0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.11 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.10/0.31 % Computer : n016.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Thu Jul 2 06:59:20 EDT 2020 0.10/0.31 % CPUTime : 0.16/0.47 % SZS status Theorem 0.16/0.47 0.16/0.47 % SZS output start Proof 0.16/0.47 Take the following subset of the input axioms: 0.16/0.48 fof(ax0, axiom, constr_CONST_0x30!=constr_CONST_1). 0.16/0.48 fof(ax1, axiom, constr_CONST_2!=constr_CONST_0x30). 0.16/0.48 fof(ax10, axiom, name_skB!=constr_CONST_0x30). 0.16/0.48 fof(ax11, axiom, constr_CONST_0x30!=name_skS). 0.16/0.48 fof(ax12, axiom, constr_CONST_1!=constr_CONST_2). 0.16/0.48 fof(ax13, axiom, constr_CONST_3!=constr_CONST_1). 0.16/0.48 fof(ax14, axiom, constr_CONST_1!=constr_CONST_4). 0.16/0.48 fof(ax15, axiom, constr_CONST_1!=name_A). 0.16/0.48 fof(ax16, axiom, constr_CONST_1!=name_B). 0.16/0.48 fof(ax17, axiom, name_I!=constr_CONST_1). 0.16/0.48 fof(ax18, axiom, constr_CONST_1!=name_c). 0.16/0.48 fof(ax19, axiom, constr_CONST_1!=name_objective). 0.16/0.48 fof(ax2, axiom, constr_CONST_0x30!=constr_CONST_3). 0.16/0.48 fof(ax20, axiom, constr_CONST_1!=name_skA). 0.16/0.48 fof(ax21, axiom, constr_CONST_1!=name_skB). 0.16/0.48 fof(ax22, axiom, name_skS!=constr_CONST_1). 0.16/0.48 fof(ax23, axiom, constr_CONST_3!=constr_CONST_2). 0.16/0.48 fof(ax24, axiom, constr_CONST_2!=constr_CONST_4). 0.16/0.48 fof(ax25, axiom, constr_CONST_2!=name_A). 0.16/0.48 fof(ax26, axiom, constr_CONST_2!=name_B). 0.16/0.48 fof(ax27, axiom, name_I!=constr_CONST_2). 0.16/0.48 fof(ax28, axiom, constr_CONST_2!=name_c). 0.16/0.48 fof(ax29, axiom, constr_CONST_2!=name_objective). 0.16/0.48 fof(ax3, axiom, constr_CONST_0x30!=constr_CONST_4). 0.16/0.48 fof(ax30, axiom, constr_CONST_2!=name_skA). 0.16/0.48 fof(ax31, axiom, constr_CONST_2!=name_skB). 0.16/0.48 fof(ax32, axiom, constr_CONST_2!=name_skS). 0.16/0.48 fof(ax33, axiom, constr_CONST_4!=constr_CONST_3). 0.16/0.48 fof(ax34, axiom, name_A!=constr_CONST_3). 0.16/0.48 fof(ax35, axiom, name_B!=constr_CONST_3). 0.16/0.48 fof(ax36, axiom, constr_CONST_3!=name_I). 0.16/0.48 fof(ax37, axiom, name_c!=constr_CONST_3). 0.16/0.48 fof(ax38, axiom, constr_CONST_3!=name_objective). 0.16/0.48 fof(ax39, axiom, name_skA!=constr_CONST_3). 0.16/0.48 fof(ax4, axiom, constr_CONST_0x30!=name_A). 0.16/0.48 fof(ax40, axiom, constr_CONST_3!=name_skB). 0.16/0.48 fof(ax41, axiom, constr_CONST_3!=name_skS). 0.16/0.48 fof(ax42, axiom, constr_CONST_4!=name_A). 0.16/0.48 fof(ax43, axiom, constr_CONST_4!=name_B). 0.16/0.48 fof(ax44, axiom, name_I!=constr_CONST_4). 0.16/0.48 fof(ax45, axiom, name_c!=constr_CONST_4). 0.16/0.48 fof(ax46, axiom, constr_CONST_4!=name_objective). 0.16/0.48 fof(ax47, axiom, constr_CONST_4!=name_skA). 0.16/0.48 fof(ax48, axiom, constr_CONST_4!=name_skB). 0.16/0.48 fof(ax49, axiom, name_skS!=constr_CONST_4). 0.16/0.48 fof(ax5, axiom, name_B!=constr_CONST_0x30). 0.16/0.48 fof(ax50, axiom, name_A!=name_B). 0.16/0.48 fof(ax51, axiom, name_A!=name_I). 0.16/0.48 fof(ax52, axiom, name_A!=name_c). 0.16/0.48 fof(ax53, axiom, name_objective!=name_A). 0.16/0.48 fof(ax54, axiom, name_A!=name_skA). 0.16/0.48 fof(ax55, axiom, name_skB!=name_A). 0.16/0.48 fof(ax56, axiom, name_A!=name_skS). 0.16/0.48 fof(ax57, axiom, name_I!=name_B). 0.16/0.48 fof(ax58, axiom, name_B!=name_c). 0.16/0.48 fof(ax59, axiom, name_objective!=name_B). 0.16/0.48 fof(ax6, axiom, constr_CONST_0x30!=name_I). 0.16/0.48 fof(ax60, axiom, name_B!=name_skA). 0.16/0.48 fof(ax61, axiom, name_skB!=name_B). 0.16/0.48 fof(ax62, axiom, name_skS!=name_B). 0.16/0.48 fof(ax63, axiom, name_I!=name_c). 0.16/0.48 fof(ax64, axiom, name_I!=name_objective). 0.16/0.48 fof(ax65, axiom, name_skA!=name_I). 0.16/0.48 fof(ax66, axiom, name_skB!=name_I). 0.16/0.48 fof(ax67, axiom, name_I!=name_skS). 0.16/0.48 fof(ax68, axiom, name_c!=name_objective). 0.16/0.48 fof(ax69, axiom, name_skA!=name_c). 0.16/0.48 fof(ax7, axiom, constr_CONST_0x30!=name_c). 0.16/0.48 fof(ax70, axiom, name_skB!=name_c). 0.16/0.48 fof(ax71, axiom, name_c!=name_skS). 0.16/0.48 fof(ax72, axiom, name_objective!=name_skA). 0.16/0.48 fof(ax73, axiom, name_objective!=name_skB). 0.16/0.48 fof(ax74, axiom, name_objective!=name_skS). 0.16/0.48 fof(ax75, axiom, name_skA!=name_skB). 0.16/0.48 fof(ax76, axiom, name_skA!=name_skS). 0.16/0.48 fof(ax77, axiom, name_skB!=name_skS). 0.16/0.48 fof(ax8, axiom, constr_CONST_0x30!=name_objective). 0.16/0.48 fof(ax82, axiom, ![VAR_X_17, VAR_Y_18, VAR_Z_0X30]: tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30))=tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30)). 0.16/0.48 fof(ax84, axiom, ![VAR_X0X30_13, VAR_X1_14]: constr_assoc_pair_2_get_0x30_bitstring(tuple_assoc_pair(VAR_X0X30_13, VAR_X1_14))=VAR_X0X30_13). 0.16/0.48 fof(ax85, axiom, ![VAR_X0X30_11, VAR_X1_12]: constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12))=VAR_X1_12). 0.16/0.48 fof(ax9, axiom, name_skA!=constr_CONST_0x30). 0.16/0.48 fof(co0, conjecture, pred_attacker(name_objective)). 0.16/0.48 0.16/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of 0.16/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 0.16/0.48 We repeatedly replace C & s=t => u=v by the two clauses: 0.16/0.48 fresh(y, y, x1...xn) = u 0.16/0.48 C => fresh(s, t, x1...xn) = v 0.16/0.48 where fresh is a fresh function symbol and x1..xn are the free 0.16/0.48 variables of u and v. 0.16/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the 0.16/0.48 input problem has no model of domain size 1). 0.16/0.48 0.16/0.48 The encoding turns the above axioms into the following unit equations and goals: 0.16/0.48 0.16/0.48 Axiom 1 (ax85): constr_assoc_pair_2_get_1(tuple_assoc_pair(X, Y)) = Y. 0.16/0.48 Axiom 2 (ax84): constr_assoc_pair_2_get_0x30_bitstring(tuple_assoc_pair(X, Y)) = X. 0.16/0.48 Axiom 3 (ax82): tuple_assoc_pair(X, tuple_assoc_pair(Y, Z)) = tuple_assoc_pair(tuple_assoc_pair(X, Y), Z). 0.16/0.48 0.16/0.48 Lemma 4: tuple_assoc_pair(X, Z) = Z. 0.16/0.48 Proof: 0.16/0.48 tuple_assoc_pair(X, Z) 0.16/0.48 = { by axiom 1 (ax85) } 0.16/0.48 constr_assoc_pair_2_get_1(tuple_assoc_pair(?, tuple_assoc_pair(X, Z))) 0.16/0.48 = { by axiom 3 (ax82) } 0.16/0.48 constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(?, X), Z)) 0.16/0.48 = { by axiom 1 (ax85) } 0.16/0.48 Z 0.16/0.48 0.16/0.48 Lemma 5: Y = ?. 0.16/0.48 Proof: 0.16/0.48 Y 0.16/0.48 = { by lemma 4 } 0.16/0.48 tuple_assoc_pair(Z, Y) 0.16/0.48 = { by axiom 2 (ax84) } 0.16/0.48 constr_assoc_pair_2_get_0x30_bitstring(tuple_assoc_pair(tuple_assoc_pair(Z, Y), X)) 0.16/0.48 = { by axiom 3 (ax82) } 0.16/0.48 constr_assoc_pair_2_get_0x30_bitstring(tuple_assoc_pair(Z, tuple_assoc_pair(Y, X))) 0.16/0.48 = { by axiom 2 (ax84) } 0.16/0.48 Z 0.16/0.48 = { by axiom 2 (ax84) } 0.16/0.48 constr_assoc_pair_2_get_0x30_bitstring(tuple_assoc_pair(Z, tuple_assoc_pair(?, X))) 0.16/0.48 = { by axiom 3 (ax82) } 0.16/0.48 constr_assoc_pair_2_get_0x30_bitstring(tuple_assoc_pair(tuple_assoc_pair(Z, ?), X)) 0.16/0.48 = { by axiom 2 (ax84) } 0.16/0.48 tuple_assoc_pair(Z, ?) 0.16/0.48 = { by lemma 4 } 0.16/0.48 ? 0.16/0.48 0.16/0.48 Goal 1 (co0): pred_attacker(name_objective) = true. 0.16/0.48 Proof: 0.16/0.48 pred_attacker(name_objective) 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 true 0.16/0.48 0.16/0.48 Goal 2 (ax30): constr_CONST_2 = name_skA. 0.16/0.48 Proof: 0.16/0.48 constr_CONST_2 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 name_skA 0.16/0.48 0.16/0.48 Goal 3 (ax26): constr_CONST_2 = name_B. 0.16/0.48 Proof: 0.16/0.48 constr_CONST_2 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 name_B 0.16/0.48 0.16/0.48 Goal 4 (ax54): name_A = name_skA. 0.16/0.48 Proof: 0.16/0.48 name_A 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 name_skA 0.16/0.48 0.16/0.48 Goal 5 (ax67): name_I = name_skS. 0.16/0.48 Proof: 0.16/0.48 name_I 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 name_skS 0.16/0.48 0.16/0.48 Goal 6 (ax4): constr_CONST_0x30 = name_A. 0.16/0.48 Proof: 0.16/0.48 constr_CONST_0x30 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 name_A 0.16/0.48 0.16/0.48 Goal 7 (ax31): constr_CONST_2 = name_skB. 0.16/0.48 Proof: 0.16/0.48 constr_CONST_2 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 name_skB 0.16/0.48 0.16/0.48 Goal 8 (ax10): name_skB = constr_CONST_0x30. 0.16/0.48 Proof: 0.16/0.48 name_skB 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 constr_CONST_0x30 0.16/0.48 0.16/0.48 Goal 9 (ax68): name_c = name_objective. 0.16/0.48 Proof: 0.16/0.48 name_c 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 name_objective 0.16/0.48 0.16/0.48 Goal 10 (ax0): constr_CONST_0x30 = constr_CONST_1. 0.16/0.48 Proof: 0.16/0.48 constr_CONST_0x30 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 constr_CONST_1 0.16/0.48 0.16/0.48 Goal 11 (ax64): name_I = name_objective. 0.16/0.48 Proof: 0.16/0.48 name_I 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 name_objective 0.16/0.48 0.16/0.48 Goal 12 (ax9): name_skA = constr_CONST_0x30. 0.16/0.48 Proof: 0.16/0.48 name_skA 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 constr_CONST_0x30 0.16/0.48 0.16/0.48 Goal 13 (ax5): name_B = constr_CONST_0x30. 0.16/0.48 Proof: 0.16/0.48 name_B 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 constr_CONST_0x30 0.16/0.48 0.16/0.48 Goal 14 (ax12): constr_CONST_1 = constr_CONST_2. 0.16/0.48 Proof: 0.16/0.48 constr_CONST_1 0.16/0.48 = { by lemma 5 } 0.16/0.48 ? 0.16/0.48 = { by lemma 5 } 0.16/0.48 constr_CONST_2 0.16/0.49 0.16/0.49 Goal 15 (ax3): constr_CONST_0x30 = constr_CONST_4. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_0x30 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_4 0.16/0.49 0.16/0.49 Goal 16 (ax8): constr_CONST_0x30 = name_objective. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_0x30 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_objective 0.16/0.49 0.16/0.49 Goal 17 (ax11): constr_CONST_0x30 = name_skS. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_0x30 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skS 0.16/0.49 0.16/0.49 Goal 18 (ax50): name_A = name_B. 0.16/0.49 Proof: 0.16/0.49 name_A 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_B 0.16/0.49 0.16/0.49 Goal 19 (ax70): name_skB = name_c. 0.16/0.49 Proof: 0.16/0.49 name_skB 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_c 0.16/0.49 0.16/0.49 Goal 20 (ax73): name_objective = name_skB. 0.16/0.49 Proof: 0.16/0.49 name_objective 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skB 0.16/0.49 0.16/0.49 Goal 21 (ax39): name_skA = constr_CONST_3. 0.16/0.49 Proof: 0.16/0.49 name_skA 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_3 0.16/0.49 0.16/0.49 Goal 22 (ax60): name_B = name_skA. 0.16/0.49 Proof: 0.16/0.49 name_B 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skA 0.16/0.49 0.16/0.49 Goal 23 (ax47): constr_CONST_4 = name_skA. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_4 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skA 0.16/0.49 0.16/0.49 Goal 24 (ax17): name_I = constr_CONST_1. 0.16/0.49 Proof: 0.16/0.49 name_I 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_1 0.16/0.49 0.16/0.49 Goal 25 (ax58): name_B = name_c. 0.16/0.49 Proof: 0.16/0.49 name_B 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_c 0.16/0.49 0.16/0.49 Goal 26 (ax57): name_I = name_B. 0.16/0.49 Proof: 0.16/0.49 name_I 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_B 0.16/0.49 0.16/0.49 Goal 27 (ax42): constr_CONST_4 = name_A. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_4 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_A 0.16/0.49 0.16/0.49 Goal 28 (ax72): name_objective = name_skA. 0.16/0.49 Proof: 0.16/0.49 name_objective 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skA 0.16/0.49 0.16/0.49 Goal 29 (ax61): name_skB = name_B. 0.16/0.49 Proof: 0.16/0.49 name_skB 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_B 0.16/0.49 0.16/0.49 Goal 30 (ax25): constr_CONST_2 = name_A. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_2 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_A 0.16/0.49 0.16/0.49 Goal 31 (ax62): name_skS = name_B. 0.16/0.49 Proof: 0.16/0.49 name_skS 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_B 0.16/0.49 0.16/0.49 Goal 32 (ax77): name_skB = name_skS. 0.16/0.49 Proof: 0.16/0.49 name_skB 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skS 0.16/0.49 0.16/0.49 Goal 33 (ax35): name_B = constr_CONST_3. 0.16/0.49 Proof: 0.16/0.49 name_B 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_3 0.16/0.49 0.16/0.49 Goal 34 (ax18): constr_CONST_1 = name_c. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_1 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_c 0.16/0.49 0.16/0.49 Goal 35 (ax53): name_objective = name_A. 0.16/0.49 Proof: 0.16/0.49 name_objective 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_A 0.16/0.49 0.16/0.49 Goal 36 (ax51): name_A = name_I. 0.16/0.49 Proof: 0.16/0.49 name_A 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_I 0.16/0.49 0.16/0.49 Goal 37 (ax75): name_skA = name_skB. 0.16/0.49 Proof: 0.16/0.49 name_skA 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skB 0.16/0.49 0.16/0.49 Goal 38 (ax76): name_skA = name_skS. 0.16/0.49 Proof: 0.16/0.49 name_skA 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skS 0.16/0.49 0.16/0.49 Goal 39 (ax23): constr_CONST_3 = constr_CONST_2. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_3 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_2 0.16/0.49 0.16/0.49 Goal 40 (ax37): name_c = constr_CONST_3. 0.16/0.49 Proof: 0.16/0.49 name_c 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_3 0.16/0.49 0.16/0.49 Goal 41 (ax27): name_I = constr_CONST_2. 0.16/0.49 Proof: 0.16/0.49 name_I 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_2 0.16/0.49 0.16/0.49 Goal 42 (ax14): constr_CONST_1 = constr_CONST_4. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_1 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_4 0.16/0.49 0.16/0.49 Goal 43 (ax15): constr_CONST_1 = name_A. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_1 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_A 0.16/0.49 0.16/0.49 Goal 44 (ax33): constr_CONST_4 = constr_CONST_3. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_4 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_3 0.16/0.49 0.16/0.49 Goal 45 (ax71): name_c = name_skS. 0.16/0.49 Proof: 0.16/0.49 name_c 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skS 0.16/0.49 0.16/0.49 Goal 46 (ax2): constr_CONST_0x30 = constr_CONST_3. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_0x30 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_3 0.16/0.49 0.16/0.49 Goal 47 (ax1): constr_CONST_2 = constr_CONST_0x30. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_2 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_0x30 0.16/0.49 0.16/0.49 Goal 48 (ax20): constr_CONST_1 = name_skA. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_1 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skA 0.16/0.49 0.16/0.49 Goal 49 (ax28): constr_CONST_2 = name_c. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_2 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_c 0.16/0.49 0.16/0.49 Goal 50 (ax40): constr_CONST_3 = name_skB. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_3 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skB 0.16/0.49 0.16/0.49 Goal 51 (ax45): name_c = constr_CONST_4. 0.16/0.49 Proof: 0.16/0.49 name_c 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_4 0.16/0.49 0.16/0.49 Goal 52 (ax21): constr_CONST_1 = name_skB. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_1 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_skB 0.16/0.49 0.16/0.49 Goal 53 (ax38): constr_CONST_3 = name_objective. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_3 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_objective 0.16/0.49 0.16/0.49 Goal 54 (ax63): name_I = name_c. 0.16/0.49 Proof: 0.16/0.49 name_I 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_c 0.16/0.49 0.16/0.49 Goal 55 (ax55): name_skB = name_A. 0.16/0.49 Proof: 0.16/0.49 name_skB 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_A 0.16/0.49 0.16/0.49 Goal 56 (ax43): constr_CONST_4 = name_B. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_4 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_B 0.16/0.49 0.16/0.49 Goal 57 (ax6): constr_CONST_0x30 = name_I. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_0x30 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_I 0.16/0.49 0.16/0.49 Goal 58 (ax24): constr_CONST_2 = constr_CONST_4. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_2 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_4 0.16/0.49 0.16/0.49 Goal 59 (ax34): name_A = constr_CONST_3. 0.16/0.49 Proof: 0.16/0.49 name_A 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_3 0.16/0.49 0.16/0.49 Goal 60 (ax19): constr_CONST_1 = name_objective. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_1 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_objective 0.16/0.49 0.16/0.49 Goal 61 (ax16): constr_CONST_1 = name_B. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_1 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_B 0.16/0.49 0.16/0.49 Goal 62 (ax36): constr_CONST_3 = name_I. 0.16/0.49 Proof: 0.16/0.49 constr_CONST_3 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 name_I 0.16/0.49 0.16/0.49 Goal 63 (ax49): name_skS = constr_CONST_4. 0.16/0.49 Proof: 0.16/0.49 name_skS 0.16/0.49 = { by lemma 5 } 0.16/0.49 ? 0.16/0.49 = { by lemma 5 } 0.16/0.49 constr_CONST_4 0.16/0.49 0.16/0.49 Goal 64 (ax13): constr_CONST_3 = constr_CONST_1. 0.16/0.49 Proof: 0.16/0.50 constr_CONST_3 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 constr_CONST_1 0.16/0.50 0.16/0.50 Goal 65 (ax41): constr_CONST_3 = name_skS. 0.16/0.50 Proof: 0.16/0.50 constr_CONST_3 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_skS 0.16/0.50 0.16/0.50 Goal 66 (ax46): constr_CONST_4 = name_objective. 0.16/0.50 Proof: 0.16/0.50 constr_CONST_4 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_objective 0.16/0.50 0.16/0.50 Goal 67 (ax74): name_objective = name_skS. 0.16/0.50 Proof: 0.16/0.50 name_objective 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_skS 0.16/0.50 0.16/0.50 Goal 68 (ax7): constr_CONST_0x30 = name_c. 0.16/0.50 Proof: 0.16/0.50 constr_CONST_0x30 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_c 0.16/0.50 0.16/0.50 Goal 69 (ax29): constr_CONST_2 = name_objective. 0.16/0.50 Proof: 0.16/0.50 constr_CONST_2 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_objective 0.16/0.50 0.16/0.50 Goal 70 (ax69): name_skA = name_c. 0.16/0.50 Proof: 0.16/0.50 name_skA 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_c 0.16/0.50 0.16/0.50 Goal 71 (ax44): name_I = constr_CONST_4. 0.16/0.50 Proof: 0.16/0.50 name_I 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 constr_CONST_4 0.16/0.50 0.16/0.50 Goal 72 (ax32): constr_CONST_2 = name_skS. 0.16/0.50 Proof: 0.16/0.50 constr_CONST_2 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_skS 0.16/0.50 0.16/0.50 Goal 73 (ax56): name_A = name_skS. 0.16/0.50 Proof: 0.16/0.50 name_A 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_skS 0.16/0.50 0.16/0.50 Goal 74 (ax52): name_A = name_c. 0.16/0.50 Proof: 0.16/0.50 name_A 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_c 0.16/0.50 0.16/0.50 Goal 75 (ax66): name_skB = name_I. 0.16/0.50 Proof: 0.16/0.50 name_skB 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_I 0.16/0.50 0.16/0.50 Goal 76 (ax65): name_skA = name_I. 0.16/0.50 Proof: 0.16/0.50 name_skA 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_I 0.16/0.50 0.16/0.50 Goal 77 (ax59): name_objective = name_B. 0.16/0.50 Proof: 0.16/0.50 name_objective 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_B 0.16/0.50 0.16/0.50 Goal 78 (ax22): name_skS = constr_CONST_1. 0.16/0.50 Proof: 0.16/0.50 name_skS 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 constr_CONST_1 0.16/0.50 0.16/0.50 Goal 79 (ax48): constr_CONST_4 = name_skB. 0.16/0.50 Proof: 0.16/0.50 constr_CONST_4 0.16/0.50 = { by lemma 5 } 0.16/0.50 ? 0.16/0.50 = { by lemma 5 } 0.16/0.50 name_skB 0.16/0.50 % SZS output end Proof 0.16/0.50 0.16/0.50 RESULT: Theorem (the conjecture is true). 0.16/0.50 EOF