%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP034-4 : TPTP v5.0.0. Released v1.0.0. % 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 20:43:32 EST 2010 % Result : Unsatisfiable 31.01s % Output : Refutation 31.01s % 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/SystemOnTPTP18386/GRP/GRP034-4+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 = 0] [nf = 0] [nu = 0] [ut = 6] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 30] [nf = 46] [nu = 0] [ut = 6] % Looking for a proof at depth = 3 ... % Entering time slice 2 % Updating parameters ... done. % Looking for a proof at depth = 1 ... % t = 32 secs [nr = 6313996] [nf = 84] [nu = 6296652] [ut = 4355] % Looking for a proof at depth = 2 ... % t = 32 secs [nr = 6314026] [nf = 130] [nu = 6296652] [ut = 4355] % Looking for a proof at depth = 3 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~subgroup_member_1(inverse_1(a_0())) % B1: product_3(x0,x1,multiply_2(x0,x1)) % B2: product_3(x0,identity_0(),x0) % B6: ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) % B7: ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) % B8: ~subgroup_member_1(x1) | ~subgroup_member_1(x0) | ~product_3(x1,inverse_1(x0),x2) | subgroup_member_1(x2) % Unit Clauses: % -------------- % U1: < d0 v4 dv2 f1 c0 t5 td2 b > product_3(x0,x1,multiply_2(x0,x1)) % U2: < d0 v2 dv1 f0 c1 t3 td1 b > product_3(x0,identity_0(),x0) % U3: < d0 v2 dv1 f0 c1 t3 td1 b > product_3(identity_0(),x0,x0) % U4: < d0 v2 dv1 f1 c1 t4 td2 b > product_3(x0,inverse_1(x0),identity_0()) % U5: < d0 v0 dv0 f0 c1 t1 td1 b > subgroup_member_1(a_0()) % U14: < d3 v2 dv1 f1 c2 t5 td2 > product_3(x0,identity_0(),multiply_2(identity_0(),x0)) % U23: < d3 v4 dv2 f2 c1 t7 td2 > product_3(multiply_2(identity_0(),x0),x1,multiply_2(x0,x1)) % U59: < d3 v4 dv2 f2 c0 t6 td2 > product_3(multiply_2(x0,x1),inverse_1(x1),x0) % U70: < d3 v2 dv1 f2 c2 t6 td3 > product_3(multiply_2(x0,inverse_1(x0)),identity_0(),identity_0()) % U162: < d3 v2 dv1 f2 c2 t6 td3 > product_3(x0,multiply_2(inverse_1(x0),identity_0()),identity_0()) % U182: < d3 v4 dv2 f3 c1 t8 td3 > product_3(multiply_2(x0,inverse_1(x0)),multiply_2(identity_0(),x1),x1) % U185: < d3 v4 dv2 f3 c1 t8 td4 > product_3(x0,multiply_2(multiply_2(inverse_1(x0),identity_0()),x1),x1) % U250: < d3 v4 dv2 f2 c0 t6 td3 > product_3(x0,multiply_2(x1,inverse_1(x1)),x0) % U260: < d3 v4 dv2 f3 c1 t8 td3 > product_3(multiply_2(identity_0(),x0),multiply_2(x1,inverse_1(x1)),x0) % U351: < d3 v4 dv2 f3 c1 t8 td4 > product_3(x0,multiply_2(identity_0(),multiply_2(x1,inverse_1(x1))),x0) % U805: < d3 v4 dv2 f3 c0 t7 td3 > product_3(x0,inverse_1(x0),multiply_2(x1,inverse_1(x1))) % U920: < d3 v2 dv1 f3 c2 t7 td4 > product_3(identity_0(),inverse_1(multiply_2(inverse_1(x0),identity_0())),x0) % U1216: < d3 v4 dv2 f3 c0 t7 td3 > product_3(inverse_1(x0),x0,multiply_2(x1,inverse_1(x1))) % U2917: < d3 v0 dv0 f2 c2 t4 td3 > subgroup_member_1(multiply_2(a_0(),inverse_1(a_0()))) % U3061: < d3 v4 dv2 f4 c0 t8 td3 > product_3(multiply_2(x0,inverse_1(x0)),inverse_1(x1),inverse_1(x1)) % U4357: < d3 v0 dv0 f4 c4 t8 td3 > ~product_3(multiply_2(a_0(),inverse_1(a_0())),inverse_1(a_0()),inverse_1(a_0())) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % product_3(x0,x1,multiply_2(x0,x1)) ....... U1 % Derivation of unit clause U2: % product_3(x0,identity_0(),x0) ....... U2 % Derivation of unit clause U3: % product_3(identity_0(),x0,x0) ....... U3 % Derivation of unit clause U4: % product_3(x0,inverse_1(x0),identity_0()) ....... U4 % Derivation of unit clause U5: % subgroup_member_1(a_0()) ....... U5 % Derivation of unit clause U14: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) ....... B6 % ~product_3(x0, x1, x2) | ~product_3(x3, x0, x4) | product_3(x4, x1, multiply_2(x3, x2)) ....... R1 [B1:L0, B6:L0] % product_3(x0,identity_0(),x0) ....... U2 % ~product_3(x0, x1, x2) | product_3(x2, identity_0(), multiply_2(x0, x1)) ....... R2 [R1:L0, U2:L0] % product_3(identity_0(),x0,x0) ....... U3 % product_3(x0, identity_0(), multiply_2(identity_0(), x0)) ....... R3 [R2:L0, U3:L0] % Derivation of unit clause U23: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) ....... B6 % ~product_3(x0, x1, x2) | ~product_3(x3, x0, x4) | product_3(x4, x1, multiply_2(x3, x2)) ....... R1 [B1:L0, B6:L0] % product_3(identity_0(),x0,x0) ....... U3 % ~product_3(x0, identity_0(), x1) | product_3(x1, x2, multiply_2(x0, x2)) ....... R2 [R1:L0, U3:L0] % product_3(x0,identity_0(),multiply_2(identity_0(),x0)) ....... U14 % product_3(multiply_2(identity_0(), x0), x1, multiply_2(x0, x1)) ....... R3 [R2:L0, U14:L0] % Derivation of unit clause U59: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) ....... B6 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x1) | product_3(multiply_2(x0, x3), x4, x2) ....... R1 [B1:L0, B6:L2] % product_3(x0,identity_0(),x0) ....... U2 % ~product_3(x0, x1, identity_0()) | product_3(multiply_2(x2, x0), x1, x2) ....... R2 [R1:L0, U2:L0] % product_3(x0,inverse_1(x0),identity_0()) ....... U4 % product_3(multiply_2(x0, x1), inverse_1(x1), x0) ....... R3 [R2:L0, U4:L0] % Derivation of unit clause U70: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) ....... B6 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x1) | product_3(multiply_2(x0, x3), x4, x2) ....... R1 [B1:L0, B6:L2] % product_3(x0,inverse_1(x0),identity_0()) ....... U4 % ~product_3(x0, x1, inverse_1(x2)) | product_3(multiply_2(x2, x0), x1, identity_0()) ....... R2 [R1:L0, U4:L0] % product_3(x0,identity_0(),x0) ....... U2 % product_3(multiply_2(x0, inverse_1(x0)), identity_0(), identity_0()) ....... R3 [R2:L0, U2:L0] % Derivation of unit clause U162: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x0) | product_3(x3, multiply_2(x4, x1), x2) ....... R1 [B1:L0, B7:L1] % product_3(x0,identity_0(),x0) ....... U2 % ~product_3(x0, x1, x2) | product_3(x0, multiply_2(x1, identity_0()), x2) ....... R2 [R1:L0, U2:L0] % product_3(x0,inverse_1(x0),identity_0()) ....... U4 % product_3(x0, multiply_2(inverse_1(x0), identity_0()), identity_0()) ....... R3 [R2:L0, U4:L0] % Derivation of unit clause U182: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x0) | product_3(x3, multiply_2(x4, x1), x2) ....... R1 [B1:L0, B7:L1] % product_3(identity_0(),x0,x0) ....... U3 % ~product_3(x0, x1, identity_0()) | product_3(x0, multiply_2(x1, x2), x2) ....... R2 [R1:L0, U3:L0] % product_3(multiply_2(x0,inverse_1(x0)),identity_0(),identity_0()) ....... U70 % product_3(multiply_2(x0, inverse_1(x0)), multiply_2(identity_0(), x1), x1) ....... R3 [R2:L0, U70:L0] % Derivation of unit clause U185: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x0) | product_3(x3, multiply_2(x4, x1), x2) ....... R1 [B1:L0, B7:L1] % product_3(identity_0(),x0,x0) ....... U3 % ~product_3(x0, x1, identity_0()) | product_3(x0, multiply_2(x1, x2), x2) ....... R2 [R1:L0, U3:L0] % product_3(x0,multiply_2(inverse_1(x0),identity_0()),identity_0()) ....... U162 % product_3(x0, multiply_2(multiply_2(inverse_1(x0), identity_0()), x1), x1) ....... R3 [R2:L0, U162:L0] % Derivation of unit clause U250: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x0) | product_3(x3, multiply_2(x4, x1), x2) ....... R1 [B1:L0, B7:L1] % product_3(multiply_2(x0,x1),inverse_1(x1),x0) ....... U59 % ~product_3(x0, x1, multiply_2(x2, x3)) | product_3(x0, multiply_2(x1, inverse_1(x3)), x2) ....... R2 [R1:L0, U59:L0] % product_3(x0,x1,multiply_2(x0,x1)) ....... U1 % product_3(x0, multiply_2(x1, inverse_1(x1)), x0) ....... R3 [R2:L0, U1:L0] % Derivation of unit clause U260: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x0) | product_3(x3, multiply_2(x4, x1), x2) ....... R1 [B1:L0, B7:L1] % product_3(multiply_2(x0,x1),inverse_1(x1),x0) ....... U59 % ~product_3(x0, x1, multiply_2(x2, x3)) | product_3(x0, multiply_2(x1, inverse_1(x3)), x2) ....... R2 [R1:L0, U59:L0] % product_3(multiply_2(identity_0(),x0),x1,multiply_2(x0,x1)) ....... U23 % product_3(multiply_2(identity_0(), x0), multiply_2(x1, inverse_1(x1)), x0) ....... R3 [R2:L0, U23:L0] % Derivation of unit clause U351: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x0) | product_3(x3, multiply_2(x4, x1), x2) ....... R1 [B1:L0, B7:L1] % product_3(x0,multiply_2(x1,inverse_1(x1)),x0) ....... U250 % ~product_3(x0, x1, x2) | product_3(x0, multiply_2(x1, multiply_2(x3, inverse_1(x3))), x2) ....... R2 [R1:L0, U250:L0] % product_3(x0,identity_0(),x0) ....... U2 % product_3(x0, multiply_2(identity_0(), multiply_2(x1, inverse_1(x1))), x0) ....... R3 [R2:L0, U2:L0] % Derivation of unit clause U805: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(multiply_2(x0, x1), x2, x3) | ~product_3(x1, x2, x4) | product_3(x0, x4, x3) ....... R1 [B1:L0, B7:L2] % product_3(multiply_2(x0,inverse_1(x0)),multiply_2(identity_0(),x1),x1) ....... U182 % ~product_3(inverse_1(x0), multiply_2(identity_0(), x1), x2) | product_3(x0, x2, x1) ....... R2 [R1:L0, U182:L0] % product_3(x0,multiply_2(identity_0(),multiply_2(x1,inverse_1(x1))),x0) ....... U351 % product_3(x0, inverse_1(x0), multiply_2(x1, inverse_1(x1))) ....... R3 [R2:L0, U351:L0] % Derivation of unit clause U920: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(multiply_2(x0, x1), x2, x3) | ~product_3(x1, x2, x4) | product_3(x0, x4, x3) ....... R1 [B1:L0, B7:L2] % product_3(multiply_2(identity_0(),x0),multiply_2(x1,inverse_1(x1)),x0) ....... U260 % ~product_3(x0, multiply_2(x1, inverse_1(x1)), x2) | product_3(identity_0(), x2, x0) ....... R2 [R1:L0, U260:L0] % product_3(x0,multiply_2(multiply_2(inverse_1(x0),identity_0()),x1),x1) ....... U185 % product_3(identity_0(), inverse_1(multiply_2(inverse_1(x0), identity_0())), x0) ....... R3 [R2:L0, U185:L0] % Derivation of unit clause U1216: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(multiply_2(x0, x1), x2, x3) | ~product_3(x1, x2, x4) | product_3(x0, x4, x3) ....... R1 [B1:L0, B7:L2] % product_3(x0,inverse_1(x0),multiply_2(x1,inverse_1(x1))) ....... U805 % ~product_3(x0, inverse_1(multiply_2(x1, x0)), x2) | product_3(x1, x2, multiply_2(x3, inverse_1(x3))) ....... R2 [R1:L0, U805:L0] % product_3(identity_0(),inverse_1(multiply_2(inverse_1(x0),identity_0())),x0) ....... U920 % product_3(inverse_1(x0), x0, multiply_2(x1, inverse_1(x1))) ....... R3 [R2:L0, U920:L0] % Derivation of unit clause U2917: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~subgroup_member_1(x1) | ~subgroup_member_1(x0) | ~product_3(x1,inverse_1(x0),x2) | subgroup_member_1(x2) ....... B8 % ~subgroup_member_1(x0) | ~subgroup_member_1(x1) | subgroup_member_1(multiply_2(x0, inverse_1(x1))) ....... R1 [B1:L0, B8:L2] % ~subgroup_member_1(x0) | subgroup_member_1(multiply_2(x0, inverse_1(x0))) ....... R2 [R1:L1, R1:L0] % subgroup_member_1(a_0()) ....... U5 % subgroup_member_1(multiply_2(a_0(), inverse_1(a_0()))) ....... R3 [R2:L0, U5:L0] % Derivation of unit clause U3061: % product_3(x0,identity_0(),x0) ....... B2 % ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) ....... B6 % ~product_3(x0, x1, identity_0()) | ~product_3(x2, x0, x3) | product_3(x3, x1, x2) ....... R1 [B2:L0, B6:L0] % product_3(x0,inverse_1(x0),identity_0()) ....... U4 % ~product_3(x0, x1, x2) | product_3(x2, inverse_1(x1), x0) ....... R2 [R1:L0, U4:L0] % product_3(inverse_1(x0),x0,multiply_2(x1,inverse_1(x1))) ....... U1216 % product_3(multiply_2(x0, inverse_1(x0)), inverse_1(x1), inverse_1(x1)) ....... R3 [R2:L0, U1216:L0] % Derivation of unit clause U4357: % ~subgroup_member_1(inverse_1(a_0())) ....... B0 % ~subgroup_member_1(x1) | ~subgroup_member_1(x0) | ~product_3(x1,inverse_1(x0),x2) | subgroup_member_1(x2) ....... B8 % ~subgroup_member_1(x0) | ~subgroup_member_1(x1) | ~product_3(x0, inverse_1(x1), inverse_1(a_0())) ....... R1 [B0:L0, B8:L3] % subgroup_member_1(multiply_2(a_0(),inverse_1(a_0()))) ....... U2917 % ~subgroup_member_1(x0) | ~product_3(multiply_2(a_0(), inverse_1(a_0())), inverse_1(x0), inverse_1(a_0())) ....... R2 [R1:L0, U2917:L0] % subgroup_member_1(a_0()) ....... U5 % ~product_3(multiply_2(a_0(), inverse_1(a_0())), inverse_1(a_0()), inverse_1(a_0())) ....... R3 [R2:L0, U5:L0] % Derivation of the empty clause: % ~product_3(multiply_2(a_0(),inverse_1(a_0())),inverse_1(a_0()),inverse_1(a_0())) ....... U4357 % product_3(multiply_2(x0,inverse_1(x0)),inverse_1(x1),inverse_1(x1)) ....... U3061 % [] ....... R1 [U4357:L0, U3061:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 6314172 % resolvents: 6314040 factors: 132 % Number of unit clauses generated: 6296663 % % unit clauses generated to total clauses generated: 99.72 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 6 [3] = 4352 % Total = 4358 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 6296663 [2] = 17420 [3] = 89 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] subgroup_member_1 (+)3 (-)3 % [1] product_3 (+)1222 (-)3130 % ------------------ % Total: (+)1225 (-)3133 % Total number of unit clauses retained: 4358 % Number of clauses skipped because of their length: 99 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 6314220 % Number of unification failures: 32975245 % Number of unit to unit unification failures: 3824614 % N literal unification failure due to lookup root_id table: 65 % N base clause resolution failure due to lookup table: 15 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 11 % N unit clauses dropped because they exceeded max values: 6292311 % N unit clauses dropped because too much nesting: 1780913 % 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: 8 % Max term depth in a unit clause: 4 % Number of states in UCFA table: 7860 % Total number of terms of all unit clauses in table: 32832 % Max allowed number of states in UCFA: 80000 % Ratio n states used/total allowed states: 0.10 % Ratio n states used/total unit clauses terms: 0.24 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 39289465 % ConstructUnitClause() = 6296663 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 7.48 secs % -------------------------------------------------------- % | | % Inferences per sec: 203683 % | | % -------------------------------------------------------- % Elapsed time: 32 secs % CPU time: 31.00 secs % %------------------------------------------------------------------------------