TSTP Solution File: LCL358-1 by CARINE---0.734
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL358-1 : TPTP v5.0.0. Released v2.3.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art01.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 00:59:23 EST 2010
% Result : Unsatisfiable 0.49s
% Output : Refutation 0.49s
% 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/SystemOnTPTP18437/LCL/LCL358-1+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 = 7] [nf = 0] [nu = 0] [ut = 4]
% Looking for a proof at depth = 2 ...
% t = 1 secs [nr = 4294] [nf = 0] [nu = 2375] [ut = 1013]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 11142] [nf = 7] [nu = 7291] [ut = 1013]
% Looking for a proof at depth = 4 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~is_a_theorem_1(implies_2(implies_2(x_0(),implies_2(implies_2(y_0(),z_0()),u_0())),implies_2(implies_2(y_0(),v_0()),implies_2(x_0(),implies_2(implies_2(v_0(),z_0()),u_0())))))
% B1: is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2))))
% B2: is_a_theorem_1(implies_2(x0,implies_2(not_1(x0),x1)))
% B4: ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U1: < d0 v6 dv3 f5 c0 t11 td4 b > is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2))))
% U3: < d0 v3 dv1 f3 c0 t6 td4 b > is_a_theorem_1(implies_2(implies_2(not_1(x0),x0),x0))
% U8: < d2 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)))
% U10: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(implies_2(x0,x2),x3),implies_2(implies_2(x1,x2),x3))))
% U11: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x0,x4)),x2),x3)))
% U12: < d2 v10 dv5 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(x3,x4),implies_2(implies_2(x2,x0),x4))))
% U13: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x3,x1),x2)),x4),implies_2(implies_2(x0,x3),x4)))
% U253: < d2 v9 dv5 f9 c0 t18 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(not_1(implies_2(implies_2(x2,x0),x3)),x4)))
% U1072: < d4 v10 dv5 f30 c20 t60 td9 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x3,x1),x2)),x4),implies_2(implies_2(x0,x3),x4)),implies_2(not_1(implies_2(implies_2(x_0(),implies_2(implies_2(y_0(),z_0()),u_0())),implies_2(implies_2(y_0(),v_0()),implies_2(x_0(),implies_2(implies_2(v_0(),z_0()),u_0()))))),implies_2(implies_2(x_0(),implies_2(implies_2(y_0(),z_0()),u_0())),implies_2(implies_2(y_0(),v_0()),implies_2(x_0(),implies_2(implies_2(v_0(),z_0()),u_0())))))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... U1
% Derivation of unit clause U3:
% is_a_theorem_1(implies_2(implies_2(not_1(x0),x0),x0)) ....... U3
% Derivation of unit clause U8:
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0]
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... U1
% 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))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U10:
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0]
% 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))) ....... U8
% is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(implies_2(implies_2(x0, x2), x3), implies_2(implies_2(x1, x2), x3)))) ....... R2 [R1:L0, U8:L0]
% Derivation of unit clause U11:
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0]
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(implies_2(x0,x2),x3),implies_2(implies_2(x1,x2),x3)))) ....... U10
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x3), implies_2(implies_2(implies_2(implies_2(x1, x4), implies_2(x0, x4)), x2), x3))) ....... R2 [R1:L0, U10:L0]
% Derivation of unit clause U12:
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x0,x4)),x2),x3))) ....... U11
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(x3, x4), implies_2(implies_2(x2, x0), x4)))) ....... R2 [R1:L0, U11:L0]
% Derivation of unit clause U13:
% is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x3,x4),implies_2(implies_2(x2,x0),x4)))) ....... U12
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x3, x1), x2)), x4), implies_2(implies_2(x0, x3), x4))) ....... R2 [R1:L0, U12:L0]
% Derivation of unit clause U253:
% is_a_theorem_1(implies_2(x0,implies_2(not_1(x0),x1))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(not_1(x0), x1)), x2)) | is_a_theorem_1(x2) ....... R1 [B2:L0, B4:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x0,x4)),x2),x3))) ....... U11
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(not_1(implies_2(implies_2(x2, x0), x3)), x4))) ....... R2 [R1:L0, U11:L0]
% Derivation of unit clause U1072:
% ~is_a_theorem_1(implies_2(implies_2(x_0(),implies_2(implies_2(y_0(),z_0()),u_0())),implies_2(implies_2(y_0(),v_0()),implies_2(x_0(),implies_2(implies_2(v_0(),z_0()),u_0()))))) ....... B0
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(x_0(), implies_2(implies_2(y_0(), z_0()), u_0())), implies_2(implies_2(y_0(), v_0()), implies_2(x_0(), implies_2(implies_2(v_0(), z_0()), u_0())))))) ....... R1 [B0:L0, B4:L2]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
% ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(x_0(), implies_2(implies_2(y_0(), z_0()), u_0())), implies_2(implies_2(y_0(), v_0()), implies_2(x_0(), implies_2(implies_2(v_0(), z_0()), u_0())))))) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(implies_2(x1, x0)) ....... R2 [R1:L0, B4:L2]
% is_a_theorem_1(implies_2(implies_2(not_1(x0),x0),x0)) ....... U3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(not_1(implies_2(implies_2(x_0(), implies_2(implies_2(y_0(), z_0()), u_0())), implies_2(implies_2(y_0(), v_0()), implies_2(x_0(), implies_2(implies_2(v_0(), z_0()), u_0()))))), implies_2(implies_2(x_0(), implies_2(implies_2(y_0(), z_0()), u_0())), implies_2(implies_2(y_0(), v_0()), implies_2(x_0(), implies_2(implies_2(v_0(), z_0()), u_0()))))))) ....... R3 [R2:L0, U3:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x3,x1),x2)),x4),implies_2(implies_2(x0,x3),x4))) ....... U13
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x3, x1), x2)), x4), implies_2(implies_2(x0, x3), x4)), implies_2(not_1(implies_2(implies_2(x_0(), implies_2(implies_2(y_0(), z_0()), u_0())), implies_2(implies_2(y_0(), v_0()), implies_2(x_0(), implies_2(implies_2(v_0(), z_0()), u_0()))))), implies_2(implies_2(x_0(), implies_2(implies_2(y_0(), z_0()), u_0())), implies_2(implies_2(y_0(), v_0()), implies_2(x_0(), implies_2(implies_2(v_0(), z_0()), u_0()))))))) ....... R4 [R3:L0, U13:L0]
% Derivation of the empty clause:
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x3,x1),x2)),x4),implies_2(implies_2(x0,x3),x4)),implies_2(not_1(implies_2(implies_2(x_0(),implies_2(implies_2(y_0(),z_0()),u_0())),implies_2(implies_2(y_0(),v_0()),implies_2(x_0(),implies_2(implies_2(v_0(),z_0()),u_0()))))),implies_2(implies_2(x_0(),implies_2(implies_2(y_0(),z_0()),u_0())),implies_2(implies_2(y_0(),v_0()),implies_2(x_0(),implies_2(implies_2(v_0(),z_0()),u_0()))))))) ....... U1072
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(not_1(implies_2(implies_2(x2,x0),x3)),x4))) ....... U253
% [] ....... R1 [U1072:L0, U253:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 12990
% resolvents: 12981 factors: 9
% Number of unit clauses generated: 9127
% % unit clauses generated to total clauses generated: 70.26
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 4 [2] = 1009 [4] = 60
% Total = 1073
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 9127 [2] = 3842 [3] = 21
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)892 (-)181
% ------------------
% Total: (+)892 (-)181
% Total number of unit clauses retained: 1073
% Number of clauses skipped because of their length: 29
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 13006
% Number of unification failures: 8068
% Number of unit to unit unification failures: 160796
% N literal unification failure due to lookup root_id table: 43
% 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: 15
% N unit clauses dropped because they exceeded max values: 1785
% N unit clauses dropped because too much nesting: 731
% 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: 64
% Max term depth in a unit clause: 12
% Number of states in UCFA table: 17526
% Total number of terms of all unit clauses in table: 38318
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.03
% Ratio n states used/total unit clauses terms: 0.46
% Number of symbols (columns) in UCFA: 42
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 21074
% ConstructUnitClause() = 2854
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.01 secs
% --------------------------------------------------------
% | |
% Inferences per sec: inf
% | |
% --------------------------------------------------------
% Elapsed time: 1 secs
% CPU time: 0.48 secs
%
%------------------------------------------------------------------------------