TSTP Solution File: LCL091-1 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL091-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art03.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 : Sat Nov 27 23:55:49 EST 2010
% Result : Unsatisfiable 173.71s
% Output : Refutation 173.71s
% 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/SystemOnTPTP23983/LCL/LCL091-1+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 = 58] [nf = 0] [nu = 20] [ut = 18]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 139] [nf = 4] [nu = 58] [ut = 18]
% Looking for a proof at depth = 4 ...
% Entering time slice 2
% Updating parameters ... done.
% Looking for a proof at depth = 1 ...
% t = 123 secs [nr = 465868] [nf = 8] [nu = 444398] [ut = 18094]
% Looking for a proof at depth = 2 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~is_a_theorem_1(implies_2(a_0(),implies_2(b_0(),a_0())))
% B1: is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0)))))
% B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U1: < d0 v9 dv5 f8 c0 t17 td5 b > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0)))))
% U3: < d2 v10 dv6 f9 c0 t19 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3)))))
% U6: < d2 v12 dv7 f11 c0 t23 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x4,x1))),implies_2(x5,implies_2(x6,implies_2(x3,implies_2(x4,x1))))))
% U7: < d2 v14 dv8 f13 c0 t27 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5))))))
% U8: < d2 v15 dv9 f14 c0 t29 td7 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(implies_2(x1,x2),implies_2(x2,x3))),implies_2(x4,implies_2(x5,implies_2(x6,x2)))),implies_2(x7,implies_2(x8,implies_2(x4,implies_2(x5,implies_2(x6,x2)))))))
% U18: < d4 v1 dv1 f8 c8 t17 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(x0,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0()))))
% U145: < d4 v11 dv7 f18 c8 t37 td7 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3)))),implies_2(implies_2(implies_2(x6,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0())))))
% U187: < d4 v10 dv6 f9 c0 t19 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(x1,x2),implies_2(x2,implies_2(implies_2(implies_2(x3,x4),x4),implies_2(x4,implies_2(x5,x4)))))))
% U205: < d4 v9 dv5 f8 c0 t17 td6 > is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(x1,implies_2(implies_2(implies_2(x2,x3),x3),implies_2(x3,implies_2(x4,x3))))))
% U217: < d4 v13 dv7 f12 c0 t25 td6 > is_a_theorem_1(implies_2(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,implies_2(x3,x2)))),implies_2(implies_2(implies_2(x4,x5),x5),implies_2(x5,implies_2(x6,x5)))))
% U319: < d4 v11 dv7 f10 c0 t21 td7 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,implies_2(implies_2(x3,x0),x0))),x4),implies_2(x5,implies_2(x6,x4))))
% U15258: < d4 v17 dv10 f24 c8 t49 td8 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x1),implies_2(x1,implies_2(x2,x1))),implies_2(implies_2(implies_2(implies_2(x3,implies_2(x4,x5)),implies_2(x5,x6)),implies_2(x7,implies_2(implies_2(x8,x5),implies_2(x5,x6)))),implies_2(implies_2(implies_2(x9,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0()))))))
% U16958: < d4 v23 dv13 f30 c8 t61 td9 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x1),implies_2(x1,implies_2(x2,x1))),implies_2(implies_2(implies_2(implies_2(x3,x4),x4),implies_2(x4,implies_2(x5,x4))),implies_2(implies_2(implies_2(implies_2(x6,implies_2(x7,x8)),implies_2(x8,x9)),implies_2(x10,implies_2(implies_2(x11,x8),implies_2(x8,x9)))),implies_2(implies_2(implies_2(x12,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0())))))))
% U22753: < d2 v11 dv7 f10 c0 t21 td7 > is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(implies_2(implies_2(x2,x3),x3),implies_2(x3,x4)),implies_2(x5,implies_2(x6,implies_2(x3,x4)))))))
% U23556: < d2 v10 dv6 f9 c0 t19 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,x3)),implies_2(x4,implies_2(x5,implies_2(x2,x3))))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... U1
% Derivation of unit clause U3:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... U1
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x5, x2), implies_2(x2, x3))))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U6:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x2, x3))) | is_a_theorem_1(implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3))))) ....... U3
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x1, x2)), implies_2(x3, implies_2(x4, x1))), implies_2(x5, implies_2(x6, implies_2(x3, implies_2(x4, x1)))))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U7:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x2, x3))) | is_a_theorem_1(implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x4,x1))),implies_2(x5,implies_2(x6,implies_2(x3,implies_2(x4,x1)))))) ....... U6
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, implies_2(x2, x3))), implies_2(implies_2(x4, x3), implies_2(x3, x5))), implies_2(x6, implies_2(x7, implies_2(implies_2(x4, x3), implies_2(x3, x5)))))) ....... R2 [R1:L0, U6:L0]
% Derivation of unit clause U8:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x2, x3))) | is_a_theorem_1(implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) ....... U7
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(implies_2(x1, x2), implies_2(x2, x3))), implies_2(x4, implies_2(x5, implies_2(x6, x2)))), implies_2(x7, implies_2(x8, implies_2(x4, implies_2(x5, implies_2(x6, x2))))))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U18:
% ~is_a_theorem_1(implies_2(a_0(),implies_2(b_0(),a_0()))) ....... B0
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(a_0(), implies_2(b_0(), a_0())))) ....... R1 [B0:L0, B2:L2]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(x0, implies_2(a_0(), implies_2(b_0(), a_0())))) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(implies_2(x1, x0)) ....... R2 [R1:L0, B2:L2]
% ~is_a_theorem_1(implies_2(x0, implies_2(a_0(), implies_2(b_0(), a_0())))) | ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(a_0(), implies_2(b_0(), a_0()))), x0)) ....... R3 [R2:L0, R2:L1]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x4,x1))),implies_2(x5,implies_2(x6,implies_2(x3,implies_2(x4,x1)))))) ....... U6
% ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, a_0()), implies_2(a_0(), implies_2(a_0(), implies_2(b_0(), a_0())))), implies_2(a_0(), implies_2(b_0(), a_0())))) ....... R4 [R3:L1, U6:L0]
% Derivation of unit clause U145:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... U1
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x5, x2), implies_2(x2, x3)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0]
% ~is_a_theorem_1(implies_2(implies_2(implies_2(x0,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0())))) ....... U18
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x5, x2), implies_2(x2, x3)))), implies_2(implies_2(implies_2(x6, a_0()), implies_2(a_0(), implies_2(a_0(), implies_2(b_0(), a_0())))), implies_2(a_0(), implies_2(b_0(), a_0()))))) ....... R4 [R3:L1, U18:L0]
% Derivation of unit clause U187:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) ....... U7
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, implies_2(x4, x3))))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3))))) ....... U3
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(x1, x2), implies_2(x2, implies_2(implies_2(implies_2(x3, x4), x4), implies_2(x4, implies_2(x5, x4))))))) ....... R4 [R3:L0, U3:L0]
% Derivation of unit clause U205:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) ....... U7
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, implies_2(x4, x3))))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(x1,x2),implies_2(x2,implies_2(implies_2(implies_2(x3,x4),x4),implies_2(x4,implies_2(x5,x4))))))) ....... U187
% is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, implies_2(x4, x3)))))) ....... R4 [R3:L0, U187:L0]
% Derivation of unit clause U217:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) ....... U7
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, implies_2(x4, x3))))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0]
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(x1,implies_2(implies_2(implies_2(x2,x3),x3),implies_2(x3,implies_2(x4,x3)))))) ....... U205
% is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x2), implies_2(x2, implies_2(x3, x2)))), implies_2(implies_2(implies_2(x4, x5), x5), implies_2(x5, implies_2(x6, x5))))) ....... R4 [R3:L0, U205:L0]
% Derivation of unit clause U319:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(implies_2(x1,x2),implies_2(x2,x3))),implies_2(x4,implies_2(x5,implies_2(x6,x2)))),implies_2(x7,implies_2(x8,implies_2(x4,implies_2(x5,implies_2(x6,x2))))))) ....... U8
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x2), implies_2(x4, implies_2(implies_2(x5, x2), x2))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U8:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... U1
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, implies_2(implies_2(x3, x0), x0))), x4), implies_2(x5, implies_2(x6, x4)))) ....... R4 [R3:L0, U1:L0]
% Derivation of unit clause U15258:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,implies_2(x3,x2)))),implies_2(implies_2(implies_2(x4,x5),x5),implies_2(x5,implies_2(x6,x5))))) ....... U217
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x1), implies_2(x1, implies_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U217:L0]
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3)))),implies_2(implies_2(implies_2(x6,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0()))))) ....... U145
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x1), implies_2(x1, implies_2(x2, x1))), implies_2(implies_2(implies_2(implies_2(x3, implies_2(x4, x5)), implies_2(x5, x6)), implies_2(x7, implies_2(implies_2(x8, x5), implies_2(x5, x6)))), implies_2(implies_2(implies_2(x9, a_0()), implies_2(a_0(), implies_2(a_0(), implies_2(b_0(), a_0())))), implies_2(a_0(), implies_2(b_0(), a_0())))))) ....... R4 [R3:L1, U145:L0]
% Derivation of unit clause U16958:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,implies_2(x3,x2)))),implies_2(implies_2(implies_2(x4,x5),x5),implies_2(x5,implies_2(x6,x5))))) ....... U217
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x1), implies_2(x1, implies_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U217:L0]
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x1),implies_2(x1,implies_2(x2,x1))),implies_2(implies_2(implies_2(implies_2(x3,implies_2(x4,x5)),implies_2(x5,x6)),implies_2(x7,implies_2(implies_2(x8,x5),implies_2(x5,x6)))),implies_2(implies_2(implies_2(x9,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0())))))) ....... U15258
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x1), implies_2(x1, implies_2(x2, x1))), implies_2(implies_2(implies_2(implies_2(x3, x4), x4), implies_2(x4, implies_2(x5, x4))), implies_2(implies_2(implies_2(implies_2(x6, implies_2(x7, x8)), implies_2(x8, x9)), implies_2(x10, implies_2(implies_2(x11, x8), implies_2(x8, x9)))), implies_2(implies_2(implies_2(x12, a_0()), implies_2(a_0(), implies_2(a_0(), implies_2(b_0(), a_0())))), implies_2(a_0(), implies_2(b_0(), a_0()))))))) ....... R4 [R3:L1, U15258:L0]
% Derivation of unit clause U22753:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,implies_2(implies_2(x3,x0),x0))),x4),implies_2(x5,implies_2(x6,x4)))) ....... U319
% is_a_theorem_1(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, x4)), implies_2(x5, implies_2(x6, implies_2(x3, x4))))))) ....... R2 [R1:L0, U319:L0]
% Derivation of unit clause U23556:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(implies_2(implies_2(x2,x3),x3),implies_2(x3,x4)),implies_2(x5,implies_2(x6,implies_2(x3,x4))))))) ....... U22753
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), x2), implies_2(x2, x3)), implies_2(x4, implies_2(x5, implies_2(x2, x3)))))) ....... R2 [R1:L0, U22753:L0]
% Derivation of the empty clause:
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,x3)),implies_2(x4,implies_2(x5,implies_2(x2,x3)))))) ....... U23556
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x1),implies_2(x1,implies_2(x2,x1))),implies_2(implies_2(implies_2(implies_2(x3,x4),x4),implies_2(x4,implies_2(x5,x4))),implies_2(implies_2(implies_2(implies_2(x6,implies_2(x7,x8)),implies_2(x8,x9)),implies_2(x10,implies_2(implies_2(x11,x8),implies_2(x8,x9)))),implies_2(implies_2(implies_2(x12,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0()))))))) ....... U16958
% [] ....... R1 [U23556:L0, U16958:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 473860
% resolvents: 473852 factors: 8
% Number of unit clauses generated: 452380
% % unit clauses generated to total clauses generated: 95.47
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 5479 [4] = 18076
% Total = 23557
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 452380 [2] = 21467 [3] = 13
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)5525 (-)18032
% ------------------
% Total: (+)5525 (-)18032
% Total number of unit clauses retained: 23557
% Number of clauses skipped because of their length: 143
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 473904
% Number of unification failures: 82713
% Number of unit to unit unification failures: 99621357
% N literal unification failure due to lookup root_id table: 34
% 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: 428668
% N unit clauses dropped because too much nesting: 11342
% N unit clauses not constrcuted because table was full: 0
% N unit clauses dropped because UCFA table was full: 0
% Max number of terms in a unit clause: 63
% Max term depth in a unit clause: 11
% Number of states in UCFA table: 347657
% Total number of terms of all unit clauses in table: 1115985
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.66
% Ratio n states used/total unit clauses terms: 0.31
% Number of symbols (columns) in UCFA: 38
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 556617
% ConstructUnitClause() = 452223
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 2.42 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 2739
% | |
% --------------------------------------------------------
% Elapsed time: 176 secs
% CPU time: 173.67 secs
%
%------------------------------------------------------------------------------