%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP124-2.004 : TPTP v5.0.0. Released v1.2.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : 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 20:56:32 EST 2010 % Result : Unsatisfiable 94.88s % Output : Refutation 94.88s % 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/SystemOnTPTP954/GRP/GRP124-2.004+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 = 0 secs [nr = 52] [nf = 0] [nu = 0] [ut = 26] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 320] [nf = 6] [nu = 164] [ut = 65] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 588] [nf = 12] [nu = 328] [ut = 65] % Looking for a proof at depth = 4 ... % t = 1 secs [nr = 1824] [nf = 42] [nu = 636] [ut = 65] % Looking for a proof at depth = 5 ... % t = 1 secs [nr = 3060] [nf = 72] [nu = 944] [ut = 65] % Looking for a proof at depth = 6 ... % t = 1 secs [nr = 4296] [nf = 102] [nu = 1252] [ut = 65] % Looking for a proof at depth = 7 ... % t = 1 secs [nr = 5532] [nf = 132] [nu = 1560] [ut = 65] % Looking for a proof at depth = 8 ... % t = 1 secs [nr = 6768] [nf = 162] [nu = 1868] [ut = 65] % Looking for a proof at depth = 9 ... % t = 1 secs [nr = 8004] [nf = 192] [nu = 2176] [ut = 65] % Looking for a proof at depth = 10 ... % t = 1 secs [nr = 9240] [nf = 222] [nu = 2484] [ut = 65] % Looking for a proof at depth = 11 ... % t = 1 secs [nr = 10476] [nf = 252] [nu = 2792] [ut = 65] % Looking for a proof at depth = 12 ... % t = 1 secs [nr = 11712] [nf = 282] [nu = 3100] [ut = 65] % Looking for a proof at depth = 13 ... % t = 1 secs [nr = 12948] [nf = 312] [nu = 3408] [ut = 65] % Looking for a proof at depth = 14 ... % t = 1 secs [nr = 14184] [nf = 342] [nu = 3716] [ut = 65] % Looking for a proof at depth = 15 ... % t = 1 secs [nr = 15420] [nf = 372] [nu = 4024] [ut = 65] % Looking for a proof at depth = 16 ... % t = 1 secs [nr = 16656] [nf = 402] [nu = 4332] [ut = 65] % Looking for a proof at depth = 17 ... % t = 1 secs [nr = 17892] [nf = 432] [nu = 4640] [ut = 65] % Looking for a proof at depth = 18 ... % t = 1 secs [nr = 19128] [nf = 462] [nu = 4948] [ut = 65] % Looking for a proof at depth = 19 ... % t = 1 secs [nr = 20364] [nf = 492] [nu = 5256] [ut = 65] % Looking for a proof at depth = 20 ... % t = 1 secs [nr = 21600] [nf = 522] [nu = 5564] [ut = 65] % Looking for a proof at depth = 21 ... % t = 1 secs [nr = 22836] [nf = 552] [nu = 5872] [ut = 65] % Looking for a proof at depth = 22 ... % t = 1 secs [nr = 24072] [nf = 582] [nu = 6180] [ut = 65] % Looking for a proof at depth = 23 ... % t = 1 secs [nr = 25308] [nf = 612] [nu = 6488] [ut = 65] % Looking for a proof at depth = 24 ... % t = 1 secs [nr = 26544] [nf = 642] [nu = 6796] [ut = 65] % Looking for a proof at depth = 25 ... % t = 1 secs [nr = 27780] [nf = 672] [nu = 7104] [ut = 65] % Looking for a proof at depth = 26 ... % t = 1 secs [nr = 29016] [nf = 702] [nu = 7412] [ut = 65] % Looking for a proof at depth = 27 ... % t = 1 secs [nr = 30252] [nf = 732] [nu = 7720] [ut = 65] % Looking for a proof at depth = 28 ... % t = 1 secs [nr = 31488] [nf = 762] [nu = 8028] [ut = 65] % Looking for a proof at depth = 29 ... % t = 1 secs [nr = 32724] [nf = 792] [nu = 8336] [ut = 65] % Looking for a proof at depth = 30 ... % t = 1 secs [nr = 33960] [nf = 822] [nu = 8644] [ut = 65] % Restarting search with different parameters. % Looking for a proof at depth = 1 ... % t = 1 secs [nr = 34012] [nf = 822] [nu = 8644] [ut = 65] % Looking for a proof at depth = 2 ... % t = 1 secs [nr = 34280] [nf = 828] [nu = 8808] [ut = 65] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 34548] [nf = 834] [nu = 8972] [ut = 65] % Looking for a proof at depth = 4 ... % t = 1 secs [nr = 35792] [nf = 864] [nu = 9280] [ut = 65] % Looking for a proof at depth = 5 ... % t = 1 secs [nr = 38717] [nf = 896] [nu = 10144] [ut = 70] % Looking for a proof at depth = 6 ... % t = 1 secs [nr = 62956] [nf = 984] [nu = 15256] [ut = 70] % Looking for a proof at depth = 7 ... % t = 29 secs [nr = 2857193] [nf = 1072] [nu = 1034291] [ut = 104] % Looking for a proof at depth = 8 ... % t = 79 secs [nr = 17800970] [nf = 2356794] [nu = 2141080] [ut = 104] % Looking for a proof at depth = 9 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~product_3(x5,x3,x4) | ~product_3(x5,x0,x1) | ~product_3(x3,x4,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) % B2: product_3(x0,x0,x0) % B3: group_element_1(e_1_0()) % B4: group_element_1(e_2_0()) % B5: group_element_1(e_3_0()) % B24: greater_2(e_4_0(),e_3_0()) % B29: ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) % B30: ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) % B31: ~greater_2(x1,x2) | ~next_2(x0,x2) | ~product_3(x0,e_1_0(),x1) % B32: ~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()) % U3: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_3_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()) % U9: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_3_0()) % U11: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_1_0()) % U12: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_2_0()) % U13: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_4_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()) % U16: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_4_0(),e_3_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()) % U40: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_1_0(),e_3_0()) % U41: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_4_0(),e_1_0(),e_4_0()) % U42: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_1_0()) % U43: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_3_0()) % U45: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_3_0(),e_1_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()) % U58: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_2_0()) % U60: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_4_0(),e_1_0(),e_1_0()) % U61: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_4_0(),e_2_0(),e_2_0()) % U64: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_4_0()) % U74: < d7 v0 dv0 f0 c3 t3 td1 > ~product_3(e_4_0(),e_1_0(),e_3_0()) % U81: < d7 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_1_0(),e_2_0()) % U84: < d7 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_4_0()) % U91: < d7 v0 dv0 f0 c3 t3 td1 > ~product_3(e_4_0(),e_2_0(),e_1_0()) % U92: < d7 v0 dv0 f0 c3 t3 td1 > product_3(e_4_0(),e_2_0(),e_3_0()) % U95: < d7 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_2_0(),e_4_0()) % U100: < d7 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_3_0(),e_2_0()) % U104: < d9 v0 dv0 f0 c2 t2 td1 > equalish_2(e_2_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 U3: % group_element_1(e_3_0()) ....... U3 % 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 U9: % ~equalish_2(e_2_0(),e_3_0()) ....... U9 % Derivation of unit clause U11: % ~equalish_2(e_3_0(),e_1_0()) ....... U11 % Derivation of unit clause U12: % ~equalish_2(e_3_0(),e_2_0()) ....... U12 % Derivation of unit clause U13: % ~equalish_2(e_3_0(),e_4_0()) ....... U13 % 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 U16: % ~equalish_2(e_4_0(),e_3_0()) ....... U16 % Derivation of unit clause U24: % next_2(e_2_0(),e_3_0()) ....... U24 % Derivation of unit clause U39: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B29: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 U40: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B29:L0] % ~equalish_2(e_1_0(),e_3_0()) ....... U6 % ~product_3(e_3_0(), e_1_0(), e_3_0()) ....... R2 [R1:L1, U6:L0] % Derivation of unit clause U41: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B29: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 U42: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B29:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U8 % ~product_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U8:L0] % Derivation of unit clause U43: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B29:L0] % ~equalish_2(e_2_0(),e_3_0()) ....... U9 % ~product_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L1, U9:L0] % Derivation of unit clause U45: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B29:L0] % ~equalish_2(e_3_0(),e_1_0()) ....... U11 % ~product_3(e_1_0(), e_3_0(), e_1_0()) ....... R2 [R1:L1, U11:L0] % Derivation of unit clause U51: % product_3(x0,x0,x0) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B30: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) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B30: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) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B30: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) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B30: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 U58: % product_3(x0,x0,x0) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B30:L0] % ~equalish_2(e_3_0(),e_2_0()) ....... U12 % ~product_3(e_3_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U12:L0] % Derivation of unit clause U60: % product_3(x0,x0,x0) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B30: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 U61: % product_3(x0,x0,x0) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B30:L0] % ~equalish_2(e_4_0(),e_2_0()) ....... U15 % ~product_3(e_4_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U15:L0] % Derivation of unit clause U64: % greater_2(e_4_0(),e_3_0()) ....... B24 % ~greater_2(x1,x2) | ~next_2(x0,x2) | ~product_3(x0,e_1_0(),x1) ....... B31 % ~next_2(x0, e_3_0()) | ~product_3(x0, e_1_0(), e_4_0()) ....... R1 [B24:L0, B31: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 U74: % group_element_1(e_1_0()) ....... B3 % ~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()) ....... B32 % ~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 [B3:L0, B32: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) ....... B30 % 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, B30: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 U81: % group_element_1(e_1_0()) ....... B3 % ~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()) ....... B32 % ~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 [B3:L0, B32: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()) ....... U74 % 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, U74:L0] % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % product_3(e_4_0(), e_1_0(), e_4_0()) | ~product_3(x0, e_1_0(), e_2_0()) | equalish_2(x0, e_4_0()) ....... R5 [R4:L0, B30:L0] % ~product_3(e_4_0(),e_1_0(),e_4_0()) ....... U41 % ~product_3(x0, e_1_0(), e_2_0()) | equalish_2(x0, e_4_0()) ....... R6 [R5:L0, U41:L0] % ~equalish_2(e_3_0(),e_4_0()) ....... U13 % ~product_3(e_3_0(), e_1_0(), e_2_0()) ....... R7 [R6:L1, U13:L0] % Derivation of unit clause U84: % group_element_1(e_1_0()) ....... B3 % ~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()) ....... B32 % ~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 [B3:L0, B32:L0] % ~product_3(e_3_0(),e_1_0(),e_1_0()) ....... U57 % ~group_element_1(e_3_0()) | product_3(e_3_0(), e_1_0(), e_2_0()) | product_3(e_3_0(), e_1_0(), e_3_0()) | product_3(e_3_0(), e_1_0(), e_4_0()) ....... R2 [R1:L1, U57:L0] % group_element_1(e_3_0()) ....... U3 % product_3(e_3_0(), e_1_0(), e_2_0()) | product_3(e_3_0(), e_1_0(), e_3_0()) | product_3(e_3_0(), e_1_0(), e_4_0()) ....... R3 [R2:L0, U3:L0] % ~product_3(e_3_0(),e_1_0(),e_2_0()) ....... U81 % product_3(e_3_0(), e_1_0(), e_3_0()) | product_3(e_3_0(), e_1_0(), e_4_0()) ....... R4 [R3:L0, U81:L0] % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % product_3(e_3_0(), e_1_0(), e_3_0()) | ~product_3(e_3_0(), x0, e_4_0()) | equalish_2(x0, e_1_0()) ....... R5 [R4:L1, B29:L0] % ~product_3(e_3_0(),e_1_0(),e_3_0()) ....... U40 % ~product_3(e_3_0(), x0, e_4_0()) | equalish_2(x0, e_1_0()) ....... R6 [R5:L0, U40:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U8 % ~product_3(e_3_0(), e_2_0(), e_4_0()) ....... R7 [R6:L1, U8:L0] % Derivation of unit clause U91: % group_element_1(e_2_0()) ....... B4 % ~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()) ....... B32 % ~group_element_1(x0) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_2_0(), e_2_0()) | product_3(x0, e_2_0(), e_3_0()) | product_3(x0, e_2_0(), e_4_0()) ....... R1 [B4:L0, B32:L0] % group_element_1(e_3_0()) ....... U3 % product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_2_0(), e_2_0()) | product_3(e_3_0(), e_2_0(), e_3_0()) | product_3(e_3_0(), e_2_0(), e_4_0()) ....... R2 [R1:L0, U3:L0] % ~product_3(e_3_0(),e_2_0(),e_2_0()) ....... U58 % product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_2_0(), e_3_0()) | product_3(e_3_0(), e_2_0(), e_4_0()) ....... R3 [R2:L1, U58:L0] % ~product_3(e_3_0(),e_2_0(),e_3_0()) ....... U43 % product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_2_0(), e_4_0()) ....... R4 [R3:L1, U43:L0] % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % product_3(e_3_0(), e_2_0(), e_4_0()) | ~product_3(x0, e_2_0(), e_1_0()) | equalish_2(x0, e_3_0()) ....... R5 [R4:L0, B30:L0] % ~product_3(e_3_0(),e_2_0(),e_4_0()) ....... U84 % ~product_3(x0, e_2_0(), e_1_0()) | equalish_2(x0, e_3_0()) ....... R6 [R5:L0, U84:L0] % ~equalish_2(e_4_0(),e_3_0()) ....... U16 % ~product_3(e_4_0(), e_2_0(), e_1_0()) ....... R7 [R6:L1, U16:L0] % Derivation of unit clause U92: % group_element_1(e_2_0()) ....... B4 % ~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()) ....... B32 % ~group_element_1(x0) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_2_0(), e_2_0()) | product_3(x0, e_2_0(), e_3_0()) | product_3(x0, e_2_0(), e_4_0()) ....... R1 [B4:L0, B32:L0] % group_element_1(e_4_0()) ....... U4 % product_3(e_4_0(), e_2_0(), e_1_0()) | product_3(e_4_0(), e_2_0(), e_2_0()) | product_3(e_4_0(), e_2_0(), e_3_0()) | product_3(e_4_0(), e_2_0(), e_4_0()) ....... R2 [R1:L0, U4:L0] % ~product_3(e_4_0(),e_2_0(),e_1_0()) ....... U91 % product_3(e_4_0(), e_2_0(), e_2_0()) | product_3(e_4_0(), e_2_0(), e_3_0()) | product_3(e_4_0(), e_2_0(), e_4_0()) ....... R3 [R2:L0, U91:L0] % ~product_3(e_4_0(),e_2_0(),e_2_0()) ....... U61 % product_3(e_4_0(), e_2_0(), e_3_0()) | product_3(e_4_0(), e_2_0(), e_4_0()) ....... R4 [R3:L0, U61:L0] % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % product_3(e_4_0(), e_2_0(), e_3_0()) | ~product_3(e_4_0(), x0, e_4_0()) | equalish_2(x0, e_2_0()) ....... R5 [R4:L1, B29:L0] % product_3(x0,x0,x0) ....... U0 % product_3(e_4_0(), e_2_0(), e_3_0()) | equalish_2(e_4_0(), e_2_0()) ....... R6 [R5:L1, U0:L0] % ~equalish_2(e_4_0(),e_2_0()) ....... U15 % product_3(e_4_0(), e_2_0(), e_3_0()) ....... R7 [R6:L1, U15:L0] % Derivation of unit clause U95: % group_element_1(e_2_0()) ....... B4 % ~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()) ....... B32 % ~group_element_1(x0) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_2_0(), e_2_0()) | product_3(x0, e_2_0(), e_3_0()) | product_3(x0, e_2_0(), e_4_0()) ....... R1 [B4:L0, B32:L0] % ~product_3(e_1_0(),e_2_0(),e_1_0()) ....... U42 % ~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:L1, U42: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()) ....... R3 [R2: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()) ....... R4 [R3:L0, U51:L0] % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B30 % product_3(e_1_0(), e_2_0(), e_4_0()) | ~product_3(x0, e_2_0(), e_3_0()) | equalish_2(x0, e_1_0()) ....... R5 [R4:L0, B30:L0] % product_3(e_4_0(),e_2_0(),e_3_0()) ....... U92 % product_3(e_1_0(), e_2_0(), e_4_0()) | equalish_2(e_4_0(), e_1_0()) ....... R6 [R5:L1, U92:L0] % ~equalish_2(e_4_0(),e_1_0()) ....... U14 % product_3(e_1_0(), e_2_0(), e_4_0()) ....... R7 [R6:L1, U14:L0] % Derivation of unit clause U100: % group_element_1(e_3_0()) ....... B5 % ~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()) ....... B32 % ~group_element_1(x0) | product_3(x0, e_3_0(), e_1_0()) | product_3(x0, e_3_0(), e_2_0()) | product_3(x0, e_3_0(), e_3_0()) | product_3(x0, e_3_0(), e_4_0()) ....... R1 [B5:L0, B32:L0] % group_element_1(e_1_0()) ....... U1 % product_3(e_1_0(), e_3_0(), e_1_0()) | product_3(e_1_0(), e_3_0(), e_2_0()) | product_3(e_1_0(), e_3_0(), e_3_0()) | product_3(e_1_0(), e_3_0(), e_4_0()) ....... R2 [R1:L0, U1:L0] % ~product_3(e_1_0(),e_3_0(),e_1_0()) ....... U45 % product_3(e_1_0(), e_3_0(), e_2_0()) | product_3(e_1_0(), e_3_0(), e_3_0()) | product_3(e_1_0(), e_3_0(), e_4_0()) ....... R3 [R2:L0, U45:L0] % ~product_3(e_1_0(),e_3_0(),e_3_0()) ....... U52 % product_3(e_1_0(), e_3_0(), e_2_0()) | product_3(e_1_0(), e_3_0(), e_4_0()) ....... R4 [R3:L1, U52:L0] % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B29 % product_3(e_1_0(), e_3_0(), e_2_0()) | ~product_3(e_1_0(), x0, e_4_0()) | equalish_2(x0, e_3_0()) ....... R5 [R4:L1, B29:L0] % product_3(e_1_0(),e_2_0(),e_4_0()) ....... U95 % product_3(e_1_0(), e_3_0(), e_2_0()) | equalish_2(e_2_0(), e_3_0()) ....... R6 [R5:L1, U95:L0] % ~equalish_2(e_2_0(),e_3_0()) ....... U9 % product_3(e_1_0(), e_3_0(), e_2_0()) ....... R7 [R6:L1, U9:L0] % Derivation of unit clause U104: % group_element_1(e_1_0()) ....... B3 % ~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()) ....... B32 % ~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 [B3:L0, B32: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(x5,x3,x4) | ~product_3(x5,x0,x1) | ~product_3(x3,x4,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B0 % 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()) | ~product_3(e_2_0(), x0, x1) | ~product_3(e_1_0(), e_3_0(), x2) | ~product_3(x0, x1, x2) | equalish_2(x0, e_1_0()) ....... R3 [R2:L2, B0:L0] % 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()) | ~product_3(e_2_0(), e_2_0(), e_2_0()) | ~product_3(e_1_0(), e_3_0(), e_2_0()) | equalish_2(e_2_0(), e_1_0()) ....... R4 [R3:L5, R3:L3] % ~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_4_0()) | ~product_3(e_2_0(), e_2_0(), e_2_0()) | ~product_3(e_1_0(), e_3_0(), e_2_0()) | equalish_2(e_2_0(), e_1_0()) ....... R5 [R4:L0, U54:L0] % ~product_3(e_2_0(),e_1_0(),e_2_0()) ....... U39 % product_3(e_2_0(), e_1_0(), e_4_0()) | ~product_3(e_2_0(), e_2_0(), e_2_0()) | ~product_3(e_1_0(), e_3_0(), e_2_0()) | equalish_2(e_2_0(), e_1_0()) ....... R6 [R5:L0, U39:L0] % ~product_3(e_2_0(),e_1_0(),e_4_0()) ....... U64 % ~product_3(e_2_0(), e_2_0(), e_2_0()) | ~product_3(e_1_0(), e_3_0(), e_2_0()) | equalish_2(e_2_0(), e_1_0()) ....... R7 [R6:L0, U64:L0] % product_3(x0,x0,x0) ....... U0 % ~product_3(e_1_0(), e_3_0(), e_2_0()) | equalish_2(e_2_0(), e_1_0()) ....... R8 [R7:L0, U0:L0] % product_3(e_1_0(),e_3_0(),e_2_0()) ....... U100 % equalish_2(e_2_0(), e_1_0()) ....... R9 [R8:L0, U100:L0] % Derivation of the empty clause: % equalish_2(e_2_0(),e_1_0()) ....... U104 % ~equalish_2(e_2_0(),e_1_0()) ....... U8 % [] ....... R1 [U104:L0, U8:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 22276199 % resolvents: 19910268 factors: 2365931 % Number of unit clauses generated: 2889324 % % unit clauses generated to total clauses generated: 12.97 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 26 [2] = 39 [5] = 5 [7] = 34 % [9] = 1 % Total = 105 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 2889324 [2] = 4171652 [3] = 9741438 [4] = 5317965 [5] = 70278 [6] = 50807 % [7] = 34735 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] group_element_1 (+)4 (-)0 % [1] equalish_2 (+)6 (-)12 % [2] greater_2 (+)6 (-)3 % [3] next_2 (+)3 (-)6 % [4] product_3 (+)17 (-)48 % ------------------ % Total: (+)36 (-)69 % Total number of unit clauses retained: 105 % Number of clauses skipped because of their length: 26607628 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 1301270 % Number of successful unifications: 22276285 % Number of unification failures: 334659102 % Number of unit to unit unification failures: 915 % N literal unification failure due to lookup root_id table: 14017293 % N base clause resolution failure due to lookup table: 4983407 % N UC-BCL resolution dropped due to lookup table: 12233475 % Max entries in substitution set: 12 % N unit clauses dropped because they exceeded max values: 1749728 % 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: 75 % Total number of terms of all unit clauses in table: 271 % 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: 0.28 % Number of symbols (columns) in UCFA: 43 % Profile 2: Number of calls to: % ============================== % PTUnify() = 356935387 % ConstructUnitClause() = 1749807 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 1.95 secs % -------------------------------------------------------- % | | % Inferences per sec: 236981 % | | % -------------------------------------------------------- % Elapsed time: 96 secs % CPU time: 94.85 secs % %------------------------------------------------------------------------------