TSTP Solution File: LCL094-1 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL094-1 : 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 : Sat Nov 27 23:56:24 EST 2010
% Result : Unsatisfiable 173.16s
% Output : Refutation 173.16s
% 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/SystemOnTPTP22558/LCL/LCL094-1+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 = 136] [nf = 0] [nu = 50] [ut = 42]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 344] [nf = 6] [nu = 167] [ut = 42]
% Looking for a proof at depth = 4 ...
% Entering time slice 2
% Updating parameters ... done.
% Looking for a proof at depth = 1 ...
% t = 153 secs [nr = 388709] [nf = 10] [nu = 367536] [ut = 18263]
% 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(implies_2(a_0(),b_0()),b_0())))
% B1: is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0)))))
% U3: < d2 v10 dv6 f9 c0 t19 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),implies_2(x2,x4)),implies_2(x5,implies_2(x2,x4)))))
% U4: < d2 v9 dv5 f8 c0 t17 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3))))
% U5: < d2 v6 dv4 f5 c0 t11 td5 > is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2)))))
% U6: < d2 v5 dv3 f4 c0 t9 td4 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(x0,x1),implies_2(x2,x1))))
% U11: < d2 v12 dv7 f11 c0 t23 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,implies_2(x2,x3)),x4),implies_2(implies_2(implies_2(implies_2(x5,x2),implies_2(x6,x2)),implies_2(x2,x3)),x4))))
% U12: < d2 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1))))))
% U13: < d2 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),x4),implies_2(x1,x4))))
% U14: < d2 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(x3,x4),x2),x3))))
% U19: < d2 v10 dv6 f9 c0 t19 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x5,x4)),x2),x3))))
% U20: < d2 v10 dv6 f9 c0 t19 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4))))
% U26: < d2 v12 dv7 f11 c0 t23 td8 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),implies_2(implies_2(implies_2(implies_2(implies_2(x3,x6),x2),x3),x4),x5))))
% U32: < d2 v14 dv8 f13 c0 t27 td9 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),x5),x6),implies_2(implies_2(implies_2(implies_2(implies_2(x7,x3),x1),x4),x5),x6))))
% U38: < d2 v16 dv9 f15 c0 t31 td10 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),x6),x7),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x3,x8),x2),x3),x4),x5),x6),x7))))
% U819: < d4 v11 dv6 f10 c0 t21 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),x3),implies_2(implies_2(implies_2(implies_2(x4,x1),implies_2(x5,x1)),implies_2(x1,x2)),x3)))
% U827: < d4 v9 dv5 f8 c0 t17 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(implies_2(implies_2(x0,x3),implies_2(x4,x3)),x1),x2)))
% U843: < d4 v15 dv8 f14 c0 t29 td9 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),x4),x5),x6),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x2,x7),x1),x2),x3),x4),x5),x6)))
% U2051: < d4 v10 dv6 f9 c0 t19 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(implies_2(x0,x3),x4),implies_2(x5,x4))))
% U2085: < d4 v11 dv7 f10 c0 t21 td8 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(x4,x3))),x5),implies_2(x6,x5)))
% U4293: < d4 v10 dv7 f9 c0 t19 td8 > is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(implies_2(implies_2(implies_2(x2,x3),x4),implies_2(x5,x4)),x2),implies_2(x6,x2)))))
% U4315: < d4 v9 dv6 f8 c0 t17 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),implies_2(x4,x3)),x1),implies_2(x5,x1))))
% U4322: < d4 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(x3,x2)),x0),implies_2(x4,x0)))
% U9315: < d4 v13 dv7 f12 c0 t25 td8 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x0),x3),implies_2(x4,x2)),x5),implies_2(implies_2(implies_2(x6,x3),implies_2(x4,x2)),x5)))
% U9574: < d4 v11 dv6 f10 c0 t21 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x3,x4)),implies_2(implies_2(implies_2(x5,x1),implies_2(x1,x2)),implies_2(x3,x4))))
% U11829: < d4 v9 dv5 f8 c0 t17 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x4)),x1),x4),implies_2(x3,x4))))
% U12075: < d4 v8 dv4 f7 c0 t15 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),x0),x3),implies_2(x2,x3)))
% U15291: < d4 v9 dv5 f8 c0 t17 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(implies_2(x2,x4),implies_2(x1,x4)))))
% U15599: < d4 v9 dv5 f8 c0 t17 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),x4),implies_2(implies_2(x3,x1),x4))))
% U15675: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3)))
% U21769: < d2 v8 dv4 f11 c4 t23 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3)),implies_2(a_0(),implies_2(implies_2(a_0(),b_0()),b_0()))))
% --------------- 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(x4,implies_2(implies_2(x3,x0),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(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), implies_2(x2, x4)), implies_2(x5, implies_2(x2, x4))))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U4:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),implies_2(x2,x4)),implies_2(x5,implies_2(x2,x4))))) ....... U3
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3)))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U5:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) ....... U4
% is_a_theorem_1(implies_2(x0, implies_2(x1, implies_2(implies_2(x1, x2), implies_2(x3, x2))))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U6:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x1,x2),implies_2(x3,x2))))) ....... U5
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(x0, x1), implies_2(x2, x1)))) ....... R2 [R1:L0, U5:L0]
% Derivation of unit clause U11:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),implies_2(x2,x4)),implies_2(x5,implies_2(x2,x4))))) ....... U3
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, implies_2(x2, x3)), x4), implies_2(implies_2(implies_2(implies_2(x5, x2), implies_2(x6, x2)), implies_2(x2, x3)), x4)))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U12:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) ....... U4
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), implies_2(implies_2(x3, x1), implies_2(x4, x1))), implies_2(x5, implies_2(implies_2(x3, x1), implies_2(x4, x1)))))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U13:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) ....... U5
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), x4), implies_2(x1, x4)))) ....... R2 [R1:L0, U5:L0]
% Derivation of unit clause U14:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(x0,x1),implies_2(x2,x1)))) ....... U6
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x3), implies_2(implies_2(implies_2(x3, x4), x2), x3)))) ....... R2 [R1:L0, U6:L0]
% Derivation of unit clause U19:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),x4),implies_2(x1,x4)))) ....... U13
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x3), implies_2(implies_2(implies_2(implies_2(x1, x4), implies_2(x5, x4)), x2), x3)))) ....... R2 [R1:L0, U13:L0]
% Derivation of unit clause U20:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(x3,x4),x2),x3)))) ....... U14
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x1), x4), implies_2(implies_2(implies_2(x5, x3), x1), x4)))) ....... R2 [R1:L0, U14:L0]
% Derivation of unit clause U26:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) ....... U20
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x4), x5), implies_2(implies_2(implies_2(implies_2(implies_2(x3, x6), x2), x3), x4), x5)))) ....... R2 [R1:L0, U20:L0]
% Derivation of unit clause U32:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),implies_2(implies_2(implies_2(implies_2(implies_2(x3,x6),x2),x3),x4),x5)))) ....... U26
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x1), x4), x5), x6), implies_2(implies_2(implies_2(implies_2(implies_2(x7, x3), x1), x4), x5), x6)))) ....... R2 [R1:L0, U26:L0]
% Derivation of unit clause U38:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),x5),x6),implies_2(implies_2(implies_2(implies_2(implies_2(x7,x3),x1),x4),x5),x6)))) ....... U32
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x4), x5), x6), x7), implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x3, x8), x2), x3), x4), x5), x6), x7)))) ....... R2 [R1:L0, U32:L0]
% Derivation of unit clause U819:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), implies_2(x2, x4)), implies_2(x5, implies_2(x2, x4)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,implies_2(x2,x3)),x4),implies_2(implies_2(implies_2(implies_2(x5,x2),implies_2(x6,x2)),implies_2(x2,x3)),x4)))) ....... U11
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), x3), implies_2(implies_2(implies_2(implies_2(x4, x1), implies_2(x5, x1)), implies_2(x1, x2)), x3))) ....... R4 [R3:L0, U11:L0]
% Derivation of unit clause U827:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), implies_2(x2, x4)), implies_2(x5, implies_2(x2, x4)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x5,x4)),x2),x3)))) ....... U19
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(implies_2(implies_2(x0, x3), implies_2(x4, x3)), x1), x2))) ....... R4 [R3:L0, U19:L0]
% Derivation of unit clause U843:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), implies_2(x2, x4)), implies_2(x5, implies_2(x2, x4)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),x6),x7),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x3,x8),x2),x3),x4),x5),x6),x7)))) ....... U38
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x3), x4), x5), x6), implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x2, x7), x1), x2), x3), x4), x5), x6))) ....... R4 [R3:L0, U38:L0]
% Derivation of unit clause U2051:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) ....... U5
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(x0, x1), implies_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U5:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(implies_2(implies_2(x0,x3),implies_2(x4,x3)),x1),x2))) ....... U827
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(implies_2(x0, x3), x4), implies_2(x5, x4)))) ....... R4 [R3:L0, U827:L0]
% Derivation of unit clause U2085:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) ....... U5
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(x0, x1), implies_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U5:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(implies_2(x0,x3),x4),implies_2(x5,x4)))) ....... U2051
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(x4, x3))), x5), implies_2(x6, x5))) ....... R4 [R3:L0, U2051:L0]
% Derivation of unit clause U4293:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(implies_2(implies_2(x1,x2),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1)))))) ....... U12
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x2, x0), implies_2(x3, x0))), implies_2(x4, implies_2(implies_2(x2, x0), implies_2(x3, x0)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U12:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(x4,x3))),x5),implies_2(x6,x5))) ....... U2085
% is_a_theorem_1(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(implies_2(implies_2(x2, x3), x4), implies_2(x5, x4)), x2), implies_2(x6, x2))))) ....... R4 [R3:L0, U2085:L0]
% Derivation of unit clause U4315:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(implies_2(implies_2(x1,x2),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1)))))) ....... U12
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x2, x0), implies_2(x3, x0))), implies_2(x4, implies_2(implies_2(x2, x0), implies_2(x3, x0)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U12:L0]
% is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(implies_2(implies_2(implies_2(x2,x3),x4),implies_2(x5,x4)),x2),implies_2(x6,x2))))) ....... U4293
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), implies_2(x4, x3)), x1), implies_2(x5, x1)))) ....... R4 [R3:L0, U4293:L0]
% Derivation of unit clause U4322:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(implies_2(implies_2(x1,x2),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1)))))) ....... U12
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x2, x0), implies_2(x3, x0))), implies_2(x4, implies_2(implies_2(x2, x0), implies_2(x3, x0)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U12:L0]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),implies_2(x4,x3)),x1),implies_2(x5,x1)))) ....... U4315
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(x3, x2)), x0), implies_2(x4, x0))) ....... R4 [R3:L0, U4315:L0]
% Derivation of unit clause U9315:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) ....... U20
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x0), x3), implies_2(implies_2(implies_2(x4, x2), x0), x3)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U20:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),x4),x5),x6),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x2,x7),x1),x2),x3),x4),x5),x6))) ....... U843
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x0), x3), implies_2(x4, x2)), x5), implies_2(implies_2(implies_2(x6, x3), implies_2(x4, x2)), x5))) ....... R4 [R3:L0, U843:L0]
% Derivation of unit clause U9574:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) ....... U20
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x0), x3), implies_2(implies_2(implies_2(x4, x2), x0), x3)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U20:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x0),x3),implies_2(x4,x2)),x5),implies_2(implies_2(implies_2(x6,x3),implies_2(x4,x2)),x5))) ....... U9315
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x3, x4)), implies_2(implies_2(implies_2(x5, x1), implies_2(x1, x2)), implies_2(x3, x4)))) ....... R4 [R3:L0, U9315:L0]
% Derivation of unit clause U11829:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),implies_2(implies_2(implies_2(implies_2(implies_2(x3,x6),x2),x3),x4),x5)))) ....... U26
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x3), x4), implies_2(implies_2(implies_2(implies_2(implies_2(x2, x5), x1), x2), x3), x4)), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U26:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(x3,x2)),x0),implies_2(x4,x0))) ....... U4322
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x4)), x1), x4), implies_2(x3, x4)))) ....... R4 [R3:L0, U4322:L0]
% Derivation of unit clause U12075:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),implies_2(implies_2(implies_2(implies_2(implies_2(x3,x6),x2),x3),x4),x5)))) ....... U26
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x3), x4), implies_2(implies_2(implies_2(implies_2(implies_2(x2, x5), x1), x2), x3), x4)), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U26:L0]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x4)),x1),x4),implies_2(x3,x4)))) ....... U11829
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), x0), x3), implies_2(x2, x3))) ....... R4 [R3:L0, U11829:L0]
% Derivation of unit clause U15291:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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,x2)),x3),implies_2(implies_2(implies_2(implies_2(x4,x1),implies_2(x5,x1)),implies_2(x1,x2)),x3))) ....... U819
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(implies_2(x3, x5), implies_2(x1, x5)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U819:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x3,x4)),implies_2(implies_2(implies_2(x5,x1),implies_2(x1,x2)),implies_2(x3,x4)))) ....... U9574
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(x1, x2)), implies_2(x3, implies_2(implies_2(x2, x4), implies_2(x1, x4))))) ....... R4 [R3:L0, U9574:L0]
% Derivation of unit clause U15599:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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,x2)),x3),implies_2(implies_2(implies_2(implies_2(x4,x1),implies_2(x5,x1)),implies_2(x1,x2)),x3))) ....... U819
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(implies_2(x3, x5), implies_2(x1, x5)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U819:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(implies_2(x2,x4),implies_2(x1,x4))))) ....... U15291
% is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), x4), implies_2(implies_2(x3, x1), x4)))) ....... R4 [R3:L0, U15291:L0]
% Derivation of unit clause U15675:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),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(x4, implies_2(implies_2(x3, x0), 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(x4, implies_2(implies_2(x3, x0), 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,x2)),x3),implies_2(implies_2(implies_2(implies_2(x4,x1),implies_2(x5,x1)),implies_2(x1,x2)),x3))) ....... U819
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(implies_2(x3, x5), implies_2(x1, x5)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U819:L0]
% is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),x4),implies_2(implies_2(x3,x1),x4)))) ....... U15599
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(x2, x0), x3))) ....... R4 [R3:L0, U15599:L0]
% Derivation of unit clause U21769:
% ~is_a_theorem_1(implies_2(a_0(),implies_2(implies_2(a_0(),b_0()),b_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(implies_2(a_0(), b_0()), b_0())))) ....... R1 [B0:L0, B2:L2]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3))) ....... U15675
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(x2, x0), x3)), implies_2(a_0(), implies_2(implies_2(a_0(), b_0()), b_0())))) ....... R2 [R1:L0, U15675:L0]
% Derivation of the empty clause:
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3)),implies_2(a_0(),implies_2(implies_2(a_0(),b_0()),b_0())))) ....... U21769
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),x0),x3),implies_2(x2,x3))) ....... U12075
% [] ....... R1 [U21769:L0, U12075:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 392367
% resolvents: 392357 factors: 10
% Number of unit clauses generated: 371183
% % unit clauses generated to total clauses generated: 94.60
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 3547 [4] = 18221
% Total = 21770
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 371183 [2] = 21171 [3] = 13
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)4322 (-)17448
% ------------------
% Total: (+)4322 (-)17448
% Total number of unit clauses retained: 21770
% Number of clauses skipped because of their length: 216
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 392455
% Number of unification failures: 55362
% Number of unit to unit unification failures: 75408151
% 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: 18
% N unit clauses dropped because they exceeded max values: 348447
% N unit clauses dropped because too much nesting: 17843
% 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: 293438
% Total number of terms of all unit clauses in table: 1024854
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.56
% Ratio n states used/total unit clauses terms: 0.29
% Number of symbols (columns) in UCFA: 38
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 447817
% ConstructUnitClause() = 370215
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 1.94 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 2268
% | |
% --------------------------------------------------------
% Elapsed time: 175 secs
% CPU time: 173.13 secs
%
%------------------------------------------------------------------------------