TSTP Solution File: COL116-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL116-1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n031.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 : Wed Aug 30 18:32:13 EDT 2023
% Result : Unsatisfiable 74.32s 9.93s
% Output : Proof 75.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COL116-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.35 % Computer : n031.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Sun Aug 27 04:52:08 EDT 2023
% 0.19/0.35 % CPUTime :
% 74.32/9.93 Command-line arguments: --no-flatten-goal
% 74.32/9.93
% 74.32/9.93 % SZS status Unsatisfiable
% 74.32/9.93
% 74.32/9.94 % SZS output start Proof
% 74.32/9.94 Take the following subset of the input axioms:
% 75.08/9.94 fof(cls_Comb_OI__contract__E_0, axiom, ![V_z]: ~c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 75.08/9.94 fof(cls_Comb_OK__contractE_0, axiom, ![V_r]: ~c_in(c_Pair(c_Comb_Ocomb_OK, V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 75.08/9.94 fof(cls_Comb_OS__contractE_0, axiom, ![V_r2]: ~c_in(c_Pair(c_Comb_Ocomb_OS, V_r2, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 75.08/9.94 fof(cls_Comb_Ocomb_Odistinct__3__iff1_0, axiom, ![V_comb1_H, V_comb2_H]: c_Comb_Ocomb_OK!=c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)).
% 75.08/9.94 fof(cls_Comb_Ocomb_Odistinct__4__iff1_0, axiom, ![V_comb1_H2, V_comb2_H2]: c_Comb_Ocomb_Oop_A_D_D(V_comb1_H2, V_comb2_H2)!=c_Comb_Ocomb_OK).
% 75.08/9.94 fof(cls_Comb_Ocomb_Odistinct__5__iff1_0, axiom, ![V_comb1_H2, V_comb2_H2]: c_Comb_Ocomb_OS!=c_Comb_Ocomb_Oop_A_D_D(V_comb1_H2, V_comb2_H2)).
% 75.08/9.94 fof(cls_Comb_Ocomb_Odistinct__6__iff1_0, axiom, ![V_comb1_H2, V_comb2_H2]: c_Comb_Ocomb_Oop_A_D_D(V_comb1_H2, V_comb2_H2)!=c_Comb_Ocomb_OS).
% 75.08/9.94 fof(cls_Comb_Oparcontract_Ointros__1_0, axiom, ![V_x]: c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 75.08/9.94 fof(cls_Datatype_Ooption_Odistinct__1__iff1_0, axiom, ![T_a, V_a_H]: c_Datatype_Ooption_ONone!=c_Datatype_Ooption_OSome(V_a_H, T_a)).
% 75.08/9.94 fof(cls_Datatype_Ooption_Odistinct__2__iff1_0, axiom, ![T_a2, V_a_H2]: c_Datatype_Ooption_OSome(V_a_H2, T_a2)!=c_Datatype_Ooption_ONone).
% 75.08/9.94 fof(cls_Datatype__Universe_OAtom__not__Scons__iff1_0, axiom, ![V_a, T_b, V_M, V_N, T_a2]: c_Datatype__Universe_OAtom(V_a, T_a2, T_b)!=c_Datatype__Universe_OScons(V_M, V_N, T_a2, T_b)).
% 75.08/9.94 fof(cls_Datatype__Universe_OIn0__not__In1__iff1_0, axiom, ![T_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OIn0(V_M2, T_a2, T_b2)!=c_Datatype__Universe_OIn1(V_N2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Datatype__Universe_OIn1__not__In0__iff1_0, axiom, ![T_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OIn1(V_N2, T_a2, T_b2)!=c_Datatype__Universe_OIn0(V_M2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Datatype__Universe_OLeaf__not__Numb__iff1_0, axiom, ![V_k, T_a2, V_a2, T_b2]: c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)!=c_Datatype__Universe_ONumb(V_k, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Datatype__Universe_OLeaf__not__Scons__iff1_0, axiom, ![T_a2, V_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)!=c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Datatype__Universe_ONumb__not__Leaf__iff1_0, axiom, ![T_a2, V_a2, T_b2, V_k2]: c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)!=c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Datatype__Universe_ONumb__not__Scons__iff1_0, axiom, ![T_a2, T_b2, V_M2, V_N2, V_k2]: c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)!=c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Datatype__Universe_OScons__not__Atom__iff1_0, axiom, ![T_a2, V_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_OAtom(V_a2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Datatype__Universe_OScons__not__Leaf__iff1_0, axiom, ![T_a2, V_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Datatype__Universe_OScons__not__Numb__iff1_0, axiom, ![T_a2, T_b2, V_M2, V_N2, V_k2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_List_ONil2__notin__lex__iff1_0, axiom, ![V_xs, V_r2, T_a2]: ~c_in(c_Pair(V_xs, c_List_Olist_ONil, tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olex(V_r2, T_a2), tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2)))).
% 75.08/9.94 fof(cls_List_ONil__notin__lex__iff1_0, axiom, ![V_ys, V_r2, T_a2]: ~c_in(c_Pair(c_List_Olist_ONil, V_ys, tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olex(V_r2, T_a2), tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2)))).
% 75.08/9.94 fof(cls_List_Olength__greater__0__conv__iff1_0, axiom, ![T_a2]: ~c_less(c_0, c_Nat_Osize(c_List_Olist_ONil, tc_List_Olist(T_a2)), tc_nat)).
% 75.08/9.94 fof(cls_List_Olist_Odistinct__1__iff1_0, axiom, ![V_list_H, T_a2, V_a_H2]: c_List_Olist_ONil!=c_List_Olist_OCons(V_a_H2, V_list_H, T_a2)).
% 75.08/9.94 fof(cls_List_Olist_Odistinct__2__iff1_0, axiom, ![T_a2, V_a_H2, V_list_H2]: c_List_Olist_OCons(V_a_H2, V_list_H2, T_a2)!=c_List_Olist_ONil).
% 75.08/9.94 fof(cls_Nat_OSuc__not__Zero__iff1_0, axiom, ![V_m]: c_Suc(V_m)!=c_0).
% 75.08/9.94 fof(cls_Nat_OZero__not__Suc__iff1_0, axiom, ![V_m2]: c_0!=c_Suc(V_m2)).
% 75.08/9.94 fof(cls_Nat_Oless__irrefl_0, axiom, ![V_n]: ~c_less(V_n, V_n, tc_nat)).
% 75.08/9.94 fof(cls_Nat_Onot__add__less1__iff1_0, axiom, ![V_i, V_j]: ~c_less(c_plus(V_i, V_j, tc_nat), V_i, tc_nat)).
% 75.08/9.94 fof(cls_Nat_Onot__add__less2__iff1_0, axiom, ![V_i2, V_j2]: ~c_less(c_plus(V_j2, V_i2, tc_nat), V_i2, tc_nat)).
% 75.08/9.94 fof(cls_Nat_Onot__less0__iff1_0, axiom, ![V_n2]: ~c_less(V_n2, c_0, tc_nat)).
% 75.08/9.94 fof(cls_Orderings_Oorder__less__irrefl__iff1_0, axiom, ![V_x2, T_a2]: (~class_Orderings_Oorder(T_a2) | ~c_less(V_x2, V_x2, T_a2))).
% 75.08/9.94 fof(cls_Set_OComplD__dest_0, axiom, ![V_A, V_c, T_a2]: (~c_in(V_c, V_A, T_a2) | ~c_in(V_c, c_uminus(V_A, tc_set(T_a2)), T_a2))).
% 75.08/9.94 fof(cls_Set_ODiffE_0, axiom, ![V_B, T_a2, V_A2, V_c2]: (~c_in(V_c2, V_B, T_a2) | ~c_in(V_c2, c_minus(V_A2, V_B, tc_set(T_a2)), T_a2))).
% 75.08/9.94 fof(cls_Set_OemptyE_0, axiom, ![T_a2, V_a2]: ~c_in(V_a2, c_emptyset, T_a2)).
% 75.08/9.94 fof(cls_Set_Onot__psubset__empty__iff1_0, axiom, ![T_a2, V_A2]: ~c_less(V_A2, c_emptyset, tc_set(T_a2))).
% 75.08/9.94 fof(cls_Set_OpsubsetE_0, axiom, ![T_a2, V_A2, V_B2]: (~c_less(V_A2, V_B2, tc_set(T_a2)) | ~c_lessequals(V_B2, V_A2, tc_set(T_a2)))).
% 75.08/9.94 fof(cls_Sum__Type_OInl__not__Inr__iff1_0, axiom, ![V_b, T_a2, V_a2, T_b2]: c_Sum__Type_OInl(V_a2, T_a2, T_b2)!=c_Sum__Type_OInr(V_b, T_b2, T_a2)).
% 75.08/9.94 fof(cls_Sum__Type_OInr__not__Inl__iff1_0, axiom, ![T_a2, V_a2, T_b2, V_b2]: c_Sum__Type_OInr(V_b2, T_b2, T_a2)!=c_Sum__Type_OInl(V_a2, T_a2, T_b2)).
% 75.08/9.94 fof(cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, axiom, ![V_y, V_r2, V_x2, T_a2]: (~c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)), T_a2) | ~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)))).
% 75.08/9.95 fof(cls_Wellfounded__Recursion_Owf__insert__iff1_1, axiom, ![V_r2, V_x2, V_y2, T_a2]: (~c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y2, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)), T_a2) | ~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)))).
% 75.08/9.95 fof(cls_conjecture_0, negated_conjecture, ![V_U]: ~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z)), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 75.08/9.95
% 75.08/9.95 Now clausify the problem and encode Horn clauses using encoding 3 of
% 75.08/9.95 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 75.08/9.95 We repeatedly replace C & s=t => u=v by the two clauses:
% 75.08/9.95 fresh(y, y, x1...xn) = u
% 75.08/9.95 C => fresh(s, t, x1...xn) = v
% 75.08/9.95 where fresh is a fresh function symbol and x1..xn are the free
% 75.08/9.95 variables of u and v.
% 75.08/9.95 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 75.08/9.95 input problem has no model of domain size 1).
% 75.08/9.95
% 75.08/9.95 The encoding turns the above axioms into the following unit equations and goals:
% 75.08/9.95
% 75.08/9.95 Axiom 1 (cls_Comb_Oparcontract_Ointros__1_0): c_in(c_Pair(X, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 75.08/9.95
% 75.08/9.95 Goal 1 (cls_conjecture_0): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z)), X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 75.08/9.95 The goal is true when:
% 75.08/9.95 X = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z))
% 75.08/9.95
% 75.08/9.95 Proof:
% 75.08/9.95 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 75.08/9.95 = { by axiom 1 (cls_Comb_Oparcontract_Ointros__1_0) }
% 75.08/9.95 true2
% 75.08/9.95 % SZS output end Proof
% 75.08/9.95
% 75.08/9.95 RESULT: Unsatisfiable (the axioms are contradictory).
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