TSTP Solution File: COL123-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL123-2 : 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 : n025.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 18:32:16 EDT 2023
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL123-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sun Aug 27 04:47:53 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.21/0.46 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.46
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 Take the following subset of the input axioms:
% 0.21/0.47 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)))).
% 0.21/0.47 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))))).
% 0.21/0.48 fof(cls_conjecture_1, negated_conjecture, c_in(c_Pair(v_y, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a))).
% 0.21/0.48 fof(cls_conjecture_2, negated_conjecture, c_in(c_Pair(v_x, v_xb, t_a, t_a), v_r, tc_prod(t_a, t_a))).
% 0.21/0.48 fof(cls_conjecture_3, negated_conjecture, ![V_U]: (c_in(c_Pair(V_U, v_xaa(V_U), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) | ~c_in(c_Pair(v_x, V_U, t_a, t_a), v_r, tc_prod(t_a, t_a)))).
% 0.21/0.48 fof(cls_conjecture_4, negated_conjecture, ![V_U2]: (c_in(c_Pair(v_y, v_xaa(V_U2), t_a, t_a), v_r, tc_prod(t_a, t_a)) | ~c_in(c_Pair(v_x, V_U2, t_a, t_a), v_r, tc_prod(t_a, t_a)))).
% 0.21/0.48 fof(cls_conjecture_5, negated_conjecture, ![V_U2]: (~c_in(c_Pair(v_z, V_U2, t_a, t_a), v_r, tc_prod(t_a, t_a)) | ~c_in(c_Pair(v_xb, V_U2, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)))).
% 0.21/0.48 fof(cls_conjecture_6, negated_conjecture, ![V_V, V_W, V_U2]: (c_in(c_Pair(V_V, v_xa(V_U2, V_V, V_W), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(c_Pair(V_U2, V_W, t_a, t_a), v_r, tc_prod(t_a, t_a)) | ~c_in(c_Pair(V_U2, V_V, t_a, t_a), v_r, tc_prod(t_a, t_a))))).
% 0.21/0.48 fof(cls_conjecture_7, negated_conjecture, ![V_U2, V_V2, V_W2]: (c_in(c_Pair(V_W2, v_xa(V_U2, V_V2, V_W2), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(c_Pair(V_U2, V_W2, t_a, t_a), v_r, tc_prod(t_a, t_a)) | ~c_in(c_Pair(V_U2, V_V2, t_a, t_a), v_r, tc_prod(t_a, t_a))))).
% 0.21/0.48
% 0.21/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.48 fresh(y, y, x1...xn) = u
% 0.21/0.48 C => fresh(s, t, x1...xn) = v
% 0.21/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.48 variables of u and v.
% 0.21/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.48 input problem has no model of domain size 1).
% 0.21/0.48
% 0.21/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.48
% 0.21/0.48 Axiom 1 (cls_conjecture_3): fresh6(X, X, Y) = true2.
% 0.21/0.48 Axiom 2 (cls_conjecture_4): fresh5(X, X, Y) = true2.
% 0.21/0.48 Axiom 3 (cls_conjecture_7): fresh(X, X, Y, Z, W) = true2.
% 0.21/0.48 Axiom 4 (cls_Transitive__Closure_Or__into__rtrancl_0): fresh8(X, X, Y, Z, W) = true2.
% 0.21/0.48 Axiom 5 (cls_conjecture_6): fresh3(X, X, Y, Z, W) = true2.
% 0.21/0.48 Axiom 6 (cls_Transitive__Closure_Ortrancl__trans_0): fresh7(X, X, Y, Z, W, V) = true2.
% 0.21/0.48 Axiom 7 (cls_conjecture_2): c_in(c_Pair(v_x, v_xb, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true2.
% 0.21/0.48 Axiom 8 (cls_conjecture_1): c_in(c_Pair(v_y, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true2.
% 0.21/0.48 Axiom 9 (cls_Transitive__Closure_Or__into__rtrancl_0): fresh8(c_in(X, Y, tc_prod(Z, Z)), true2, X, Y, Z) = c_in(X, c_Transitive__Closure_Ortrancl(Y, Z), tc_prod(Z, Z)).
% 0.21/0.48 Axiom 10 (cls_Transitive__Closure_Ortrancl__trans_0): fresh9(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)).
% 0.21/0.48 Axiom 11 (cls_conjecture_6): fresh4(X, X, Y, Z, W) = c_in(c_Pair(Y, v_xa(Z, Y, W), t_a, t_a), v_r, tc_prod(t_a, t_a)).
% 0.21/0.48 Axiom 12 (cls_conjecture_7): fresh2(X, X, Y, Z, W) = c_in(c_Pair(Y, v_xa(Z, W, Y), t_a, t_a), v_r, tc_prod(t_a, t_a)).
% 0.21/0.48 Axiom 13 (cls_conjecture_3): fresh6(c_in(c_Pair(v_x, X, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, X) = c_in(c_Pair(X, v_xaa(X), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)).
% 0.21/0.48 Axiom 14 (cls_conjecture_4): fresh5(c_in(c_Pair(v_x, X, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, X) = c_in(c_Pair(v_y, v_xaa(X), t_a, t_a), v_r, tc_prod(t_a, t_a)).
% 0.21/0.48 Axiom 15 (cls_conjecture_6): fresh4(c_in(c_Pair(X, Y, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, Z, X, Y) = fresh3(c_in(c_Pair(X, Z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, Z, X, Y).
% 0.21/0.48 Axiom 16 (cls_conjecture_7): fresh2(c_in(c_Pair(X, Y, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, Z, X, Y) = fresh(c_in(c_Pair(X, Z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, Z, X, Y).
% 0.21/0.48 Axiom 17 (cls_Transitive__Closure_Ortrancl__trans_0): fresh9(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true2, Y, V, Z, W, X) = fresh7(c_in(c_Pair(Y, V, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true2, V, Z, W, X).
% 0.21/0.48
% 0.21/0.48 Lemma 18: c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)) = true2.
% 0.21/0.48 Proof:
% 0.21/0.48 c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a))
% 0.21/0.48 = { by axiom 14 (cls_conjecture_4) R->L }
% 0.21/0.48 fresh5(c_in(c_Pair(v_x, v_xb, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, v_xb)
% 0.21/0.48 = { by axiom 7 (cls_conjecture_2) }
% 0.21/0.48 fresh5(true2, true2, v_xb)
% 0.21/0.48 = { by axiom 2 (cls_conjecture_4) }
% 0.21/0.48 true2
% 0.21/0.48
% 0.21/0.48 Goal 1 (cls_conjecture_5): tuple(c_in(c_Pair(v_z, X, t_a, t_a), v_r, tc_prod(t_a, t_a)), c_in(c_Pair(v_xb, X, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a))) = tuple(true2, true2).
% 0.21/0.48 The goal is true when:
% 0.21/0.48 X = v_xa(v_y, v_z, v_xaa(v_xb))
% 0.21/0.48
% 0.21/0.48 Proof:
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)))
% 0.21/0.48 = { by axiom 10 (cls_Transitive__Closure_Ortrancl__trans_0) R->L }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh9(true2, true2, v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 1 (cls_conjecture_3) R->L }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh9(fresh6(true2, true2, v_xb), true2, v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 7 (cls_conjecture_2) R->L }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh9(fresh6(c_in(c_Pair(v_x, v_xb, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, v_xb), true2, v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 13 (cls_conjecture_3) }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh9(c_in(c_Pair(v_xb, v_xaa(v_xb), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 17 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh7(c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true2, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 9 (cls_Transitive__Closure_Or__into__rtrancl_0) R->L }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh7(fresh8(c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, t_a), true2, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 12 (cls_conjecture_7) R->L }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh7(fresh8(fresh2(true2, true2, v_xaa(v_xb), v_y, v_z), true2, c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, t_a), true2, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 8 (cls_conjecture_1) R->L }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh7(fresh8(fresh2(c_in(c_Pair(v_y, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, v_xaa(v_xb), v_y, v_z), true2, c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, t_a), true2, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 16 (cls_conjecture_7) }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh7(fresh8(fresh(c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, v_xaa(v_xb), v_y, v_z), true2, c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, t_a), true2, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by lemma 18 }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh7(fresh8(fresh(true2, true2, v_xaa(v_xb), v_y, v_z), true2, c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, t_a), true2, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 3 (cls_conjecture_7) }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh7(fresh8(true2, true2, c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, t_a), true2, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 4 (cls_Transitive__Closure_Or__into__rtrancl_0) }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), fresh7(true2, true2, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, v_r, v_xb))
% 0.21/0.48 = { by axiom 6 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.21/0.48 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true2)
% 0.21/0.48 = { by axiom 11 (cls_conjecture_6) R->L }
% 0.21/0.48 tuple(fresh4(true2, true2, v_z, v_y, v_xaa(v_xb)), true2)
% 0.21/0.48 = { by lemma 18 R->L }
% 0.21/0.48 tuple(fresh4(c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, v_z, v_y, v_xaa(v_xb)), true2)
% 0.21/0.48 = { by axiom 15 (cls_conjecture_6) }
% 0.21/0.48 tuple(fresh3(c_in(c_Pair(v_y, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true2, v_z, v_y, v_xaa(v_xb)), true2)
% 0.21/0.48 = { by axiom 8 (cls_conjecture_1) }
% 0.21/0.48 tuple(fresh3(true2, true2, v_z, v_y, v_xaa(v_xb)), true2)
% 0.21/0.48 = { by axiom 5 (cls_conjecture_6) }
% 0.21/0.48 tuple(true2, true2)
% 0.21/0.48 % SZS output end Proof
% 0.21/0.48
% 0.21/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------