TSTP Solution File: SWW970+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW970+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 : n026.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 00:56:24 EDT 2023
% Result : Theorem 0.16s 0.62s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW970+1 : TPTP v8.1.2. Released v7.4.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 20:49:19 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.62 Command-line arguments: --no-flatten-goal
% 0.16/0.62
% 0.16/0.62 % SZS status Theorem
% 0.16/0.62
% 0.16/0.62 % SZS output start Proof
% 0.16/0.62 Take the following subset of the input axioms:
% 0.16/0.62 fof(ax135, axiom, ![VAR_ENC_A_KAB_T_330X30]: ((pred_eq_bitstring_bitstring(name_A, constr_tuple_3_get_0x30(constr_cbc_dec_3(VAR_ENC_A_KAB_T_330X30, name_Kbs))) & pred_attacker(tuple_client_B_in_1(VAR_ENC_A_KAB_T_330X30))) => pred_attacker(tuple_client_B_out_2(name_objective)))).
% 0.16/0.62 fof(ax79, axiom, ![VAR_X_67, VAR_Y_68]: pred_eq_bitstring_bitstring(VAR_X_67, VAR_Y_68)).
% 0.16/0.62 fof(ax83, axiom, pred_attacker(tuple_true)).
% 0.16/0.62 fof(ax93, axiom, ![VAR_V_112]: (pred_attacker(tuple_client_B_out_2(VAR_V_112)) => pred_attacker(VAR_V_112))).
% 0.16/0.62 fof(ax94, axiom, ![VAR_V_115]: (pred_attacker(VAR_V_115) => pred_attacker(tuple_client_B_in_1(VAR_V_115)))).
% 0.16/0.62 fof(co0, conjecture, pred_attacker(name_objective)).
% 0.16/0.62
% 0.16/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.62 fresh(y, y, x1...xn) = u
% 0.16/0.62 C => fresh(s, t, x1...xn) = v
% 0.16/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.62 variables of u and v.
% 0.16/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.62 input problem has no model of domain size 1).
% 0.16/0.62
% 0.16/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.62
% 0.16/0.63 Axiom 1 (ax83): pred_attacker(tuple_true) = true.
% 0.16/0.63 Axiom 2 (ax79): pred_eq_bitstring_bitstring(X, Y) = true.
% 0.16/0.63 Axiom 3 (ax135): fresh21(X, X) = true.
% 0.16/0.63 Axiom 4 (ax135): fresh22(X, X, Y) = pred_attacker(tuple_client_B_out_2(name_objective)).
% 0.16/0.63 Axiom 5 (ax93): fresh6(X, X, Y) = true.
% 0.16/0.63 Axiom 6 (ax94): fresh5(X, X, Y) = true.
% 0.16/0.63 Axiom 7 (ax94): fresh5(pred_attacker(X), true, X) = pred_attacker(tuple_client_B_in_1(X)).
% 0.16/0.63 Axiom 8 (ax93): fresh6(pred_attacker(tuple_client_B_out_2(X)), true, X) = pred_attacker(X).
% 0.16/0.63 Axiom 9 (ax135): fresh22(pred_attacker(tuple_client_B_in_1(X)), true, X) = fresh21(pred_eq_bitstring_bitstring(name_A, constr_tuple_3_get_0x30(constr_cbc_dec_3(X, name_Kbs))), true).
% 0.16/0.63
% 0.16/0.63 Goal 1 (co0): pred_attacker(name_objective) = true.
% 0.16/0.63 Proof:
% 0.16/0.63 pred_attacker(name_objective)
% 0.16/0.63 = { by axiom 8 (ax93) R->L }
% 0.16/0.63 fresh6(pred_attacker(tuple_client_B_out_2(name_objective)), true, name_objective)
% 0.16/0.63 = { by axiom 4 (ax135) R->L }
% 0.16/0.63 fresh6(fresh22(true, true, tuple_true), true, name_objective)
% 0.16/0.63 = { by axiom 6 (ax94) R->L }
% 0.16/0.63 fresh6(fresh22(fresh5(true, true, tuple_true), true, tuple_true), true, name_objective)
% 0.16/0.63 = { by axiom 1 (ax83) R->L }
% 0.16/0.63 fresh6(fresh22(fresh5(pred_attacker(tuple_true), true, tuple_true), true, tuple_true), true, name_objective)
% 0.16/0.63 = { by axiom 7 (ax94) }
% 0.16/0.63 fresh6(fresh22(pred_attacker(tuple_client_B_in_1(tuple_true)), true, tuple_true), true, name_objective)
% 0.16/0.63 = { by axiom 9 (ax135) }
% 0.16/0.63 fresh6(fresh21(pred_eq_bitstring_bitstring(name_A, constr_tuple_3_get_0x30(constr_cbc_dec_3(tuple_true, name_Kbs))), true), true, name_objective)
% 0.16/0.63 = { by axiom 2 (ax79) }
% 0.16/0.63 fresh6(fresh21(true, true), true, name_objective)
% 0.16/0.63 = { by axiom 3 (ax135) }
% 0.16/0.63 fresh6(true, true, name_objective)
% 0.16/0.63 = { by axiom 5 (ax93) }
% 0.16/0.63 true
% 0.16/0.63 % SZS output end Proof
% 0.16/0.63
% 0.16/0.63 RESULT: Theorem (the conjecture is true).
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