TSTP Solution File: SWW474+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW474+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 : 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 41.44s 5.76s
% Output : Proof 41.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW474+1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 22:34:25 EDT 2023
% 0.14/0.34 % CPUTime :
% 41.44/5.76 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 41.44/5.76
% 41.44/5.76 % SZS status Theorem
% 41.44/5.76
% 41.44/5.77 % SZS output start Proof
% 41.44/5.77 Take the following subset of the input axioms:
% 41.44/5.77 fof(conj_0, hypothesis, hBOOL(hoare_165779456gleton)).
% 41.44/5.77 fof(conj_1, hypothesis, hBOOL(wT_bodies)).
% 41.44/5.77 fof(conj_5, hypothesis, hAPP_p799580910on_com(body, pn)=some_com(y)).
% 41.44/5.77 fof(conj_7, conjecture, hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body))), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool)))).
% 41.44/5.77 fof(fact_0_empty, axiom, ![G]: hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G), bot_bo620288102e_bool))).
% 41.44/5.77 fof(fact_103_MGF, axiom, ![C_1]: (hBOOL(hoare_165779456gleton) => (hBOOL(wT_bodies) => (hBOOL(wt(C_1)) => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, C_1), bot_bo620288102e_bool))))))).
% 41.44/5.77 fof(fact_288_WT__bodiesD, axiom, ![Pn, B_2]: (hBOOL(wT_bodies) => (hAPP_p799580910on_com(body, Pn)=some_com(B_2) => hBOOL(wt(B_2))))).
% 41.44/5.77 fof(fact_4_cut, axiom, ![Ts, G_1, G2]: (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1), Ts)) => (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G2), G_1)) => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G2), Ts))))).
% 41.44/5.77
% 41.44/5.77 Now clausify the problem and encode Horn clauses using encoding 3 of
% 41.44/5.77 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 41.44/5.77 We repeatedly replace C & s=t => u=v by the two clauses:
% 41.44/5.77 fresh(y, y, x1...xn) = u
% 41.44/5.77 C => fresh(s, t, x1...xn) = v
% 41.44/5.77 where fresh is a fresh function symbol and x1..xn are the free
% 41.44/5.77 variables of u and v.
% 41.44/5.77 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 41.44/5.77 input problem has no model of domain size 1).
% 41.44/5.77
% 41.44/5.77 The encoding turns the above axioms into the following unit equations and goals:
% 41.44/5.77
% 41.44/5.77 Axiom 1 (conj_1): hBOOL(wT_bodies) = true2.
% 41.44/5.77 Axiom 2 (conj_0): hBOOL(hoare_165779456gleton) = true2.
% 41.44/5.77 Axiom 3 (conj_5): hAPP_p799580910on_com(body, pn) = some_com(y).
% 41.44/5.77 Axiom 4 (fact_103_MGF): fresh434(X, X, Y) = true2.
% 41.44/5.77 Axiom 5 (fact_288_WT__bodiesD): fresh199(X, X, Y) = true2.
% 41.44/5.77 Axiom 6 (fact_0_empty): hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(X), bot_bo620288102e_bool)) = true2.
% 41.44/5.77 Axiom 7 (fact_103_MGF): fresh432(X, X, Y) = fresh433(hBOOL(wT_bodies), true2, Y).
% 41.44/5.77 Axiom 8 (fact_288_WT__bodiesD): fresh200(X, X, Y, Z) = hBOOL(wt(Z)).
% 41.44/5.77 Axiom 9 (fact_4_cut): fresh163(X, X, Y, Z) = true2.
% 41.44/5.77 Axiom 10 (fact_103_MGF): fresh433(X, X, Y) = fresh434(hBOOL(wt(Y)), true2, Y).
% 41.44/5.77 Axiom 11 (fact_4_cut): fresh164(X, X, Y, Z, W) = hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(Y), W)).
% 41.44/5.77 Axiom 12 (fact_288_WT__bodiesD): fresh200(hBOOL(wT_bodies), true2, X, Y) = fresh199(hAPP_p799580910on_com(body, X), some_com(Y), Y).
% 41.44/5.77 Axiom 13 (fact_103_MGF): fresh432(hBOOL(hoare_165779456gleton), true2, X) = hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, X), bot_bo620288102e_bool))).
% 41.44/5.77 Axiom 14 (fact_4_cut): fresh164(hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(X), Y)), true2, Z, X, Y) = fresh163(hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(Z), X)), true2, Z, Y).
% 41.44/5.77
% 41.44/5.77 Goal 1 (conj_7): hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body))), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))) = true2.
% 41.44/5.77 Proof:
% 41.44/5.77 hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body))), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool)))
% 41.44/5.77 = { by axiom 11 (fact_4_cut) R->L }
% 41.44/5.77 fresh164(true2, true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 4 (fact_103_MGF) R->L }
% 41.44/5.77 fresh164(fresh434(true2, true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 5 (fact_288_WT__bodiesD) R->L }
% 41.44/5.77 fresh164(fresh434(fresh199(some_com(y), some_com(y), y), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 3 (conj_5) R->L }
% 41.44/5.77 fresh164(fresh434(fresh199(hAPP_p799580910on_com(body, pn), some_com(y), y), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 12 (fact_288_WT__bodiesD) R->L }
% 41.44/5.77 fresh164(fresh434(fresh200(hBOOL(wT_bodies), true2, pn, y), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 1 (conj_1) }
% 41.44/5.77 fresh164(fresh434(fresh200(true2, true2, pn, y), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 8 (fact_288_WT__bodiesD) }
% 41.44/5.77 fresh164(fresh434(hBOOL(wt(y)), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 10 (fact_103_MGF) R->L }
% 41.44/5.77 fresh164(fresh433(true2, true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 1 (conj_1) R->L }
% 41.44/5.77 fresh164(fresh433(hBOOL(wT_bodies), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 7 (fact_103_MGF) R->L }
% 41.44/5.77 fresh164(fresh432(true2, true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 2 (conj_0) R->L }
% 41.44/5.77 fresh164(fresh432(hBOOL(hoare_165779456gleton), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 13 (fact_103_MGF) }
% 41.44/5.77 fresh164(hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 14 (fact_4_cut) }
% 41.44/5.77 fresh163(hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body))), bot_bo620288102e_bool)), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 6 (fact_0_empty) }
% 41.44/5.77 fresh163(true2, true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
% 41.44/5.77 = { by axiom 9 (fact_4_cut) }
% 41.44/5.77 true2
% 41.44/5.77 % SZS output end Proof
% 41.44/5.77
% 41.44/5.77 RESULT: Theorem (the conjecture is true).
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