%------------------------------------------------------------------------------ % 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 % %------------------------------------------------------------------------------