TSTP Solution File: SCT002-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT002-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n032.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 14:21:52 EDT 2023
% Result : Unsatisfiable 23.57s 3.47s
% Output : Proof 23.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SCT002-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.29 % Computer : n032.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Thu Aug 24 16:29:57 EDT 2023
% 0.11/0.29 % CPUTime :
% 23.57/3.47 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 23.57/3.47
% 23.57/3.47 % SZS status Unsatisfiable
% 23.57/3.47
% 23.57/3.48 % SZS output start Proof
% 23.57/3.48 Take the following subset of the input axioms:
% 23.57/3.48 fof(cls_DiffE_1, axiom, ![V_A, T_a, V_B, V_c]: (~hBOOL(c_in(V_c, V_B, T_a)) | ~hBOOL(c_in(V_c, c_HOL_Ominus__class_Ominus(V_A, V_B, tc_fun(T_a, tc_bool)), T_a)))).
% 23.57/3.48 fof(cls_acyclic__def_0, axiom, ![V_x, V_r, T_a2]: (~hBOOL(c_in(c_Pair(V_x, V_x, T_a2, T_a2), c_Transitive__Closure_Otrancl(V_r, T_a2), tc_prod(T_a2, T_a2))) | ~c_Wellfounded_Oacyclic(V_r, T_a2))).
% 23.57/3.48 fof(cls_acyclic__insert_1, axiom, ![V_y, V_r2, T_a2, V_x2]: (~hBOOL(c_in(c_Pair(V_x2, V_y, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2))) | ~c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(V_y, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)), T_a2))).
% 23.57/3.48 fof(cls_bex__empty_0, axiom, ![V_P, T_a2, V_x2]: (~hBOOL(hAPP(V_P, V_x2)) | ~hBOOL(c_in(V_x2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2)))).
% 23.57/3.48 fof(cls_bot1E_0, axiom, ![T_a2, V_x2]: ~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), V_x2))).
% 23.57/3.48 fof(cls_bot2E_0, axiom, ![T_b, V_y2, T_a2, V_x2]: ~hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_fun(T_b, tc_bool))), V_x2), V_y2))).
% 23.57/3.48 fof(cls_conjecture_1, negated_conjecture, c_Relation_Otrans(v_L, tc_Arrow__Order__Mirabelle_Oalt)).
% 23.57/3.48 fof(cls_conjecture_2, negated_conjecture, ![V_x2]: ~hBOOL(c_in(c_Pair(V_x2, V_x2, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))).
% 23.57/3.48 fof(cls_conjecture_3, negated_conjecture, hBOOL(c_in(c_Pair(v_y, v_x, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))).
% 23.57/3.48 fof(cls_conjecture_4, negated_conjecture, hBOOL(c_in(c_Pair(v_x, v_y, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))).
% 23.57/3.48 fof(cls_disjoint__iff__not__equal_0, axiom, ![T_a2, V_x2, V_A2, V_B2]: (~hBOOL(c_in(V_x2, V_B2, T_a2)) | (~hBOOL(c_in(V_x2, V_A2, T_a2)) | c_Lattices_Olower__semilattice__class_Oinf(V_A2, V_B2, tc_fun(T_a2, tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool))))).
% 23.57/3.48 fof(cls_emptyE_0, axiom, ![V_a, T_a2]: ~hBOOL(c_in(V_a, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2))).
% 23.57/3.48 fof(cls_empty__iff_0, axiom, ![T_a2, V_c2]: ~hBOOL(c_in(V_c2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2))).
% 23.57/3.48 fof(cls_empty__not__insert_0, axiom, ![V_a2, T_a2, V_A2]: c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool))!=c_Set_Oinsert(V_a2, V_A2, T_a2)).
% 23.57/3.48 fof(cls_ex__in__conv_0, axiom, ![T_a2, V_x2]: ~hBOOL(c_in(V_x2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2))).
% 23.57/3.48 fof(cls_insert__not__empty_0, axiom, ![V_a2, T_a2, V_A2]: c_Set_Oinsert(V_a2, V_A2, T_a2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool))).
% 23.57/3.48 fof(cls_irrefl__def_0, axiom, ![V_r2, T_a2, V_x2]: (~hBOOL(c_in(c_Pair(V_x2, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2))) | ~c_Relation_Oirrefl(V_r2, T_a2))).
% 23.57/3.48 fof(cls_irrefl__tranclI_0, axiom, ![V_r2, T_a2, V_x2]: (c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r2, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_fun(tc_prod(T_a2, T_a2), tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a2, T_a2), tc_bool)) | ~hBOOL(c_in(c_Pair(V_x2, V_x2, T_a2, T_a2), c_Transitive__Closure_Otrancl(V_r2, T_a2), tc_prod(T_a2, T_a2))))).
% 23.57/3.48 fof(cls_transD_0, axiom, ![V_b, V_a2, V_r2, T_a2, V_c2]: (hBOOL(c_in(c_Pair(V_a2, V_c2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2))) | (~hBOOL(c_in(c_Pair(V_b, V_c2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2))) | (~hBOOL(c_in(c_Pair(V_a2, V_b, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2))) | ~c_Relation_Otrans(V_r2, T_a2))))).
% 23.57/3.48 fof(cls_wfE__min_1, axiom, ![V_R, V_Q, V_y2, T_a2, V_x2]: (~hBOOL(c_in(V_y2, V_Q, T_a2)) | (~hBOOL(c_in(c_Pair(V_y2, c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(V_Q, V_R, T_a2), T_a2, T_a2), V_R, tc_prod(T_a2, T_a2))) | (~hBOOL(c_in(V_x2, V_Q, T_a2)) | ~c_Wellfounded_Owf(V_R, T_a2))))).
% 23.57/3.48 fof(cls_wf__asym_0, axiom, ![V_a2, V_r2, T_a2, V_x2]: (~hBOOL(c_in(c_Pair(V_x2, V_a2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2))) | (~hBOOL(c_in(c_Pair(V_a2, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2))) | ~c_Wellfounded_Owf(V_r2, T_a2)))).
% 23.57/3.48 fof(cls_wf__eq__minimal_1, axiom, ![V_xa, V_r2, V_y2, T_a2, V_Q2]: (~hBOOL(c_in(V_y2, V_Q2, T_a2)) | (~hBOOL(c_in(c_Pair(V_y2, c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(V_Q2, V_r2, T_a2), T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2))) | (~hBOOL(c_in(V_xa, V_Q2, T_a2)) | ~c_Wellfounded_Owf(V_r2, T_a2))))).
% 23.57/3.48 fof(cls_wf__insert_1, axiom, ![V_r2, V_y2, T_a2, V_x2]: (~hBOOL(c_in(c_Pair(V_x2, V_y2, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2))) | ~c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(V_y2, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)), T_a2))).
% 23.57/3.48 fof(cls_wf__irrefl_0, axiom, ![V_a2, V_r2, T_a2]: (~hBOOL(c_in(c_Pair(V_a2, V_a2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2))) | ~c_Wellfounded_Owf(V_r2, T_a2))).
% 23.57/3.48
% 23.57/3.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 23.57/3.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 23.57/3.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 23.57/3.48 fresh(y, y, x1...xn) = u
% 23.57/3.48 C => fresh(s, t, x1...xn) = v
% 23.57/3.48 where fresh is a fresh function symbol and x1..xn are the free
% 23.57/3.48 variables of u and v.
% 23.57/3.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 23.57/3.48 input problem has no model of domain size 1).
% 23.57/3.48
% 23.57/3.48 The encoding turns the above axioms into the following unit equations and goals:
% 23.57/3.48
% 23.57/3.48 Axiom 1 (cls_conjecture_1): c_Relation_Otrans(v_L, tc_Arrow__Order__Mirabelle_Oalt) = true2.
% 23.57/3.48 Axiom 2 (cls_transD_0): fresh471(X, X, Y, Z, W, V) = true2.
% 23.57/3.48 Axiom 3 (cls_transD_0): fresh111(X, X, Y, Z, W, V, U) = hBOOL(c_in(c_Pair(Y, Z, W, W), V, tc_prod(W, W))).
% 23.57/3.48 Axiom 4 (cls_conjecture_4): hBOOL(c_in(c_Pair(v_x, v_y, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) = true2.
% 23.57/3.48 Axiom 5 (cls_conjecture_3): hBOOL(c_in(c_Pair(v_y, v_x, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) = true2.
% 23.57/3.48 Axiom 6 (cls_transD_0): fresh470(X, X, Y, Z, W, V, U) = fresh471(hBOOL(c_in(c_Pair(Y, U, W, W), V, tc_prod(W, W))), true2, Y, Z, W, V).
% 23.57/3.48 Axiom 7 (cls_transD_0): fresh470(c_Relation_Otrans(X, Y), true2, Z, W, Y, X, V) = fresh111(hBOOL(c_in(c_Pair(V, W, Y, Y), X, tc_prod(Y, Y))), true2, Z, W, Y, X, V).
% 23.57/3.48
% 23.57/3.48 Goal 1 (cls_conjecture_2): hBOOL(c_in(c_Pair(X, X, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) = true2.
% 23.57/3.48 The goal is true when:
% 23.57/3.48 X = v_y
% 23.57/3.48
% 23.57/3.48 Proof:
% 23.57/3.48 hBOOL(c_in(c_Pair(v_y, v_y, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))
% 23.57/3.48 = { by axiom 3 (cls_transD_0) R->L }
% 23.57/3.48 fresh111(true2, true2, v_y, v_y, tc_Arrow__Order__Mirabelle_Oalt, v_L, v_x)
% 23.57/3.48 = { by axiom 4 (cls_conjecture_4) R->L }
% 23.57/3.48 fresh111(hBOOL(c_in(c_Pair(v_x, v_y, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))), true2, v_y, v_y, tc_Arrow__Order__Mirabelle_Oalt, v_L, v_x)
% 23.57/3.48 = { by axiom 7 (cls_transD_0) R->L }
% 23.57/3.48 fresh470(c_Relation_Otrans(v_L, tc_Arrow__Order__Mirabelle_Oalt), true2, v_y, v_y, tc_Arrow__Order__Mirabelle_Oalt, v_L, v_x)
% 23.57/3.48 = { by axiom 1 (cls_conjecture_1) }
% 23.57/3.48 fresh470(true2, true2, v_y, v_y, tc_Arrow__Order__Mirabelle_Oalt, v_L, v_x)
% 23.57/3.48 = { by axiom 6 (cls_transD_0) }
% 23.57/3.48 fresh471(hBOOL(c_in(c_Pair(v_y, v_x, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))), true2, v_y, v_y, tc_Arrow__Order__Mirabelle_Oalt, v_L)
% 23.57/3.48 = { by axiom 5 (cls_conjecture_3) }
% 23.57/3.48 fresh471(true2, true2, v_y, v_y, tc_Arrow__Order__Mirabelle_Oalt, v_L)
% 23.57/3.48 = { by axiom 2 (cls_transD_0) }
% 23.57/3.48 true2
% 23.57/3.48 % SZS output end Proof
% 23.57/3.48
% 23.57/3.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------