TSTP Solution File: LCL102-1 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL102-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art02.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 00:00:12 EST 2010
% Result : Unsatisfiable 0.43s
% Output : Refutation 0.43s
% 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/SystemOnTPTP1562/LCL/LCL102-1+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 = 7] [nf = 0] [nu = 0] [ut = 4]
% 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(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3))
% B2: is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))))
% B3: is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x0))))
% B4: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U2: < d0 v6 dv3 f5 c0 t11 td4 b > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))))
% U5: < d2 v6 dv3 f13 c8 t27 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))
% U13: < d2 v14 dv7 f21 c8 t43 td7 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))
% U20: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))))
% U24: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(x1,x3))),equivalent_2(x2,x3)))
% U62: < d2 v20 dv10 f27 c8 t55 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),x6),x6),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x9,x7),equivalent_2(x9,x8))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))))
% U91: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),equivalent_2(x1,equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x3,x4))))
% U114: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),equivalent_2(x2,equivalent_2(x3,x5))))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x4,x5)))))
% U232: < d2 v16 dv8 f23 c8 t47 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x4)),equivalent_2(x0,x4)),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x7,x5),equivalent_2(x7,x6))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))
% U256: < d2 v8 dv4 f15 c8 t31 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x0),equivalent_2(x3,x1)),x2)),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))
% U275: < d2 v2 dv1 f9 c8 t19 td5 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,a_0()),equivalent_2(x0,b_0())),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))
% U314: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x1,x3),x0),equivalent_2(x3,x2))))
% U444: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x3))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U2:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U2
% Derivation of unit clause U5:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) ....... B0
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R1 [B0:L0, B4:L2]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R2 [R1:L0, U2:L0]
% Derivation of unit clause U13:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3), x3), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B4:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U5
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3), x3), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x6, x4), equivalent_2(x6, x5))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R2 [R1:L1, U5:L0]
% Derivation of unit clause U20:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U2
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3)))) ....... R2 [R1:L0, U2:L0]
% Derivation of unit clause U24:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3)))) ....... U20
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x0, equivalent_2(x1, x3))), equivalent_2(x2, x3))) ....... R2 [R1:L0, U20:L0]
% Derivation of unit clause U62:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B4:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) ....... U13
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)), x6), x6), equivalent_2(equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x9, x7), equivalent_2(x9, x8))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))))) ....... R2 [R1:L1, U13:L0]
% Derivation of unit clause U91:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(x1,x3))),equivalent_2(x2,x3))) ....... U24
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), equivalent_2(x1, equivalent_2(x2, x4)))), equivalent_2(x0, equivalent_2(x3, x4)))) ....... R2 [R1:L0, U24:L0]
% Derivation of unit clause U114:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),equivalent_2(x1,equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x3,x4)))) ....... U91
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), equivalent_2(x2, equivalent_2(x3, x5))))), equivalent_2(x0, equivalent_2(x1, equivalent_2(x4, x5))))) ....... R2 [R1:L0, U91:L0]
% Derivation of unit clause U232:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),x6),x6),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x9,x7),equivalent_2(x9,x8))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))) ....... U62
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x4)), equivalent_2(x0, x4)), equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x7, x5), equivalent_2(x7, x6))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R2 [R1:L1, U62:L0]
% Derivation of unit clause U256:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x4)),equivalent_2(x0,x4)),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x7,x5),equivalent_2(x7,x6))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) ....... U232
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x3, x0), equivalent_2(x3, x1)), x2)), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R2 [R1:L1, U232:L0]
% Derivation of unit clause U275:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x0),equivalent_2(x3,x1)),x2)),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U256
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, a_0()), equivalent_2(x0, b_0())), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))) ....... R2 [R1:L1, U256:L0]
% Derivation of unit clause U314:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x0)))) ....... B3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), x0))), x3)) | is_a_theorem_1(x3) ....... R1 [B3:L0, B4:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),equivalent_2(x2,equivalent_2(x3,x5))))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x4,x5))))) ....... U114
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x1, x3), x0), equivalent_2(x3, x2)))) ....... R2 [R1:L0, U114:L0]
% Derivation of unit clause U444:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x0)))) ....... B3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), x0))), x3)) | is_a_theorem_1(x3) ....... R1 [B3:L0, B4:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x1,x3),x0),equivalent_2(x3,x2)))) ....... U314
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x3)))) ....... R2 [R1:L0, U314:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x3)))) ....... U444
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,a_0()),equivalent_2(x0,b_0())),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) ....... U275
% [] ....... R1 [U444:L0, U275:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 566
% resolvents: 566 factors: 0
% Number of unit clauses generated: 553
% % unit clauses generated to total clauses generated: 97.70
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 4 [2] = 441
% Total = 445
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 553 [2] = 13
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)334 (-)111
% ------------------
% Total: (+)334 (-)111
% Total number of unit clauses retained: 445
% Number of clauses skipped because of their length: 5
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 590
% Number of unification failures: 84
% Number of unit to unit unification failures: 37067
% N literal unification failure due to lookup root_id table: 9
% 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: 9
% N unit clauses dropped because they exceeded max values: 112
% N unit clauses dropped because too much nesting: 23
% 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: 6558
% Total number of terms of all unit clauses in table: 15067
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.01
% Ratio n states used/total unit clauses terms: 0.44
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 674
% ConstructUnitClause() = 553
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.00 secs
% --------------------------------------------------------
% | |
% Inferences per sec: inf
% | |
% --------------------------------------------------------
% Elapsed time: 0 secs
% CPU time: 0.41 secs
%
%------------------------------------------------------------------------------