TSTP Solution File: SWW473+6 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW473+6 : TPTP v8.1.2. Released v5.3.0.
% 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 : n029.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 00:55:10 EDT 2023
% Result : Theorem 102.43s 13.47s
% Output : Proof 102.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWW473+6 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.31 % Computer : n029.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sun Aug 27 18:40:56 EDT 2023
% 0.12/0.31 % CPUTime :
% 102.43/13.47 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 102.43/13.47
% 102.43/13.47 % SZS status Theorem
% 102.43/13.47
% 102.43/13.49 % SZS output start Proof
% 102.43/13.49 Take the following subset of the input axioms:
% 102.43/13.49 fof(conj_1, hypothesis, hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))).
% 102.43/13.49 fof(conj_4, hypothesis, hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u))).
% 102.43/13.49 fof(conj_6, conjecture, hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))).
% 102.43/13.49 fof(fact_63_insert__code, axiom, ![X_b, A_3, X_1, Y_1]: (hBOOL(hAPP(X_b, bool, hAPP(fun(X_b, bool), fun(X_b, bool), hAPP(X_b, fun(fun(X_b, bool), fun(X_b, bool)), insert(X_b), Y_1), A_3), X_1)) <=> (ti(X_b, Y_1)=ti(X_b, X_1) | hBOOL(hAPP(X_b, bool, A_3, X_1))))).
% 102.43/13.49 fof(fact_66_insert__absorb, axiom, ![A_2, X_b2, A_3_2]: (hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(X_b2, fun(fun(X_b2, bool), bool), member(X_b2), A_2), A_3_2)) => hAPP(fun(X_b2, bool), fun(X_b2, bool), hAPP(X_b2, fun(fun(X_b2, bool), fun(X_b2, bool)), insert(X_b2), A_2), A_3_2)=ti(fun(X_b2, bool), A_3_2))).
% 102.43/13.49 fof(fact_75_mem__def, axiom, ![X_b2, A_3_2, X_1_2]: (hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(X_b2, fun(fun(X_b2, bool), bool), member(X_b2), X_1_2), A_3_2)) <=> hBOOL(hAPP(X_b2, bool, A_3_2, X_1_2)))).
% 102.43/13.49 fof(fact_86_insert__subset, axiom, ![B_2, X_b2, A_3_2, X_1_2]: (hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(fun(X_b2, bool), fun(fun(X_b2, bool), bool), ord_less_eq(fun(X_b2, bool)), hAPP(fun(X_b2, bool), fun(X_b2, bool), hAPP(X_b2, fun(fun(X_b2, bool), fun(X_b2, bool)), insert(X_b2), X_1_2), A_3_2)), B_2)) <=> (hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(X_b2, fun(fun(X_b2, bool), bool), member(X_b2), X_1_2), B_2)) & hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(fun(X_b2, bool), fun(fun(X_b2, bool), bool), ord_less_eq(fun(X_b2, bool)), A_3_2), B_2))))).
% 102.43/13.49 fof(fact_90_image__insert, axiom, ![X_c, F, X_b2, A_2_2, B_2_2]: hAPP(fun(X_c, bool), fun(X_b2, bool), hAPP(fun(X_c, X_b2), fun(fun(X_c, bool), fun(X_b2, bool)), image(X_c, X_b2), F), hAPP(fun(X_c, bool), fun(X_c, bool), hAPP(X_c, fun(fun(X_c, bool), fun(X_c, bool)), insert(X_c), A_2_2), B_2_2))=hAPP(fun(X_b2, bool), fun(X_b2, bool), hAPP(X_b2, fun(fun(X_b2, bool), fun(X_b2, bool)), insert(X_b2), hAPP(X_c, X_b2, F, A_2_2)), hAPP(fun(X_c, bool), fun(X_b2, bool), hAPP(fun(X_c, X_b2), fun(fun(X_c, bool), fun(X_b2, bool)), image(X_c, X_b2), F), B_2_2))).
% 102.43/13.49 fof(tsy_v_U_res, hypothesis, ti(fun(pname, bool), u)=u).
% 102.43/13.49
% 102.43/13.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 102.43/13.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 102.43/13.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 102.43/13.49 fresh(y, y, x1...xn) = u
% 102.43/13.49 C => fresh(s, t, x1...xn) = v
% 102.43/13.49 where fresh is a fresh function symbol and x1..xn are the free
% 102.43/13.49 variables of u and v.
% 102.43/13.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 102.43/13.49 input problem has no model of domain size 1).
% 102.43/13.49
% 102.43/13.49 The encoding turns the above axioms into the following unit equations and goals:
% 102.43/13.49
% 102.43/13.49 Axiom 1 (tsy_v_U_res): ti(fun(pname, bool), u) = u.
% 102.43/13.49 Axiom 2 (fact_66_insert__absorb): fresh83(X, X, Y, Z, W) = ti(fun(Y, bool), W).
% 102.43/13.49 Axiom 3 (fact_75_mem__def): fresh68(X, X, Y, Z, W) = true2.
% 102.43/13.49 Axiom 4 (fact_86_insert__subset): fresh710(X, X, Y, Z, W, V) = true2.
% 102.43/13.49 Axiom 5 (fact_63_insert__code): fresh86(X, X, Y, Z, W, V) = true2.
% 102.43/13.49 Axiom 6 (fact_75_mem__def): fresh68(hBOOL(hAPP(X, bool, Y, Z)), true2, X, Z, Y) = hBOOL(hAPP(fun(X, bool), bool, hAPP(X, fun(fun(X, bool), bool), member(X), Z), Y)).
% 102.43/13.49 Axiom 7 (conj_4): hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u)) = true2.
% 102.43/13.49 Axiom 8 (fact_66_insert__absorb): fresh83(hBOOL(hAPP(fun(X, bool), bool, hAPP(X, fun(fun(X, bool), bool), member(X), Y), Z)), true2, X, Y, Z) = hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), Y), Z).
% 102.43/13.49 Axiom 9 (fact_63_insert__code): fresh86(ti(X, Y), ti(X, Z), X, Y, W, Z) = hBOOL(hAPP(X, bool, hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), Y), W), Z)).
% 102.43/13.49 Axiom 10 (fact_86_insert__subset): fresh709(X, X, Y, Z, W, V) = fresh710(hBOOL(hAPP(fun(Y, bool), bool, hAPP(Y, fun(fun(Y, bool), bool), member(Y), Z), V)), true2, Y, Z, W, V).
% 102.43/13.49 Axiom 11 (fact_86_insert__subset): fresh709(hBOOL(hAPP(fun(X, bool), bool, hAPP(fun(X, bool), fun(fun(X, bool), bool), ord_less_eq(fun(X, bool)), Y), Z)), true2, X, W, Y, Z) = hBOOL(hAPP(fun(X, bool), bool, hAPP(fun(X, bool), fun(fun(X, bool), bool), ord_less_eq(fun(X, bool)), hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), W), Y)), Z)).
% 102.43/13.49 Axiom 12 (conj_1): hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))) = true2.
% 102.43/13.49 Axiom 13 (fact_90_image__insert): hAPP(fun(X, bool), fun(Y, bool), hAPP(fun(X, Y), fun(fun(X, bool), fun(Y, bool)), image(X, Y), Z), hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), W), V)) = hAPP(fun(Y, bool), fun(Y, bool), hAPP(Y, fun(fun(Y, bool), fun(Y, bool)), insert(Y), hAPP(X, Y, Z, W)), hAPP(fun(X, bool), fun(Y, bool), hAPP(fun(X, Y), fun(fun(X, bool), fun(Y, bool)), image(X, Y), Z), V)).
% 102.43/13.49
% 102.43/13.49 Goal 1 (conj_6): hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))) = true2.
% 102.43/13.49 Proof:
% 102.43/13.49 hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
% 102.43/13.49 = { by axiom 11 (fact_86_insert__subset) R->L }
% 102.43/13.49 fresh709(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 102.43/13.49 = { by axiom 12 (conj_1) }
% 102.43/13.49 fresh709(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 102.43/13.49 = { by axiom 1 (tsy_v_U_res) R->L }
% 102.43/13.49 fresh709(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), ti(fun(pname, bool), u)))
% 102.43/13.49 = { by axiom 2 (fact_66_insert__absorb) R->L }
% 102.43/13.49 fresh709(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), fresh83(true2, true2, pname, pn, u)))
% 102.43/13.49 = { by axiom 7 (conj_4) R->L }
% 102.43/13.49 fresh709(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), fresh83(hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u)), true2, pname, pn, u)))
% 102.43/13.49 = { by axiom 8 (fact_66_insert__absorb) }
% 102.43/13.49 fresh709(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), hAPP(fun(pname, bool), fun(pname, bool), hAPP(pname, fun(fun(pname, bool), fun(pname, bool)), insert(pname), pn), u)))
% 102.43/13.49 = { by axiom 13 (fact_90_image__insert) }
% 102.43/13.49 fresh709(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
% 102.43/13.49 = { by axiom 10 (fact_86_insert__subset) }
% 102.43/13.49 fresh710(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(x_a, fun(fun(x_a, bool), bool), member(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
% 102.43/13.49 = { by axiom 6 (fact_75_mem__def) R->L }
% 102.43/13.50 fresh710(fresh68(hBOOL(hAPP(x_a, bool, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), hAPP(pname, x_a, mgt_call, pn))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
% 102.43/13.50 = { by axiom 9 (fact_63_insert__code) R->L }
% 102.43/13.50 fresh710(fresh68(fresh86(ti(x_a, hAPP(pname, x_a, mgt_call, pn)), ti(x_a, hAPP(pname, x_a, mgt_call, pn)), x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u), hAPP(pname, x_a, mgt_call, pn)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
% 102.43/13.50 = { by axiom 5 (fact_63_insert__code) }
% 102.43/13.50 fresh710(fresh68(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
% 102.43/13.50 = { by axiom 3 (fact_75_mem__def) }
% 102.43/13.50 fresh710(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
% 102.43/13.50 = { by axiom 4 (fact_86_insert__subset) }
% 102.43/13.50 true2
% 102.43/13.50 % SZS output end Proof
% 102.43/13.50
% 102.43/13.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------