TSTP Solution File: COL104-2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL104-2 : 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 : n007.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 18:32:09 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL104-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 05:03:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Take the following subset of the input axioms:
% 0.19/0.40 fof(cls_Comb_Ocontract_OAp2_0, axiom, ![V_x, V_y, V_z]: (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_z, V_x), c_Comb_Ocomb_Oop_A_D_D(V_z, V_y), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))).
% 0.19/0.40 fof(cls_Transitive__Closure_Or__into__rtrancl_0, axiom, ![V_p, V_r, T_a]: (~c_in(V_p, V_r, tc_prod(T_a, T_a)) | c_in(V_p, c_Transitive__Closure_Ortrancl(V_r, T_a), tc_prod(T_a, T_a)))).
% 0.19/0.41 fof(cls_Transitive__Closure_Ortrancl__trans_0, axiom, ![V_b, V_c, V_a, V_r2, T_a2]: (~c_in(c_Pair(V_b, V_c, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)) | (~c_in(c_Pair(V_a, V_b, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)) | c_in(c_Pair(V_a, V_c, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2))))).
% 0.19/0.41 fof(cls_conjecture_1, negated_conjecture, c_in(c_Pair(v_y, v_za, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.19/0.41 fof(cls_conjecture_2, negated_conjecture, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.19/0.41 fof(cls_conjecture_3, negated_conjecture, ~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.19/0.41
% 0.19/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.41 fresh(y, y, x1...xn) = u
% 0.19/0.41 C => fresh(s, t, x1...xn) = v
% 0.19/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.41 variables of u and v.
% 0.19/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.41 input problem has no model of domain size 1).
% 0.19/0.41
% 0.19/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.41
% 0.19/0.41 Axiom 1 (cls_Transitive__Closure_Or__into__rtrancl_0): fresh4(X, X, Y, Z, W) = true.
% 0.19/0.41 Axiom 2 (cls_Comb_Ocontract_OAp2_0): fresh3(X, X, Y, Z, W) = true.
% 0.19/0.41 Axiom 3 (cls_Transitive__Closure_Ortrancl__trans_0): fresh(X, X, Y, Z, W, V) = true.
% 0.19/0.41 Axiom 4 (cls_conjecture_1): c_in(c_Pair(v_y, v_za, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.19/0.41 Axiom 5 (cls_Transitive__Closure_Or__into__rtrancl_0): fresh4(c_in(X, Y, tc_prod(Z, Z)), true, X, Y, Z) = c_in(X, c_Transitive__Closure_Ortrancl(Y, Z), tc_prod(Z, Z)).
% 0.19/0.41 Axiom 6 (cls_Transitive__Closure_Ortrancl__trans_0): fresh2(X, X, Y, Z, W, V, U) = c_in(c_Pair(U, Z, W, W), c_Transitive__Closure_Ortrancl(V, W), tc_prod(W, W)).
% 0.19/0.41 Axiom 7 (cls_Comb_Ocontract_OAp2_0): fresh3(c_in(c_Pair(X, Y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, X, Y, Z) = c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(Z, X), c_Comb_Ocomb_Oop_A_D_D(Z, Y), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)).
% 0.19/0.41 Axiom 8 (cls_conjecture_2): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.19/0.41 Axiom 9 (cls_Transitive__Closure_Ortrancl__trans_0): fresh2(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true, Y, V, Z, W, X) = fresh(c_in(c_Pair(Y, V, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true, V, Z, W, X).
% 0.19/0.41
% 0.19/0.41 Goal 1 (cls_conjecture_3): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.19/0.41 Proof:
% 0.19/0.41 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.19/0.41 = { by axiom 6 (cls_Transitive__Closure_Ortrancl__trans_0) R->L }
% 0.19/0.41 fresh2(true, true, c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, c_Comb_Ocontract, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x))
% 0.19/0.41 = { by axiom 8 (cls_conjecture_2) R->L }
% 0.19/0.41 fresh2(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, c_Comb_Ocontract, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x))
% 0.19/0.41 = { by axiom 9 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.19/0.41 fresh(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, c_Comb_Ocontract, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x))
% 0.19/0.41 = { by axiom 5 (cls_Transitive__Closure_Or__into__rtrancl_0) R->L }
% 0.19/0.41 fresh(fresh4(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_Comb_Ocomb), true, c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, c_Comb_Ocontract, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x))
% 0.19/0.41 = { by axiom 7 (cls_Comb_Ocontract_OAp2_0) R->L }
% 0.19/0.41 fresh(fresh4(fresh3(c_in(c_Pair(v_y, v_za, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, v_y, v_za, v_z), true, c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_Comb_Ocomb), true, c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, c_Comb_Ocontract, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x))
% 0.19/0.41 = { by axiom 4 (cls_conjecture_1) }
% 0.19/0.41 fresh(fresh4(fresh3(true, true, v_y, v_za, v_z), true, c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_Comb_Ocomb), true, c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, c_Comb_Ocontract, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x))
% 0.19/0.41 = { by axiom 2 (cls_Comb_Ocontract_OAp2_0) }
% 0.19/0.41 fresh(fresh4(true, true, c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_y), c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_Comb_Ocomb), true, c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, c_Comb_Ocontract, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x))
% 0.19/0.41 = { by axiom 1 (cls_Transitive__Closure_Or__into__rtrancl_0) }
% 0.19/0.41 fresh(true, true, c_Comb_Ocomb_Oop_A_D_D(v_z, v_za), tc_Comb_Ocomb, c_Comb_Ocontract, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x))
% 0.19/0.41 = { by axiom 3 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.19/0.41 true
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------