TSTP Solution File: SCT074-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT074-1 : 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 : n014.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 14:22:03 EDT 2023
% Result : Unsatisfiable 20.07s 3.00s
% Output : Proof 20.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT074-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 16:16:33 EDT 2023
% 0.16/0.34 % CPUTime :
% 20.07/3.00 Command-line arguments: --no-flatten-goal
% 20.07/3.00
% 20.07/3.00 % SZS status Unsatisfiable
% 20.07/3.00
% 20.07/3.01 % SZS output start Proof
% 20.07/3.01 Take the following subset of the input axioms:
% 20.07/3.01 fof(cls_CHAINED_0, axiom, c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))).
% 20.07/3.01 fof(cls_CHAINED_0_01, axiom, c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 20.07/3.01 fof(cls_DiffE_1, axiom, ![T_a, V_A, V_B, V_c]: (~c_in(V_c, V_B, T_a) | ~c_in(V_c, c_HOL_Ominus__class_Ominus(V_A, V_B, tc_fun(T_a, tc_bool)), T_a))).
% 20.07/3.01 fof(cls_Lin__irrefl_0, axiom, ![V_a, V_b, V_L]: (~c_in(c_Pair(V_b, V_a, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(V_a, V_b, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_L, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | ~c_in(V_L, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))))).
% 20.07/3.01 fof(cls_acyclic__def_0, axiom, ![V_r, V_x, T_a2]: (~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))).
% 20.07/3.01 fof(cls_acyclic__insert_1, axiom, ![V_y, V_r2, T_a2, V_x2]: (~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))).
% 20.07/3.01 fof(cls_bex__empty_0, axiom, ![V_P, T_a2, V_x2]: (~hBOOL(hAPP(V_P, V_x2)) | ~c_in(V_x2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2))).
% 20.07/3.01 fof(cls_bot1E_0, axiom, ![T_a2, V_x2]: ~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), V_x2))).
% 20.07/3.01 fof(cls_conjecture_0, negated_conjecture, c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 20.07/3.01 fof(cls_disjoint__iff__not__equal_0, axiom, ![T_a2, V_x2, V_A2, V_B2]: (~c_in(V_x2, V_B2, T_a2) | (~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))))).
% 20.07/3.01 fof(cls_emptyE_0, axiom, ![V_a2, T_a2]: ~c_in(V_a2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2)).
% 20.07/3.01 fof(cls_empty__iff_0, axiom, ![T_a2, V_c2]: ~c_in(V_c2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2)).
% 20.07/3.01 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)).
% 20.07/3.01 fof(cls_ex__in__conv_0, axiom, ![T_a2, V_x2]: ~c_in(V_x2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), T_a2)).
% 20.07/3.01 fof(cls_in__mkbot_0, axiom, ![V_xa, V_x2, V_L2]: ~c_in(c_Pair(V_xa, V_x2, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Arrow__Order__Mirabelle_Omkbot(V_L2, V_x2), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 20.07/3.01 fof(cls_in__mkbot_1, axiom, ![V_x2, V_L2]: ~c_in(c_Pair(V_x2, V_x2, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Arrow__Order__Mirabelle_Omkbot(V_L2, V_x2), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 20.07/3.01 fof(cls_in__mktop_0, axiom, ![V_y2, V_x2, V_L2]: ~c_in(c_Pair(V_x2, V_y2, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Arrow__Order__Mirabelle_Omktop(V_L2, V_x2), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 20.07/3.01 fof(cls_in__mktop_1, axiom, ![V_x2, V_L2]: ~c_in(c_Pair(V_x2, V_x2, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Arrow__Order__Mirabelle_Omktop(V_L2, V_x2), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 20.07/3.01 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))).
% 20.07/3.01 fof(cls_irrefl__def_0, axiom, ![V_r2, T_a2, V_x2]: (~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))).
% 20.07/3.01 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)) | ~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)))).
% 20.07/3.01 fof(cls_wfE__min_1, axiom, ![V_R, V_Q, V_y2, T_a2, V_x2]: (~c_in(V_y2, V_Q, T_a2) | (~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)) | (~c_in(V_x2, V_Q, T_a2) | ~c_Wellfounded_Owf(V_R, T_a2))))).
% 20.07/3.01 fof(cls_wf__asym_0, axiom, ![V_a2, V_r2, T_a2, V_x2]: (~c_in(c_Pair(V_x2, V_a2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)) | (~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)))).
% 20.07/3.01 fof(cls_wf__eq__minimal_1, axiom, ![V_r2, V_y2, T_a2, V_Q2, V_xa2]: (~c_in(V_y2, V_Q2, T_a2) | (~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)) | (~c_in(V_xa2, V_Q2, T_a2) | ~c_Wellfounded_Owf(V_r2, T_a2))))).
% 20.07/3.01 fof(cls_wf__insert_1, axiom, ![V_r2, V_y2, T_a2, V_x2]: (~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))).
% 20.07/3.01 fof(cls_wf__irrefl_0, axiom, ![V_a2, V_r2, T_a2]: (~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))).
% 20.07/3.01
% 20.07/3.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 20.07/3.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 20.07/3.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 20.07/3.01 fresh(y, y, x1...xn) = u
% 20.07/3.01 C => fresh(s, t, x1...xn) = v
% 20.07/3.01 where fresh is a fresh function symbol and x1..xn are the free
% 20.07/3.01 variables of u and v.
% 20.07/3.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 20.07/3.01 input problem has no model of domain size 1).
% 20.07/3.01
% 20.07/3.01 The encoding turns the above axioms into the following unit equations and goals:
% 20.07/3.01
% 20.07/3.01 Axiom 1 (cls_CHAINED_0): c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)) = true2.
% 20.07/3.01 Axiom 2 (cls_subset__equiv__class_0): fresh530(X, X, Y, Z, W, V) = c_in(c_Pair(Y, Z, W, W), V, tc_prod(W, W)).
% 20.07/3.01 Axiom 3 (cls_eq__equiv__class__iff2_0): fresh587(X, X, Y, Z, W, V) = c_in(c_Pair(Y, V, Z, Z), W, tc_prod(Z, Z)).
% 20.07/3.01 Axiom 4 (cls_CHAINED_0_01): c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) = true2.
% 20.07/3.01 Axiom 5 (cls_conjecture_0): c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) = true2.
% 20.07/3.01
% 20.07/3.01 Lemma 6: fresh530(X, X, Y, Z, W, V) = fresh587(U, U, Y, W, V, Z).
% 20.07/3.01 Proof:
% 20.07/3.01 fresh530(X, X, Y, Z, W, V)
% 20.07/3.01 = { by axiom 2 (cls_subset__equiv__class_0) }
% 20.07/3.01 c_in(c_Pair(Y, Z, W, W), V, tc_prod(W, W))
% 20.07/3.01 = { by axiom 3 (cls_eq__equiv__class__iff2_0) R->L }
% 20.07/3.02 fresh587(U, U, Y, W, V, Z)
% 20.07/3.02
% 20.07/3.02 Goal 1 (cls_Lin__irrefl_0): tuple2(c_in(X, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_in(c_Pair(Y, Z, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), X, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_in(c_Pair(Z, Y, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), X, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) = tuple2(true2, true2, true2).
% 20.07/3.02 The goal is true when:
% 20.07/3.02 X = v_Lab____
% 20.07/3.02 Y = v_a____
% 20.07/3.02 Z = v_b____
% 20.07/3.02
% 20.07/3.02 Proof:
% 20.07/3.02 tuple2(c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))
% 20.07/3.02 = { by axiom 2 (cls_subset__equiv__class_0) R->L }
% 20.07/3.02 tuple2(c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), fresh530(U, U, v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____), c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))
% 20.07/3.02 = { by lemma 6 }
% 20.07/3.02 tuple2(c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), fresh587(W, W, v_a____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____, v_b____), c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))
% 20.07/3.02 = { by axiom 2 (cls_subset__equiv__class_0) R->L }
% 20.07/3.02 tuple2(c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), fresh587(W, W, v_a____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____, v_b____), fresh530(V, V, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____))
% 20.07/3.02 = { by lemma 6 }
% 20.07/3.02 tuple2(c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), fresh587(W, W, v_a____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____, v_b____), fresh587(Y, Y, v_b____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____, v_a____))
% 20.07/3.02 = { by lemma 6 R->L }
% 20.07/3.02 tuple2(c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), fresh530(Z, Z, v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____), fresh587(Y, Y, v_b____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____, v_a____))
% 20.07/3.02 = { by axiom 2 (cls_subset__equiv__class_0) }
% 20.07/3.02 tuple2(c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), fresh587(Y, Y, v_b____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____, v_a____))
% 20.07/3.02 = { by axiom 4 (cls_CHAINED_0_01) }
% 20.07/3.02 tuple2(c_in(v_Lab____, c_Arrow__Order__Mirabelle_OLin, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), true2, fresh587(Y, Y, v_b____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____, v_a____))
% 20.07/3.02 = { by axiom 1 (cls_CHAINED_0) }
% 20.07/3.02 tuple2(true2, true2, fresh587(Y, Y, v_b____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____, v_a____))
% 20.07/3.02 = { by lemma 6 R->L }
% 20.07/3.02 tuple2(true2, true2, fresh530(X, X, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, v_Lab____))
% 20.07/3.02 = { by axiom 2 (cls_subset__equiv__class_0) }
% 20.07/3.02 tuple2(true2, true2, c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_Lab____, tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))
% 20.07/3.02 = { by axiom 5 (cls_conjecture_0) }
% 20.07/3.02 tuple2(true2, true2, true2)
% 20.07/3.02 % SZS output end Proof
% 20.07/3.02
% 20.07/3.02 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------