TSTP Solution File: SWW473+1 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : SWW473+1 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n024.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 : Mon Jun 24 18:27:08 EDT 2024
% Result : Theorem 281.29s 35.73s
% Output : Proof 281.29s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW473+1 : TPTP v8.2.0. Released v5.3.0.
% 0.07/0.13 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.13/0.34 % Computer : n024.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 : Wed Jun 19 06:14:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 281.29/35.73 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 281.29/35.73
% 281.29/35.73 % SZS status Theorem
% 281.29/35.73
% 281.29/35.74 % SZS output start Proof
% 281.29/35.74 Take the following subset of the input axioms:
% 281.29/35.74 fof(conj_1, hypothesis, hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, g), image_pname_a(mgt_call, u)))).
% 281.29/35.74 fof(conj_4, hypothesis, hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u))).
% 281.29/35.74 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)))).
% 281.29/35.74 fof(fact_261_imageI, axiom, ![F, X_2, A2]: (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, X_2), A2)) => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, hAPP_pname_a(F, X_2)), image_pname_a(F, A2))))).
% 281.29/35.74 fof(fact_274_insert__subset, axiom, ![B, X_2_2, A2_2]: (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(X_2_2, A2_2)), B)) <=> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, X_2_2), B)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, A2_2), B))))).
% 281.29/35.74
% 281.29/35.74 Now clausify the problem and encode Horn clauses using encoding 3 of
% 281.29/35.74 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 281.29/35.74 We repeatedly replace C & s=t => u=v by the two clauses:
% 281.29/35.74 fresh(y, y, x1...xn) = u
% 281.29/35.74 C => fresh(s, t, x1...xn) = v
% 281.29/35.74 where fresh is a fresh function symbol and x1..xn are the free
% 281.29/35.74 variables of u and v.
% 281.29/35.74 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 281.29/35.74 input problem has no model of domain size 1).
% 281.29/35.74
% 281.29/35.74 The encoding turns the above axioms into the following unit equations and goals:
% 281.29/35.74
% 281.29/35.74 Axiom 1 (conj_4): hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u)) = true2.
% 281.29/35.74 Axiom 2 (fact_261_imageI): fresh202(X, X, Y, Z, W) = true2.
% 281.29/35.74 Axiom 3 (fact_274_insert__subset): fresh189(X, X, Y, Z, W) = true2.
% 281.29/35.74 Axiom 4 (conj_1): hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, g), image_pname_a(mgt_call, u))) = true2.
% 281.29/35.74 Axiom 5 (fact_274_insert__subset): fresh190(X, X, Y, Z, W) = hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(Y, Z)), W)).
% 281.29/35.74 Axiom 6 (fact_261_imageI): fresh202(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, X), Y)), true2, Z, X, Y) = hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, hAPP_pname_a(Z, X)), image_pname_a(Z, Y))).
% 281.29/35.74 Axiom 7 (fact_274_insert__subset): fresh190(hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, X), Y)), true2, Z, X, Y) = fresh189(hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, Z), Y)), true2, Z, X, Y).
% 281.29/35.74
% 281.29/35.74 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.
% 281.29/35.74 Proof:
% 281.29/35.74 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)))
% 281.29/35.74 = { by axiom 5 (fact_274_insert__subset) R->L }
% 281.29/35.74 fresh190(true2, true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
% 281.29/35.74 = { by axiom 4 (conj_1) R->L }
% 281.29/35.74 fresh190(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))
% 281.29/35.74 = { by axiom 7 (fact_274_insert__subset) }
% 281.29/35.74 fresh189(hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, hAPP_pname_a(mgt_call, pn)), image_pname_a(mgt_call, u))), true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
% 281.29/35.74 = { by axiom 6 (fact_261_imageI) R->L }
% 281.29/35.74 fresh189(fresh202(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u)), true2, mgt_call, pn, u), true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
% 281.29/35.74 = { by axiom 1 (conj_4) }
% 281.29/35.74 fresh189(fresh202(true2, true2, mgt_call, pn, u), true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
% 281.29/35.74 = { by axiom 2 (fact_261_imageI) }
% 281.29/35.74 fresh189(true2, true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
% 281.29/35.74 = { by axiom 3 (fact_274_insert__subset) }
% 281.29/35.74 true2
% 281.29/35.74 % SZS output end Proof
% 281.29/35.74
% 281.29/35.74 RESULT: Theorem (the conjecture is true).
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