TSTP Solution File: LCL123-1 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL123-1 : TPTP v5.0.0. Bugfixed v2.3.0.
% 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 : Sun Nov 28 00:08:34 EST 2010
% Result : Unsatisfiable 7.31s
% Output : Refutation 7.31s
% 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/SystemOnTPTP22492/LCL/LCL123-1+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 = 71] [nf = 0] [nu = 26] [ut = 21]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 165] [nf = 5] [nu = 70] [ut = 21]
% 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())),equivalent_2(e_0(),equivalent_2(b_0(),f_0()))),equivalent_2(a_0(),equivalent_2(e_0(),equivalent_2(c_0(),f_0())))))
% B1: is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))))
% 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 f9 c10 t19 td5 b nc > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),equivalent_2(e_0(),equivalent_2(b_0(),f_0()))),equivalent_2(a_0(),equivalent_2(e_0(),equivalent_2(c_0(),f_0())))))
% U1: < d0 v8 dv4 f7 c0 t15 td6 b > is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))))
% U3: < d2 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))))
% U4: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))))
% U5: < d2 v10 dv5 f9 c0 t19 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),x1)))
% U10: < d2 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),x1)),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)))))
% U74: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2)))
% U75: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),equivalent_2(equivalent_2(x0,x5),equivalent_2(x1,x5))))
% U77: < d4 v8 dv4 f7 c0 t15 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x3),equivalent_2(x2,x3))))
% U97: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))),x1),x2)))
% U101: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))),x2)))
% U102: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),x1)))
% U105: < d4 v18 dv9 f17 c0 t35 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x6,x8),equivalent_2(x7,x8)))),x1)))
% U118: < d4 v4 dv2 f3 c0 t7 td3 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1)))
% U122: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),equivalent_2(equivalent_2(x0,x5),equivalent_2(x4,x5))))
% U123: < d4 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),equivalent_2(equivalent_2(x0,x6),equivalent_2(x1,x6))))
% U135: < d4 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))),x3)))
% U137: < d4 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),equivalent_2(equivalent_2(x0,x3),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6))))))
% U138: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),x4),equivalent_2(equivalent_2(x0,equivalent_2(x1,x3)),x4)))
% U140: < d4 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))),equivalent_2(x0,equivalent_2(x1,x3))))
% U143: < d4 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),equivalent_2(equivalent_2(equivalent_2(x0,x5),x6),equivalent_2(equivalent_2(x1,x5),x6))))
% U145: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))))))
% U147: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x3),x4),equivalent_2(equivalent_2(x1,x3),x4)),x2)))
% U166: < d4 v14 dv7 f13 c0 t27 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6))),x3)),x1),x2)))
% U214: < d4 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),equivalent_2(equivalent_2(equivalent_2(x1,x4),equivalent_2(x2,x4)),x3))),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)))),x0))
% U258: < d4 v18 dv9 f17 c0 t35 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4))),x1)),x5),equivalent_2(equivalent_2(x0,x5),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x6,x8),equivalent_2(x7,x8))))))
% U313: < d4 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))),x2)))
% U329: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(x0,equivalent_2(x1,x3))))
% U339: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),equivalent_2(equivalent_2(x1,x2),x3))))
% U352: < d4 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),equivalent_2(equivalent_2(equivalent_2(x4,x7),equivalent_2(x5,x7)),x6)))))
% U417: < d4 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),equivalent_2(equivalent_2(equivalent_2(x4,x7),equivalent_2(x5,x7)),x6))))
% U460: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x4),equivalent_2(x1,x4)),x5),equivalent_2(x2,x5)),x3)))
% U1189: < d4 v10 dv5 f9 c0 t19 td7 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,x3)))),equivalent_2(equivalent_2(x2,x4),x1))))
% U1533: < d4 v18 dv9 f27 c10 t55 td7 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))),equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x6,x8),equivalent_2(x7,x8))))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),equivalent_2(e_0(),equivalent_2(b_0(),f_0()))),equivalent_2(a_0(),equivalent_2(e_0(),equivalent_2(c_0(),f_0()))))))
% U1675: < d4 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(x0,equivalent_2(x1,x3))),equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,x6)))),equivalent_2(equivalent_2(x5,x7),x4)))
% U1764: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),equivalent_2(equivalent_2(equivalent_2(x1,x2),x4),equivalent_2(x3,x4)))))
% U2386: < d4 v18 dv9 f17 c0 t35 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)))),x1),x2),x3),x8),equivalent_2(x4,x8))))
% U5507: < d4 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),x5),x6),x7),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x4),x8),equivalent_2(x5,x8)),x6),x7)))
% U6148: < d4 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x3,x2)),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)))),x1),x8),equivalent_2(x3,x8)),x4)))
% U6368: < d4 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),x5),equivalent_2(x6,x5)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x4),x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))))
% U12601: < d4 v18 dv9 f17 c0 t35 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5))),x7),equivalent_2(x8,x7)),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x3)),equivalent_2(x4,x6)),x8)))
% --------------- 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())),equivalent_2(e_0(),equivalent_2(b_0(),f_0()))),equivalent_2(a_0(),equivalent_2(e_0(),equivalent_2(c_0(),f_0()))))) ....... U0
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... U1
% Derivation of unit clause U3:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6))))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U4:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6))))) ....... U3
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2)))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U5:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U4
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U10:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),x1))) ....... U5
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1)), equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x5, x7), equivalent_2(x6, x7))))) ....... R2 [R1:L0, U5:L0]
% Derivation of unit clause U74:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6))))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U4
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x0, x3), equivalent_2(x1, x3)), x2))) ....... R4 [R3:L0, U4:L0]
% Derivation of unit clause U75:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6))))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),x1))) ....... U5
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), equivalent_2(equivalent_2(x0, x5), equivalent_2(x1, x5)))) ....... R4 [R3:L0, U5:L0]
% Derivation of unit clause U77:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6))))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x3), equivalent_2(x2, x3)))) ....... R4 [R3:L0, U74:L0]
% Derivation of unit clause U97:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U4
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U4:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U4
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5)))), x1), x2))) ....... R4 [R3:L0, U4:L0]
% Derivation of unit clause U101:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U4
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U4:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5)))), x2))) ....... R4 [R3:L0, U74:L0]
% Derivation of unit clause U102:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U4
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U4:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),equivalent_2(equivalent_2(x0,x5),equivalent_2(x1,x5)))) ....... U75
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))), x2)), x1))) ....... R4 [R3:L0, U75:L0]
% Derivation of unit clause U105:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U4
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U4:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),x1))) ....... U102
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))), x2)), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x6, x8), equivalent_2(x7, x8)))), x1))) ....... R4 [R3:L0, U102:L0]
% Derivation of unit clause U118:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),x1))) ....... U5
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), equivalent_2(x0, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6))))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U5:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x3),equivalent_2(x2,x3)))) ....... U77
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x1))) ....... R4 [R3:L0, U77:L0]
% Derivation of unit clause U122:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),x1)),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7))))) ....... U10
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U10:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))),x1),x2))) ....... U97
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), equivalent_2(equivalent_2(x0, x5), equivalent_2(x4, x5)))) ....... R4 [R3:L0, U97:L0]
% Derivation of unit clause U123:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),x1)),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7))))) ....... U10
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U10:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),x1))) ....... U102
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))), x2)), equivalent_2(equivalent_2(x0, x6), equivalent_2(x1, x6)))) ....... R4 [R3:L0, U102:L0]
% Derivation of unit clause U135:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U74:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U4
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3), equivalent_2(equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6)))), x3))) ....... R4 [R3:L0, U4:L0]
% Derivation of unit clause U137:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U74:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), x2)), equivalent_2(equivalent_2(x0, x3), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6)))))) ....... R4 [R3:L0, U74:L0]
% Derivation of unit clause U138:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U74:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x3),equivalent_2(x2,x3)))) ....... U77
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), x4), equivalent_2(equivalent_2(x0, equivalent_2(x1, x3)), x4))) ....... R4 [R3:L0, U77:L0]
% Derivation of unit clause U140:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U74:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))),x2))) ....... U101
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6)))), equivalent_2(x0, equivalent_2(x1, x3)))) ....... R4 [R3:L0, U101:L0]
% Derivation of unit clause U143:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U74:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x6,x8),equivalent_2(x7,x8)))),x1))) ....... U105
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), equivalent_2(equivalent_2(equivalent_2(x0, x5), x6), equivalent_2(equivalent_2(x1, x5), x6)))) ....... R4 [R3:L0, U105:L0]
% Derivation of unit clause U145:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U74:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1))) ....... U118
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5)))))) ....... R4 [R3:L0, U118:L0]
% Derivation of unit clause U147:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),x2))) ....... U74
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U74:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),equivalent_2(equivalent_2(x0,x6),equivalent_2(x1,x6)))) ....... U123
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x3), x4), equivalent_2(equivalent_2(x1, x3), x4)), x2))) ....... R4 [R3:L0, U123:L0]
% Derivation of unit clause U166:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x3),equivalent_2(x2,x3)))) ....... U77
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U77:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)))),equivalent_2(equivalent_2(equivalent_2(x0,x5),x6),equivalent_2(equivalent_2(x1,x5),x6)))) ....... U143
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x3), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6))), x3)), x1), x2))) ....... R4 [R3:L0, U143:L0]
% Derivation of unit clause U214:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),x1))) ....... U102
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4))), x1)), equivalent_2(x0, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x5, x7), equivalent_2(x6, x7))))), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U102:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))),x2))) ....... U101
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), equivalent_2(equivalent_2(equivalent_2(x1, x4), equivalent_2(x2, x4)), x3))), equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x5, x7), equivalent_2(x6, x7)))), x0)) ....... R4 [R3:L0, U101:L0]
% Derivation of unit clause U258:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1))) ....... U118
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U118:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6))),x3)),x1),x2))) ....... U166
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4))), x1)), x5), equivalent_2(equivalent_2(x0, x5), equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x6, x8), equivalent_2(x7, x8)))))) ....... R4 [R3:L0, U166:L0]
% Derivation of unit clause U313:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))),x3))) ....... U135
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), equivalent_2(equivalent_2(equivalent_2(x0, x5), equivalent_2(x1, x5)), equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x6, x8), equivalent_2(x7, x8))))), x9)) | is_a_theorem_1(x9) ....... R3 [R2:L0, U135:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),equivalent_2(equivalent_2(x0,x5),equivalent_2(x4,x5)))) ....... U122
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x3), equivalent_2(x1, x3)), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6)))), x2))) ....... R4 [R3:L0, U122:L0]
% Derivation of unit clause U329:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),equivalent_2(equivalent_2(x0,x3),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))))) ....... U137
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6)))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U137:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))),equivalent_2(x0,equivalent_2(x1,x3)))) ....... U140
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), equivalent_2(x0, equivalent_2(x1, x3)))) ....... R4 [R3:L0, U140:L0]
% Derivation of unit clause U339:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),equivalent_2(equivalent_2(x0,x3),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))))) ....... U137
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6)))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U137:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),equivalent_2(equivalent_2(equivalent_2(x1,x4),equivalent_2(x2,x4)),x3))),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)))),x0)) ....... U214
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x0, x2), x3), equivalent_2(equivalent_2(x1, x2), x3)))) ....... R4 [R3:L0, U214:L0]
% Derivation of unit clause U352:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),x4),equivalent_2(equivalent_2(x0,equivalent_2(x1,x3)),x4))) ....... U138
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6))))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U138:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))),x2))) ....... U101
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x4, x5), x6), equivalent_2(equivalent_2(equivalent_2(x4, x7), equivalent_2(x5, x7)), x6))))) ....... R4 [R3:L0, U101:L0]
% Derivation of unit clause U417:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))))) ....... U145
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6)))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U145:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),equivalent_2(equivalent_2(equivalent_2(x4,x7),equivalent_2(x5,x7)),x6))))) ....... U352
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), equivalent_2(equivalent_2(equivalent_2(x4, x5), x6), equivalent_2(equivalent_2(equivalent_2(x4, x7), equivalent_2(x5, x7)), x6)))) ....... R4 [R3:L0, U352:L0]
% Derivation of unit clause U460:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x3),x4),equivalent_2(equivalent_2(x1,x3),x4)),x2))) ....... U147
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), x2)), equivalent_2(equivalent_2(x0, x3), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x4, x6), equivalent_2(x5, x6))))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U147:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),x2)),equivalent_2(equivalent_2(x0,x6),equivalent_2(x1,x6)))) ....... U123
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x4), equivalent_2(x1, x4)), x5), equivalent_2(x2, x5)), x3))) ....... R4 [R3:L0, U123:L0]
% Derivation of unit clause U1189:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... 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(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4))),x1)),x5),equivalent_2(equivalent_2(x0,x5),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x6,x8),equivalent_2(x7,x8)))))) ....... U258
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4))), x1)), equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x5, x7), equivalent_2(x6, x7))))), equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x8, x10), equivalent_2(x9, x10)))), x11)) | is_a_theorem_1(x11) ....... R3 [R2:L0, U258:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))),equivalent_2(x0,equivalent_2(x1,x3)))) ....... U140
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, x3)))), equivalent_2(equivalent_2(x2, x4), x1)))) ....... R4 [R3:L0, U140:L0]
% Derivation of unit clause U1533:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(x1,x3)),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x4,x6),equivalent_2(x5,x6)))),x2))) ....... U313
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5)))), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x6, x8), equivalent_2(x7, x8))))), x9)) | is_a_theorem_1(x9) ....... R3 [R2:L0, U313:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),equivalent_2(e_0(),equivalent_2(b_0(),f_0()))),equivalent_2(a_0(),equivalent_2(e_0(),equivalent_2(c_0(),f_0()))))) ....... U0
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5)))), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x6, x8), equivalent_2(x7, x8))))), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(b_0(), c_0())), equivalent_2(e_0(), equivalent_2(b_0(), f_0()))), equivalent_2(a_0(), equivalent_2(e_0(), equivalent_2(c_0(), f_0())))))) ....... R4 [R3:L1, U0:L0]
% Derivation of unit clause U1675:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(x0,equivalent_2(x1,x3)))) ....... U329
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), equivalent_2(x0, equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U329:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,x3)))),equivalent_2(equivalent_2(x2,x4),x1)))) ....... U1189
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), equivalent_2(x0, equivalent_2(x1, x3))), equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(x7, x6)))), equivalent_2(equivalent_2(x5, x7), x4))) ....... R4 [R3:L0, U1189:L0]
% Derivation of unit clause U1764:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(x0,equivalent_2(x1,x3)))) ....... U329
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), equivalent_2(x0, equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U329:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(x0,equivalent_2(x1,x3))),equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,x6)))),equivalent_2(equivalent_2(x5,x7),x4))) ....... U1675
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x0, x2), x3), equivalent_2(equivalent_2(equivalent_2(x1, x2), x4), equivalent_2(x3, x4))))) ....... R4 [R3:L0, U1675:L0]
% Derivation of unit clause U2386:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),equivalent_2(equivalent_2(x1,x2),x3)))) ....... U339
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5)))), x1), x2)), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U339:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),equivalent_2(equivalent_2(equivalent_2(x1,x2),x4),equivalent_2(x3,x4))))) ....... U1764
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), x4), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x5, x7), equivalent_2(x6, x7)))), x1), x2), x3), x8), equivalent_2(x4, x8)))) ....... R4 [R3:L0, U1764:L0]
% Derivation of unit clause U5507:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),equivalent_2(equivalent_2(equivalent_2(x4,x7),equivalent_2(x5,x7)),x6)))) ....... U417
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x0, x3), equivalent_2(x1, x3)), x2)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U417:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)))),x1),x2),x3),x8),equivalent_2(x4,x8)))) ....... U2386
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), x5), x6), x7), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x4), x8), equivalent_2(x5, x8)), x6), x7))) ....... R4 [R3:L0, U2386:L0]
% Derivation of unit clause U6148:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),equivalent_2(equivalent_2(equivalent_2(x4,x7),equivalent_2(x5,x7)),x6)))) ....... U417
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x0, x3), equivalent_2(x1, x3)), x2)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U417:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),x5),x6),x7),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x4),x8),equivalent_2(x5,x8)),x6),x7))) ....... U5507
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(x3, x2)), x4), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x5, x7), equivalent_2(x6, x7)))), x1), x8), equivalent_2(x3, x8)), x4))) ....... R4 [R3:L0, U5507:L0]
% Derivation of unit clause U6368:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3))))),equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),equivalent_2(equivalent_2(equivalent_2(x4,x7),equivalent_2(x5,x7)),x6)))) ....... U417
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x0, x3), equivalent_2(x1, x3)), x2)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U417:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x3,x2)),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)))),x1),x8),equivalent_2(x3,x8)),x4))) ....... U6148
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), x5), equivalent_2(x6, x5)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x4), x7), equivalent_2(x8, x7)), equivalent_2(x6, x8)))) ....... R4 [R3:L0, U6148:L0]
% Derivation of unit clause U12601:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))))) ....... 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(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | is_a_theorem_1(x4) ....... 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x4),equivalent_2(x1,x4)),x5),equivalent_2(x2,x5)),x3))) ....... U460
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3), equivalent_2(x4, x3)), equivalent_2(equivalent_2(equivalent_2(x0, x2), x4), equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x5, x7), equivalent_2(x6, x7))))), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U460:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),x5),equivalent_2(x6,x5)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x4),x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))) ....... U6368
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5))), x7), equivalent_2(x8, x7)), equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x3)), equivalent_2(x4, x6)), x8))) ....... R4 [R3:L0, U6368:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2))),equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5))),x7),equivalent_2(x8,x7)),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x3)),equivalent_2(x4,x6)),x8))) ....... U12601
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))),equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x6,x8),equivalent_2(x7,x8))))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),equivalent_2(e_0(),equivalent_2(b_0(),f_0()))),equivalent_2(a_0(),equivalent_2(e_0(),equivalent_2(c_0(),f_0())))))) ....... U1533
% [] ....... R1 [U12601:L0, U1533:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 43395
% resolvents: 43386 factors: 9
% Number of unit clauses generated: 43126
% % unit clauses generated to total clauses generated: 99.38
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 19 [4] = 12581
% Total = 12602
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 43126 [2] = 258 [3] = 11
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)12347 (-)255
% ------------------
% Total: (+)12347 (-)255
% Total number of unit clauses retained: 12602
% Number of clauses skipped because of their length: 174
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 43543
% Number of unification failures: 139680
% Number of unit to unit unification failures: 3148381
% 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: 23
% N unit clauses dropped because they exceeded max values: 30405
% N unit clauses dropped because too much nesting: 62
% 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: 12
% Number of states in UCFA table: 225513
% Total number of terms of all unit clauses in table: 548510
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.43
% Ratio n states used/total unit clauses terms: 0.41
% Number of symbols (columns) in UCFA: 41
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 183223
% ConstructUnitClause() = 43005
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.22 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 6199
% | |
% --------------------------------------------------------
% Elapsed time: 7 secs
% CPU time: 7.29 secs
%
%------------------------------------------------------------------------------