TSTP Solution File: SCT126+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT126+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : Thu Aug 31 14:22:11 EDT 2023
% Result : Theorem 177.76s 23.19s
% Output : Proof 177.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT126+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 15:14:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 177.76/23.19 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 177.76/23.19
% 177.76/23.19 % SZS status Theorem
% 177.76/23.19
% 177.76/23.19 % SZS output start Proof
% 177.76/23.19 Take the following subset of the input axioms:
% 177.76/23.19 fof(conj_0, conjecture, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(v_F, v_Q____)), c_Arrow__Order__Mirabelle_OLin))).
% 177.76/23.19 fof(fact__096Q_A_058_AProf_096, axiom, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_Q____), c_Arrow__Order__Mirabelle_OProf))).
% 177.76/23.19 fof(fact_assms_I1_J, axiom, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_F), c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin))))).
% 177.76/23.19 fof(fact_funcset__mem, axiom, ![V_f_2, V_x_2, T_a, V_B_2, V_A_2, T_b]: (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))) => (hBOOL(hAPP(hAPP(c_member(T_a), V_x_2), V_A_2)) => hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, V_x_2)), V_B_2))))).
% 177.76/23.19 fof(fact_mem__def, axiom, ![V_x_2_2, T_a2, V_A_2_2]: (hBOOL(hAPP(hAPP(c_member(T_a2), V_x_2_2), V_A_2_2)) <=> hBOOL(hAPP(V_A_2_2, V_x_2_2)))).
% 177.76/23.19
% 177.76/23.19 Now clausify the problem and encode Horn clauses using encoding 3 of
% 177.76/23.19 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 177.76/23.19 We repeatedly replace C & s=t => u=v by the two clauses:
% 177.76/23.19 fresh(y, y, x1...xn) = u
% 177.76/23.19 C => fresh(s, t, x1...xn) = v
% 177.76/23.19 where fresh is a fresh function symbol and x1..xn are the free
% 177.76/23.19 variables of u and v.
% 177.76/23.19 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 177.76/23.19 input problem has no model of domain size 1).
% 177.76/23.19
% 177.76/23.19 The encoding turns the above axioms into the following unit equations and goals:
% 177.76/23.19
% 177.76/23.19 Axiom 1 (fact_mem__def_1): fresh183(X, X, Y, Z) = true2.
% 177.76/23.19 Axiom 2 (fact_mem__def): fresh184(X, X, Y, Z, W) = true2.
% 177.76/23.19 Axiom 3 (fact_funcset__mem): fresh292(X, X, Y, Z, W, V) = true2.
% 177.76/23.19 Axiom 4 (fact_funcset__mem): fresh293(X, X, Y, Z, W, V, U, T) = hBOOL(hAPP(hAPP(c_member(U), hAPP(V, Y)), Z)).
% 177.76/23.19 Axiom 5 (fact_mem__def): fresh184(hBOOL(hAPP(X, Y)), true2, X, Y, Z) = hBOOL(hAPP(hAPP(c_member(Z), Y), X)).
% 177.76/23.19 Axiom 6 (fact_mem__def_1): fresh183(hBOOL(hAPP(hAPP(c_member(X), Y), Z)), true2, Z, Y) = hBOOL(hAPP(Z, Y)).
% 177.76/23.19 Axiom 7 (fact__096Q_A_058_AProf_096): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_Q____), c_Arrow__Order__Mirabelle_OProf)) = true2.
% 177.76/23.19 Axiom 8 (fact_funcset__mem): fresh293(hBOOL(hAPP(hAPP(c_member(tc_fun(X, Y)), Z), c_FuncSet_OPi(X, Y, W, c_COMBK(tc_fun(Y, tc_HOL_Obool), X, V)))), true2, U, V, W, Z, Y, X) = fresh292(hBOOL(hAPP(hAPP(c_member(X), U), W)), true2, U, V, Z, Y).
% 177.76/23.19 Axiom 9 (fact_assms_I1_J): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_F), c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin)))) = true2.
% 177.76/23.19
% 177.76/23.19 Goal 1 (conj_0): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(v_F, v_Q____)), c_Arrow__Order__Mirabelle_OLin)) = true2.
% 177.76/23.19 Proof:
% 177.76/23.19 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(v_F, v_Q____)), c_Arrow__Order__Mirabelle_OLin))
% 177.76/23.19 = { by axiom 4 (fact_funcset__mem) R->L }
% 177.76/23.19 fresh293(true2, true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)))
% 177.76/23.19 = { by axiom 9 (fact_assms_I1_J) R->L }
% 177.76/23.19 fresh293(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_F), c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin)))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)))
% 177.76/23.19 = { by axiom 8 (fact_funcset__mem) }
% 177.76/23.19 fresh292(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_Q____), c_Arrow__Order__Mirabelle_OProf)), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
% 177.76/23.19 = { by axiom 5 (fact_mem__def) R->L }
% 177.76/23.19 fresh292(fresh184(hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf, v_Q____)), true2, c_Arrow__Order__Mirabelle_OProf, v_Q____, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
% 177.76/23.19 = { by axiom 6 (fact_mem__def_1) R->L }
% 177.76/23.19 fresh292(fresh184(fresh183(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_Q____), c_Arrow__Order__Mirabelle_OProf)), true2, c_Arrow__Order__Mirabelle_OProf, v_Q____), true2, c_Arrow__Order__Mirabelle_OProf, v_Q____, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
% 177.76/23.19 = { by axiom 7 (fact__096Q_A_058_AProf_096) }
% 177.76/23.19 fresh292(fresh184(fresh183(true2, true2, c_Arrow__Order__Mirabelle_OProf, v_Q____), true2, c_Arrow__Order__Mirabelle_OProf, v_Q____, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
% 177.76/23.20 = { by axiom 1 (fact_mem__def_1) }
% 177.76/23.20 fresh292(fresh184(true2, true2, c_Arrow__Order__Mirabelle_OProf, v_Q____, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
% 177.76/23.20 = { by axiom 2 (fact_mem__def) }
% 177.76/23.20 fresh292(true2, true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
% 177.76/23.20 = { by axiom 3 (fact_funcset__mem) }
% 177.76/23.20 true2
% 177.76/23.20 % SZS output end Proof
% 177.76/23.20
% 177.76/23.20 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------