%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL102-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art02.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 00:00:12 EST 2010 % Result : Unsatisfiable 0.43s % Output : Refutation 0.43s % 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/SystemOnTPTP1562/LCL/LCL102-1+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 = 0 secs [nr = 7] [nf = 0] [nu = 0] [ut = 4] % Looking for a proof at depth = 2 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) % B2: is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) % B3: is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x0)))) % B4: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U2: < d0 v6 dv3 f5 c0 t11 td4 b > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) % U5: < d2 v6 dv3 f13 c8 t27 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) % U13: < d2 v14 dv7 f21 c8 t43 td7 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) % U20: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3)))) % U24: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(x1,x3))),equivalent_2(x2,x3))) % U62: < d2 v20 dv10 f27 c8 t55 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),x6),x6),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x9,x7),equivalent_2(x9,x8))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))) % U91: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),equivalent_2(x1,equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x3,x4)))) % U114: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),equivalent_2(x2,equivalent_2(x3,x5))))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x4,x5))))) % U232: < d2 v16 dv8 f23 c8 t47 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x4)),equivalent_2(x0,x4)),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x7,x5),equivalent_2(x7,x6))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) % U256: < d2 v8 dv4 f15 c8 t31 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x0),equivalent_2(x3,x1)),x2)),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) % U275: < d2 v2 dv1 f9 c8 t19 td5 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,a_0()),equivalent_2(x0,b_0())),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) % U314: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x1,x3),x0),equivalent_2(x3,x2)))) % U444: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x3)))) % --------------- Start of Proof --------------- % Derivation of unit clause U2: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U2 % Derivation of unit clause U5: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R1 [B0:L0, B4:L2] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U13: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3), x3), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B4:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U5 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3), x3), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x6, x4), equivalent_2(x6, x5))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R2 [R1:L1, U5:L0] % Derivation of unit clause U20: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U2 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3)))) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U24: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3)))) ....... U20 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x0, equivalent_2(x1, x3))), equivalent_2(x2, x3))) ....... R2 [R1:L0, U20:L0] % Derivation of unit clause U62: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B4:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) ....... U13 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)), x6), x6), equivalent_2(equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x9, x7), equivalent_2(x9, x8))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))))) ....... R2 [R1:L1, U13:L0] % Derivation of unit clause U91: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(x1,x3))),equivalent_2(x2,x3))) ....... U24 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), equivalent_2(x1, equivalent_2(x2, x4)))), equivalent_2(x0, equivalent_2(x3, x4)))) ....... R2 [R1:L0, U24:L0] % Derivation of unit clause U114: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),equivalent_2(x1,equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x3,x4)))) ....... U91 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), equivalent_2(x2, equivalent_2(x3, x5))))), equivalent_2(x0, equivalent_2(x1, equivalent_2(x4, x5))))) ....... R2 [R1:L0, U91:L0] % Derivation of unit clause U232: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),x6),x6),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x9,x7),equivalent_2(x9,x8))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))) ....... U62 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x4)), equivalent_2(x0, x4)), equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x7, x5), equivalent_2(x7, x6))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R2 [R1:L1, U62:L0] % Derivation of unit clause U256: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x4)),equivalent_2(x0,x4)),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x7,x5),equivalent_2(x7,x6))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) ....... U232 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(x3, x0), equivalent_2(x3, x1)), x2)), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R2 [R1:L1, U232:L0] % Derivation of unit clause U275: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))) ....... R1 [B2:L0, B4:L1] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(x3,x0),equivalent_2(x3,x1)),x2)),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U256 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, a_0()), equivalent_2(x0, b_0())), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))) ....... R2 [R1:L1, U256:L0] % Derivation of unit clause U314: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x0)))) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), x0))), x3)) | is_a_theorem_1(x3) ....... R1 [B3:L0, B4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),equivalent_2(x2,equivalent_2(x3,x5))))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x4,x5))))) ....... U114 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x1, x3), x0), equivalent_2(x3, x2)))) ....... R2 [R1:L0, U114:L0] % Derivation of unit clause U444: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x0)))) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), x0))), x3)) | is_a_theorem_1(x3) ....... R1 [B3:L0, B4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x1,x3),x0),equivalent_2(x3,x2)))) ....... U314 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x3)))) ....... R2 [R1:L0, U314:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x3)))) ....... U444 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,a_0()),equivalent_2(x0,b_0())),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) ....... U275 % [] ....... R1 [U444:L0, U275:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 566 % resolvents: 566 factors: 0 % Number of unit clauses generated: 553 % % unit clauses generated to total clauses generated: 97.70 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 4 [2] = 441 % Total = 445 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 553 [2] = 13 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)334 (-)111 % ------------------ % Total: (+)334 (-)111 % Total number of unit clauses retained: 445 % Number of clauses skipped because of their length: 5 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 590 % Number of unification failures: 84 % Number of unit to unit unification failures: 37067 % N literal unification failure due to lookup root_id table: 9 % 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: 9 % N unit clauses dropped because they exceeded max values: 112 % N unit clauses dropped because too much nesting: 23 % 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: 63 % Max term depth in a unit clause: 12 % Number of states in UCFA table: 6558 % Total number of terms of all unit clauses in table: 15067 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.01 % Ratio n states used/total unit clauses terms: 0.44 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 674 % ConstructUnitClause() = 553 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.41 secs % %------------------------------------------------------------------------------