TSTP Solution File: SWW473+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW473+1 : 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 : n031.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 00:55:08 EDT 2023
% Result : Theorem 16.26s 2.47s
% Output : Proof 16.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW473+1 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 20:00:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 16.26/2.47 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 16.26/2.47
% 16.26/2.47 % SZS status Theorem
% 16.26/2.47
% 16.26/2.47 % SZS output start Proof
% 16.26/2.47 Take the following subset of the input axioms:
% 16.26/2.47 fof(conj_1, hypothesis, hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, g), image_pname_a(mgt_call, u)))).
% 16.26/2.47 fof(conj_4, hypothesis, hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u))).
% 16.26/2.47 fof(conj_6, conjecture, hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, u)))).
% 16.26/2.47 fof(fact_223_insert__absorb, axiom, ![A_1, A2]: (is_fun_pname_bool(A2) => (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, A_1), A2)) => insert_pname(A_1, A2)=A2))).
% 16.26/2.47 fof(fact_283_insert__mono, axiom, ![C, D, A_1_2]: (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, C), D)) => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(A_1_2, C)), insert_a(A_1_2, D))))).
% 16.26/2.47 fof(fact_284_image__insert, axiom, ![F, B, A_1_2]: image_pname_a(F, insert_pname(A_1_2, B))=insert_a(hAPP_pname_a(F, A_1_2), image_pname_a(F, B))).
% 16.26/2.47 fof(gsy_v_U, hypothesis, is_fun_pname_bool(u)).
% 16.26/2.47
% 16.26/2.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.26/2.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.26/2.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.26/2.47 fresh(y, y, x1...xn) = u
% 16.26/2.47 C => fresh(s, t, x1...xn) = v
% 16.26/2.47 where fresh is a fresh function symbol and x1..xn are the free
% 16.26/2.47 variables of u and v.
% 16.26/2.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.26/2.47 input problem has no model of domain size 1).
% 16.26/2.47
% 16.26/2.47 The encoding turns the above axioms into the following unit equations and goals:
% 16.26/2.47
% 16.26/2.47 Axiom 1 (gsy_v_U): is_fun_pname_bool(u) = true2.
% 16.26/2.47 Axiom 2 (conj_4): hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u)) = true2.
% 16.26/2.47 Axiom 3 (fact_284_image__insert): image_pname_a(X, insert_pname(Y, Z)) = insert_a(hAPP_pname_a(X, Y), image_pname_a(X, Z)).
% 16.26/2.47 Axiom 4 (fact_223_insert__absorb): fresh243(X, X, Y, Z) = insert_pname(Y, Z).
% 16.26/2.47 Axiom 5 (fact_223_insert__absorb): fresh19(X, X, Y, Z) = Z.
% 16.26/2.47 Axiom 6 (conj_1): hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, g), image_pname_a(mgt_call, u))) = true2.
% 16.26/2.47 Axiom 7 (fact_283_insert__mono): fresh180(X, X, Y, Z, W) = true2.
% 16.26/2.47 Axiom 8 (fact_223_insert__absorb): fresh243(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, X), Y)), true2, X, Y) = fresh19(is_fun_pname_bool(Y), true2, X, Y).
% 16.26/2.47 Axiom 9 (fact_283_insert__mono): fresh180(hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, X), Y)), true2, Z, X, Y) = hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(Z, X)), insert_a(Z, Y))).
% 16.26/2.47
% 16.26/2.47 Goal 1 (conj_6): hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, u))) = true2.
% 16.26/2.47 Proof:
% 16.26/2.47 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, u)))
% 16.26/2.47 = { by axiom 5 (fact_223_insert__absorb) R->L }
% 16.26/2.47 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, fresh19(true2, true2, pn, u))))
% 16.26/2.47 = { by axiom 1 (gsy_v_U) R->L }
% 16.26/2.47 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, fresh19(is_fun_pname_bool(u), true2, pn, u))))
% 16.26/2.47 = { by axiom 8 (fact_223_insert__absorb) R->L }
% 16.26/2.47 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, fresh243(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u)), true2, pn, u))))
% 16.26/2.47 = { by axiom 2 (conj_4) }
% 16.26/2.47 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, fresh243(true2, true2, pn, u))))
% 16.26/2.47 = { by axiom 4 (fact_223_insert__absorb) }
% 16.26/2.47 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, insert_pname(pn, u))))
% 16.26/2.47 = { by axiom 3 (fact_284_image__insert) }
% 16.26/2.47 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), insert_a(hAPP_pname_a(mgt_call, pn), image_pname_a(mgt_call, u))))
% 16.26/2.47 = { by axiom 9 (fact_283_insert__mono) R->L }
% 16.26/2.47 fresh180(hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, g), image_pname_a(mgt_call, u))), true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
% 16.26/2.47 = { by axiom 6 (conj_1) }
% 16.26/2.47 fresh180(true2, true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
% 16.26/2.47 = { by axiom 7 (fact_283_insert__mono) }
% 16.26/2.47 true2
% 16.26/2.47 % SZS output end Proof
% 16.26/2.47
% 16.26/2.47 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------