',[status(thm)],[1111,1789,theory(equality)]) ).
cnf(1797,plain,
and(n19,not(n14)) = xor(n19,and(i3,n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1750,theory(equality)]),1121,theory(equality)]) ).
cnf(1838,plain,
and(n14,not(n15)) = and(i3,xor(i2,n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1733,theory(equality)]),142,theory(equality)]) ).
cnf(1840,plain,
and(n7,not(n16)) = and(n9,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1741,theory(equality)]),1168,constructor10,1475,987,138,theory(equality)]) ).
cnf(1845,plain,
and(n24,n16) = and(n2,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,1747,theory(equality)]),115,theory(equality)]) ).
cnf(1848,plain,
and(n16,not(i1)) = and(not(n15),n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1747,theory(equality)]),1767,1729,theory(equality)]) ).
cnf(1849,plain,
and(n16,not(n6)) = and(n16,not(i1)),
inference('REWRITE',[status(thm)],[1132,1848,theory(equality)]) ).
cnf(1852,plain,
and(not(n19),n16) = and(n16,not(i1)),
inference('REWRITE',[status(thm)],[1789,1848,theory(equality)]) ).
cnf(1853,plain,
and(n16,not(n23)) = and(n16,not(i1)),
inference('REWRITE',[status(thm)],[1790,1848,theory(equality)]) ).
cnf(1863,plain,
and(n14,not(n19)) = and(n14,not(n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1748,theory(equality)]),1838,142,theory(equality)]) ).
cnf(1878,plain,
and(n24,and(X,n16)) = and(X,and(n2,n15)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1845,theory(equality)]) ).
cnf(1879,plain,
and(and(i1,X),and(a1,n16)) = and(X,and(n2,n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1845,theory(equality)]),1697,609,theory(equality)]) ).
cnf(1889,plain,
and(a1,n19) = and(n2,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[190,881,theory(equality)]),629,107,488,theory(equality)]) ).
cnf(1906,plain,
and(n24,n16) = and(a1,n19),
inference('REWRITE',[status(thm)],[1845,1889,theory(equality)]) ).
cnf(1918,plain,
and(n24,and(X,n16)) = and(X,and(a1,n19)),
inference('REWRITE',[status(thm)],[1878,1889,theory(equality)]) ).
cnf(1919,plain,
and(and(i1,X),and(a1,n16)) = and(X,and(a1,n19)),
inference('REWRITE',[status(thm)],[1879,1889,theory(equality)]) ).
cnf(1922,plain,
and(n21,and(X,n2)) = and(n21,and(X,i3)),
inference('PARAMODULATE',[status(thm)],[190,115,theory(equality)]) ).
cnf(1923,plain,
and(n21,and(X,a1)) = and(inv2,and(X,a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[190,117,theory(equality)]),906,theory(equality)]) ).
cnf(1943,plain,
and(and(i3,n15),and(inv1,X)) = and(X,and(a1,n19)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1889,theory(equality)]),732,theory(equality)]) ).
cnf(1947,plain,
and(and(i3,n15),and(a1,n16)) = and(a1,n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_simplification2,1906,theory(equality)]),1697,1943,theory(equality)]) ).
cnf(1949,plain,
and(n21,not(and(X,inv2))) = and(n21,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,195,theory(equality)]),145,theory(equality)]) ).
cnf(1954,plain,
and(i1,n15) = n15,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[108,200,theory(equality)]),constructor18,theory(equality)]) ).
cnf(1963,plain,
and(n15,not(i1)) = n0,
inference('PARAMODULATE',[status(thm)],[1199,1954,theory(equality)]) ).
cnf(1965,plain,
and(n15,and(i1,X)) = and(X,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1954,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(1966,plain,
and(a1,n15) = and(inv1,n15),
inference('REWRITE',[status(thm)],[1678,1965,theory(equality)]) ).
cnf(1968,plain,
and(n21,n15) = and(a1,n15),
inference('REWRITE',[status(thm)],[392,1966,theory(equality)]) ).
cnf(1976,plain,
and(n24,n15) = and(a1,n15),
inference('REWRITE',[status(thm)],[472,1966,theory(equality)]) ).
cnf(1980,plain,
or(n24,and(a1,n15)) = n24,
inference('REWRITE',[status(thm)],[499,1966,theory(equality)]) ).
cnf(1981,plain,
and(n24,and(X,n15)) = and(X,and(a1,n15)),
inference('REWRITE',[status(thm)],[501,1966,theory(equality)]) ).
cnf(1982,plain,
and(a1,n15) = and(inv2,and(i1,a1)),
inference('REWRITE',[status(thm)],[918,1966,theory(equality)]) ).
cnf(1996,plain,
and(n15,n20) = and(n15,not(a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1968,theory(equality)]),145,1144,theory(equality)]) ).
cnf(1997,plain,
and(and(inv1,X),n15) = and(X,and(a1,n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1968,theory(equality)]),56,450,theory(equality)]) ).
cnf(2002,plain,
and(n24,not(n15)) = xor(n24,and(a1,n15)),
inference('PARAMODULATE',[status(thm)],[145,1976,theory(equality)]) ).
cnf(2014,plain,
and(i1,n19) = n19,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[107,210,theory(equality)]),constructor22,theory(equality)]) ).
cnf(2015,plain,
and(n23,not(and(i1,X))) = and(n23,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,210,theory(equality)]),145,theory(equality)]) ).
cnf(2022,plain,
n19 = and(n19,i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[112,2014,theory(equality)]),54,theory(equality)]) ).
cnf(2023,plain,
and(i3,n15) = and(n19,i2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[111,2014,theory(equality)]),1779,theory(equality)]) ).
cnf(2034,plain,
and(i3,xor(n19,X)) = xor(n19,and(X,i3)),
inference('PARAMODULATE',[status(thm)],[and_xor_simplification,2022,theory(equality)]) ).
cnf(2035,plain,
and(n19,not(n14)) = and(i3,xor(n19,n15)),
inference('REWRITE',[status(thm)],[1797,2034,theory(equality)]) ).
cnf(2037,plain,
and(n19,not(i2)) = and(n19,not(n14)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,2023,theory(equality)]),2035,2034,theory(equality)]) ).
cnf(2038,plain,
and(n19,not(n16)) = and(n19,not(i2)),
inference('REWRITE',[status(thm)],[1121,2037,theory(equality)]) ).
cnf(2065,plain,
and(n24,not(and(i1,X))) = and(n24,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,220,theory(equality)]),145,theory(equality)]) ).
cnf(2090,plain,
and(n2,and(i1,a1)) = and(n23,a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[240,859,theory(equality)]),880,theory(equality)]) ).
cnf(2098,plain,
and(n2,not(and(X,i3))) = and(n2,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,245,theory(equality)]),145,theory(equality)]) ).
cnf(2103,plain,
and(n14,not(and(i2,X))) = and(n14,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,250,theory(equality)]),145,theory(equality)]) ).
cnf(2108,plain,
and(n14,not(and(X,i3))) = and(n14,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,255,theory(equality)]),145,theory(equality)]) ).
cnf(2162,plain,
and(i2,not(and(X,a1))) = xor(i2,and(X,a1)),
inference('PARAMODULATE',[status(thm)],[145,266,theory(equality)]) ).
cnf(2163,plain,
and(i2,not(n24)) = and(i2,not(and(i1,a1))),
inference('REWRITE',[status(thm)],[1180,2162,theory(equality)]) ).
cnf(2164,plain,
and(i2,not(n2)) = and(i2,not(and(i3,a1))),
inference('REWRITE',[status(thm)],[1156,2162,theory(equality)]) ).
cnf(2220,plain,
and(n6,not(i3)) = xor(n23,n22),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[xor_simplification1,931,theory(equality)]),1045,theory(equality)]) ).
cnf(2302,plain,
and(not(n2),and(X,n23)) = and(X,and(n20,n23)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1117,theory(equality)]) ).
cnf(2310,plain,
and(not(n2),and(X,n14)) = and(X,and(n20,n14)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1127,theory(equality)]) ).
cnf(2315,plain,
and(not(a1),and(X,n14)) = and(X,and(n20,n14)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1130,theory(equality)]) ).
cnf(2324,plain,
and(not(n2),and(X,n7)) = and(X,and(n20,n7)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,1138,theory(equality)]) ).
cnf(2355,plain,
and(not(n23),and(not(i1),X)) = and(not(i1),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1298,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(2362,plain,
and(not(n23),and(not(i3),X)) = and(not(i3),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1302,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(2393,plain,
and(not(n6),not(xor(n7,X))) = and(not(n6),not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_xor_simplification,1328,theory(equality)]),145,99,theory(equality)]) ).
cnf(2396,plain,
and(not(n6),not(and(X,n7))) = not(n6),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1329,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(2429,plain,
and(not(n6),and(not(i2),X)) = and(not(i2),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1351,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(2445,plain,
and(not(i2),not(xor(a1,X))) = and(not(i2),not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_xor_simplification,1365,theory(equality)]),145,99,theory(equality)]) ).
cnf(2448,plain,
and(not(i2),not(and(X,a1))) = not(i2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1366,theory(equality)]),xor_definition1,theory(equality)]) ).
cnf(2524,plain,
and(n7,n22) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,1640,theory(equality)]),xor_definition1,52,theory(equality)]) ).
cnf(2737,plain,
or(xor(X,Y),or(X,Y)) = or(or(X,Y),and(X,Y)),
inference('PARAMODULATE',[status(thm)],[1228,93,theory(equality)]) ).
cnf(2738,plain,
or(or(X,Y),and(X,Y)) = or(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1202,93,theory(equality)]),1200,theory(equality)]) ).
cnf(2739,plain,
or(xor(X,Y),or(X,Y)) = or(X,Y),
inference('REWRITE',[status(thm)],[2737,2738,theory(equality)]) ).
cnf(2798,plain,
and(or(X,Y),xor(X,Y)) = and(or(X,Y),not(and(X,Y))),
inference('PARAMODULATE',[status(thm)],[147,93,theory(equality)]) ).
cnf(3127,plain,
xor(X,Y) = and(or(X,Y),not(and(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[94,94,theory(equality)]),2798,93,2739,theory(equality)]) ).
cnf(3263,plain,
not(and(or(X,Y),not(and(X,Y)))) = and(not(and(Y,not(X))),not(and(X,not(Y)))),
inference('REWRITE',[status(thm)],[99,1655,3127,theory(equality)]) ).
cnf(3273,plain,
or(X,Y) = or(Y,and(or(X,Y),not(and(X,Y)))),
inference('REWRITE',[status(thm)],[1202,3127,theory(equality)]) ).
cnf(3278,plain,
or(and(X,not(Y)),and(or(X,Y),not(and(X,Y)))) = and(or(X,Y),not(and(X,Y))),
inference('REWRITE',[status(thm)],[1638,3127,theory(equality)]) ).
cnf(3322,plain,
and(not(and(not(a1),X)),not(i2)) = and(not(i2),not(X)),
inference('REWRITE',[status(thm)],[2445,2448,and_commutativity,3263,3127,theory(equality)]) ).
cnf(3406,plain,
and(i2,not(and(i1,X))) = and(i2,not(and(X,n6))),
inference('REWRITE',[status(thm)],[1192,111,and_simplification1,516,515,3127,theory(equality)]) ).
cnf(3485,plain,
and(i3,not(n24)) = and(i3,not(and(i1,n2))),
inference('REWRITE',[status(thm)],[1154,726,112,737,3127,theory(equality)]) ).
cnf(3486,plain,
and(i3,not(n21)) = and(i3,not(and(inv2,n2))),
inference('REWRITE',[status(thm)],[1147,442,and_simplification1,468,463,3127,theory(equality)]) ).
cnf(3534,plain,
and(n24,not(n15)) = and(n24,not(and(a1,n15))),
inference('REWRITE',[status(thm)],[2002,74,1997,1981,1980,3127,theory(equality)]) ).
cnf(3542,plain,
and(n24,not(n14)) = and(n24,not(and(n23,a1))),
inference('REWRITE',[status(thm)],[1161,210,914,923,3127,theory(equality)]) ).
cnf(3668,plain,
and(n6,not(n2)) = and(n6,not(and(n23,a1))),
inference('REWRITE',[status(thm)],[1173,210,874,894,3127,theory(equality)]) ).
cnf(3821,plain,
and(not(and(not(n7),X)),not(n6)) = and(not(n6),not(X)),
inference('REWRITE',[status(thm)],[2393,2396,and_commutativity,3263,3127,theory(equality)]) ).
cnf(3990,plain,
and(inv2,not(and(inv1,X))) = and(inv2,not(and(X,n21))),
inference('REWRITE',[status(thm)],[1184,110,and_simplification1,450,448,3127,theory(equality)]) ).
cnf(4194,plain,
and(n6,not(i3)) = and(or(n23,n22),not(and(n23,n22))),
inference('REWRITE',[status(thm)],[2220,3127,theory(equality)]) ).
cnf(4199,plain,
n10 = or(n7,and(n10,not(and(n23,a1)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,constructor13,theory(equality)]),883,theory(equality)]) ).
cnf(4200,plain,
n22 = or(n6,and(n22,not(n7))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,constructor25,theory(equality)]),512,theory(equality)]) ).
cnf(4378,plain,
n21 = or(and(inv2,a1),and(not(a1),n21)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,456,theory(equality)]),1949,and_simplification2,1923,theory(equality)]) ).
cnf(4380,plain,
n21 = or(and(inv2,n2),and(not(i3),n21)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,465,theory(equality)]),1151,1949,442,195,1922,theory(equality)]) ).
cnf(4388,plain,
n24 = or(and(i1,n21),and(n9,n24)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,471,theory(equality)]),1148,2065,444,220,theory(equality)]) ).
cnf(4390,plain,
n24 = or(and(i1,n2),and(not(i3),n24)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,718,theory(equality)]),1178,2065,739,220,theory(equality)]) ).
cnf(4391,plain,
n23 = or(and(i1,n2),and(n20,n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,736,theory(equality)]),1117,2015,726,210,theory(equality)]) ).
cnf(4394,plain,
n24 = or(and(i1,a1),and(not(a1),n24)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,912,theory(equality)]),2065,857,220,theory(equality)]) ).
cnf(4401,plain,
n14 = or(and(i3,n15),and(n14,not(n15))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,1764,theory(equality)]),2108,1733,255,theory(equality)]) ).
cnf(4406,plain,
n2 = or(and(i3,a1),and(not(a1),n2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3273,772,theory(equality)]),2098,and_simplification2,852,theory(equality)]) ).
cnf(6461,plain,
and(not(n2),and(X,n21)) = and(X,and(not(i3),n21)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1151,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(6510,plain,
inv1 = and(not(n14),not(n22)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1225,273,theory(equality)]),constructor29,theory(equality)]) ).
cnf(6511,plain,
not(n22) = and(not(n6),not(n23)),
inference('PARAMODULATE',[status(thm)],[1225,277,theory(equality)]) ).
cnf(6512,plain,
not(n18) = and(not(n19),not(n25)),
inference('PARAMODULATE',[status(thm)],[1225,constructor21,theory(equality)]) ).
cnf(6513,plain,
not(n17) = and(not(n21),not(n18)),
inference('PARAMODULATE',[status(thm)],[1225,280,theory(equality)]) ).
cnf(6514,plain,
not(n12) = and(not(n11),not(n16)),
inference('PARAMODULATE',[status(thm)],[1225,constructor15,theory(equality)]) ).
cnf(6515,plain,
not(n13) = and(not(n21),not(n12)),
inference('PARAMODULATE',[status(thm)],[1225,279,theory(equality)]) ).
cnf(6516,plain,
not(n8) = and(not(a1),not(n10)),
inference('PARAMODULATE',[status(thm)],[1225,constructor11,theory(equality)]) ).
cnf(6517,plain,
inv2 = and(not(n2),not(n8)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1225,284,theory(equality)]),constructor30,theory(equality)]) ).
cnf(6518,plain,
not(n10) = and(not(n24),not(n7)),
inference('PARAMODULATE',[status(thm)],[1225,constructor13,theory(equality)]) ).
cnf(6519,plain,
not(n5) = and(not(n4),not(n21)),
inference('PARAMODULATE',[status(thm)],[1225,constructor8,theory(equality)]) ).
cnf(6520,plain,
not(n4) = and(not(n3),not(n15)),
inference('PARAMODULATE',[status(thm)],[1225,283,theory(equality)]) ).
cnf(6521,plain,
not(n3) = and(not(a1),not(n24)),
inference('PARAMODULATE',[status(thm)],[1225,constructor6,theory(equality)]) ).
cnf(6522,plain,
not(n25) = and(not(n2),not(n24)),
inference('PARAMODULATE',[status(thm)],[1225,constructor28,theory(equality)]) ).
cnf(6523,plain,
not(n11) = and(not(a1),not(n2)),
inference('PARAMODULATE',[status(thm)],[1225,constructor14,theory(equality)]) ).
cnf(6524,plain,
not(and(not(X),not(Y))) = or(X,Y),
inference('PARAMODULATE',[status(thm)],[52,1225,theory(equality)]) ).
cnf(6829,plain,
n2 = not(and(not(and(i3,a1)),not(and(not(a1),n2)))),
inference('REWRITE',[status(thm)],[4406,6524,theory(equality)]) ).
cnf(6862,plain,
n24 = not(and(not(and(i1,a1)),not(and(not(a1),n24)))),
inference('REWRITE',[status(thm)],[4394,6524,theory(equality)]) ).
cnf(6863,plain,
n24 = not(and(not(and(i1,n2)),not(and(not(i3),n24)))),
inference('REWRITE',[status(thm)],[4390,6524,theory(equality)]) ).
cnf(6892,plain,
n21 = not(and(not(and(inv2,n2)),not(and(not(i3),n21)))),
inference('REWRITE',[status(thm)],[4380,6524,theory(equality)]) ).
cnf(6893,plain,
n21 = not(and(not(and(inv2,a1)),not(and(not(a1),n21)))),
inference('REWRITE',[status(thm)],[4378,6524,theory(equality)]) ).
cnf(6954,plain,
n10 = not(and(not(n7),not(and(n10,not(and(n23,a1)))))),
inference('REWRITE',[status(thm)],[4199,6524,theory(equality)]) ).
cnf(6958,plain,
n24 = not(and(not(and(i1,n21)),not(and(n9,n24)))),
inference('REWRITE',[status(thm)],[4388,6524,theory(equality)]) ).
cnf(6998,plain,
n14 = not(and(not(and(i3,n15)),not(and(n14,not(n15))))),
inference('REWRITE',[status(thm)],[4401,6524,theory(equality)]) ).
cnf(7092,plain,
n23 = not(and(not(and(i1,n2)),not(and(n20,n23)))),
inference('REWRITE',[status(thm)],[4391,6524,theory(equality)]) ).
cnf(7108,plain,
n22 = not(and(not(n6),not(n22))),
inference('REWRITE',[status(thm)],[4200,3821,6524,theory(equality)]) ).
cnf(7899,plain,
not(and(not(and(not(X),not(Y))),not(and(X,Y)))) = and(not(and(Y,not(X))),not(and(X,not(Y)))),
inference('REWRITE',[status(thm)],[3263,6524,theory(equality)]) ).
cnf(7937,plain,
not(and(not(and(Y,not(X))),not(and(X,not(Y))))) = and(not(and(not(X),not(Y))),not(and(X,Y))),
inference('REWRITE',[status(thm)],[3278,and_simplification2,7899,6524,theory(equality)]) ).
cnf(9120,plain,
and(n6,not(i3)) = not(and(not(and(n22,not(n23))),not(and(n23,not(n22))))),
inference('REWRITE',[status(thm)],[4194,7937,6524,theory(equality)]) ).
cnf(9310,plain,
and(not(n22),inv1) = inv1,
inference('PARAMODULATE',[status(thm)],[and_simplification2,6510,theory(equality)]) ).
cnf(9311,plain,
and(i3,a1) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6510,theory(equality)]),767,52,theory(equality)]) ).
cnf(9314,plain,
and(n14,n2) = n0,
inference('REWRITE',[status(thm)],[770,9311,theory(equality)]) ).
cnf(9316,plain,
and(a1,n14) = n0,
inference('REWRITE',[status(thm)],[780,9311,theory(equality)]) ).
cnf(9317,plain,
and(a1,n2) = n0,
inference('REWRITE',[status(thm)],[825,9311,theory(equality)]) ).
cnf(9318,plain,
and(n2,and(X,a1)) = n0,
inference('REWRITE',[status(thm)],[852,and_definition1,9311,theory(equality)]) ).
cnf(9319,plain,
n0 = and(n23,a1),
inference('REWRITE',[status(thm)],[2090,9318,theory(equality)]) ).
cnf(9342,plain,
and(n24,not(n14)) = n24,
inference('REWRITE',[status(thm)],[3542,and_definition3,50,9319,theory(equality)]) ).
cnf(9343,plain,
and(n24,not(n7)) = n24,
inference('REWRITE',[status(thm)],[1169,9342,theory(equality)]) ).
cnf(9346,plain,
and(n6,not(n2)) = n6,
inference('REWRITE',[status(thm)],[3668,and_definition3,50,9319,theory(equality)]) ).
cnf(9351,plain,
n10 = not(and(not(n7),not(n10))),
inference('REWRITE',[status(thm)],[6954,and_definition3,50,9319,theory(equality)]) ).
cnf(9375,plain,
and(a1,n16) = n0,
inference('REWRITE',[status(thm)],[1708,and_definition1,9311,theory(equality)]) ).
cnf(9379,plain,
and(n21,and(X,n16)) = n0,
inference('REWRITE',[status(thm)],[1704,and_definition1,9375,theory(equality)]) ).
cnf(9384,plain,
n0 = and(X,and(a1,n19)),
inference('REWRITE',[status(thm)],[1919,and_definition1,9375,theory(equality)]) ).
cnf(9398,plain,
and(n24,and(X,n16)) = n0,
inference('REWRITE',[status(thm)],[1918,9384,theory(equality)]) ).
cnf(9416,plain,
n0 = and(a1,n19),
inference('REWRITE',[status(thm)],[1947,and_definition1,9375,theory(equality)]) ).
cnf(9417,plain,
n0 = and(n2,n15),
inference('REWRITE',[status(thm)],[1889,9416,theory(equality)]) ).
cnf(9477,plain,
and(i2,not(n2)) = i2,
inference('REWRITE',[status(thm)],[2164,and_definition3,50,9311,theory(equality)]) ).
cnf(9480,plain,
n2 = and(not(a1),n2),
inference('REWRITE',[status(thm)],[6829,52,and_definition3,50,9311,theory(equality)]) ).
cnf(9523,plain,
and(inv1,n22) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6510,theory(equality)]),52,theory(equality)]) ).
cnf(9524,plain,
and(not(n22),and(not(n14),X)) = and(inv1,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,6510,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(9547,plain,
n7 = and(n20,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[526,9477,theory(equality)]),1138,510,theory(equality)]) ).
cnf(9548,plain,
and(n7,not(n2)) = n7,
inference('REWRITE',[status(thm)],[1138,9547,theory(equality)]) ).
cnf(9549,plain,
and(n7,not(n24)) = n7,
inference('REWRITE',[status(thm)],[1170,9547,theory(equality)]) ).
cnf(9551,plain,
and(not(n2),and(X,n7)) = and(X,n7),
inference('REWRITE',[status(thm)],[2324,9547,theory(equality)]) ).
cnf(9558,plain,
n14 = and(n20,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[250,9477,theory(equality)]),1127,72,theory(equality)]) ).
cnf(9561,plain,
and(not(n2),and(X,n14)) = and(X,n14),
inference('REWRITE',[status(thm)],[2310,9558,theory(equality)]) ).
cnf(9563,plain,
and(not(a1),and(X,n14)) = and(X,n14),
inference('REWRITE',[status(thm)],[2315,9558,theory(equality)]) ).
cnf(9571,plain,
and(a1,not(i3)) = a1,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[117,9477,theory(equality)]),constructor4,1182,theory(equality)]) ).
cnf(9573,plain,
and(a1,not(n2)) = a1,
inference('REWRITE',[status(thm)],[1182,9571,theory(equality)]) ).
cnf(9603,plain,
and(not(n2),inv2) = inv2,
inference('PARAMODULATE',[status(thm)],[and_simplification2,6517,theory(equality)]) ).
cnf(9604,plain,
and(not(n8),inv2) = inv2,
inference('PARAMODULATE',[status(thm)],[and_simplification2,6517,theory(equality)]) ).
cnf(9606,plain,
and(inv2,n2) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6517,theory(equality)]),52,theory(equality)]) ).
cnf(9607,plain,
and(i3,n21) = n0,
inference('REWRITE',[status(thm)],[442,9606,theory(equality)]) ).
cnf(9612,plain,
and(i3,not(n21)) = i3,
inference('REWRITE',[status(thm)],[3486,and_definition3,50,9606,theory(equality)]) ).
cnf(9613,plain,
n21 = and(not(i3),n21),
inference('REWRITE',[status(thm)],[6892,52,and_definition3,50,9606,theory(equality)]) ).
cnf(9615,plain,
and(not(n2),and(X,n21)) = and(X,n21),
inference('REWRITE',[status(thm)],[6461,9613,theory(equality)]) ).
cnf(9635,plain,
and(not(n8),and(not(n2),X)) = and(X,inv2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,6517,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(9638,plain,
n0 = and(inv1,n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[215,9607,theory(equality)]),346,and_definition1,theory(equality)]) ).
cnf(9642,plain,
and(n21,and(X,n19)) = n0,
inference('REWRITE',[status(thm)],[383,and_definition1,9638,theory(equality)]) ).
cnf(9687,plain,
n2 = and(n2,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[245,9612,theory(equality)]),1150,71,theory(equality)]) ).
cnf(9703,plain,
not(n22) = and(not(n6),not(n22)),
inference('PARAMODULATE',[status(thm)],[52,7108,theory(equality)]) ).
cnf(9708,plain,
n2 = and(not(n22),n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[240,9310,theory(equality)]),70,theory(equality)]) ).
cnf(9726,plain,
and(not(n2),and(X,n6)) = and(X,n6),
inference('PARAMODULATE',[status(thm)],[and_commutativity,9346,theory(equality)]) ).
cnf(9730,plain,
not(n10) = and(not(n7),not(n10)),
inference('PARAMODULATE',[status(thm)],[52,9351,theory(equality)]) ).
cnf(9747,plain,
and(not(a1),and(X,n2)) = and(X,n2),
inference('PARAMODULATE',[status(thm)],[and_commutativity,9480,theory(equality)]) ).
cnf(9775,plain,
and(not(n2),and(X,inv2)) = and(X,inv2),
inference('PARAMODULATE',[status(thm)],[and_commutativity,9603,theory(equality)]) ).
cnf(9801,plain,
and(not(n22),n6) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,9703,theory(equality)]),52,theory(equality)]) ).
cnf(9805,plain,
and(not(n22),and(X,n6)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9801,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9809,plain,
and(not(n10),n7) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,9730,theory(equality)]),52,theory(equality)]) ).
cnf(9826,plain,
and(n23,not(n22)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6511,theory(equality)]),52,theory(equality)]) ).
cnf(9827,plain,
and(n6,not(i3)) = and(n22,not(n23)),
inference('REWRITE',[status(thm)],[9120,52,and_definition3,50,9826,theory(equality)]) ).
cnf(9836,plain,
and(not(n22),and(X,n23)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9826,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9841,plain,
and(not(n18),n19) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6512,theory(equality)]),52,theory(equality)]) ).
cnf(9843,plain,
and(not(n18),n25) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6512,theory(equality)]),52,theory(equality)]) ).
cnf(9850,plain,
and(not(n18),and(X,n25)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9843,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9856,plain,
and(not(n17),n21) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6513,theory(equality)]),52,theory(equality)]) ).
cnf(9857,plain,
and(not(n17),n18) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6513,theory(equality)]),52,theory(equality)]) ).
cnf(9865,plain,
and(not(n17),and(X,n18)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9857,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9870,plain,
and(not(n12),n11) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6514,theory(equality)]),52,theory(equality)]) ).
cnf(9875,plain,
and(not(n12),and(X,n11)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9870,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9883,plain,
and(not(n13),n21) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6515,theory(equality)]),52,theory(equality)]) ).
cnf(9884,plain,
and(not(n13),n12) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6515,theory(equality)]),52,theory(equality)]) ).
cnf(9891,plain,
and(not(n13),and(X,n12)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9884,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9896,plain,
and(not(n8),a1) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6516,theory(equality)]),52,theory(equality)]) ).
cnf(9897,plain,
and(not(n8),n10) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6516,theory(equality)]),52,theory(equality)]) ).
cnf(9901,plain,
and(not(n8),and(X,a1)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9896,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9904,plain,
and(not(n8),and(X,n10)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9897,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9908,plain,
and(n24,not(n10)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6518,theory(equality)]),52,theory(equality)]) ).
cnf(9913,plain,
and(not(n10),and(X,n24)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9908,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9918,plain,
and(not(n5),n4) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6519,theory(equality)]),52,theory(equality)]) ).
cnf(9919,plain,
and(not(n5),n21) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6519,theory(equality)]),52,theory(equality)]) ).
cnf(9923,plain,
and(not(n5),and(X,n4)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9918,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9931,plain,
and(not(n4),n3) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6520,theory(equality)]),52,theory(equality)]) ).
cnf(9932,plain,
and(not(n4),n15) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6520,theory(equality)]),52,theory(equality)]) ).
cnf(9936,plain,
and(not(n4),and(X,n3)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9931,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(9945,plain,
and(not(n3),n24) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6521,theory(equality)]),52,theory(equality)]) ).
cnf(9961,plain,
and(not(n25),n24) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6522,theory(equality)]),52,theory(equality)]) ).
cnf(9972,plain,
and(a1,not(n11)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,6523,theory(equality)]),52,theory(equality)]) ).
cnf(9973,plain,
and(not(n2),and(not(a1),X)) = and(X,not(n11)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,6523,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(10001,plain,
and(not(n22),and(X,n2)) = and(X,n2),
inference('PARAMODULATE',[status(thm)],[and_commutativity,9708,theory(equality)]) ).
cnf(10163,plain,
and(not(n22),and(i1,a1)) = n0,
inference('PARAMODULATE',[status(thm)],[9805,859,theory(equality)]) ).
cnf(10243,plain,
and(and(i1,X),n21) = and(n24,and(X,n21)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[607,110,theory(equality)]),60,609,113,and_commutativity,theory(equality)]) ).
cnf(10266,plain,
and(not(n24),and(X,n2)) = and(X,and(n2,not(i1))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,1179,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(10431,plain,
and(i1,n2) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9836,714,theory(equality)]),10001,theory(equality)]) ).
cnf(10439,plain,
and(n24,n2) = n0,
inference('REWRITE',[status(thm)],[739,10431,theory(equality)]) ).
cnf(10442,plain,
and(i3,not(n24)) = i3,
inference('REWRITE',[status(thm)],[3485,and_definition3,50,10431,theory(equality)]) ).
cnf(10444,plain,
n24 = and(not(i3),n24),
inference('REWRITE',[status(thm)],[6863,52,and_definition3,50,10431,theory(equality)]) ).
cnf(10446,plain,
and(n24,not(n2)) = n24,
inference('REWRITE',[status(thm)],[1178,10444,theory(equality)]) ).
cnf(10454,plain,
n23 = and(n20,n23),
inference('REWRITE',[status(thm)],[7092,52,and_definition3,50,10431,theory(equality)]) ).
cnf(10458,plain,
and(not(n2),and(X,n23)) = and(X,n23),
inference('REWRITE',[status(thm)],[2302,10454,theory(equality)]) ).
cnf(10498,plain,
n2 = and(n2,not(i1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[245,10442,theory(equality)]),1179,71,theory(equality)]) ).
cnf(10505,plain,
and(not(n24),and(X,n2)) = and(X,n2),
inference('REWRITE',[status(thm)],[10266,10498,theory(equality)]) ).
cnf(10509,plain,
and(not(n24),and(X,i3)) = and(X,i3),
inference('PARAMODULATE',[status(thm)],[and_commutativity,10442,theory(equality)]) ).
cnf(10561,plain,
and(not(n10),and(i1,n21)) = n0,
inference('PARAMODULATE',[status(thm)],[9913,443,theory(equality)]) ).
cnf(10653,plain,
and(n21,and(X,n15)) = and(n15,and(X,a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1968,theory(equality)]),and_commutativity,118,theory(equality)]) ).
cnf(10658,plain,
and(not(n19),and(X,n23)) = and(n9,and(X,n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,963,theory(equality)]),118,theory(equality)]) ).
cnf(10681,plain,
and(not(n15),and(X,n6)) = and(n9,and(X,n6)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1049,theory(equality)]),118,theory(equality)]) ).
cnf(10685,plain,
and(and(inv1,X),n15) = and(n15,and(X,a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1966,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(10687,plain,
and(not(n2),and(X,i3)) = and(n20,and(X,i3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1067,theory(equality)]),118,theory(equality)]) ).
cnf(10695,plain,
and(not(n21),and(inv1,X)) = and(n9,and(inv1,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1054,theory(equality)]),118,theory(equality)]) ).
cnf(10725,plain,
and(not(n24),and(X,n6)) = and(n6,and(X,n20)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1143,theory(equality)]),and_commutativity,118,theory(equality)]) ).
cnf(10727,plain,
and(and(inv1,X),and(n21,Y)) = and(X,and(n21,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,190,theory(equality)]),118,theory(equality)]) ).
cnf(10731,plain,
and(not(n21),and(X,n15)) = and(n20,and(X,n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1144,theory(equality)]),118,theory(equality)]) ).
cnf(10733,plain,
and(not(a1),and(X,n15)) = and(n20,and(X,n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1996,theory(equality)]),118,theory(equality)]) ).
cnf(10746,plain,
and(X,and(n20,n6)) = and(and(n20,n6),and(not(n24),X)),
inference('PARAMODULATE',[status(thm)],[118,1143,theory(equality)]) ).
cnf(10748,plain,
and(X,and(n15,n20)) = and(and(n15,n20),and(not(n21),X)),
inference('PARAMODULATE',[status(thm)],[118,1144,theory(equality)]) ).
cnf(10788,plain,
and(not(a1),and(X,n6)) = and(n6,and(X,n20)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1171,theory(equality)]),and_commutativity,118,theory(equality)]) ).
cnf(10851,plain,
and(not(n6),and(X,n23)) = and(not(i2),and(X,n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1090,theory(equality)]),118,theory(equality)]) ).
cnf(10868,plain,
and(and(X,n14),not(n7)) = and(not(i1),and(X,n14)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1099,theory(equality)]),118,theory(equality)]) ).
cnf(10873,plain,
and(not(n6),and(X,n16)) = and(not(i1),and(X,n16)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1849,theory(equality)]),118,theory(equality)]) ).
cnf(10877,plain,
and(not(n23),and(X,n16)) = and(not(i1),and(X,n16)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1853,theory(equality)]),118,theory(equality)]) ).
cnf(10908,plain,
and(not(n6),and(X,n24)) = and(not(a1),and(X,n24)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1142,theory(equality)]),118,theory(equality)]) ).
cnf(10921,plain,
and(X,and(n16,not(i1))) = and(and(n16,not(i1)),and(not(n6),X)),
inference('PARAMODULATE',[status(thm)],[118,1849,theory(equality)]) ).
cnf(10937,plain,
and(X,and(not(a1),n24)) = and(and(not(a1),n24),and(not(n6),X)),
inference('PARAMODULATE',[status(thm)],[118,1142,theory(equality)]) ).
cnf(10939,plain,
and(and(X,n23),not(n7)) = and(not(i2),and(X,n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,1102,theory(equality)]),118,theory(equality)]) ).
cnf(10987,plain,
and(i1,a1) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[864,9310,theory(equality)]),10163,859,theory(equality)]) ).
cnf(10996,plain,
and(a1,n15) = n0,
inference('REWRITE',[status(thm)],[1982,and_definition1,10987,theory(equality)]) ).
cnf(10999,plain,
and(n21,n15) = n0,
inference('REWRITE',[status(thm)],[1968,10996,theory(equality)]) ).
cnf(11001,plain,
and(n24,n15) = n0,
inference('REWRITE',[status(thm)],[1976,10996,theory(equality)]) ).
cnf(11003,plain,
and(n24,not(n15)) = n24,
inference('REWRITE',[status(thm)],[3534,and_definition3,50,10996,theory(equality)]) ).
cnf(11039,plain,
and(i2,not(n24)) = i2,
inference('REWRITE',[status(thm)],[2163,and_definition3,50,10987,theory(equality)]) ).
cnf(11041,plain,
n24 = and(not(a1),n24),
inference('REWRITE',[status(thm)],[6862,52,and_definition3,50,10987,theory(equality)]) ).
cnf(11053,plain,
and(X,n24) = and(not(a1),and(X,n24)),
inference('REWRITE',[status(thm)],[10937,10908,and_commutativity,11041,theory(equality)]) ).
cnf(11086,plain,
and(n15,and(X,a1)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,10999,theory(equality)]),and_definition1,10653,theory(equality)]) ).
cnf(11088,plain,
and(and(inv1,X),n15) = n0,
inference('REWRITE',[status(thm)],[10685,11086,theory(equality)]) ).
cnf(11096,plain,
n6 = and(n20,n6),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[205,11039,theory(equality)]),1143,63,theory(equality)]) ).
cnf(11097,plain,
and(n6,not(n24)) = n6,
inference('REWRITE',[status(thm)],[1143,11096,theory(equality)]) ).
cnf(11100,plain,
and(X,n6) = and(n6,and(X,n20)),
inference('REWRITE',[status(thm)],[10746,10725,and_commutativity,11096,theory(equality)]) ).
cnf(11102,plain,
and(not(a1),and(X,n6)) = and(X,n6),
inference('REWRITE',[status(thm)],[10788,11100,theory(equality)]) ).
cnf(11107,plain,
and(a1,not(i1)) = a1,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[117,11039,theory(equality)]),constructor4,1153,theory(equality)]) ).
cnf(11108,plain,
and(a1,not(n24)) = a1,
inference('REWRITE',[status(thm)],[1153,11107,theory(equality)]) ).
cnf(11121,plain,
and(not(n24),and(i2,X)) = and(i2,X),
inference('PARAMODULATE',[status(thm)],[and_commutativity,11039,theory(equality)]) ).
cnf(11152,plain,
and(n15,n20) = n15,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[108,11100,theory(equality)]),constructor18,theory(equality)]) ).
cnf(11161,plain,
and(X,n15) = and(n20,and(X,n15)),
inference('REWRITE',[status(thm)],[10748,10731,and_commutativity,11152,theory(equality)]) ).
cnf(11163,plain,
and(not(a1),and(X,n15)) = and(X,n15),
inference('REWRITE',[status(thm)],[10733,11161,theory(equality)]) ).
cnf(11197,plain,
a1 = and(a1,not(n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9319,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(11198,plain,
and(a1,not(n7)) = a1,
inference('REWRITE',[status(thm)],[1186,11197,theory(equality)]) ).
cnf(11206,plain,
n22 = and(n22,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9523,theory(equality)]),270,and_definition3,50,theory(equality)]) ).
cnf(11227,plain,
n7 = and(n7,n10),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9809,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11230,plain,
i1 = and(not(a1),i1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,10987,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(11231,plain,
n6 = and(n6,n22),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9801,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11257,plain,
n19 = and(n19,n18),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9841,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11273,plain,
n12 = and(n13,n12),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9884,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11276,plain,
n11 = and(n12,n11),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9870,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11279,plain,
n10 = and(n8,n10),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9897,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11305,plain,
n15 = and(n4,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9932,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11315,plain,
n24 = and(n24,n10),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9908,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11318,plain,
n24 = and(n3,n24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9945,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11321,plain,
n24 = and(n25,n24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9961,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11327,plain,
n3 = and(n4,n3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9931,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11338,plain,
a1 = and(n8,a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9896,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11344,plain,
a1 = and(n11,a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9972,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11347,plain,
and(a1,not(and(i2,X))) = and(a1,not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[117,1196,theory(equality)]),117,theory(equality)]) ).
cnf(11365,plain,
and(not(n24),not(and(i1,n20))) = not(i1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,1042,theory(equality)]),1343,theory(equality)]) ).
cnf(11391,plain,
and(n20,not(n22)) = and(not(n22),n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6510,theory(equality)]),52,270,theory(equality)]) ).
cnf(11394,plain,
and(not(n2),n9) = and(not(n2),n8),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6517,theory(equality)]),52,271,theory(equality)]) ).
cnf(11442,plain,
and(inv1,X) = and(not(n15),and(inv1,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11088,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(11450,plain,
and(not(n6),n22) = and(n23,not(i2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6511,theory(equality)]),1090,52,theory(equality)]) ).
cnf(11456,plain,
and(n18,not(n19)) = and(not(n19),n25),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6512,theory(equality)]),52,theory(equality)]) ).
cnf(11458,plain,
and(n18,not(n25)) = and(not(n25),n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6512,theory(equality)]),52,theory(equality)]) ).
cnf(11459,plain,
and(n17,not(n21)) = and(not(n21),n18),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6513,theory(equality)]),52,theory(equality)]) ).
cnf(11460,plain,
and(n17,not(n18)) = and(n21,not(n18)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6513,theory(equality)]),52,theory(equality)]) ).
cnf(11462,plain,
and(n12,not(n11)) = and(not(n11),n16),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6514,theory(equality)]),52,theory(equality)]) ).
cnf(11468,plain,
and(n13,not(n21)) = and(not(n21),n12),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6515,theory(equality)]),52,theory(equality)]) ).
cnf(11473,plain,
and(n13,not(n12)) = and(not(n12),n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6515,theory(equality)]),52,theory(equality)]) ).
cnf(11474,plain,
and(n8,not(a1)) = and(not(a1),n10),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6516,theory(equality)]),52,theory(equality)]) ).
cnf(11479,plain,
and(n8,not(n10)) = and(not(n10),a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6516,theory(equality)]),52,theory(equality)]) ).
cnf(11484,plain,
and(n10,not(n24)) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6518,theory(equality)]),9549,52,theory(equality)]) ).
cnf(11489,plain,
and(n10,not(n7)) = n24,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6518,theory(equality)]),9343,52,theory(equality)]) ).
cnf(11499,plain,
and(n5,not(n21)) = and(not(n21),n4),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6519,theory(equality)]),52,theory(equality)]) ).
cnf(11504,plain,
and(n4,not(n3)) = and(not(n3),n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6520,theory(equality)]),52,theory(equality)]) ).
cnf(11509,plain,
and(n4,not(n15)) = and(not(n15),n3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6520,theory(equality)]),52,theory(equality)]) ).
cnf(11514,plain,
and(n3,not(a1)) = n24,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6521,theory(equality)]),11041,52,theory(equality)]) ).
cnf(11519,plain,
and(n3,not(n24)) = a1,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6521,theory(equality)]),11108,52,theory(equality)]) ).
cnf(11524,plain,
and(n25,not(n2)) = n24,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6522,theory(equality)]),10446,52,theory(equality)]) ).
cnf(11534,plain,
and(n11,not(a1)) = n2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6523,theory(equality)]),9480,52,theory(equality)]) ).
cnf(11539,plain,
and(n11,not(n2)) = a1,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,6523,theory(equality)]),9573,52,theory(equality)]) ).
cnf(11709,plain,
and(X,n25) = and(n25,and(X,n18)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9850,theory(equality)]),and_commutativity,52,and_definition3,50,theory(equality)]) ).
cnf(11724,plain,
and(X,n18) = and(n18,and(X,n17)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9865,theory(equality)]),and_commutativity,52,and_definition3,50,theory(equality)]) ).
cnf(11726,plain,
and(X,n12) = and(and(X,n12),n13),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,9891,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11836,plain,
and(not(n8),n7) = n0,
inference('PARAMODULATE',[status(thm)],[9904,11227,theory(equality)]) ).
cnf(11847,plain,
and(n22,and(X,n20)) = and(X,n22),
inference('PARAMODULATE',[status(thm)],[and_commutativity,11206,theory(equality)]) ).
cnf(11853,plain,
and(not(n17),n19) = n0,
inference('PARAMODULATE',[status(thm)],[9865,11257,theory(equality)]) ).
cnf(11856,plain,
and(not(n13),n11) = n0,
inference('PARAMODULATE',[status(thm)],[9891,11276,theory(equality)]) ).
cnf(11859,plain,
and(not(n5),n15) = n0,
inference('PARAMODULATE',[status(thm)],[9923,11305,theory(equality)]) ).
cnf(11861,plain,
and(not(n4),n24) = n0,
inference('PARAMODULATE',[status(thm)],[9936,11318,theory(equality)]) ).
cnf(11862,plain,
and(not(n18),n24) = n0,
inference('PARAMODULATE',[status(thm)],[9850,11321,theory(equality)]) ).
cnf(11866,plain,
and(not(n12),a1) = n0,
inference('PARAMODULATE',[status(thm)],[9875,11344,theory(equality)]) ).
cnf(11876,plain,
and(not(n24),and(X,n10)) = and(X,n7),
inference('PARAMODULATE',[status(thm)],[and_commutativity,11484,theory(equality)]) ).
cnf(11886,plain,
and(not(a1),and(X,n3)) = and(X,n24),
inference('PARAMODULATE',[status(thm)],[and_commutativity,11514,theory(equality)]) ).
cnf(11896,plain,
and(not(n2),and(X,n25)) = and(X,n24),
inference('PARAMODULATE',[status(thm)],[and_commutativity,11524,theory(equality)]) ).
cnf(11906,plain,
and(not(a1),and(X,n11)) = and(X,n2),
inference('PARAMODULATE',[status(thm)],[and_commutativity,11534,theory(equality)]) ).
cnf(11911,plain,
and(not(n2),and(X,n11)) = and(X,a1),
inference('PARAMODULATE',[status(thm)],[and_commutativity,11539,theory(equality)]) ).
cnf(11961,plain,
n7 = and(n7,n8),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11836,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11980,plain,
not(n17) = and(not(n17),not(n19)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11853,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(11994,plain,
n11 = and(n11,n13),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11856,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(11997,plain,
and(n13,and(X,n11)) = and(X,n11),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,11994,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(11999,plain,
not(n5) = and(not(n5),not(n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11859,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(12006,plain,
n24 = and(n24,n4),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11861,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(12013,plain,
n24 = and(n24,n18),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11862,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(12042,plain,
a1 = and(a1,n12),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11866,theory(equality)]),52,and_definition3,50,theory(equality)]) ).
cnf(12046,plain,
and(n12,and(X,a1)) = and(X,a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,12042,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(12155,plain,
and(n20,not(and(not(n22),n14))) = n22,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11391,theory(equality)]),11206,52,theory(equality)]) ).
cnf(12164,plain,
and(not(n2),and(n9,X)) = and(not(n2),and(X,n8)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11394,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12175,plain,
and(not(n6),and(X,n22)) = and(X,and(n23,not(i2))),
inference('PARAMODULATE',[status(thm)],[and_commutativity,11450,theory(equality)]) ).
cnf(12176,plain,
and(n22,not(and(n23,not(i2)))) = n6,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11450,theory(equality)]),11231,52,theory(equality)]) ).
cnf(12182,plain,
and(not(n19),and(X,n25)) = and(not(n19),and(X,n18)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11456,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12187,plain,
and(not(n25),and(n18,n21)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9642,11458,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(12188,plain,
and(not(n25),and(n9,n18)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1254,11458,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(12208,plain,
and(not(n21),and(X,n18)) = and(not(n21),and(X,n17)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11459,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12216,plain,
and(not(n18),and(n9,n17)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1266,11460,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(12238,plain,
and(not(n11),and(n12,n21)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9379,11462,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(12239,plain,
and(not(n11),and(n9,n12)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1262,11462,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(12240,plain,
and(not(n11),and(n24,n12)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9398,11462,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(12269,plain,
and(not(n21),and(X,n13)) = and(and(X,n13),and(not(n21),n12)),
inference('PARAMODULATE',[status(thm)],[118,11468,theory(equality)]) ).
cnf(12270,plain,
and(not(n21),and(X,n13)) = and(not(n21),and(X,n12)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11468,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12272,plain,
and(not(n21),and(X,n12)) = and(and(X,n13),and(not(n21),n12)),
inference('REWRITE',[status(thm)],[12269,12270,theory(equality)]) ).
cnf(12279,plain,
and(not(n12),and(n9,n13)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1266,11473,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(12299,plain,
and(not(n12),and(X,n21)) = and(not(n12),and(X,n13)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11473,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12307,plain,
and(not(a1),and(X,n8)) = and(not(a1),and(X,n10)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11474,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12314,plain,
and(n8,not(and(not(n10),a1))) = n10,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11479,theory(equality)]),11279,52,theory(equality)]) ).
cnf(12316,plain,
and(not(n10),and(X,n8)) = and(not(n10),and(X,a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11479,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12335,plain,
and(not(n21),and(X,n5)) = and(not(n21),and(X,n4)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11499,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12342,plain,
and(n4,not(and(not(n3),n15))) = n3,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,11504,theory(equality)]),11327,52,theory(equality)]) ).
cnf(12344,plain,
and(not(n3),and(X,n4)) = and(not(n3),and(X,n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11504,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12353,plain,
and(not(n15),and(X,n4)) = and(not(n15),and(X,n3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,11509,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12380,plain,
and(n18,n21) = and(n21,n25),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12187,theory(equality)]),11709,52,and_definition3,50,theory(equality)]) ).
cnf(12395,plain,
and(n9,n18) = and(n9,n25),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12188,theory(equality)]),11709,52,and_definition3,50,theory(equality)]) ).
cnf(12399,plain,
and(n9,not(n18)) = and(not(n25),n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12395,theory(equality)]),1196,theory(equality)]) ).
cnf(12403,plain,
and(n9,and(X,n25)) = and(and(X,n25),and(n9,n18)),
inference('PARAMODULATE',[status(thm)],[118,12395,theory(equality)]) ).
cnf(12405,plain,
and(n9,and(X,n25)) = and(n9,and(X,n18)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,12395,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12406,plain,
and(n9,and(X,n18)) = and(and(X,n25),and(n9,n18)),
inference('REWRITE',[status(thm)],[12403,12405,theory(equality)]) ).
cnf(12451,plain,
and(n9,n17) = and(n9,n18),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12216,theory(equality)]),11724,52,and_definition3,50,theory(equality)]) ).
cnf(12455,plain,
and(n9,n17) = and(n9,n25),
inference('REWRITE',[status(thm)],[12395,12451,theory(equality)]) ).
cnf(12459,plain,
and(n9,and(X,n18)) = and(and(X,n25),and(n9,n17)),
inference('REWRITE',[status(thm)],[12406,12451,theory(equality)]) ).
cnf(12463,plain,
and(n9,not(n17)) = and(n9,not(n18)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12451,theory(equality)]),1196,theory(equality)]) ).
cnf(12464,plain,
and(n9,not(n17)) = and(not(n25),n9),
inference('REWRITE',[status(thm)],[12399,12463,theory(equality)]) ).
cnf(12470,plain,
and(n9,and(X,n18)) = and(n9,and(X,n17)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,12451,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12472,plain,
and(n9,and(X,n17)) = and(and(X,n25),and(n9,n17)),
inference('REWRITE',[status(thm)],[12459,12470,theory(equality)]) ).
cnf(12477,plain,
and(n12,n21) = and(and(inv1,n12),and(n11,inv2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12238,theory(equality)]),450,52,and_definition3,50,theory(equality)]) ).
cnf(12483,plain,
and(n9,n12) = and(n9,n11),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12239,theory(equality)]),11276,and_commutativity,52,and_definition3,50,theory(equality)]) ).
cnf(12488,plain,
and(n9,and(X,n12)) = and(n9,and(X,n11)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,12483,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12519,plain,
and(n9,n13) = and(n9,n11),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12279,theory(equality)]),12483,11273,and_commutativity,52,and_definition3,50,theory(equality)]) ).
cnf(12521,plain,
and(not(n11),n9) = and(n9,not(n13)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12519,theory(equality)]),1196,theory(equality)]) ).
cnf(12523,plain,
and(n9,and(X,n13)) = and(and(X,n13),and(n9,n11)),
inference('PARAMODULATE',[status(thm)],[118,12519,theory(equality)]) ).
cnf(12524,plain,
and(n9,and(X,n13)) = and(n9,and(X,n11)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,12519,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(12525,plain,
and(n9,and(X,n11)) = and(and(X,n13),and(n9,n11)),
inference('REWRITE',[status(thm)],[12523,12524,theory(equality)]) ).
cnf(12579,plain,
and(inv2,not(and(n9,X))) = inv2,
inference('PARAMODULATE',[status(thm)],[1547,constructor30,theory(equality)]) ).
cnf(12580,plain,
and(X,not(and(Y,not(X)))) = X,
inference('PARAMODULATE',[status(thm)],[1547,52,theory(equality)]) ).
cnf(12620,plain,
and(n16,not(and(n19,not(i2)))) = n16,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1547,2038,theory(equality)]),52,theory(equality)]) ).
cnf(12661,plain,
and(n15,not(and(n16,not(i1)))) = n15,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1547,1848,theory(equality)]),52,theory(equality)]) ).
cnf(12862,plain,
and(n19,not(and(n14,not(n15)))) = n19,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1547,1863,theory(equality)]),52,theory(equality)]) ).
cnf(12951,plain,
n7 = and(n9,n7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9551,1840,theory(equality)]),9548,11961,12164,theory(equality)]) ).
cnf(12975,plain,
and(i3,n15) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1199,12951,theory(equality)]),619,constructor30,theory(equality)]) ).
cnf(13001,plain,
n0 = and(n23,n15),
inference('REWRITE',[status(thm)],[1778,12975,theory(equality)]) ).
cnf(13010,plain,
n14 = and(n14,not(n15)),
inference('REWRITE',[status(thm)],[6998,52,and_definition3,50,12975,theory(equality)]) ).
cnf(13012,plain,
and(n19,not(i2)) = n19,
inference('REWRITE',[status(thm)],[12862,2037,13010,theory(equality)]) ).
cnf(13024,plain,
and(n16,not(i1)) = n16,
inference('REWRITE',[status(thm)],[12620,1852,13012,theory(equality)]) ).
cnf(13029,plain,
and(n16,not(n23)) = n16,
inference('REWRITE',[status(thm)],[1853,13024,theory(equality)]) ).
cnf(13030,plain,
and(X,n16) = and(not(i1),and(X,n16)),
inference('REWRITE',[status(thm)],[10921,10873,and_commutativity,13024,theory(equality)]) ).
cnf(13033,plain,
and(not(n23),and(X,n16)) = and(X,n16),
inference('REWRITE',[status(thm)],[10877,13030,theory(equality)]) ).
cnf(13045,plain,
and(n15,not(i3)) = n15,
inference('REWRITE',[status(thm)],[12661,1772,13024,theory(equality)]) ).
cnf(13129,plain,
i3 = and(i3,not(n15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12975,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(13313,plain,
and(n8,n14) = and(n14,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9561,1011,theory(equality)]),9561,12164,theory(equality)]) ).
cnf(13314,plain,
and(n14,not(n16)) = and(n8,n14),
inference('REWRITE',[status(thm)],[1011,13313,theory(equality)]) ).
cnf(13380,plain,
and(n21,not(n11)) = and(not(a1),n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9615,1146,theory(equality)]),9973,theory(equality)]) ).
cnf(13394,plain,
and(not(n23),and(X,n22)) = and(X,and(n6,not(i3))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,9827,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(13451,plain,
and(not(n12),and(i1,n13)) = and(not(n12),and(n24,n13)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10243,11473,theory(equality)]),12299,and_commutativity,theory(equality)]) ).
cnf(13497,plain,
and(n8,n23) = and(n23,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10458,963,theory(equality)]),10458,12164,theory(equality)]) ).
cnf(13498,plain,
and(n23,not(n19)) = and(n8,n23),
inference('REWRITE',[status(thm)],[963,13497,theory(equality)]) ).
cnf(13524,plain,
and(n9,and(X,n23)) = and(n8,and(X,n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,13498,theory(equality)]),118,10658,theory(equality)]) ).
cnf(13572,plain,
and(i1,n21) = and(and(i1,n10),n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,10561,theory(equality)]),607,constructor27,450,52,and_definition3,50,theory(equality)]) ).
cnf(13810,plain,
and(n24,n12) = and(n24,n11),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,12240,theory(equality)]),11276,and_commutativity,52,and_definition3,50,theory(equality)]) ).
cnf(13811,plain,
and(n24,n11) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11053,13810,theory(equality)]),10439,11906,theory(equality)]) ).
cnf(13812,plain,
and(n24,n12) = n0,
inference('REWRITE',[status(thm)],[13810,13811,theory(equality)]) ).
cnf(13813,plain,
n24 = and(n24,not(n12)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,13812,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(13870,plain,
and(not(n23),and(n12,not(n11))) = and(n12,not(n11)),
inference('PARAMODULATE',[status(thm)],[13033,11462,theory(equality)]) ).
cnf(14054,plain,
and(inv2,a1) = and(n21,n11),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,13380,theory(equality)]),446,52,1196,theory(equality)]) ).
cnf(14055,plain,
and(n11,not(and(not(a1),n21))) = n11,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1547,13380,theory(equality)]),52,theory(equality)]) ).
cnf(14063,plain,
and(and(inv1,X),and(n11,inv2)) = and(X,and(inv2,a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,14054,theory(equality)]),450,theory(equality)]) ).
cnf(14064,plain,
and(n12,n21) = and(inv2,a1),
inference('REWRITE',[status(thm)],[12477,12046,14063,theory(equality)]) ).
cnf(14096,plain,
and(not(a1),n21) = and(n13,not(n12)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,14064,theory(equality)]),11473,1949,theory(equality)]) ).
cnf(14101,plain,
and(not(a1),n21) = and(not(n12),n21),
inference('REWRITE',[status(thm)],[11473,14096,theory(equality)]) ).
cnf(14114,plain,
and(not(n12),and(i1,n13)) = and(i1,n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10243,14101,theory(equality)]),11230,10243,12299,and_commutativity,theory(equality)]) ).
cnf(14115,plain,
and(i1,n21) = and(not(n12),and(n24,n13)),
inference('REWRITE',[status(thm)],[13451,14114,theory(equality)]) ).
cnf(14117,plain,
and(n12,not(and(not(a1),n21))) = n12,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1547,14101,theory(equality)]),52,theory(equality)]) ).
cnf(14129,plain,
and(and(i1,not(i2)),and(n8,i3)) = and(not(n6),and(n8,n22)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13524,1090,theory(equality)]),12175,587,13524,theory(equality)]) ).
cnf(14130,plain,
and(and(i1,not(X)),and(n8,i3)) = and(and(n8,n23),not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13524,1196,theory(equality)]),and_commutativity,587,13524,theory(equality)]) ).
cnf(14131,plain,
and(and(n8,n23),not(i2)) = and(not(n6),and(n8,n22)),
inference('REWRITE',[status(thm)],[14129,14130,theory(equality)]) ).
cnf(14175,plain,
and(not(n12),and(X,n24)) = and(X,n24),
inference('PARAMODULATE',[status(thm)],[and_commutativity,13813,theory(equality)]) ).
cnf(14176,plain,
and(i1,n21) = and(n24,n13),
inference('REWRITE',[status(thm)],[14115,14175,theory(equality)]) ).
cnf(14181,plain,
and(n9,n24) = and(n24,not(n13)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,14176,theory(equality)]),1148,2065,theory(equality)]) ).
cnf(14219,plain,
and(n13,not(and(n9,n24))) = n13,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1547,14181,theory(equality)]),52,theory(equality)]) ).
cnf(14341,plain,
and(and(X,inv2),and(not(n11),n14)) = and(X,and(n12,not(n11))),
inference('PARAMODULATE',[status(thm)],[427,11462,theory(equality)]) ).
cnf(14371,plain,
and(inv2,a1) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9901,450,theory(equality)]),9604,74,theory(equality)]) ).
cnf(14373,plain,
and(a1,n21) = n0,
inference('REWRITE',[status(thm)],[446,14371,theory(equality)]) ).
cnf(14377,plain,
n21 = and(not(a1),n21),
inference('REWRITE',[status(thm)],[6893,52,and_definition3,50,14371,theory(equality)]) ).
cnf(14390,plain,
and(n11,not(n21)) = n11,
inference('REWRITE',[status(thm)],[14055,14377,theory(equality)]) ).
cnf(14398,plain,
and(not(n21),n12) = n12,
inference('REWRITE',[status(thm)],[14117,14377,theory(equality)]) ).
cnf(14403,plain,
and(not(n21),and(X,n12)) = and(X,n12),
inference('REWRITE',[status(thm)],[12272,11726,and_commutativity,14398,theory(equality)]) ).
cnf(14404,plain,
and(not(n21),and(X,n13)) = and(X,n12),
inference('REWRITE',[status(thm)],[12270,14403,theory(equality)]) ).
cnf(14435,plain,
and(n21,n10) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9904,450,theory(equality)]),110,9604,theory(equality)]) ).
cnf(14449,plain,
and(and(i1,X),and(not(n10),n21)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9913,450,theory(equality)]),121,10727,443,theory(equality)]) ).
cnf(14491,plain,
a1 = and(a1,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,14373,theory(equality)]),1152,and_definition3,50,theory(equality)]) ).
cnf(14494,plain,
and(inv2,not(a1)) = inv2,
inference('PARAMODULATE',[status(thm)],[12579,14491,theory(equality)]) ).
cnf(14504,plain,
n21 = and(not(n10),n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,14435,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(14505,plain,
and(and(i1,X),n21) = n0,
inference('REWRITE',[status(thm)],[14449,14504,theory(equality)]) ).
cnf(14506,plain,
and(i1,n21) = n0,
inference('REWRITE',[status(thm)],[13572,14505,theory(equality)]) ).
cnf(14507,plain,
n0 = and(inv2,n24),
inference('REWRITE',[status(thm)],[443,14506,theory(equality)]) ).
cnf(14508,plain,
and(n24,n21) = n0,
inference('REWRITE',[status(thm)],[444,14506,theory(equality)]) ).
cnf(14509,plain,
n24 = and(n9,n24),
inference('REWRITE',[status(thm)],[6958,52,and_definition3,50,14506,theory(equality)]) ).
cnf(14518,plain,
and(n13,not(n24)) = n13,
inference('REWRITE',[status(thm)],[14219,14509,theory(equality)]) ).
cnf(14561,plain,
inv2 = and(inv2,not(n24)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,14507,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(14791,plain,
and(and(i1,X),and(Y,i3)) = and(X,and(Y,n23)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,587,theory(equality)]) ).
cnf(14807,plain,
and(and(i1,X),and(i3,not(n6))) = and(not(i2),and(X,n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[587,1046,theory(equality)]),10939,theory(equality)]) ).
cnf(15063,plain,
and(and(X,i3),and(inv1,not(i1))) = and(X,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[731,1056,theory(equality)]),10505,theory(equality)]) ).
cnf(15156,plain,
and(and(i2,X),and(Y,i3)) = and(X,and(Y,n14)),
inference('PARAMODULATE',[status(thm)],[and_commutativity,787,theory(equality)]) ).
cnf(15168,plain,
and(and(i2,X),and(i3,not(n6))) = and(not(i1),and(X,n14)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[787,1046,theory(equality)]),10868,theory(equality)]) ).
cnf(15541,plain,
and(n6,n8) = and(n6,n9),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9726,1049,theory(equality)]),9726,12164,theory(equality)]) ).
cnf(15542,plain,
and(n6,not(n15)) = and(n6,n8),
inference('REWRITE',[status(thm)],[1049,15541,theory(equality)]) ).
cnf(15569,plain,
and(n9,and(X,n6)) = and(n8,and(X,n6)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,15542,theory(equality)]),118,10681,theory(equality)]) ).
cnf(15570,plain,
and(not(n15),and(X,n6)) = and(n8,and(X,n6)),
inference('REWRITE',[status(thm)],[10681,15569,theory(equality)]) ).
cnf(15759,plain,
and(n10,n6) = and(n6,n8),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11102,15542,theory(equality)]),11102,12307,theory(equality)]) ).
cnf(15762,plain,
and(n6,not(n15)) = and(n10,n6),
inference('REWRITE',[status(thm)],[15542,15759,theory(equality)]) ).
cnf(15797,plain,
and(not(n10),n6) = n15,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,15762,theory(equality)]),57,52,1196,theory(equality)]) ).
cnf(15798,plain,
and(n8,and(X,n6)) = and(n6,and(X,n10)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,15762,theory(equality)]),and_commutativity,118,15570,theory(equality)]) ).
cnf(15816,plain,
and(n8,not(and(n10,n6))) = and(n8,not(n6)),
inference('PARAMODULATE',[status(thm)],[1196,15759,theory(equality)]) ).
cnf(15819,plain,
and(n10,n6) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15798,11097,theory(equality)]),68,11484,15759,theory(equality)]) ).
cnf(15854,plain,
and(n8,not(n7)) = and(n8,not(n6)),
inference('REWRITE',[status(thm)],[15816,15819,theory(equality)]) ).
cnf(15878,plain,
and(n6,not(i3)) = n15,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,15819,theory(equality)]),15797,1044,theory(equality)]) ).
cnf(15907,plain,
and(not(n23),and(X,n22)) = and(X,n15),
inference('REWRITE',[status(thm)],[13394,15878,theory(equality)]) ).
cnf(16195,plain,
n7 = and(n10,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1418,11876,theory(equality)]),9547,theory(equality)]) ).
cnf(16199,plain,
n7 = and(n10,i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10509,11876,theory(equality)]),69,theory(equality)]) ).
cnf(16202,plain,
n7 = and(i2,n10),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11121,11876,theory(equality)]),521,theory(equality)]) ).
cnf(16217,plain,
n7 = and(n10,n22),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11847,16195,theory(equality)]),2524,theory(equality)]) ).
cnf(16218,plain,
n24 = and(n10,inv1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16195,theory(equality)]),constructor29,11489,theory(equality)]) ).
cnf(16234,plain,
and(i3,not(n6)) = and(not(n10),i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16199,theory(equality)]),1046,theory(equality)]) ).
cnf(16241,plain,
and(and(i1,X),and(not(n10),i3)) = and(not(i2),and(X,n23)),
inference('REWRITE',[status(thm)],[14807,16234,theory(equality)]) ).
cnf(16245,plain,
and(and(i2,X),and(not(n10),i3)) = and(not(i1),and(X,n14)),
inference('REWRITE',[status(thm)],[15168,16234,theory(equality)]) ).
cnf(16263,plain,
a1 = and(not(n10),a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11347,16202,theory(equality)]),11198,theory(equality)]) ).
cnf(16264,plain,
and(n8,not(n10)) = a1,
inference('REWRITE',[status(thm)],[11479,16263,theory(equality)]) ).
cnf(16267,plain,
and(not(a1),n10) = n10,
inference('REWRITE',[status(thm)],[12314,11474,16263,theory(equality)]) ).
cnf(16268,plain,
and(n8,not(a1)) = n10,
inference('REWRITE',[status(thm)],[11474,16267,theory(equality)]) ).
cnf(16280,plain,
and(not(n10),and(X,a1)) = and(X,a1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,16264,theory(equality)]),12316,theory(equality)]) ).
cnf(16281,plain,
and(not(n10),and(X,n8)) = and(X,a1),
inference('REWRITE',[status(thm)],[12316,16280,theory(equality)]) ).
cnf(16285,plain,
and(not(a1),and(X,n10)) = and(X,n10),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,16268,theory(equality)]),12307,theory(equality)]) ).
cnf(16286,plain,
and(not(a1),and(X,n8)) = and(X,n10),
inference('REWRITE',[status(thm)],[12307,16285,theory(equality)]) ).
cnf(16290,plain,
n24 = and(n10,not(n22)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16217,theory(equality)]),11489,theory(equality)]) ).
cnf(16311,plain,
and(inv1,not(i1)) = and(inv1,not(n10)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16218,theory(equality)]),1056,theory(equality)]) ).
cnf(16369,plain,
and(not(n24),not(n22)) = and(not(n22),not(n10)),
inference('PARAMODULATE',[status(thm)],[1196,16290,theory(equality)]) ).
cnf(16380,plain,
n0 = and(n3,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1428,11886,theory(equality)]),1057,theory(equality)]) ).
cnf(16383,plain,
n0 = and(n3,n2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9747,11886,theory(equality)]),10439,theory(equality)]) ).
cnf(16386,plain,
n0 = and(n15,n3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11163,11886,theory(equality)]),11001,theory(equality)]) ).
cnf(16394,plain,
and(n3,n21) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[450,11886,theory(equality)]),14508,110,14494,theory(equality)]) ).
cnf(16405,plain,
n3 = and(n3,inv1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16380,theory(equality)]),constructor29,and_definition3,50,theory(equality)]) ).
cnf(16417,plain,
n3 = and(n3,not(n2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16383,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(16418,plain,
n2 = and(n2,not(n3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16383,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(16421,plain,
and(and(X,i3),n3) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[732,16383,theory(equality)]),and_definition1,16405,theory(equality)]) ).
cnf(16428,plain,
n15 = and(not(n3),n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16386,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(16429,plain,
and(n4,not(n3)) = n15,
inference('REWRITE',[status(thm)],[11504,16428,theory(equality)]) ).
cnf(16432,plain,
and(not(n15),n3) = n3,
inference('REWRITE',[status(thm)],[12342,11509,16428,theory(equality)]) ).
cnf(16433,plain,
and(n4,not(n15)) = n3,
inference('REWRITE',[status(thm)],[11509,16432,theory(equality)]) ).
cnf(16450,plain,
n3 = and(n3,not(n21)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16394,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(16455,plain,
and(not(n3),and(X,n15)) = and(X,n15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,16429,theory(equality)]),12344,theory(equality)]) ).
cnf(16456,plain,
and(not(n3),and(X,n4)) = and(X,n15),
inference('REWRITE',[status(thm)],[12344,16455,theory(equality)]) ).
cnf(16460,plain,
and(not(n15),and(X,n3)) = and(X,n3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,16433,theory(equality)]),12353,theory(equality)]) ).
cnf(16461,plain,
and(not(n15),and(X,n4)) = and(X,n3),
inference('REWRITE',[status(thm)],[12353,16460,theory(equality)]) ).
cnf(16470,plain,
n0 = and(n3,inv2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,16405,theory(equality)]),16394,theory(equality)]) ).
cnf(16472,plain,
n3 = and(n9,n3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10695,16405,theory(equality)]),16450,theory(equality)]) ).
cnf(16477,plain,
inv2 = and(inv2,not(n3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16470,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(16502,plain,
and(and(X,i3),and(not(n3),inv1)) = and(X,n2),
inference('PARAMODULATE',[status(thm)],[732,16418,theory(equality)]) ).
cnf(16536,plain,
n0 = and(n3,i3),
inference('PARAMODULATE',[status(thm)],[and_simplification2,16421,theory(equality)]) ).
cnf(16540,plain,
i3 = and(not(n3),i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16536,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(16578,plain,
n0 = and(n25,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1423,11896,theory(equality)]),1057,theory(equality)]) ).
cnf(16613,plain,
n0 = and(n18,n21),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9615,11896,theory(equality)]),12380,14508,theory(equality)]) ).
cnf(16634,plain,
n0 = and(n25,inv2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9775,11896,theory(equality)]),14507,theory(equality)]) ).
cnf(16641,plain,
and(not(n2),and(n8,n17)) = n24,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11896,12455,theory(equality)]),14509,12164,theory(equality)]) ).
cnf(16651,plain,
n25 = and(inv1,n25),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16578,theory(equality)]),constructor29,and_definition3,50,theory(equality)]) ).
cnf(16675,plain,
n18 = and(n17,not(n21)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16613,theory(equality)]),11459,and_definition3,50,theory(equality)]) ).
cnf(16680,plain,
n18 = and(not(n21),n18),
inference('REWRITE',[status(thm)],[11459,16675,theory(equality)]) ).
cnf(16714,plain,
n25 = and(n9,n17),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,16634,theory(equality)]),12455,271,and_definition3,50,theory(equality)]) ).
cnf(16715,plain,
n25 = and(n9,n18),
inference('REWRITE',[status(thm)],[12451,16714,theory(equality)]) ).
cnf(16721,plain,
and(n9,and(X,n17)) = and(X,n25),
inference('REWRITE',[status(thm)],[12472,and_simplification2,16714,theory(equality)]) ).
cnf(16725,plain,
n19 = and(n18,not(n25)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1670,16634,theory(equality)]),11458,and_definition3,50,theory(equality)]) ).
cnf(16746,plain,
and(not(n21),and(X,n17)) = and(X,n18),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,16680,theory(equality)]),12208,theory(equality)]) ).
cnf(16758,plain,
and(n18,not(n19)) = n25,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1391,16715,theory(equality)]),11456,theory(equality)]) ).
cnf(16763,plain,
n25 = and(not(n19),n25),
inference('REWRITE',[status(thm)],[11456,16758,theory(equality)]) ).
cnf(16771,plain,
and(not(n19),and(X,n18)) = and(X,n25),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,16763,theory(equality)]),12182,theory(equality)]) ).
cnf(17009,plain,
n0 = and(n11,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1428,11906,theory(equality)]),1071,theory(equality)]) ).
cnf(17010,plain,
n0 = and(n11,n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9563,11906,theory(equality)]),9314,theory(equality)]) ).
cnf(17076,plain,
n11 = and(n11,inv1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17009,theory(equality)]),constructor29,and_definition3,50,theory(equality)]) ).
cnf(17083,plain,
n14 = and(not(n11),n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17010,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(17084,plain,
and(X,n16) = and(X,and(n12,not(n11))),
inference('REWRITE',[status(thm)],[14341,109,17083,theory(equality)]) ).
cnf(17086,plain,
n16 = and(n12,not(n11)),
inference('REWRITE',[status(thm)],[13870,13029,17084,theory(equality)]) ).
cnf(17153,plain,
n11 = and(n9,n11),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10695,17076,theory(equality)]),14390,theory(equality)]) ).
cnf(17160,plain,
and(n9,and(X,n11)) = and(X,n11),
inference('REWRITE',[status(thm)],[12525,11997,and_commutativity,17153,theory(equality)]) ).
cnf(17161,plain,
and(n9,and(X,n12)) = and(X,n11),
inference('REWRITE',[status(thm)],[12488,17160,theory(equality)]) ).
cnf(17640,plain,
and(inv1,n12) = n11,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10695,14403,theory(equality)]),17076,17161,theory(equality)]) ).
cnf(17646,plain,
n16 = and(n12,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17640,theory(equality)]),270,17086,theory(equality)]) ).
cnf(17651,plain,
and(not(n16),n20) = and(n20,not(n12)),
inference('PARAMODULATE',[status(thm)],[1196,17646,theory(equality)]) ).
cnf(17681,plain,
n16 = and(n13,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1412,14404,theory(equality)]),17646,theory(equality)]) ).
cnf(17704,plain,
and(n20,not(n12)) = and(n20,not(n13)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17681,theory(equality)]),17651,theory(equality)]) ).
cnf(17837,plain,
and(not(n6),and(n8,n22)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[587,16281,theory(equality)]),9319,14131,16241,theory(equality)]) ).
cnf(17838,plain,
and(and(n8,n23),not(i2)) = n0,
inference('REWRITE',[status(thm)],[14131,17837,theory(equality)]) ).
cnf(17839,plain,
and(n8,n2) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[731,16281,theory(equality)]),9317,15063,16311,theory(equality)]) ).
cnf(17845,plain,
and(not(i1),and(n8,n14)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[787,16281,theory(equality)]),9316,16245,theory(equality)]) ).
cnf(17857,plain,
n8 = and(not(n2),n8),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17839,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(17858,plain,
and(not(n2),n9) = n8,
inference('REWRITE',[status(thm)],[11394,17857,theory(equality)]) ).
cnf(17872,plain,
and(not(n2),and(X,n8)) = and(X,n8),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,17858,theory(equality)]),12164,theory(equality)]) ).
cnf(17874,plain,
and(n8,n17) = n24,
inference('REWRITE',[status(thm)],[16641,17872,theory(equality)]) ).
cnf(17875,plain,
and(not(n2),and(n9,X)) = and(X,n8),
inference('REWRITE',[status(thm)],[12164,17872,theory(equality)]) ).
cnf(17885,plain,
and(n8,n18) = n24,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11724,17874,theory(equality)]),12013,theory(equality)]) ).
cnf(17887,plain,
and(n8,not(n24)) = and(n8,not(n17)),
inference('PARAMODULATE',[status(thm)],[1196,17874,theory(equality)]) ).
cnf(17897,plain,
and(n8,n23) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17838,theory(equality)]),11961,114,constructor9,14791,52,and_definition3,50,theory(equality)]) ).
cnf(17899,plain,
and(n23,not(n19)) = n7,
inference('REWRITE',[status(thm)],[13498,17897,theory(equality)]) ).
cnf(17970,plain,
and(n23,not(i2)) = n19,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17899,theory(equality)]),54,52,1102,theory(equality)]) ).
cnf(17993,plain,
and(not(n6),and(X,n22)) = and(X,n19),
inference('REWRITE',[status(thm)],[12175,17970,theory(equality)]) ).
cnf(17995,plain,
and(n22,not(n19)) = n6,
inference('REWRITE',[status(thm)],[12176,17970,theory(equality)]) ).
cnf(18011,plain,
and(n8,not(n6)) = and(n8,not(n23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17897,theory(equality)]),15854,theory(equality)]) ).
cnf(18014,plain,
and(n8,not(n7)) = and(n8,not(n23)),
inference('REWRITE',[status(thm)],[15854,18011,theory(equality)]) ).
cnf(18024,plain,
and(not(i2),and(X,n23)) = and(X,n19),
inference('PARAMODULATE',[status(thm)],[and_commutativity,17970,theory(equality)]) ).
cnf(18027,plain,
and(not(n6),and(X,n23)) = and(X,n19),
inference('REWRITE',[status(thm)],[10851,18024,theory(equality)]) ).
cnf(18048,plain,
and(n8,n25) = n24,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11709,17885,theory(equality)]),11321,theory(equality)]) ).
cnf(18097,plain,
and(n8,not(n17)) = and(n8,not(n25)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18048,theory(equality)]),17887,theory(equality)]) ).
cnf(18106,plain,
and(n8,n14) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,17845,theory(equality)]),11961,114,constructor9,15156,52,and_definition3,50,theory(equality)]) ).
cnf(18108,plain,
and(n14,not(n16)) = n7,
inference('REWRITE',[status(thm)],[13314,18106,theory(equality)]) ).
cnf(18182,plain,
and(n14,not(i1)) = n16,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18108,theory(equality)]),58,52,1099,theory(equality)]) ).
cnf(18183,plain,
n16 = and(n14,not(n6)),
inference('REWRITE',[status(thm)],[1097,18182,theory(equality)]) ).
cnf(18236,plain,
and(n8,not(n23)) = and(n8,not(n14)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18106,theory(equality)]),18014,theory(equality)]) ).
cnf(18241,plain,
and(n8,not(n7)) = and(n8,not(n14)),
inference('REWRITE',[status(thm)],[18014,18236,theory(equality)]) ).
cnf(18321,plain,
and(n3,n10) = n24,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11886,16285,theory(equality)]),11315,theory(equality)]) ).
cnf(18327,plain,
a1 = and(n3,not(n10)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18321,theory(equality)]),11519,theory(equality)]) ).
cnf(18328,plain,
n7 = and(n10,not(n3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18321,theory(equality)]),11484,theory(equality)]) ).
cnf(18334,plain,
not(n8) = and(not(n10),not(n3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18327,theory(equality)]),6516,theory(equality)]) ).
cnf(18348,plain,
n7 = and(n8,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1428,16286,theory(equality)]),16195,theory(equality)]) ).
cnf(18366,plain,
and(n8,not(n14)) = and(n8,inv1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18348,theory(equality)]),constructor29,18241,theory(equality)]) ).
cnf(18373,plain,
and(n8,not(n7)) = and(n8,inv1),
inference('REWRITE',[status(thm)],[18241,18366,theory(equality)]) ).
cnf(18385,plain,
and(n8,and(X,n20)) = and(X,n7),
inference('PARAMODULATE',[status(thm)],[and_commutativity,18348,theory(equality)]) ).
cnf(18413,plain,
and(n4,n21) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[450,16456,theory(equality)]),10999,110,16477,theory(equality)]) ).
cnf(18421,plain,
and(n4,n23) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[587,16456,theory(equality)]),13001,112,16540,theory(equality)]) ).
cnf(18423,plain,
and(n4,n2) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[731,16456,theory(equality)]),9417,16502,theory(equality)]) ).
cnf(18440,plain,
n4 = and(not(n21),n4),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18413,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(18441,plain,
and(n5,not(n21)) = n4,
inference('REWRITE',[status(thm)],[11499,18440,theory(equality)]) ).
cnf(18464,plain,
n0 = and(n4,n19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18027,18421,theory(equality)]),and_definition1,theory(equality)]) ).
cnf(18470,plain,
n4 = and(n4,not(n2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18423,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(18479,plain,
and(not(n21),and(X,n4)) = and(X,n4),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[and_commutativity,18441,theory(equality)]),12335,theory(equality)]) ).
cnf(18480,plain,
and(not(n21),and(X,n5)) = and(X,n4),
inference('REWRITE',[status(thm)],[12335,18479,theory(equality)]) ).
cnf(18492,plain,
n4 = and(n4,not(n19)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18464,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(18523,plain,
and(not(n2),and(X,n4)) = and(X,n4),
inference('PARAMODULATE',[status(thm)],[and_commutativity,18470,theory(equality)]) ).
cnf(18553,plain,
and(not(n19),and(X,n4)) = and(X,n4),
inference('PARAMODULATE',[status(thm)],[and_commutativity,18492,theory(equality)]) ).
cnf(18562,plain,
n3 = and(n9,n4),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1397,16461,theory(equality)]),16472,theory(equality)]) ).
cnf(18563,plain,
and(n4,inv1) = n3,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11442,16461,theory(equality)]),16405,theory(equality)]) ).
cnf(18580,plain,
n15 = and(n4,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18563,theory(equality)]),270,16429,theory(equality)]) ).
cnf(18626,plain,
and(n20,n18) = and(n17,n20),
inference('PARAMODULATE',[status(thm)],[1412,16746,theory(equality)]) ).
cnf(18637,plain,
and(inv1,n18) = n25,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10695,16746,theory(equality)]),16651,16721,theory(equality)]) ).
cnf(18650,plain,
n19 = and(n17,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18637,theory(equality)]),18626,270,16725,theory(equality)]) ).
cnf(18659,plain,
and(n17,not(n19)) = and(n17,inv1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18650,theory(equality)]),constructor29,theory(equality)]) ).
cnf(19005,plain,
and(n11,n8) = a1,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11911,17872,theory(equality)]),11338,theory(equality)]) ).
cnf(19006,plain,
and(n8,i3) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10687,17872,theory(equality)]),69,18385,and_commutativity,theory(equality)]) ).
cnf(19011,plain,
n2 = and(n11,not(n8)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,19005,theory(equality)]),11534,theory(equality)]) ).
cnf(19012,plain,
n10 = and(n8,not(n11)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,19005,theory(equality)]),16268,theory(equality)]) ).
cnf(19014,plain,
and(n8,inv1) = and(n8,not(i3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,19006,theory(equality)]),18373,theory(equality)]) ).
cnf(19018,plain,
inv2 = and(not(n8),not(n11)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,19011,theory(equality)]),6517,theory(equality)]) ).
cnf(19065,plain,
n3 = and(n4,n8),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17875,18562,theory(equality)]),16417,theory(equality)]) ).
cnf(19130,plain,
and(n8,not(n3)) = and(n8,not(n4)),
inference('PARAMODULATE',[status(thm)],[1196,19065,theory(equality)]) ).
cnf(19311,plain,
and(n17,n4) = and(n4,n18),
inference('PARAMODULATE',[status(thm)],[16746,18479,theory(equality)]) ).
cnf(19317,plain,
and(n17,n3) = and(n18,n3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16461,19311,theory(equality)]),16461,theory(equality)]) ).
cnf(19318,plain,
and(n17,n4) = and(n4,n25),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16771,19311,theory(equality)]),18553,theory(equality)]) ).
cnf(19337,plain,
and(n17,n4) = n24,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11896,19318,theory(equality)]),12006,18523,theory(equality)]) ).
cnf(19338,plain,
n24 = and(n4,n18),
inference('REWRITE',[status(thm)],[19311,19337,theory(equality)]) ).
cnf(19340,plain,
n24 = and(n17,n3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16461,19338,theory(equality)]),19317,11003,theory(equality)]) ).
cnf(19352,plain,
a1 = and(n3,not(n17)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,19340,theory(equality)]),11519,theory(equality)]) ).
cnf(19392,plain,
n3 = and(n9,n5),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1407,18480,theory(equality)]),18562,theory(equality)]) ).
cnf(19393,plain,
n15 = and(n5,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1412,18480,theory(equality)]),18580,theory(equality)]) ).
cnf(19418,plain,
and(n9,not(n3)) = and(n9,not(n5)),
inference('PARAMODULATE',[status(thm)],[1196,19392,theory(equality)]) ).
cnf(19427,plain,
and(n5,not(n15)) = and(inv1,n5),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,19393,theory(equality)]),constructor29,theory(equality)]) ).
cnf(19665,plain,
and(not(n11),n9) = n10,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,19018,theory(equality)]),19012,52,271,theory(equality)]) ).
cnf(19667,plain,
n10 = and(n9,not(n13)),
inference('REWRITE',[status(thm)],[12521,19665,theory(equality)]) ).
cnf(19680,plain,
and(not(n13),and(n9,X)) = and(X,n10),
inference('PARAMODULATE',[status(thm)],[and_commutativity,19667,theory(equality)]) ).
cnf(19764,plain,
and(not(n15),not(and(inv1,n5))) = not(n5),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,19427,theory(equality)]),11999,theory(equality)]) ).
cnf(19905,plain,
and(i2,not(and(not(n22),i1))) = i2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3406,9801,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(19952,plain,
and(not(n22),and(i1,not(i2))) = and(not(n22),i1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12580,19905,theory(equality)]),and_commutativity,theory(equality)]) ).
cnf(20139,plain,
and(inv2,not(and(inv1,not(n17)))) = inv2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3990,9856,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(20140,plain,
and(inv2,not(and(inv1,not(n13)))) = inv2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3990,9883,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(20141,plain,
and(inv2,not(and(inv1,not(n5)))) = inv2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3990,9919,theory(equality)]),and_definition3,50,theory(equality)]) ).
cnf(20192,plain,
and(not(n22),not(i2)) = and(inv1,not(a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9524,1320,theory(equality)]),1083,theory(equality)]) ).
cnf(20193,plain,
and(not(n22),not(i3)) = and(inv1,not(i3)),
inference('PARAMODULATE',[status(thm)],[9524,1324,theory(equality)]) ).
cnf(20205,plain,
and(not(n22),and(not(i2),X)) = and(X,and(inv1,not(a1))),
inference('PARAMODULATE',[status(thm)],[and_commutativity,20192,theory(equality)]) ).
cnf(20206,plain,
n24 = and(not(n22),i1),
inference('REWRITE',[status(thm)],[19952,constructor27,11230,and_commutativity,20205,theory(equality)]) ).
cnf(20208,plain,
and(not(i2),n20) = and(not(i2),n22),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,20192,theory(equality)]),52,270,3322,theory(equality)]) ).
cnf(20212,plain,
and(not(n22),not(n10)) = and(not(n22),not(i1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,20206,theory(equality)]),16369,theory(equality)]) ).
cnf(20213,plain,
and(not(n24),not(n22)) = and(not(n22),not(i1)),
inference('REWRITE',[status(thm)],[16369,20212,theory(equality)]) ).
cnf(20216,plain,
and(i1,n20) = and(i1,n22),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,20206,theory(equality)]),52,1042,theory(equality)]) ).
cnf(20226,plain,
and(n20,not(i3)) = and(not(i3),n22),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,20193,theory(equality)]),52,270,1196,theory(equality)]) ).
cnf(20231,plain,
and(not(i2),n20) = n19,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17993,20208,theory(equality)]),13012,2429,theory(equality)]) ).
cnf(20259,plain,
n19 = and(not(i2),n22),
inference('REWRITE',[status(thm)],[20208,20231,theory(equality)]) ).
cnf(20275,plain,
n6 = and(n22,i2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,20259,theory(equality)]),52,17995,theory(equality)]) ).
cnf(20299,plain,
n16 = and(not(n22),n14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2103,20275,theory(equality)]),18183,theory(equality)]) ).
cnf(20303,plain,
and(n20,not(n12)) = n22,
inference('REWRITE',[status(thm)],[12155,17651,20299,theory(equality)]) ).
cnf(20308,plain,
n22 = and(n20,not(n13)),
inference('REWRITE',[status(thm)],[17704,20303,theory(equality)]) ).
cnf(20461,plain,
and(not(i3),not(n8)) = and(not(i3),inv2),
inference('PARAMODULATE',[status(thm)],[9635,1358,theory(equality)]) ).
cnf(20463,plain,
and(not(n8),not(n25)) = inv2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9635,6522,theory(equality)]),14561,theory(equality)]) ).
cnf(20477,plain,
and(n9,not(n17)) = and(n8,not(n17)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,20463,theory(equality)]),18097,52,12464,271,theory(equality)]) ).
cnf(20485,plain,
and(not(i3),n9) = and(n8,inv1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,20461,theory(equality)]),19014,52,271,1196,theory(equality)]) ).
cnf(20491,plain,
and(n9,not(and(n8,inv1))) = and(n9,i3),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,20485,theory(equality)]),52,theory(equality)]) ).
cnf(20497,plain,
and(not(n17),and(n9,X)) = and(not(n17),and(X,n8)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,20477,theory(equality)]),118,and_commutativity,theory(equality)]) ).
cnf(21589,plain,
and(n20,not(i3)) = n15,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15907,20226,theory(equality)]),13045,2362,theory(equality)]) ).
cnf(21608,plain,
n15 = and(not(i3),n22),
inference('REWRITE',[status(thm)],[20226,21589,theory(equality)]) ).
cnf(21625,plain,
and(not(i3),not(n15)) = and(inv1,not(i3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,21608,theory(equality)]),20193,theory(equality)]) ).
cnf(22246,plain,
and(n8,not(n3)) = n7,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18334,theory(equality)]),18328,52,theory(equality)]) ).
cnf(22247,plain,
n7 = and(n8,not(n4)),
inference('REWRITE',[status(thm)],[19130,22246,theory(equality)]) ).
cnf(22256,plain,
and(n8,inv1) = n3,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,22247,theory(equality)]),19065,52,18373,theory(equality)]) ).
cnf(22299,plain,
and(n9,not(n3)) = and(n9,i3),
inference('REWRITE',[status(thm)],[20491,22256,theory(equality)]) ).
cnf(22303,plain,
and(n9,i3) = and(n9,not(n5)),
inference('REWRITE',[status(thm)],[19418,22299,theory(equality)]) ).
cnf(22396,plain,
and(not(n5),and(n9,X)) = and(n9,and(X,i3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,22303,theory(equality)]),and_commutativity,118,theory(equality)]) ).
cnf(22509,plain,
and(not(n19),not(and(n17,inv1))) = not(n17),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,18659,theory(equality)]),11980,theory(equality)]) ).
cnf(22894,plain,
a1 = and(inv1,not(n17)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12580,20139,theory(equality)]),19352,22256,20497,and_commutativity,271,theory(equality)]) ).
cnf(22896,plain,
and(inv1,not(a1)) = and(n17,inv1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,22894,theory(equality)]),52,theory(equality)]) ).
cnf(22897,plain,
and(n17,inv1) = and(inv1,not(i2)),
inference('REWRITE',[status(thm)],[1083,22896,theory(equality)]) ).
cnf(22898,plain,
and(i2,not(and(n17,inv1))) = i2,
inference('REWRITE',[status(thm)],[1362,22896,theory(equality)]) ).
cnf(22952,plain,
and(not(i2),not(and(n17,inv1))) = n19,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,22897,theory(equality)]),20231,270,theory(equality)]) ).
cnf(22971,plain,
not(n17) = i2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,22952,theory(equality)]),22898,52,22509,theory(equality)]) ).
cnf(23123,plain,
not(i2) = n17,
inference('PARAMODULATE',[status(thm)],[52,22971,theory(equality)]) ).
cnf(23124,plain,
( ~ circuit(not(i1))
| ~ circuit(not(i3)) ),
inference('REWRITE',[status(thm)],[prove_inversion,46,23123,theory(equality)]) ).
cnf(23512,plain,
n24 = and(inv1,not(n13)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12580,20140,theory(equality)]),16218,19680,and_commutativity,271,theory(equality)]) ).
cnf(23554,plain,
and(not(n13),not(n24)) = n22,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,23512,theory(equality)]),20308,270,theory(equality)]) ).
cnf(23575,plain,
and(not(n22),not(i1)) = n13,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,23554,theory(equality)]),14518,52,20213,theory(equality)]) ).
cnf(23577,plain,
and(not(n24),not(n22)) = n13,
inference('REWRITE',[status(thm)],[20213,23575,theory(equality)]) ).
cnf(23624,plain,
n2 = and(inv1,not(n5)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12580,20141,theory(equality)]),9687,constructor5,22396,and_commutativity,271,theory(equality)]) ).
cnf(23628,plain,
and(inv1,not(i3)) = and(inv1,n5),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,23624,theory(equality)]),52,1070,theory(equality)]) ).
cnf(23662,plain,
and(not(i3),not(n15)) = and(inv1,n5),
inference('REWRITE',[status(thm)],[21625,23628,theory(equality)]) ).
cnf(24129,plain,
not(n5) = i3,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,23662,theory(equality)]),13129,52,19764,theory(equality)]) ).
cnf(24264,plain,
not(i3) = n5,
inference('PARAMODULATE',[status(thm)],[52,24129,theory(equality)]) ).
cnf(24530,plain,
~ circuit(not(i1)),
inference('REWRITE',[status(thm)],[23124,48,24264,theory(equality)]) ).
cnf(30736,plain,
and(n22,not(i1)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15907,2355,theory(equality)]),1963,theory(equality)]) ).
cnf(30750,plain,
n22 = and(i1,n20),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1196,30736,theory(equality)]),20216,52,and_definition3,50,theory(equality)]) ).
cnf(30776,plain,
n13 = not(i1),
inference('REWRITE',[status(thm)],[11365,23577,30750,theory(equality)]) ).
cnf(31346,plain,
$false,
inference('REWRITE',[status(thm)],[24530,44,30776,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HWV002-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n012.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 : Fri Jun 17 03:54:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 *
% 0.19/0.47 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-17T03:54:24
% 0.19/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-06-17T03:54:24
% 0.19/0.49
% 0.19/0.49 ; Recognized left identity assertion (= (|xor| |n0| ?X) ?X).
% 0.19/0.49 ; Recognized right identity assertion (= (|xor| ?X |n0|) ?X).
% 0.19/0.49 ; Recognized left identity assertion (= (|and| |n1| ?X) ?X).
% 0.19/0.49 ; Recognized right identity assertion (= (|and| ?X |n1|) ?X).
% 0.19/0.49 ; Recognized commutativity assertion (= (|xor| ?X ?Y) (|xor| ?Y ?X)).
% 0.19/0.49 ; Recognized commutativity assertion (= (|and| ?X ?Y) (|and| ?Y ?X)).
% 0.19/0.49 ; Declaring xor to be commutative.
% 136.41/136.61 ; Declaring and to be commutative.
% 136.41/136.61
% 136.41/136.61 #||
% 136.41/136.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 136.41/136.61 % SZS output start Refutation
% See solution above
% 136.80/136.96 ||#
% 136.80/136.96
% 136.80/136.96 ; Summary of computation:
% 136.80/136.97 ; 455092 formulas have been input or derived (from 3466 formulas).
% 136.80/136.97 ; 31346 ( 7%) were retained. Of these,
% 136.80/136.97 ; 17748 (57%) were simplified or subsumed later,
% 136.80/136.97 ; 13598 (43%) are still being kept.
% 136.80/136.97 ;
% 136.80/136.97 ; Run time in seconds excluding printing time:
% 136.80/136.97 ; 0.005 0% Read assertion file (1 call)
% 136.80/136.97 ; 0.002 0% Assert (51 calls)
% 136.80/136.97 ; 6.231 5% Process new row (385,314 calls)
% 136.80/136.97 ; 0.379 0% Resolution (6,930 calls)
% 136.80/136.97 ; 13.162 10% Paramodulation (3,465 calls)
% 136.80/136.97 ; 0.000 0% Condensing (2 calls)
% 136.80/136.97 ; 0.000 0% Forward subsumption (2 calls)
% 136.80/136.97 ; 0.000 0% Backward subsumption (2 calls)
% 136.80/136.97 ; 61.868 45% Forward simplification (382,545 calls)
% 136.80/136.97 ; 10.940 8% Backward simplification (31,343 calls)
% 136.80/136.97 ; 42.267 31% Ordering (8,098,992 calls)
% 136.80/136.97 ; 0.002 0% Sortal reasoning (32 calls)
% 136.80/136.97 ; 0.000 0% Purity testing (1 call)
% 136.80/136.97 ; 1.277 1% Other
% 136.80/136.97 ; 136.133 Total
% 136.80/136.97 ; 136.490 Real time
% 136.80/136.97 ;
% 136.80/136.97 ; Term-hash-array has 101,192 terms in all.
% 136.80/136.97 ; Feature-vector-row-index has 0 entries (1 at peak, 2 added, 2 deleted).
% 136.80/136.97 ; Feature-vector-row-index has 1 node (11 at peak, 19 added, 18 deleted).
% 136.80/136.97 ; Retrieved 0 possibly forward subsuming rows in 2 calls.
% 136.80/136.97 ; Retrieved 0 possibly backward subsumed rows in 2 calls.
% 136.80/136.97 ; Path-index has 45,259 entries (47,274 at peak, 122,444 added, 77,185 deleted).
% 136.80/136.97 ; Path-index has 4,456 nodes (6,424 at peak, 12,230 added, 7,774 deleted).
% 136.80/136.97 ; Trie-index has 45,259 entries (47,274 at peak, 122,444 added, 77,185 deleted).
% 136.80/136.97 ; Trie-index has 305,772 nodes (318,581 at peak, 962,645 added, 656,873 deleted).
% 136.80/136.97 ; Retrieved 5,467,914 generalization terms in 3,258,305 calls.
% 136.80/136.97 ; Retrieved 895,472 instance terms in 44,000 calls.
% 136.80/136.97 ; Retrieved 4,227,914 unifiable terms in 25,599 calls.
% 136.80/136.97 ;
% 136.80/136.97 ; The agenda of backward simplifiable rows to process has 224 entries:
% 136.80/136.97 ; 224 with value 0
% 136.80/136.97 ; The agenda of rows to process has 42 entries:
% 136.80/136.97 ; 6 with value 22 1 with value 25 4 with value 27
% 136.80/136.97 ; 1 with value 23 10 with value 26 4 with value 74
% 136.80/136.97 ; 16 with value 24
% 136.80/136.97 ; The agenda of rows to give has 11447 entries:
% 136.80/136.97 ; 1 with value (4 9) 70 with value (4 43) 43 with value (4 75)
% 136.80/136.97 ; 2 with value (4 11) 33 with value (4 44) 50 with value (4 76)
% 136.80/136.97 ; 5 with value (4 13) 70 with value (4 45) 14 with value (4 77)
% 136.80/136.97 ; 1 with value (4 14) 66 with value (4 46) 24 with value (4 78)
% 136.80/136.97 ; 4 with value (4 15) 59 with value (4 47) 12 with value (4 79)
% 136.80/136.97 ; 10 with value (4 16) 44 with value (4 48) 31 with value (4 80)
% 136.80/136.97 ; 2 with value (4 17) 31 with value (4 49) 20 with value (4 81)
% 136.80/136.97 ; 11 with value (4 18) 35 with value (4 50) 23 with value (4 82)
% 136.80/136.97 ; 17 with value (4 19) 39 with value (4 51) 59 with value (4 83)
% 136.80/136.97 ; 602 with value (4 20) 84 with value (4 52) 29 with value (4 84)
% 136.80/136.97 ; 688 with value (4 21) 83 with value (4 53) 36 with value (4 85)
% 136.80/136.97 ; 501 with value (4 22) 69 with value (4 54) 34 with value (4 86)
% 136.80/136.97 ; 964 with value (4 23) 33 with value (4 55) 18 with value (4 87)
% 136.80/136.97 ; 1016 with value (4 24) 105 with value (4 56) 5 with value (4 88)
% 136.80/136.97 ; 901 with value (4 25) 73 with value (4 57) 18 with value (4 89)
% 136.80/136.97 ; 653 with value (4 26) 54 with value (4 58) 10 with value (4 90)
% 136.80/136.97 ; 573 with value (4 27) 58 with value (4 59) 13 with value (4 91)
% 136.80/136.97 ; 715 with value (4 28) 62 with value (4 60) 23 with value (4 92)
% 136.80/136.97 ; 1173 with value (4 29) 45 with value (4 61) 9 with value (4 93)
% 136.80/136.97 ; 695 with value (4 30) 111 with value (4 62) 5 with value (4 95)
% 136.80/136.97 ; 101 with value (4 31) 89 with value (4 63) 11 with value (4 96)
% 136.80/136.97 ; 22 with value (4 32) 54 with value (4 64) 5 with value (4 97)
% 136.80/136.97 ; 45 with value (4 33) 59 with value (4 65) 9 with value (4 100)
% 136.80/136.97 ; 12 with value (4 34) 48 with value (4 66) 4 with value (4 108)
% 136.80/136.97 ; 35 with value (4 35) 60 with value (4 67) 1 with value (4 112)
% 136.80/136.97 ; 8 with value (4 36) 50 with value (4 68) 1 with value (4 137)
% 136.80/136.97 ; 46 with value (4 37) 42 with value (4 69) 1 with value (4 140)
% 136.80/136.97 ; 28 with value (4 38) 42 with value (4 70) 2 with value (4 157)
% 136.80/136.97 ; 28 with value (4 39) 43 with value (4 71) 1 with value (4 159)
% 136.80/136.97 ; 8 with value (4 40) 60 with value (4 72) 2 with value (4 160)
% 136.80/136.97 ; 33 with value (4 41) 113 with value (4 73) 2 with value (4 176)
% 136.80/136.97 ; 35 with value (4 42) 112 with value (4 74) 1 with value (4 194)
% 136.80/136.97 Evaluation took:
% 136.80/136.97 136.494 seconds of real time
% 136.80/136.97 124.19304 seconds of user run time
% 136.80/136.97 12.303469 seconds of system run time
% 136.80/136.97 [Run times include 28.114 seconds GC run time.]
% 136.80/136.97 0 calls to %EVAL
% 136.80/136.97 0 page faults and
% 136.80/136.97 9,392,002,016 bytes consed.
% 136.80/136.97 :PROOF-FOUND
% 136.80/136.97 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-17T03:56:40
% 136.80/136.97 :PROOF-FOUND
% 136.80/136.97 *
%------------------------------------------------------------------------------