TSTP Solution File: SWW951+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW951+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 : n006.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 00:56:21 EDT 2023
% Result : Theorem 0.19s 0.54s
% Output : Proof 0.19s
% 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 : SWW951+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
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 21:03:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.54 Command-line arguments: --flatten
% 0.19/0.54
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 Take the following subset of the input axioms:
% 0.19/0.54 fof(ax41, axiom, pred_attacker(tuple_true)).
% 0.19/0.54 fof(ax46, axiom, ![VAR_V_35]: (pred_attacker(tuple_T_out_4(VAR_V_35)) => pred_attacker(VAR_V_35))).
% 0.19/0.54 fof(ax49, axiom, ![VAR_V_44]: (pred_attacker(VAR_V_44) => pred_attacker(tuple_T_in_3(VAR_V_44)))).
% 0.19/0.54 fof(ax51, axiom, ![VAR_V_50X30]: (pred_attacker(VAR_V_50X30) => pred_attacker(tuple_T_in_1(VAR_V_50X30)))).
% 0.19/0.54 fof(ax57, axiom, pred_attacker(constr_CONST_0x30)).
% 0.19/0.54 fof(ax64, axiom, ![VAR_K_XOR_K1_10X305, VAR_R1_10X306]: ((pred_attacker(tuple_T_in_3(VAR_K_XOR_K1_10X305)) & pred_attacker(tuple_T_in_1(VAR_R1_10X306))) => pred_attacker(tuple_T_out_4(name_objective)))).
% 0.19/0.54 fof(co0, conjecture, pred_attacker(name_objective)).
% 0.19/0.54
% 0.19/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.54 fresh(y, y, x1...xn) = u
% 0.19/0.54 C => fresh(s, t, x1...xn) = v
% 0.19/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.55 variables of u and v.
% 0.19/0.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.55 input problem has no model of domain size 1).
% 0.19/0.55
% 0.19/0.55 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.55
% 0.19/0.55 Axiom 1 (ax41): pred_attacker(tuple_true) = true.
% 0.19/0.55 Axiom 2 (ax57): pred_attacker(constr_CONST_0x30) = true.
% 0.19/0.55 Axiom 3 (ax64): fresh(X, X) = true.
% 0.19/0.55 Axiom 4 (ax46): fresh14(X, X, Y) = true.
% 0.19/0.55 Axiom 5 (ax49): fresh11(X, X, Y) = true.
% 0.19/0.55 Axiom 6 (ax51): fresh9(X, X, Y) = true.
% 0.19/0.55 Axiom 7 (ax64): fresh2(X, X, Y) = pred_attacker(tuple_T_out_4(name_objective)).
% 0.19/0.55 Axiom 8 (ax49): fresh11(pred_attacker(X), true, X) = pred_attacker(tuple_T_in_3(X)).
% 0.19/0.55 Axiom 9 (ax51): fresh9(pred_attacker(X), true, X) = pred_attacker(tuple_T_in_1(X)).
% 0.19/0.55 Axiom 10 (ax46): fresh14(pred_attacker(tuple_T_out_4(X)), true, X) = pred_attacker(X).
% 0.19/0.55 Axiom 11 (ax64): fresh2(pred_attacker(tuple_T_in_1(X)), true, Y) = fresh(pred_attacker(tuple_T_in_3(Y)), true).
% 0.19/0.55
% 0.19/0.55 Lemma 12: pred_attacker(constr_CONST_0x30) = pred_attacker(tuple_true).
% 0.19/0.55 Proof:
% 0.19/0.55 pred_attacker(constr_CONST_0x30)
% 0.19/0.55 = { by axiom 2 (ax57) }
% 0.19/0.55 true
% 0.19/0.55 = { by axiom 1 (ax41) R->L }
% 0.19/0.55 pred_attacker(tuple_true)
% 0.19/0.55
% 0.19/0.55 Goal 1 (co0): pred_attacker(name_objective) = true.
% 0.19/0.55 Proof:
% 0.19/0.55 pred_attacker(name_objective)
% 0.19/0.55 = { by axiom 10 (ax46) R->L }
% 0.19/0.55 fresh14(pred_attacker(tuple_T_out_4(name_objective)), true, name_objective)
% 0.19/0.55 = { by axiom 1 (ax41) R->L }
% 0.19/0.55 fresh14(pred_attacker(tuple_T_out_4(name_objective)), pred_attacker(tuple_true), name_objective)
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 fresh14(pred_attacker(tuple_T_out_4(name_objective)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 7 (ax64) R->L }
% 0.19/0.55 fresh14(fresh2(pred_attacker(constr_CONST_0x30), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 fresh14(fresh2(pred_attacker(tuple_true), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 1 (ax41) }
% 0.19/0.55 fresh14(fresh2(true, pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 6 (ax51) R->L }
% 0.19/0.55 fresh14(fresh2(fresh9(pred_attacker(constr_CONST_0x30), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 fresh14(fresh2(fresh9(pred_attacker(tuple_true), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 fresh14(fresh2(fresh9(pred_attacker(tuple_true), pred_attacker(tuple_true), tuple_true), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 1 (ax41) }
% 0.19/0.55 fresh14(fresh2(fresh9(pred_attacker(tuple_true), true, tuple_true), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 9 (ax51) }
% 0.19/0.55 fresh14(fresh2(pred_attacker(tuple_T_in_1(tuple_true)), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 fresh14(fresh2(pred_attacker(tuple_T_in_1(tuple_true)), pred_attacker(tuple_true), tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 1 (ax41) }
% 0.19/0.55 fresh14(fresh2(pred_attacker(tuple_T_in_1(tuple_true)), true, tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 11 (ax64) }
% 0.19/0.55 fresh14(fresh(pred_attacker(tuple_T_in_3(tuple_true)), true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 1 (ax41) R->L }
% 0.19/0.55 fresh14(fresh(pred_attacker(tuple_T_in_3(tuple_true)), pred_attacker(tuple_true)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 fresh14(fresh(pred_attacker(tuple_T_in_3(tuple_true)), pred_attacker(constr_CONST_0x30)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 8 (ax49) R->L }
% 0.19/0.55 fresh14(fresh(fresh11(pred_attacker(tuple_true), true, tuple_true), pred_attacker(constr_CONST_0x30)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 1 (ax41) R->L }
% 0.19/0.55 fresh14(fresh(fresh11(pred_attacker(tuple_true), pred_attacker(tuple_true), tuple_true), pred_attacker(constr_CONST_0x30)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 fresh14(fresh(fresh11(pred_attacker(tuple_true), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 fresh14(fresh(fresh11(pred_attacker(constr_CONST_0x30), pred_attacker(constr_CONST_0x30), tuple_true), pred_attacker(constr_CONST_0x30)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 5 (ax49) }
% 0.19/0.55 fresh14(fresh(true, pred_attacker(constr_CONST_0x30)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 1 (ax41) R->L }
% 0.19/0.55 fresh14(fresh(pred_attacker(tuple_true), pred_attacker(constr_CONST_0x30)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 fresh14(fresh(pred_attacker(constr_CONST_0x30), pred_attacker(constr_CONST_0x30)), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 3 (ax64) }
% 0.19/0.55 fresh14(true, pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 1 (ax41) R->L }
% 0.19/0.55 fresh14(pred_attacker(tuple_true), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 fresh14(pred_attacker(constr_CONST_0x30), pred_attacker(constr_CONST_0x30), name_objective)
% 0.19/0.55 = { by axiom 4 (ax46) }
% 0.19/0.55 true
% 0.19/0.55 % SZS output end Proof
% 0.19/0.55
% 0.19/0.55 RESULT: Theorem (the conjecture is true).
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