TSTP Solution File: SWW962+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW962+1 : TPTP v8.1.2. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:56:23 EDT 2023
% Result : Theorem 0.10s 0.49s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWW962+1 : TPTP v8.1.2. Released v7.4.0.
% 0.00/0.08 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.06/0.26 % Computer : n025.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.27 % CPULimit : 300
% 0.06/0.27 % WCLimit : 300
% 0.06/0.27 % DateTime : Sun Aug 27 21:12:23 EDT 2023
% 0.06/0.27 % CPUTime :
% 0.10/0.49 Command-line arguments: --no-flatten-goal
% 0.10/0.49
% 0.10/0.49 % SZS status Theorem
% 0.10/0.49
% 0.10/0.50 % SZS output start Proof
% 0.10/0.50 Take the following subset of the input axioms:
% 0.10/0.50 fof(ax0, axiom, constr_CONST_0x30!=constr_CONST_1).
% 0.10/0.50 fof(ax1, axiom, constr_CONST_0x30!=constr_CONST_2).
% 0.10/0.50 fof(ax10, axiom, constr_CONST_0x30!=name_skB).
% 0.10/0.50 fof(ax11, axiom, constr_CONST_0x30!=name_skS).
% 0.10/0.50 fof(ax12, axiom, constr_CONST_1!=constr_CONST_2).
% 0.10/0.50 fof(ax13, axiom, constr_CONST_1!=constr_CONST_3).
% 0.10/0.50 fof(ax14, axiom, constr_CONST_1!=constr_CONST_4).
% 0.10/0.50 fof(ax15, axiom, constr_CONST_1!=name_A).
% 0.10/0.50 fof(ax16, axiom, constr_CONST_1!=name_B).
% 0.10/0.50 fof(ax17, axiom, constr_CONST_1!=name_I).
% 0.10/0.50 fof(ax18, axiom, constr_CONST_1!=name_c).
% 0.10/0.50 fof(ax19, axiom, constr_CONST_1!=name_objective).
% 0.10/0.50 fof(ax2, axiom, constr_CONST_0x30!=constr_CONST_3).
% 0.10/0.50 fof(ax20, axiom, constr_CONST_1!=name_skA).
% 0.10/0.50 fof(ax21, axiom, constr_CONST_1!=name_skB).
% 0.10/0.50 fof(ax22, axiom, constr_CONST_1!=name_skS).
% 0.10/0.50 fof(ax23, axiom, constr_CONST_2!=constr_CONST_3).
% 0.10/0.50 fof(ax24, axiom, constr_CONST_2!=constr_CONST_4).
% 0.10/0.50 fof(ax25, axiom, constr_CONST_2!=name_A).
% 0.10/0.50 fof(ax26, axiom, constr_CONST_2!=name_B).
% 0.10/0.50 fof(ax27, axiom, constr_CONST_2!=name_I).
% 0.10/0.50 fof(ax28, axiom, constr_CONST_2!=name_c).
% 0.10/0.50 fof(ax29, axiom, constr_CONST_2!=name_objective).
% 0.10/0.50 fof(ax3, axiom, constr_CONST_0x30!=constr_CONST_4).
% 0.10/0.50 fof(ax30, axiom, constr_CONST_2!=name_skA).
% 0.10/0.50 fof(ax31, axiom, constr_CONST_2!=name_skB).
% 0.10/0.50 fof(ax32, axiom, constr_CONST_2!=name_skS).
% 0.10/0.50 fof(ax33, axiom, constr_CONST_3!=constr_CONST_4).
% 0.10/0.50 fof(ax34, axiom, constr_CONST_3!=name_A).
% 0.10/0.50 fof(ax35, axiom, constr_CONST_3!=name_B).
% 0.10/0.50 fof(ax36, axiom, constr_CONST_3!=name_I).
% 0.10/0.50 fof(ax37, axiom, constr_CONST_3!=name_c).
% 0.10/0.50 fof(ax38, axiom, constr_CONST_3!=name_objective).
% 0.10/0.50 fof(ax39, axiom, constr_CONST_3!=name_skA).
% 0.10/0.50 fof(ax4, axiom, constr_CONST_0x30!=name_A).
% 0.10/0.50 fof(ax40, axiom, constr_CONST_3!=name_skB).
% 0.10/0.50 fof(ax41, axiom, constr_CONST_3!=name_skS).
% 0.10/0.50 fof(ax42, axiom, constr_CONST_4!=name_A).
% 0.10/0.50 fof(ax43, axiom, constr_CONST_4!=name_B).
% 0.10/0.50 fof(ax44, axiom, constr_CONST_4!=name_I).
% 0.10/0.50 fof(ax45, axiom, constr_CONST_4!=name_c).
% 0.10/0.50 fof(ax46, axiom, constr_CONST_4!=name_objective).
% 0.10/0.50 fof(ax47, axiom, constr_CONST_4!=name_skA).
% 0.10/0.50 fof(ax48, axiom, constr_CONST_4!=name_skB).
% 0.10/0.50 fof(ax49, axiom, constr_CONST_4!=name_skS).
% 0.10/0.50 fof(ax5, axiom, constr_CONST_0x30!=name_B).
% 0.10/0.50 fof(ax50, axiom, name_A!=name_B).
% 0.10/0.50 fof(ax51, axiom, name_A!=name_I).
% 0.10/0.50 fof(ax52, axiom, name_A!=name_c).
% 0.10/0.50 fof(ax53, axiom, name_A!=name_objective).
% 0.10/0.50 fof(ax54, axiom, name_A!=name_skA).
% 0.10/0.50 fof(ax55, axiom, name_A!=name_skB).
% 0.10/0.50 fof(ax56, axiom, name_A!=name_skS).
% 0.10/0.50 fof(ax57, axiom, name_B!=name_I).
% 0.10/0.50 fof(ax58, axiom, name_B!=name_c).
% 0.10/0.50 fof(ax59, axiom, name_B!=name_objective).
% 0.10/0.50 fof(ax6, axiom, constr_CONST_0x30!=name_I).
% 0.10/0.50 fof(ax60, axiom, name_B!=name_skA).
% 0.10/0.50 fof(ax61, axiom, name_B!=name_skB).
% 0.10/0.50 fof(ax62, axiom, name_B!=name_skS).
% 0.10/0.50 fof(ax63, axiom, name_I!=name_c).
% 0.10/0.50 fof(ax64, axiom, name_I!=name_objective).
% 0.10/0.50 fof(ax65, axiom, name_I!=name_skA).
% 0.10/0.50 fof(ax66, axiom, name_I!=name_skB).
% 0.10/0.50 fof(ax67, axiom, name_I!=name_skS).
% 0.10/0.50 fof(ax68, axiom, name_c!=name_objective).
% 0.10/0.51 fof(ax69, axiom, name_c!=name_skA).
% 0.10/0.51 fof(ax7, axiom, constr_CONST_0x30!=name_c).
% 0.10/0.51 fof(ax70, axiom, name_c!=name_skB).
% 0.10/0.51 fof(ax71, axiom, name_c!=name_skS).
% 0.10/0.51 fof(ax72, axiom, name_objective!=name_skA).
% 0.10/0.51 fof(ax73, axiom, name_objective!=name_skB).
% 0.10/0.51 fof(ax74, axiom, name_objective!=name_skS).
% 0.10/0.51 fof(ax75, axiom, name_skA!=name_skB).
% 0.10/0.51 fof(ax76, axiom, name_skA!=name_skS).
% 0.10/0.51 fof(ax77, axiom, name_skB!=name_skS).
% 0.10/0.51 fof(ax8, axiom, constr_CONST_0x30!=name_objective).
% 0.10/0.51 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)).
% 0.10/0.51 fof(ax83, axiom, ![VAR_X0X30_15, VAR_X1_16]: constr_assoc_pair_2_get_1_bitstring(tuple_assoc_pair(VAR_X0X30_15, VAR_X1_16))=VAR_X1_16).
% 0.10/0.51 fof(ax86, axiom, ![VAR_X0X30_9, VAR_X1_10X30]: constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9, VAR_X1_10X30))=VAR_X0X30_9).
% 0.10/0.51 fof(ax9, axiom, constr_CONST_0x30!=name_skA).
% 0.10/0.51 fof(co0, conjecture, ![VAR_V_711]: pred_attacker(tuple_2(name_Nb(VAR_V_711), name_objective))).
% 0.10/0.51
% 0.10/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.10/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.10/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.10/0.51 fresh(y, y, x1...xn) = u
% 0.10/0.51 C => fresh(s, t, x1...xn) = v
% 0.10/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.10/0.51 variables of u and v.
% 0.10/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.10/0.51 input problem has no model of domain size 1).
% 0.10/0.51
% 0.10/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.10/0.51
% 0.10/0.51 Axiom 1 (ax86): constr_assoc_pair_2_get_0x30(tuple_assoc_pair(X, Y)) = X.
% 0.10/0.51 Axiom 2 (ax83): constr_assoc_pair_2_get_1_bitstring(tuple_assoc_pair(X, Y)) = Y.
% 0.10/0.51 Axiom 3 (ax82): tuple_assoc_pair(X, tuple_assoc_pair(Y, Z)) = tuple_assoc_pair(tuple_assoc_pair(X, Y), Z).
% 0.10/0.51
% 0.10/0.51 Lemma 4: tuple_assoc_pair(X, Y) = X.
% 0.10/0.51 Proof:
% 0.10/0.51 tuple_assoc_pair(X, Y)
% 0.10/0.51 = { by axiom 1 (ax86) R->L }
% 0.10/0.51 constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(X, Y), Z))
% 0.10/0.51 = { by axiom 3 (ax82) R->L }
% 0.10/0.51 constr_assoc_pair_2_get_0x30(tuple_assoc_pair(X, tuple_assoc_pair(Y, Z)))
% 0.10/0.51 = { by axiom 1 (ax86) }
% 0.10/0.51 X
% 0.10/0.51
% 0.10/0.51 Lemma 5: Y = X.
% 0.10/0.51 Proof:
% 0.10/0.51 Y
% 0.10/0.51 = { by axiom 2 (ax83) R->L }
% 0.10/0.51 constr_assoc_pair_2_get_1_bitstring(tuple_assoc_pair(Z, Y))
% 0.10/0.51 = { by lemma 4 }
% 0.10/0.51 constr_assoc_pair_2_get_1_bitstring(Z)
% 0.10/0.51 = { by lemma 4 R->L }
% 0.10/0.51 constr_assoc_pair_2_get_1_bitstring(tuple_assoc_pair(Z, X))
% 0.10/0.51 = { by axiom 2 (ax83) }
% 0.10/0.51 X
% 0.10/0.51
% 0.10/0.51 Goal 1 (co0): pred_attacker(tuple_2(name_Nb(var_v_711), name_objective)) = true.
% 0.10/0.51 Proof:
% 0.10/0.51 pred_attacker(tuple_2(name_Nb(var_v_711), name_objective))
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 true
% 0.10/0.51
% 0.10/0.51 Goal 2 (ax77): name_skB = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 name_skB
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 3 (ax76): name_skA = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 name_skA
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 4 (ax75): name_skA = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 name_skA
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 5 (ax74): name_objective = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 name_objective
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 6 (ax73): name_objective = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 name_objective
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 7 (ax72): name_objective = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 name_objective
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 8 (ax71): name_c = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 name_c
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 9 (ax70): name_c = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 name_c
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 10 (ax69): name_c = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 name_c
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 11 (ax68): name_c = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 name_c
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 12 (ax67): name_I = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 name_I
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 13 (ax66): name_I = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 name_I
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 14 (ax65): name_I = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 name_I
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 15 (ax64): name_I = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 name_I
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 16 (ax63): name_I = name_c.
% 0.10/0.51 Proof:
% 0.10/0.51 name_I
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_c
% 0.10/0.51
% 0.10/0.51 Goal 17 (ax62): name_B = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 name_B
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 18 (ax61): name_B = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 name_B
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 19 (ax60): name_B = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 name_B
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 20 (ax59): name_B = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 name_B
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 21 (ax58): name_B = name_c.
% 0.10/0.51 Proof:
% 0.10/0.51 name_B
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_c
% 0.10/0.51
% 0.10/0.51 Goal 22 (ax57): name_B = name_I.
% 0.10/0.51 Proof:
% 0.10/0.51 name_B
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_I
% 0.10/0.51
% 0.10/0.51 Goal 23 (ax56): name_A = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 name_A
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 24 (ax55): name_A = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 name_A
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 25 (ax54): name_A = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 name_A
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 26 (ax53): name_A = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 name_A
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 27 (ax52): name_A = name_c.
% 0.10/0.51 Proof:
% 0.10/0.51 name_A
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_c
% 0.10/0.51
% 0.10/0.51 Goal 28 (ax51): name_A = name_I.
% 0.10/0.51 Proof:
% 0.10/0.51 name_A
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_I
% 0.10/0.51
% 0.10/0.51 Goal 29 (ax50): name_A = name_B.
% 0.10/0.51 Proof:
% 0.10/0.51 name_A
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_B
% 0.10/0.51
% 0.10/0.51 Goal 30 (ax49): constr_CONST_4 = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_4
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 31 (ax48): constr_CONST_4 = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_4
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 32 (ax47): constr_CONST_4 = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_4
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 33 (ax46): constr_CONST_4 = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_4
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 34 (ax45): constr_CONST_4 = name_c.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_4
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_c
% 0.10/0.51
% 0.10/0.51 Goal 35 (ax44): constr_CONST_4 = name_I.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_4
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_I
% 0.10/0.51
% 0.10/0.51 Goal 36 (ax43): constr_CONST_4 = name_B.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_4
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_B
% 0.10/0.51
% 0.10/0.51 Goal 37 (ax42): constr_CONST_4 = name_A.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_4
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_A
% 0.10/0.51
% 0.10/0.51 Goal 38 (ax41): constr_CONST_3 = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 39 (ax40): constr_CONST_3 = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 40 (ax39): constr_CONST_3 = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 41 (ax38): constr_CONST_3 = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 42 (ax37): constr_CONST_3 = name_c.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_c
% 0.10/0.51
% 0.10/0.51 Goal 43 (ax36): constr_CONST_3 = name_I.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_I
% 0.10/0.51
% 0.10/0.51 Goal 44 (ax35): constr_CONST_3 = name_B.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_B
% 0.10/0.51
% 0.10/0.51 Goal 45 (ax34): constr_CONST_3 = name_A.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_A
% 0.10/0.51
% 0.10/0.51 Goal 46 (ax33): constr_CONST_3 = constr_CONST_4.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_3
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_4
% 0.10/0.51
% 0.10/0.51 Goal 47 (ax32): constr_CONST_2 = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 48 (ax31): constr_CONST_2 = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 49 (ax30): constr_CONST_2 = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 50 (ax29): constr_CONST_2 = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 51 (ax28): constr_CONST_2 = name_c.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_c
% 0.10/0.51
% 0.10/0.51 Goal 52 (ax27): constr_CONST_2 = name_I.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_I
% 0.10/0.51
% 0.10/0.51 Goal 53 (ax26): constr_CONST_2 = name_B.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_B
% 0.10/0.51
% 0.10/0.51 Goal 54 (ax25): constr_CONST_2 = name_A.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_A
% 0.10/0.51
% 0.10/0.51 Goal 55 (ax24): constr_CONST_2 = constr_CONST_4.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_4
% 0.10/0.51
% 0.10/0.51 Goal 56 (ax23): constr_CONST_2 = constr_CONST_3.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_2
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_3
% 0.10/0.51
% 0.10/0.51 Goal 57 (ax22): constr_CONST_1 = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 58 (ax21): constr_CONST_1 = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 59 (ax20): constr_CONST_1 = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 60 (ax19): constr_CONST_1 = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 61 (ax18): constr_CONST_1 = name_c.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_c
% 0.10/0.51
% 0.10/0.51 Goal 62 (ax17): constr_CONST_1 = name_I.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_I
% 0.10/0.51
% 0.10/0.51 Goal 63 (ax16): constr_CONST_1 = name_B.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_B
% 0.10/0.51
% 0.10/0.51 Goal 64 (ax15): constr_CONST_1 = name_A.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_A
% 0.10/0.51
% 0.10/0.51 Goal 65 (ax14): constr_CONST_1 = constr_CONST_4.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_4
% 0.10/0.51
% 0.10/0.51 Goal 66 (ax13): constr_CONST_1 = constr_CONST_3.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_3
% 0.10/0.51
% 0.10/0.51 Goal 67 (ax12): constr_CONST_1 = constr_CONST_2.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_2
% 0.10/0.51
% 0.10/0.51 Goal 68 (ax11): constr_CONST_0x30 = name_skS.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skS
% 0.10/0.51
% 0.10/0.51 Goal 69 (ax10): constr_CONST_0x30 = name_skB.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skB
% 0.10/0.51
% 0.10/0.51 Goal 70 (ax9): constr_CONST_0x30 = name_skA.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_skA
% 0.10/0.51
% 0.10/0.51 Goal 71 (ax8): constr_CONST_0x30 = name_objective.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_objective
% 0.10/0.51
% 0.10/0.51 Goal 72 (ax7): constr_CONST_0x30 = name_c.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_c
% 0.10/0.51
% 0.10/0.51 Goal 73 (ax6): constr_CONST_0x30 = name_I.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_I
% 0.10/0.51
% 0.10/0.51 Goal 74 (ax5): constr_CONST_0x30 = name_B.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_B
% 0.10/0.51
% 0.10/0.51 Goal 75 (ax4): constr_CONST_0x30 = name_A.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 name_A
% 0.10/0.51
% 0.10/0.51 Goal 76 (ax3): constr_CONST_0x30 = constr_CONST_4.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_4
% 0.10/0.51
% 0.10/0.51 Goal 77 (ax2): constr_CONST_0x30 = constr_CONST_3.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_3
% 0.10/0.51
% 0.10/0.51 Goal 78 (ax1): constr_CONST_0x30 = constr_CONST_2.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_2
% 0.10/0.51
% 0.10/0.51 Goal 79 (ax0): constr_CONST_0x30 = constr_CONST_1.
% 0.10/0.51 Proof:
% 0.10/0.51 constr_CONST_0x30
% 0.10/0.51 = { by lemma 5 }
% 0.10/0.51 constr_CONST_1
% 0.10/0.51 % SZS output end Proof
% 0.10/0.51
% 0.10/0.51 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------