TSTP Solution File: GRP126-2.004 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : GRP126-2.004 : TPTP v5.0.0. Released v1.2.0.
% 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 : Sat Nov 27 21:08:44 EST 2010
% Result : Unsatisfiable 139.58s
% Output : Refutation 139.58s
% 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/SystemOnTPTP20399/GRP/GRP126-2.004+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 = 52] [nf = 0] [nu = 0] [ut = 26]
% Looking for a proof at depth = 2 ...
% t = 1 secs [nr = 324] [nf = 8] [nu = 166] [ut = 65]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 770] [nf = 362] [nu = 356] [ut = 65]
% Looking for a proof at depth = 4 ...
% t = 1 secs [nr = 3290] [nf = 716] [nu = 1922] [ut = 65]
% Looking for a proof at depth = 5 ...
% t = 1 secs [nr = 7930] [nf = 5454] [nu = 3488] [ut = 65]
% Looking for a proof at depth = 6 ...
% t = 1 secs [nr = 31402] [nf = 10192] [nu = 17102] [ut = 65]
% Looking for a proof at depth = 7 ...
% t = 1 secs [nr = 77898] [nf = 62378] [nu = 30716] [ut = 65]
% Looking for a proof at depth = 8 ...
% t = 1 secs [nr = 293842] [nf = 114564] [nu = 152530] [ut = 65]
% Looking for a proof at depth = 9 ...
% t = 3 secs [nr = 735338] [nf = 643518] [nu = 274344] [ut = 65]
% Looking for a proof at depth = 10 ...
% t = 9 secs [nr = 2757546] [nf = 1172472] [nu = 1412046] [ut = 65]
% Looking for a proof at depth = 11 ...
% t = 23 secs [nr = 6949546] [nf = 6145154] [nu = 2549748] [ut = 65]
% Looking for a proof at depth = 12 ...
% t = 81 secs [nr = 26274090] [nf = 11117836] [nu = 13427946] [ut = 65]
% Looking for a proof at depth = 13 ...
% Entering time slice 2
% Updating parameters ... done.
% Looking for a proof at depth = 1 ...
% t = 123 secs [nr = 38867297] [nf = 25341046] [nu = 17064102] [ut = 65]
% Looking for a proof at depth = 2 ...
% t = 123 secs [nr = 38867630] [nf = 25341054] [nu = 17064292] [ut = 65]
% Looking for a proof at depth = 3 ...
% t = 123 secs [nr = 38868087] [nf = 25341432] [nu = 17064482] [ut = 65]
% Looking for a proof at depth = 4 ...
% t = 123 secs [nr = 38873697] [nf = 25341810] [nu = 17067458] [ut = 65]
% Looking for a proof at depth = 5 ...
% t = 123 secs [nr = 38890354] [nf = 25360274] [nu = 17072222] [ut = 70]
% Looking for a proof at depth = 6 ...
% t = 128 secs [nr = 40484690] [nf = 25392492] [nu = 18038800] [ut = 75]
% Looking for a proof at depth = 7 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~product_3(x1,x0,x3) | ~product_3(x0,x1,x2) | product_3(x2,x3,x1)
% B1: product_3(x0,x0,x0)
% B2: group_element_1(e_1_0())
% B23: greater_2(e_4_0(),e_3_0())
% B28: ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3)
% B29: ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3)
% B30: ~greater_2(x1,x2) | ~next_2(x0,x2) | ~product_3(x0,e_1_0(),x1)
% B31: ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) | product_3(x0,x1,e_4_0())
% Unit Clauses:
% --------------
% U0: < d0 v3 dv1 f0 c0 t3 td1 b > product_3(x0,x0,x0)
% U1: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_1_0())
% U2: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_2_0())
% U4: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_4_0())
% U5: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_2_0())
% U6: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_3_0())
% U7: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_4_0())
% U8: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_1_0())
% U11: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_1_0())
% U14: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_4_0(),e_1_0())
% U15: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_4_0(),e_2_0())
% U24: < d0 v0 dv0 f0 c2 t2 td1 b > next_2(e_2_0(),e_3_0())
% U39: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_2_0())
% U41: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_4_0(),e_1_0(),e_4_0())
% U51: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_2_0())
% U52: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_3_0(),e_3_0())
% U54: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_1_0())
% U57: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_1_0(),e_1_0())
% U60: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_4_0(),e_1_0(),e_1_0())
% U64: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_4_0())
% U66: < d5 v0 dv0 f0 c3 t3 td1 > product_3(e_2_0(),e_1_0(),e_3_0())
% U74: < d6 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_3_0())
% U75: < d7 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_2_0(),e_4_0())
% U76: < d7 v0 dv0 f0 c3 t3 td1 > product_3(e_4_0(),e_3_0(),e_2_0())
% U79: < d7 v0 dv0 f0 c3 t3 td1 > ~product_3(e_4_0(),e_1_0(),e_3_0())
% U84: < d7 v0 dv0 f0 c2 t2 td1 > equalish_2(e_3_0(),e_1_0())
% --------------- Start of Proof ---------------
% Derivation of unit clause U0:
% product_3(x0,x0,x0) ....... U0
% Derivation of unit clause U1:
% group_element_1(e_1_0()) ....... U1
% Derivation of unit clause U2:
% group_element_1(e_2_0()) ....... U2
% Derivation of unit clause U4:
% group_element_1(e_4_0()) ....... U4
% Derivation of unit clause U5:
% ~equalish_2(e_1_0(),e_2_0()) ....... U5
% Derivation of unit clause U6:
% ~equalish_2(e_1_0(),e_3_0()) ....... U6
% Derivation of unit clause U7:
% ~equalish_2(e_1_0(),e_4_0()) ....... U7
% Derivation of unit clause U8:
% ~equalish_2(e_2_0(),e_1_0()) ....... U8
% Derivation of unit clause U11:
% ~equalish_2(e_3_0(),e_1_0()) ....... U11
% Derivation of unit clause U14:
% ~equalish_2(e_4_0(),e_1_0()) ....... U14
% Derivation of unit clause U15:
% ~equalish_2(e_4_0(),e_2_0()) ....... U15
% Derivation of unit clause U24:
% next_2(e_2_0(),e_3_0()) ....... U24
% Derivation of unit clause U39:
% product_3(x0,x0,x0) ....... B1
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B28
% ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B1:L0, B28:L0]
% ~equalish_2(e_1_0(),e_2_0()) ....... U5
% ~product_3(e_2_0(), e_1_0(), e_2_0()) ....... R2 [R1:L1, U5:L0]
% Derivation of unit clause U41:
% product_3(x0,x0,x0) ....... B1
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B28
% ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B1:L0, B28:L0]
% ~equalish_2(e_1_0(),e_4_0()) ....... U7
% ~product_3(e_4_0(), e_1_0(), e_4_0()) ....... R2 [R1:L1, U7:L0]
% Derivation of unit clause U51:
% product_3(x0,x0,x0) ....... B1
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B29
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B29:L0]
% ~equalish_2(e_1_0(),e_2_0()) ....... U5
% ~product_3(e_1_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U5:L0]
% Derivation of unit clause U52:
% product_3(x0,x0,x0) ....... B1
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B29
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B29:L0]
% ~equalish_2(e_1_0(),e_3_0()) ....... U6
% ~product_3(e_1_0(), e_3_0(), e_3_0()) ....... R2 [R1:L1, U6:L0]
% Derivation of unit clause U54:
% product_3(x0,x0,x0) ....... B1
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B29
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B29:L0]
% ~equalish_2(e_2_0(),e_1_0()) ....... U8
% ~product_3(e_2_0(), e_1_0(), e_1_0()) ....... R2 [R1:L1, U8:L0]
% Derivation of unit clause U57:
% product_3(x0,x0,x0) ....... B1
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B29
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B29:L0]
% ~equalish_2(e_3_0(),e_1_0()) ....... U11
% ~product_3(e_3_0(), e_1_0(), e_1_0()) ....... R2 [R1:L1, U11:L0]
% Derivation of unit clause U60:
% product_3(x0,x0,x0) ....... B1
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B29
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B29:L0]
% ~equalish_2(e_4_0(),e_1_0()) ....... U14
% ~product_3(e_4_0(), e_1_0(), e_1_0()) ....... R2 [R1:L1, U14:L0]
% Derivation of unit clause U64:
% greater_2(e_4_0(),e_3_0()) ....... B23
% ~greater_2(x1,x2) | ~next_2(x0,x2) | ~product_3(x0,e_1_0(),x1) ....... B30
% ~next_2(x0, e_3_0()) | ~product_3(x0, e_1_0(), e_4_0()) ....... R1 [B23:L0, B30:L0]
% next_2(e_2_0(),e_3_0()) ....... U24
% ~product_3(e_2_0(), e_1_0(), e_4_0()) ....... R2 [R1:L0, U24:L0]
% Derivation of unit clause U66:
% group_element_1(e_1_0()) ....... B2
% ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) | product_3(x0,x1,e_4_0()) ....... B31
% ~group_element_1(x0) | product_3(x0, e_1_0(), e_1_0()) | product_3(x0, e_1_0(), e_2_0()) | product_3(x0, e_1_0(), e_3_0()) | product_3(x0, e_1_0(), e_4_0()) ....... R1 [B2:L0, B31:L0]
% group_element_1(e_2_0()) ....... U2
% product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_3_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R2 [R1:L0, U2:L0]
% ~product_3(e_2_0(),e_1_0(),e_1_0()) ....... U54
% product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_3_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R3 [R2:L0, U54:L0]
% ~product_3(e_2_0(),e_1_0(),e_2_0()) ....... U39
% product_3(e_2_0(), e_1_0(), e_3_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R4 [R3:L0, U39:L0]
% ~product_3(e_2_0(),e_1_0(),e_4_0()) ....... U64
% product_3(e_2_0(), e_1_0(), e_3_0()) ....... R5 [R4:L1, U64:L0]
% Derivation of unit clause U74:
% ~product_3(x1,x0,x3) | ~product_3(x0,x1,x2) | product_3(x2,x3,x1) ....... B0
% ~product_3(x0, x0, x1) | product_3(x1, x1, x0) ....... R1 [B0:L0, B0:L1]
% ~product_3(x1,x0,x3) | ~product_3(x0,x1,x2) | product_3(x2,x3,x1) ....... B0
% ~product_3(x0, x0, x1) | ~product_3(x1, x1, x2) | product_3(x2, x0, x1) ....... R2 [R1:L1, B0:L0]
% product_3(x0,x0,x0) ....... U0
% ~product_3(x0, x0, x1) | product_3(x1, x0, x0) ....... R3 [R2:L0, U0:L0]
% ~product_3(x1,x0,x3) | ~product_3(x0,x1,x2) | product_3(x2,x3,x1) ....... B0
% product_3(x0, x1, x1) | ~product_3(x0, x2, x1) | ~product_3(x2, x0, x1) ....... R4 [R3:L0, B0:L2]
% ~product_3(e_1_0(),e_3_0(),e_3_0()) ....... U52
% ~product_3(e_1_0(), x0, e_3_0()) | ~product_3(x0, e_1_0(), e_3_0()) ....... R5 [R4:L0, U52:L0]
% product_3(e_2_0(),e_1_0(),e_3_0()) ....... U66
% ~product_3(e_1_0(), e_2_0(), e_3_0()) ....... R6 [R5:L1, U66:L0]
% Derivation of unit clause U75:
% ~product_3(x1,x0,x3) | ~product_3(x0,x1,x2) | product_3(x2,x3,x1) ....... B0
% ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) | product_3(x0,x1,e_4_0()) ....... B31
% ~product_3(x0, x1, x2) | product_3(x2, e_1_0(), x1) | ~group_element_1(x0) | ~group_element_1(x1) | product_3(x1, x0, e_2_0()) | product_3(x1, x0, e_3_0()) | product_3(x1, x0, e_4_0()) ....... R1 [B0:L0, B31:L2]
% product_3(e_2_0(),e_1_0(),e_3_0()) ....... U66
% product_3(e_3_0(), e_1_0(), e_1_0()) | ~group_element_1(e_2_0()) | ~group_element_1(e_1_0()) | product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_1_0(), e_2_0(), e_3_0()) | product_3(e_1_0(), e_2_0(), e_4_0()) ....... R2 [R1:L0, U66:L0]
% ~product_3(e_3_0(),e_1_0(),e_1_0()) ....... U57
% ~group_element_1(e_2_0()) | ~group_element_1(e_1_0()) | product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_1_0(), e_2_0(), e_3_0()) | product_3(e_1_0(), e_2_0(), e_4_0()) ....... R3 [R2:L0, U57:L0]
% group_element_1(e_2_0()) ....... U2
% ~group_element_1(e_1_0()) | product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_1_0(), e_2_0(), e_3_0()) | product_3(e_1_0(), e_2_0(), e_4_0()) ....... R4 [R3:L0, U2:L0]
% group_element_1(e_1_0()) ....... U1
% product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_1_0(), e_2_0(), e_3_0()) | product_3(e_1_0(), e_2_0(), e_4_0()) ....... R5 [R4:L0, U1:L0]
% ~product_3(e_1_0(),e_2_0(),e_2_0()) ....... U51
% product_3(e_1_0(), e_2_0(), e_3_0()) | product_3(e_1_0(), e_2_0(), e_4_0()) ....... R6 [R5:L0, U51:L0]
% ~product_3(e_1_0(),e_2_0(),e_3_0()) ....... U74
% product_3(e_1_0(), e_2_0(), e_4_0()) ....... R7 [R6:L0, U74:L0]
% Derivation of unit clause U76:
% ~product_3(x1,x0,x3) | ~product_3(x0,x1,x2) | product_3(x2,x3,x1) ....... B0
% ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) | product_3(x0,x1,e_4_0()) ....... B31
% ~product_3(x0, x1, x2) | product_3(x2, e_3_0(), x1) | ~group_element_1(x0) | ~group_element_1(x1) | product_3(x1, x0, e_1_0()) | product_3(x1, x0, e_2_0()) | product_3(x1, x0, e_4_0()) ....... R1 [B0:L0, B31:L4]
% product_3(e_1_0(),e_2_0(),e_4_0()) ....... U75
% product_3(e_4_0(), e_3_0(), e_2_0()) | ~group_element_1(e_1_0()) | ~group_element_1(e_2_0()) | product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R2 [R1:L0, U75:L0]
% group_element_1(e_1_0()) ....... U1
% product_3(e_4_0(), e_3_0(), e_2_0()) | ~group_element_1(e_2_0()) | product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R3 [R2:L1, U1:L0]
% group_element_1(e_2_0()) ....... U2
% product_3(e_4_0(), e_3_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R4 [R3:L1, U2:L0]
% ~product_3(e_2_0(),e_1_0(),e_1_0()) ....... U54
% product_3(e_4_0(), e_3_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R5 [R4:L1, U54:L0]
% ~product_3(e_2_0(),e_1_0(),e_2_0()) ....... U39
% product_3(e_4_0(), e_3_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R6 [R5:L1, U39:L0]
% ~product_3(e_2_0(),e_1_0(),e_4_0()) ....... U64
% product_3(e_4_0(), e_3_0(), e_2_0()) ....... R7 [R6:L1, U64:L0]
% Derivation of unit clause U79:
% group_element_1(e_1_0()) ....... B2
% ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) | product_3(x0,x1,e_4_0()) ....... B31
% ~group_element_1(x0) | product_3(x0, e_1_0(), e_1_0()) | product_3(x0, e_1_0(), e_2_0()) | product_3(x0, e_1_0(), e_3_0()) | product_3(x0, e_1_0(), e_4_0()) ....... R1 [B2:L0, B31:L0]
% group_element_1(e_2_0()) ....... U2
% product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_3_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R2 [R1:L0, U2:L0]
% ~product_3(e_2_0(),e_1_0(),e_1_0()) ....... U54
% product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_3_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R3 [R2:L0, U54:L0]
% ~product_3(e_2_0(),e_1_0(),e_2_0()) ....... U39
% product_3(e_2_0(), e_1_0(), e_3_0()) | product_3(e_2_0(), e_1_0(), e_4_0()) ....... R4 [R3:L0, U39:L0]
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B29
% product_3(e_2_0(), e_1_0(), e_4_0()) | ~product_3(x0, e_1_0(), e_3_0()) | equalish_2(x0, e_2_0()) ....... R5 [R4:L0, B29:L0]
% ~product_3(e_2_0(),e_1_0(),e_4_0()) ....... U64
% ~product_3(x0, e_1_0(), e_3_0()) | equalish_2(x0, e_2_0()) ....... R6 [R5:L0, U64:L0]
% ~equalish_2(e_4_0(),e_2_0()) ....... U15
% ~product_3(e_4_0(), e_1_0(), e_3_0()) ....... R7 [R6:L1, U15:L0]
% Derivation of unit clause U84:
% group_element_1(e_1_0()) ....... B2
% ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) | product_3(x0,x1,e_4_0()) ....... B31
% ~group_element_1(x0) | product_3(x0, e_1_0(), e_1_0()) | product_3(x0, e_1_0(), e_2_0()) | product_3(x0, e_1_0(), e_3_0()) | product_3(x0, e_1_0(), e_4_0()) ....... R1 [B2:L0, B31:L0]
% group_element_1(e_4_0()) ....... U4
% product_3(e_4_0(), e_1_0(), e_1_0()) | product_3(e_4_0(), e_1_0(), e_2_0()) | product_3(e_4_0(), e_1_0(), e_3_0()) | product_3(e_4_0(), e_1_0(), e_4_0()) ....... R2 [R1:L0, U4:L0]
% ~product_3(e_4_0(),e_1_0(),e_1_0()) ....... U60
% product_3(e_4_0(), e_1_0(), e_2_0()) | product_3(e_4_0(), e_1_0(), e_3_0()) | product_3(e_4_0(), e_1_0(), e_4_0()) ....... R3 [R2:L0, U60:L0]
% ~product_3(e_4_0(),e_1_0(),e_3_0()) ....... U79
% product_3(e_4_0(), e_1_0(), e_2_0()) | product_3(e_4_0(), e_1_0(), e_4_0()) ....... R4 [R3:L1, U79:L0]
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B28
% product_3(e_4_0(), e_1_0(), e_4_0()) | ~product_3(e_4_0(), x0, e_2_0()) | equalish_2(x0, e_1_0()) ....... R5 [R4:L0, B28:L0]
% ~product_3(e_4_0(),e_1_0(),e_4_0()) ....... U41
% ~product_3(e_4_0(), x0, e_2_0()) | equalish_2(x0, e_1_0()) ....... R6 [R5:L0, U41:L0]
% product_3(e_4_0(),e_3_0(),e_2_0()) ....... U76
% equalish_2(e_3_0(), e_1_0()) ....... R7 [R6:L0, U76:L0]
% Derivation of the empty clause:
% equalish_2(e_3_0(),e_1_0()) ....... U84
% ~equalish_2(e_3_0(),e_1_0()) ....... U11
% [] ....... R1 [U84:L0, U11:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 72541605
% resolvents: 43905311 factors: 28636294
% Number of unit clauses generated: 19064931
% % unit clauses generated to total clauses generated: 26.28
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 26 [2] = 39 [5] = 5 [6] = 5 [7] = 10
% Total = 85
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 19064931 [2] = 37947060 [3] = 14971732 [4] = 519911 [5] = 36626 [6] = 1301
% [7] = 44
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] group_element_1 (+)4 (-)0
% [1] equalish_2 (+)6 (-)12
% [2] greater_2 (+)6 (-)2
% [3] next_2 (+)3 (-)2
% [4] product_3 (+)9 (-)41
% ------------------
% Total: (+)28 (-)57
% Total number of unit clauses retained: 85
% Number of clauses skipped because of their length: 70755972
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 98331
% Number of successful unifications: 72541660
% Number of unification failures: 103973075
% Number of unit to unit unification failures: 453
% N literal unification failure due to lookup root_id table: 150323710
% N base clause resolution failure due to lookup table: 9525284
% N UC-BCL resolution dropped due to lookup table: 586488
% Max entries in substitution set: 32
% N unit clauses dropped because they exceeded max values: 11940712
% N unit clauses dropped because too much nesting: 0
% 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: 3
% Max term depth in a unit clause: 1
% Number of states in UCFA table: 64
% Total number of terms of all unit clauses in table: 216
% Max allowed number of states in UCFA: 80000
% Ratio n states used/total allowed states: 0.00
% Ratio n states used/total unit clauses terms: 0.30
% Number of symbols (columns) in UCFA: 43
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 176514735
% ConstructUnitClause() = 11940771
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 13.03 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 521882
% | |
% --------------------------------------------------------
% Elapsed time: 142 secs
% CPU time: 139.56 secs
%
%------------------------------------------------------------------------------