TSTP Solution File: LCL107-1 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL107-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Nov 28 00:00:53 EST 2010
% Result : Unsatisfiable 2.53s
% Output : Refutation 2.53s
% 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/SystemOnTPTP23383/LCL/LCL107-1+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 = 1 secs [nr = 3] [nf = 0] [nu = 0] [ut = 2]
% Looking for a proof at depth = 2 ...
% t = 1 secs [nr = 62] [nf = 0] [nu = 26] [ut = 19]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 150] [nf = 4] [nu = 73] [ut = 19]
% 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(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6))))
% B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U1: < d0 v14 dv7 f13 c0 t27 td7 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6))))
% U2: < d2 v14 dv7 f21 c8 t43 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))
% U4: < d2 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x1),equivalent_2(x2,x0)),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),x3)))
% U6: < d2 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7)))
% U7: < d2 v18 dv9 f17 c0 t35 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7)))
% U15: < d2 v20 dv10 f27 c8 t55 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(),equivalent_2(a_0(),b_0())),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))),equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(equivalent_2(x9,x8),equivalent_2(x9,x7)),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))
% U96: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x1,equivalent_2(x3,x4))),x5),x5))
% U99: < d4 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)))
% U102: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),x5),x5))
% U104: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x4)),x0),equivalent_2(x4,x3))))
% U106: < d4 v20 dv10 f19 c0 t39 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x3)),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x5,x7))),equivalent_2(x4,equivalent_2(x6,x7))),equivalent_2(equivalent_2(equivalent_2(x8,x0),equivalent_2(x8,x1)),equivalent_2(x2,x9)))),equivalent_2(x3,x9)))
% U111: < d4 v8 dv4 f7 c0 t15 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(x3,x1),equivalent_2(x3,x2))))
% U116: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x1,x3),x0),equivalent_2(x3,x2))))
% U118: < d4 v16 dv8 f15 c0 t31 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)))),equivalent_2(x2,equivalent_2(x3,equivalent_2(x5,x6)))))),equivalent_2(x1,x7)),x7))
% U458: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x1,equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)))),equivalent_2(x2,equivalent_2(x0,equivalent_2(x4,x5)))))
% U2875: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x4))),equivalent_2(x0,equivalent_2(x3,x4))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... U1
% Derivation of unit clause U2:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) ....... B0
% ~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(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R1 [B0:L0, B2:L2]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U4:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x1), equivalent_2(x2, x0)), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x6, x4), equivalent_2(x6, x5))), x3))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U6:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x1),equivalent_2(x2,x0)),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),x3))) ....... U4
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6))), equivalent_2(x3, equivalent_2(x5, x6))), x7)), equivalent_2(equivalent_2(x1, x2), x7))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U7:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(equivalent_2(x8, x5), equivalent_2(x8, x6)), x7))) ....... R2 [R1:L0, U6:L0]
% Derivation of unit clause U15:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(), equivalent_2(a_0(), b_0())), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6)))), equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(equivalent_2(x9, x8), equivalent_2(x9, x7)), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R2 [R1:L1, U2:L0]
% Derivation of unit clause U96:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)))), equivalent_2(x1, equivalent_2(x3, x4))), x5), x5)) ....... R4 [R3:L0, U6:L0]
% Derivation of unit clause U99:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x1,equivalent_2(x3,x4))),x5),x5)) ....... U96
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2))) ....... R4 [R3:L0, U96:L0]
% Derivation of unit clause U102:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U99
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)))), equivalent_2(x0, equivalent_2(x1, equivalent_2(x3, x4)))), x5), x5)) ....... R4 [R3:L0, U99:L0]
% Derivation of unit clause U104:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),x5),x5)) ....... U102
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x4)), x0), equivalent_2(x4, x3)))) ....... R4 [R3:L0, U102:L0]
% Derivation of unit clause U106:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x4)),x0),equivalent_2(x4,x3)))) ....... U104
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x3)), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(x5, x7))), equivalent_2(x4, equivalent_2(x6, x7))), equivalent_2(equivalent_2(equivalent_2(x8, x0), equivalent_2(x8, x1)), equivalent_2(x2, x9)))), equivalent_2(x3, x9))) ....... R4 [R3:L0, U104:L0]
% Derivation of unit clause U111:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U7
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, x4)), equivalent_2(equivalent_2(x2, x3), x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(equivalent_2(x3, x1), equivalent_2(x3, x2)))) ....... R4 [R3:L0, U7:L0]
% Derivation of unit clause U116:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U7
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, x4)), equivalent_2(equivalent_2(x2, x3), x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),x5),x5)) ....... U102
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x1, x3), x0), equivalent_2(x3, x2)))) ....... R4 [R3:L0, U102:L0]
% Derivation of unit clause U118:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U7
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, x4)), equivalent_2(equivalent_2(x2, x3), x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x3)),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x5,x7))),equivalent_2(x4,equivalent_2(x6,x7))),equivalent_2(equivalent_2(equivalent_2(x8,x0),equivalent_2(x8,x1)),equivalent_2(x2,x9)))),equivalent_2(x3,x9))) ....... U106
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, equivalent_2(equivalent_2(x2, equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)))), equivalent_2(x2, equivalent_2(x3, equivalent_2(x5, x6)))))), equivalent_2(x1, x7)), x7)) ....... R4 [R3:L0, U106:L0]
% Derivation of unit clause U458:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)))),equivalent_2(x2,equivalent_2(x3,equivalent_2(x5,x6)))))),equivalent_2(x1,x7)),x7)) ....... U118
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(equivalent_2(x4, x0), equivalent_2(x4, equivalent_2(x2, x3)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U118:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x1,x3),x0),equivalent_2(x3,x2)))) ....... U116
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(x1, equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)))), equivalent_2(x2, equivalent_2(x0, equivalent_2(x4, x5))))) ....... R4 [R3:L0, U116:L0]
% Derivation of unit clause U2875:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x1,equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)))),equivalent_2(x2,equivalent_2(x0,equivalent_2(x4,x5))))) ....... U458
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x1), equivalent_2(x2, x0)), equivalent_2(x3, x4))), equivalent_2(equivalent_2(x5, x3), equivalent_2(x5, x4))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U458:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(x3,x1),equivalent_2(x3,x2)))) ....... U111
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x4))), equivalent_2(x0, equivalent_2(x3, x4)))) ....... R4 [R3:L0, U111:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x4))),equivalent_2(x0,equivalent_2(x3,x4)))) ....... U2875
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(),equivalent_2(a_0(),b_0())),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))),equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(equivalent_2(x9,x8),equivalent_2(x9,x7)),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) ....... U15
% [] ....... R1 [U2875:L0, U15:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 17582
% resolvents: 17574 factors: 8
% Number of unit clauses generated: 17390
% % unit clauses generated to total clauses generated: 98.91
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 17 [4] = 2857
% Total = 2876
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 17390 [2] = 181 [3] = 11
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)2365 (-)511
% ------------------
% Total: (+)2365 (-)511
% Total number of unit clauses retained: 2876
% Number of clauses skipped because of their length: 116
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 17632
% Number of unification failures: 41804
% Number of unit to unit unification failures: 1208008
% 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: 29
% N unit clauses dropped because they exceeded max values: 14374
% N unit clauses dropped because too much nesting: 28
% 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: 13
% Number of states in UCFA table: 56558
% Total number of terms of all unit clauses in table: 130756
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.11
% Ratio n states used/total unit clauses terms: 0.43
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 59436
% ConstructUnitClause() = 17248
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.13 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 8791
% | |
% --------------------------------------------------------
% Elapsed time: 3 secs
% CPU time: 2.52 secs
%
%------------------------------------------------------------------------------