TSTP Solution File: LCL018-1 by CARINE---0.734
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL018-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sat Nov 27 23:22:39 EST 2010
% Result : Unsatisfiable 82.80s
% Output : Refutation 82.80s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Command entered:
% /home/graph/tptp/Systems/CARINE---0.734/carine /tmp/SystemOnTPTP15063/LCL/LCL018-1+noeq.car t=300 xo=off uct=32000
% CARINE version 0.734 (Dec 2003)
% Initializing tables ... done.
% Parsing ... done.
% Calculating time slices ... done.
% Building Lookup Tables ... done.
% Looking for a proof at depth = 1 ...
% t = 0 secs [nr = 3] [nf = 0] [nu = 0] [ut = 2]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 92] [nf = 0] [nu = 45] [ut = 32]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 214] [nf = 4] [nu = 115] [ut = 32]
% Looking for a proof at depth = 4 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)))
% B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U0: < d0 v0 dv0 f5 c6 t11 td5 b nc > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))
% U1: < d0 v6 dv3 f5 c0 t11 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)))
% U4: < d2 v6 dv3 f5 c0 t11 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x2))))
% U5: < d2 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2))),x1)))
% U6: < d2 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0))
% U7: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5))))
% U8: < d2 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(x4,equivalent_2(x6,x3)),x6))),x5)))
% U17: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x0)),x2),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3)))))
% U18: < d2 v12 dv6 f11 c0 t23 td11 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,equivalent_2(equivalent_2(x3,equivalent_2(x5,x2)),x5))),x4))),x1)))
% U216: < d4 v10 dv5 f9 c0 t19 td9 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x2),x4)))),x1)))
% U218: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x5),x4)),equivalent_2(x6,x5)),x6)))
% U219: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))))
% U221: < d4 v14 dv7 f13 c0 t27 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3)))),equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x5),x4),x6)))),x0))
% U628: < d4 v16 dv8 f15 c0 t31 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x3,equivalent_2(equivalent_2(x6,equivalent_2(x7,x5)),x7))))),x4)))
% U790: < d4 v14 dv7 f13 c0 t27 td9 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3)),x0),equivalent_2(equivalent_2(x2,equivalent_2(x6,x1)),x6)))))
% U1001: < d4 v16 dv8 f15 c0 t31 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x3),x2)),equivalent_2(x4,x3)),x4)),equivalent_2(equivalent_2(equivalent_2(x5,equivalent_2(x6,x7)),x6),equivalent_2(x7,x5))),x0))
% U1004: < d4 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,equivalent_2(equivalent_2(x6,equivalent_2(x8,x5)),x8))),x7))),x4))
% U1218: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x5),x4),x6)))),x0))
% U1900: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5)))))
% U2362: < d4 v8 dv4 f7 c0 t15 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0))
% U2498: < d4 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(x7,x6),x5),x7)))),equivalent_2(equivalent_2(x1,equivalent_2(x8,x0)),x8))))
% U2506: < d4 v20 dv10 f19 c0 t39 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5)))),equivalent_2(equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(x7,x6),x8),x7)),equivalent_2(x9,x8)),x9)))
% U2859: < d4 v6 dv3 f5 c0 t11 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x0),x2),x1)))
% U2860: < d4 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1)))
% U2861: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),x1),equivalent_2(x3,x2))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0))
% U2863: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5)))
% U2876: < d4 v6 dv3 f5 c0 t11 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x0,equivalent_2(x2,x1)),x2))))
% U2884: < d4 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1),x0))
% U2889: < d4 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),x1),equivalent_2(x3,x2)),equivalent_2(x4,x0)),x4)))
% U2892: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),x4),equivalent_2(x6,x5)))),x3))
% U2894: < d4 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)))
% U2895: < d4 v2 dv1 f1 c0 t3 td2 > is_a_theorem_1(equivalent_2(x0,x0))
% U3548: < d4 v12 dv6 f11 c0 t23 td10 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x3),x2)),equivalent_2(x4,x3)),x4),equivalent_2(x5,x0)),x5)))
% U3975: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),x4),equivalent_2(x6,x5))),x0))
% U4054: < d4 v12 dv6 f17 c6 t35 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))))
% U4263: < d4 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,equivalent_2(equivalent_2(equivalent_2(x8,x6),x5),x8))),x7))),x4))
% U4675: < d4 v20 dv10 f25 c6 t51 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x1),x0),x3))),x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6,x7),x8),x6),equivalent_2(x8,x7)),equivalent_2(equivalent_2(x5,equivalent_2(x9,x4)),x9))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))))
% U5237: < d4 v6 dv3 f5 c0 t11 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2))))
% U5398: < d4 v26 dv13 f31 c6 t63 td10 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),x11),x9),equivalent_2(x11,x10)),equivalent_2(equivalent_2(x8,equivalent_2(x12,x7)),x12))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))))))
% U19296: < d4 v16 dv8 f15 c0 t31 td11 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4)),equivalent_2(equivalent_2(equivalent_2(x7,x3),x2),x7)))),x0),x1)))
% --------------- Start of Proof ---------------
% Derivation of unit clause U0:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))) ....... U0
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1
% Derivation of unit clause U4:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1
% is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2)))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U5:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x2)))) ....... U4
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), equivalent_2(equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), x3), equivalent_2(x4, x2))), x1))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U6:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2))),x1))) ....... U5
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4))), x0)) ....... R2 [R1:L0, U5:L0]
% Derivation of unit clause U7:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0)) ....... U6
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), x3), equivalent_2(x4, x2)), equivalent_2(equivalent_2(x1, equivalent_2(x5, x0)), x5)))) ....... R2 [R1:L0, U6:L0]
% Derivation of unit clause U8:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, equivalent_2(equivalent_2(x4, equivalent_2(x6, x3)), x6))), x5))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U17:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1)) | is_a_theorem_1(equivalent_2(x2, x0)) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0)) ....... U6
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x0)), x2), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, x5)), x4), equivalent_2(x5, x3))))) ....... R2 [R1:L0, U6:L0]
% Derivation of unit clause U18:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1)) | is_a_theorem_1(equivalent_2(x2, x0)) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(x4,equivalent_2(x6,x3)),x6))),x5))) ....... U8
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, equivalent_2(equivalent_2(x3, equivalent_2(x5, x2)), x5))), x4))), x1))) ....... R2 [R1:L0, U8:L0]
% Derivation of unit clause U216:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x2)))) ....... U4
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), equivalent_2(x2, equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(x4, x3), x2), x4)))), x1))) ....... R4 [R3:L0, U4:L0]
% Derivation of unit clause U218:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(x4, x3), x5), x4)), equivalent_2(x6, x5)), x6))) ....... R4 [R3:L0, U7:L0]
% Derivation of unit clause U219:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x0)),x2),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3))))) ....... U17
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4)))) ....... R4 [R3:L0, U17:L0]
% Derivation of unit clause U221:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x2),x4)))),x1))) ....... U216
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x2), x1), x3)))), equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(x6, x5), x4), x6)))), x0)) ....... R4 [R3:L0, U216:L0]
% Derivation of unit clause U628:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(x4,equivalent_2(x6,x3)),x6))),x5))) ....... U8
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(x1, equivalent_2(x3, x0)), x3))), x2), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U8:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(x3, equivalent_2(equivalent_2(x6, equivalent_2(x7, x5)), x7))))), x4))) ....... R4 [R3:L0, U7:L0]
% Derivation of unit clause U790:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x0)),x2),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3))))) ....... U17
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(x1, equivalent_2(x3, x0)), x3))), x2), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U17:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, x5)), x4), equivalent_2(x5, x3)), x0), equivalent_2(equivalent_2(x2, equivalent_2(x6, x1)), x6))))) ....... R4 [R3:L0, U1:L0]
% Derivation of unit clause U1001:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x5),x4)),equivalent_2(x6,x5)),x6))) ....... U218
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U218:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2))),x1))) ....... U5
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x3), x2)), equivalent_2(x4, x3)), x4)), equivalent_2(equivalent_2(equivalent_2(x5, equivalent_2(x6, x7)), x6), equivalent_2(x7, x5))), x0)) ....... R4 [R3:L0, U5:L0]
% Derivation of unit clause U1004:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x5),x4)),equivalent_2(x6,x5)),x6))) ....... U218
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U218:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,equivalent_2(equivalent_2(x3,equivalent_2(x5,x2)),x5))),x4))),x1))) ....... U18
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x7, equivalent_2(equivalent_2(x6, equivalent_2(x8, x5)), x8))), x7))), x4)) ....... R4 [R3:L0, U18:L0]
% Derivation of unit clause U1218:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4)))) ....... U219
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U219:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x2),x4)))),x1))) ....... U216
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x2), equivalent_2(x3, x1))), equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(x6, x5), x4), x6)))), x0)) ....... R4 [R3:L0, U216:L0]
% Derivation of unit clause U1900:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x3,equivalent_2(equivalent_2(x6,equivalent_2(x7,x5)),x7))))),x4))) ....... U628
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(x0, equivalent_2(equivalent_2(x3, equivalent_2(x4, x2)), x4))))), x1), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U628:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3)))),equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x5),x4),x6)))),x0)) ....... U221
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x4), x3), x5))))) ....... R4 [R3:L0, U221:L0]
% Derivation of unit clause U2362:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x5),x4),x6)))),x0)) ....... U1218
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, x5)), x4), equivalent_2(x5, x3)), x2)), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1218:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x3),x2)),equivalent_2(x4,x3)),x4)),equivalent_2(equivalent_2(equivalent_2(x5,equivalent_2(x6,x7)),x6),equivalent_2(x7,x5))),x0)) ....... U1001
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x2), x1), x3))), x0)) ....... R4 [R3:L0, U1001:L0]
% Derivation of unit clause U2498:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5))))) ....... U1900
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1900:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3)),x0),equivalent_2(equivalent_2(x2,equivalent_2(x6,x1)),x6))))) ....... U790
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), x3), equivalent_2(x4, x2)), equivalent_2(x5, equivalent_2(x6, equivalent_2(equivalent_2(equivalent_2(x7, x6), x5), x7)))), equivalent_2(equivalent_2(x1, equivalent_2(x8, x0)), x8)))) ....... R4 [R3:L0, U790:L0]
% Derivation of unit clause U2506:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5))))) ....... U1900
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1900:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(x7,x6),x5),x7)))),equivalent_2(equivalent_2(x1,equivalent_2(x8,x0)),x8)))) ....... U2498
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x4), x3), x5)))), equivalent_2(equivalent_2(equivalent_2(x6, equivalent_2(equivalent_2(equivalent_2(x7, x6), x8), x7)), equivalent_2(x9, x8)), x9))) ....... R4 [R3:L0, U2498:L0]
% Derivation of unit clause U2859:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), x0), x2), x1))) ....... R4 [R3:L0, U1:L0]
% Derivation of unit clause U2860:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x2)))) ....... U4
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x2), equivalent_2(x4, x3))), x1))) ....... R4 [R3:L0, U4:L0]
% Derivation of unit clause U2861:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2))),x1))) ....... U5
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), x1), equivalent_2(x3, x2))), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4))), x0)) ....... R4 [R3:L0, U5:L0]
% Derivation of unit clause U2863:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(x6, x4), x3), x6))), x5))) ....... R4 [R3:L0, U7:L0]
% Derivation of unit clause U2876:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,equivalent_2(equivalent_2(x6,equivalent_2(x8,x5)),x8))),x7))),x4)) ....... U1004
% is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x0, equivalent_2(x2, x1)), x2)))) ....... R4 [R3:L0, U1004:L0]
% Derivation of unit clause U2884:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x0),x2),x1))) ....... U2859
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x2), equivalent_2(x4, x3))), x1), x0)) ....... R4 [R3:L0, U2859:L0]
% Derivation of unit clause U2889:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x0,equivalent_2(x2,x1)),x2)))) ....... U2876
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), x1), equivalent_2(x3, x2)), equivalent_2(x4, x0)), x4))) ....... R4 [R3:L0, U2876:L0]
% Derivation of unit clause U2892:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),x1),equivalent_2(x3,x2)),equivalent_2(x4,x0)),x4))) ....... U2889
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), x6), x4), equivalent_2(x6, x5)))), x3)) ....... R4 [R3:L0, U2889:L0]
% Derivation of unit clause U2894:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),x4),equivalent_2(x6,x5)))),x3)) ....... U2892
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1))) ....... R4 [R3:L0, U2892:L0]
% Derivation of unit clause U2895:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1))) ....... U2894
% is_a_theorem_1(equivalent_2(x0, x0)) ....... R4 [R3:L0, U2894:L0]
% Derivation of unit clause U3548:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5)))),equivalent_2(equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(x7,x6),x8),x7)),equivalent_2(x9,x8)),x9))) ....... U2506
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U2506:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x0,equivalent_2(x2,x1)),x2)))) ....... U2876
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x3), x2)), equivalent_2(x4, x3)), x4), equivalent_2(x5, x0)), x5))) ....... R4 [R3:L0, U2876:L0]
% Derivation of unit clause U3975:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1))) ....... U2860
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), x6), x4), equivalent_2(x6, x5))), x0), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U2860:L0]
% is_a_theorem_1(equivalent_2(x0,x0)) ....... U2895
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), x6), x4), equivalent_2(x6, x5))), x0)) ....... R4 [R3:L0, U2895:L0]
% Derivation of unit clause U4054:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),x1),equivalent_2(x3,x2))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0)) ....... U2861
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x2), equivalent_2(x4, x3)), equivalent_2(equivalent_2(x1, equivalent_2(x5, x0)), x5))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U2861:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))) ....... U0
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x2), equivalent_2(x4, x3)), equivalent_2(equivalent_2(x1, equivalent_2(x5, x0)), x5))), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(b_0(), c_0())), c_0()), equivalent_2(b_0(), a_0())))) ....... R4 [R3:L1, U0:L0]
% Derivation of unit clause U4263:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5))) ....... U2863
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x1), x0), x3))), x2), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U2863:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x3),x2)),equivalent_2(x4,x3)),x4),equivalent_2(x5,x0)),x5))) ....... U3548
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x7, equivalent_2(equivalent_2(equivalent_2(x8, x6), x5), x8))), x7))), x4)) ....... R4 [R3:L0, U3548:L0]
% Derivation of unit clause U4675:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5))) ....... U2863
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x1), x0), x3))), x2), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U2863:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))) ....... U4054
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x1), x0), x3))), x2), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6, x7), x8), x6), equivalent_2(x8, x7)), equivalent_2(equivalent_2(x5, equivalent_2(x9, x4)), x9))), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(b_0(), c_0())), c_0()), equivalent_2(b_0(), a_0()))))) ....... R4 [R3:L1, U4054:L0]
% Derivation of unit clause U5237:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1),x0)) ....... U2884
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2884:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,equivalent_2(equivalent_2(equivalent_2(x8,x6),x5),x8))),x7))),x4)) ....... U4263
% is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x0), x1), x2)))) ....... R4 [R3:L0, U4263:L0]
% Derivation of unit clause U5398:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1),x0)) ....... U2884
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2884:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x1),x0),x3))),x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6,x7),x8),x6),equivalent_2(x8,x7)),equivalent_2(equivalent_2(x5,equivalent_2(x9,x4)),x9))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))))) ....... U4675
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(x6, x4), x3), x6))), x5), equivalent_2(equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9, x10), x11), x9), equivalent_2(x11, x10)), equivalent_2(equivalent_2(x8, equivalent_2(x12, x7)), x12))), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(b_0(), c_0())), c_0()), equivalent_2(b_0(), a_0())))))) ....... R4 [R3:L1, U4675:L0]
% Derivation of unit clause U19296:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),x4),equivalent_2(x6,x5))),x0)) ....... U3975
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), x3), equivalent_2(x4, x2)), equivalent_2(equivalent_2(equivalent_2(x5, x1), x0), x5))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U3975:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2)))) ....... U5237
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4)), equivalent_2(equivalent_2(equivalent_2(x7, x3), x2), x7)))), x0), x1))) ....... R4 [R3:L0, U5237:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4)),equivalent_2(equivalent_2(equivalent_2(x7,x3),x2),x7)))),x0),x1))) ....... U19296
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),x11),x9),equivalent_2(x11,x10)),equivalent_2(equivalent_2(x8,equivalent_2(x12,x7)),x12))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))))) ....... U5398
% [] ....... R1 [U19296:L0, U5398:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 409836
% resolvents: 409828 factors: 8
% Number of unit clauses generated: 409609
% % unit clauses generated to total clauses generated: 99.94
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 30 [4] = 19265
% Total = 19297
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 409609 [2] = 216 [3] = 11
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)3105 (-)16192
% ------------------
% Total: (+)3105 (-)16192
% Total number of unit clauses retained: 19297
% Number of clauses skipped because of their length: 129
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 409974
% Number of unification failures: 43193
% Number of unit to unit unification failures: 50265028
% N literal unification failure due to lookup root_id table: 26
% N base clause resolution failure due to lookup table: 0
% N UC-BCL resolution dropped due to lookup table: 0
% Max entries in substitution set: 22
% N unit clauses dropped because they exceeded max values: 390017
% N unit clauses dropped because too much nesting: 63997
% N unit clauses not constrcuted because table was full: 0
% N unit clauses dropped because UCFA table was full: 0
% Max number of terms in a unit clause: 63
% Max term depth in a unit clause: 11
% Number of states in UCFA table: 327112
% Total number of terms of all unit clauses in table: 1031435
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.62
% Ratio n states used/total unit clauses terms: 0.32
% Number of symbols (columns) in UCFA: 39
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 453167
% ConstructUnitClause() = 409312
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 1.93 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 4998
% | |
% --------------------------------------------------------
% Elapsed time: 84 secs
% CPU time: 82.79 secs
%
%------------------------------------------------------------------------------