TSTP Solution File: LCL103-1 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL103-1 : 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 00:00:22 EST 2010
% Result : Unsatisfiable 20.27s
% Output : Refutation 20.27s
% 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/SystemOnTPTP23091/LCL/LCL103-1+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 = 5] [nf = 0] [nu = 0] [ut = 3]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 1313] [nf = 0] [nu = 612] [ut = 396]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 3696] [nf = 7] [nu = 2285] [ut = 396]
% 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(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0()))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2))))
% B2: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2))
% B3: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U1: < d0 v8 dv4 f7 c0 t15 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2))))
% U2: < d0 v6 dv3 f5 c0 t11 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2))
% U6: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x2,x4),x1)))))
% U7: < d2 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x0,x5),equivalent_2(equivalent_2(x6,x3),equivalent_2(equivalent_2(x2,x6),x4))))))
% U8: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x2,x5),x1))))))
% U9: < d2 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x0,x6),equivalent_2(equivalent_2(x7,x3),equivalent_2(equivalent_2(x2,x7),x4)))))))
% U10: < d2 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x3,x6),x1)))))))
% U11: < d2 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x4,x7),equivalent_2(equivalent_2(x8,x2),equivalent_2(equivalent_2(x1,x8),x3))))))))
% U12: < d2 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x0,x6),equivalent_2(equivalent_2(x7,x3),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x2,x8),x4))))))))
% U13: < d2 v16 dv8 f15 c0 t31 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x3,x7),x1))))))))
% U14: < d2 v20 dv10 f19 c0 t39 td10 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),equivalent_2(equivalent_2(x9,x2),equivalent_2(equivalent_2(x1,x9),x3)))))))))
% U15: < d2 v20 dv10 f19 c0 t39 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x0,x7),equivalent_2(equivalent_2(x8,x3),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x2,x9),x4)))))))))
% U16: < d2 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),x3),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),x1)))))))))
% U17: < d2 v22 dv11 f21 c0 t43 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(equivalent_2(x5,x6),x4),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x5,x9),equivalent_2(equivalent_2(x10,x2),equivalent_2(equivalent_2(x1,x10),x3))))))))))
% U18: < d2 v22 dv11 f21 c0 t43 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),equivalent_2(equivalent_2(x9,x2),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x1,x10),x3))))))))))
% U19: < d2 v22 dv11 f21 c0 t43 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x0,x7),equivalent_2(equivalent_2(x8,x3),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x2,x10),x4))))))))))
% U20: < d2 v20 dv10 f19 c0 t39 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),x3),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x4,x9),x1))))))))))
% U31: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x3)))
% U89: < d2 v22 dv11 f21 c0 t43 td10 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x3))),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(equivalent_2(x5,x6),x4),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x5,x10),x3)))))))))
% U142: < d2 v24 dv12 f23 c0 t47 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x3),x5))))),equivalent_2(equivalent_2(equivalent_2(x6,x7),x0),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x6,x11),x5))))))))
% U193: < d2 v26 dv13 f25 c0 t51 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x6),x8))))))),equivalent_2(equivalent_2(x9,x1),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x12,x11),equivalent_2(equivalent_2(x0,x12),x8)))))))
% U240: < d2 v26 dv13 f25 c0 t51 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x7),x9)))))))),equivalent_2(equivalent_2(x10,x0),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x12,x11),equivalent_2(equivalent_2(equivalent_2(x2,x1),x12),x9))))))
% U296: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x0,x4),x2)))))
% U7709: < d4 v10 dv5 f17 c8 t35 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),x4))),equivalent_2(equivalent_2(x4,equivalent_2(x3,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0()))))
% U10110: < d4 v20 dv10 f27 c8 t55 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x2,x4),x1)))),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x7,x5),equivalent_2(equivalent_2(x8,x7),x9))),equivalent_2(equivalent_2(x9,equivalent_2(x8,x6)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0())))))
% U11255: < d4 v18 dv9 f17 c0 t35 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x4),x6))))),equivalent_2(equivalent_2(x7,x0),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x3,x2)),x8),x6)))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... U1
% Derivation of unit clause U2:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... U2
% Derivation of unit clause U6:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x2, x4), x1))))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U7:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x2,x4),x1))))) ....... U6
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x0, x5), equivalent_2(equivalent_2(x6, x3), equivalent_2(equivalent_2(x2, x6), x4)))))) ....... R2 [R1:L0, U6:L0]
% Derivation of unit clause U8:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x0,x5),equivalent_2(equivalent_2(x6,x3),equivalent_2(equivalent_2(x2,x6),x4)))))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x2, x5), x1)))))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U9:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x2,x5),x1)))))) ....... U8
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x0, x6), equivalent_2(equivalent_2(x7, x3), equivalent_2(equivalent_2(x2, x7), x4))))))) ....... R2 [R1:L0, U8:L0]
% Derivation of unit clause U10:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x0,x6),equivalent_2(equivalent_2(x7,x3),equivalent_2(equivalent_2(x2,x7),x4))))))) ....... U9
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(equivalent_2(x3, x4), x2), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x3, x6), x1))))))) ....... R2 [R1:L0, U9:L0]
% Derivation of unit clause U11:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x3,x6),x1))))))) ....... U10
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), x0), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x4, x7), equivalent_2(equivalent_2(x8, x2), equivalent_2(equivalent_2(x1, x8), x3)))))))) ....... R2 [R1:L0, U10:L0]
% Derivation of unit clause U12:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x4,x7),equivalent_2(equivalent_2(x8,x2),equivalent_2(equivalent_2(x1,x8),x3)))))))) ....... U11
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x0, x6), equivalent_2(equivalent_2(x7, x3), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x2, x8), x4)))))))) ....... R2 [R1:L0, U11:L0]
% Derivation of unit clause U13:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x0,x6),equivalent_2(equivalent_2(x7,x3),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x2,x8),x4)))))))) ....... U12
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(equivalent_2(x3, x4), x2), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x3, x7), x1)))))))) ....... R2 [R1:L0, U12:L0]
% Derivation of unit clause U14:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x3,x7),x1)))))))) ....... U13
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), x0), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x4, x8), equivalent_2(equivalent_2(x9, x2), equivalent_2(equivalent_2(x1, x9), x3))))))))) ....... R2 [R1:L0, U13:L0]
% Derivation of unit clause U15:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),equivalent_2(equivalent_2(x9,x2),equivalent_2(equivalent_2(x1,x9),x3))))))))) ....... U14
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x0, x7), equivalent_2(equivalent_2(x8, x3), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x2, x9), x4))))))))) ....... R2 [R1:L0, U14:L0]
% Derivation of unit clause U16:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x0,x7),equivalent_2(equivalent_2(x8,x3),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x2,x9),x4))))))))) ....... U15
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(x3, x2), equivalent_2(equivalent_2(equivalent_2(x4, x5), x3), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x4, x8), x1))))))))) ....... R2 [R1:L0, U15:L0]
% Derivation of unit clause U17:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),x3),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),x1))))))))) ....... U16
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(x4, x0), equivalent_2(equivalent_2(equivalent_2(x5, x6), x4), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x5, x9), equivalent_2(equivalent_2(x10, x2), equivalent_2(equivalent_2(x1, x10), x3)))))))))) ....... R2 [R1:L0, U16:L0]
% Derivation of unit clause U18:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(equivalent_2(x5,x6),x4),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x5,x9),equivalent_2(equivalent_2(x10,x2),equivalent_2(equivalent_2(x1,x10),x3)))))))))) ....... U17
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), x0), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x4, x8), equivalent_2(equivalent_2(x9, x2), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x1, x10), x3)))))))))) ....... R2 [R1:L0, U17:L0]
% Derivation of unit clause U19:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),equivalent_2(equivalent_2(x9,x2),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x1,x10),x3)))))))))) ....... U18
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x0, x7), equivalent_2(equivalent_2(x8, x3), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x2, x10), x4)))))))))) ....... R2 [R1:L0, U18:L0]
% Derivation of unit clause U20:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x0,x7),equivalent_2(equivalent_2(x8,x3),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x2,x10),x4)))))))))) ....... U19
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(x3, x2), equivalent_2(equivalent_2(equivalent_2(x4, x5), x3), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x4, x9), x1)))))))))) ....... R2 [R1:L0, U19:L0]
% Derivation of unit clause U31:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), x2)) | is_a_theorem_1(equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))) ....... R1 [B1:L0, B3:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... U2
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x3))) ....... R2 [R1:L0, U2:L0]
% Derivation of unit clause U89:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),x3),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x4,x9),x1)))))))))) ....... U20
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), x3))), equivalent_2(equivalent_2(x4, x0), equivalent_2(equivalent_2(equivalent_2(x5, x6), x4), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x5, x10), x3))))))))) ....... R2 [R1:L0, U20:L0]
% Derivation of unit clause U142:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x3))),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(equivalent_2(x5,x6),x4),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x5,x10),x3))))))))) ....... U89
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x3), x5))))), equivalent_2(equivalent_2(equivalent_2(x6, x7), x0), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x11, x10), equivalent_2(equivalent_2(x6, x11), x5)))))))) ....... R2 [R1:L0, U89:L0]
% Derivation of unit clause U193:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x3),x5))))),equivalent_2(equivalent_2(equivalent_2(x6,x7),x0),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x6,x11),x5)))))))) ....... U142
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x2), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x6), x8))))))), equivalent_2(equivalent_2(x9, x1), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x11, x10), equivalent_2(equivalent_2(x12, x11), equivalent_2(equivalent_2(x0, x12), x8))))))) ....... R2 [R1:L0, U142:L0]
% Derivation of unit clause U240:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x6),x8))))))),equivalent_2(equivalent_2(x9,x1),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x12,x11),equivalent_2(equivalent_2(x0,x12),x8))))))) ....... U193
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x7), x9)))))))), equivalent_2(equivalent_2(x10, x0), equivalent_2(equivalent_2(x11, x10), equivalent_2(equivalent_2(x12, x11), equivalent_2(equivalent_2(equivalent_2(x2, x1), x12), x9)))))) ....... R2 [R1:L0, U193:L0]
% Derivation of unit clause U296:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2))) | is_a_theorem_1(x2) ....... R1 [B2:L0, B3:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x3,x6),x1))))))) ....... U10
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x0, x4), x2))))) ....... R2 [R1:L0, U10:L0]
% Derivation of unit clause U7709:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0())) ....... B0
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0()))) ....... R1 [B0:L0, B3:L2]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0())))) ....... R2 [R1:L1, B3:L2]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x0,x4),x2))))) ....... U296
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), equivalent_2(equivalent_2(x4, x2), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x1, x5), x3)))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0())))) ....... R3 [R2:L0, U296:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x3))) ....... U31
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(x3, x2), x4))), equivalent_2(equivalent_2(x4, equivalent_2(x3, x1)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0())))) ....... R4 [R3:L1, U31:L0]
% Derivation of unit clause U10110:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x2, x4), x1)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U1:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),x4))),equivalent_2(equivalent_2(x4,equivalent_2(x3,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0())))) ....... U7709
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x2, x4), x1)))), equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x7, x5), equivalent_2(equivalent_2(x8, x7), x9))), equivalent_2(equivalent_2(x9, equivalent_2(x8, x6)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0()))))) ....... R4 [R3:L1, U7709:L0]
% Derivation of unit clause U11255:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x0,x5),equivalent_2(equivalent_2(x6,x3),equivalent_2(equivalent_2(x2,x6),x4)))))) ....... U7
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x2, x5), x1))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U7:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x7),x9)))))))),equivalent_2(equivalent_2(x10,x0),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x12,x11),equivalent_2(equivalent_2(equivalent_2(x2,x1),x12),x9)))))) ....... U240
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x4), x6))))), equivalent_2(equivalent_2(x7, x0), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x3, x2)), x8), x6))))) ....... R4 [R3:L0, U240:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x4),x6))))),equivalent_2(equivalent_2(x7,x0),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x3,x2)),x8),x6))))) ....... U11255
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x2,x4),x1)))),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x7,x5),equivalent_2(equivalent_2(x8,x7),x9))),equivalent_2(equivalent_2(x9,equivalent_2(x8,x6)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0()))))) ....... U10110
% [] ....... R1 [U11255:L0, U10110:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 358035
% resolvents: 358024 factors: 11
% Number of unit clauses generated: 355341
% % unit clauses generated to total clauses generated: 99.25
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 3 [2] = 393 [4] = 10860
% Total = 11256
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 355341 [2] = 2677 [3] = 17
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)918 (-)10338
% ------------------
% Total: (+)918 (-)10338
% Total number of unit clauses retained: 11256
% Number of clauses skipped because of their length: 1289
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 358089
% Number of unification failures: 436592
% Number of unit to unit unification failures: 9489583
% N literal unification failure due to lookup root_id table: 35
% 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: 24
% N unit clauses dropped because they exceeded max values: 332912
% N unit clauses dropped because too much nesting: 95850
% 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: 232089
% Total number of terms of all unit clauses in table: 607756
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.44
% Ratio n states used/total unit clauses terms: 0.38
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 794681
% ConstructUnitClause() = 344165
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 1.52 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 17902
% | |
% --------------------------------------------------------
% Elapsed time: 21 secs
% CPU time: 20.24 secs
%
%------------------------------------------------------------------------------