TSTP Solution File: COL109-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL109-2 : 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 : 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 : Wed Aug 30 18:32:11 EDT 2023
% Result : Unsatisfiable 31.21s 4.39s
% Output : Proof 31.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL109-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 03:59:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 31.21/4.39 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 31.21/4.39
% 31.21/4.39 % SZS status Unsatisfiable
% 31.21/4.39
% 31.21/4.40 % SZS output start Proof
% 31.21/4.40 Take the following subset of the input axioms:
% 31.21/4.40 fof(cls_Comb_Oparcontract_Ointros__3_0, axiom, ![V_x, V_y, V_z]: c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, V_x), V_y), V_z), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_z)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 31.21/4.40 fof(cls_Comb_Oparcontract_Ointros__4_0, axiom, ![V_w, V_x2, V_y2, V_z2]: (~c_in(c_Pair(V_z2, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x2, V_y2, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x2, V_z2), c_Comb_Ocomb_Oop_A_D_D(V_y2, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))).
% 31.21/4.40 fof(cls_conjecture_0, negated_conjecture, c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 31.21/4.40 fof(cls_conjecture_1, negated_conjecture, c_in(c_Pair(v_xb, v_x_H, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 31.21/4.40 fof(cls_conjecture_2, negated_conjecture, c_in(c_Pair(v_yb, v_y_Ha, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 31.21/4.40 fof(cls_conjecture_3, 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)) | ~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))).
% 31.21/4.40
% 31.21/4.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 31.21/4.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 31.21/4.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 31.21/4.40 fresh(y, y, x1...xn) = u
% 31.21/4.40 C => fresh(s, t, x1...xn) = v
% 31.21/4.40 where fresh is a fresh function symbol and x1..xn are the free
% 31.21/4.40 variables of u and v.
% 31.21/4.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 31.21/4.40 input problem has no model of domain size 1).
% 31.21/4.40
% 31.21/4.40 The encoding turns the above axioms into the following unit equations and goals:
% 31.21/4.40
% 31.21/4.40 Axiom 1 (cls_Comb_Oparcontract_Ointros__4_0): fresh2(X, X, Y, Z, W, V) = true2.
% 31.21/4.40 Axiom 2 (cls_conjecture_0): c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 31.21/4.40 Axiom 3 (cls_conjecture_1): c_in(c_Pair(v_xb, v_x_H, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 31.21/4.40 Axiom 4 (cls_conjecture_2): c_in(c_Pair(v_yb, v_y_Ha, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 31.21/4.40 Axiom 5 (cls_Comb_Oparcontract_Ointros__4_0): fresh(X, X, Y, Z, W, V) = c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(W, Y), c_Comb_Ocomb_Oop_A_D_D(V, Z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)).
% 31.21/4.40 Axiom 6 (cls_Comb_Oparcontract_Ointros__4_0): fresh(c_in(c_Pair(X, Y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, Z, W, X, Y) = fresh2(c_in(c_Pair(Z, W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, Z, W, X, Y).
% 31.21/4.40 Axiom 7 (cls_Comb_Oparcontract_Ointros__3_0): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, X), Y), Z), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(X, Z), c_Comb_Ocomb_Oop_A_D_D(Y, Z)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 31.21/4.40
% 31.21/4.40 Lemma 8: fresh(c_in(c_Pair(X, Y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_z, v_w, X, Y) = true2.
% 31.21/4.40 Proof:
% 31.21/4.40 fresh(c_in(c_Pair(X, Y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_z, v_w, X, Y)
% 31.21/4.40 = { by axiom 6 (cls_Comb_Oparcontract_Ointros__4_0) }
% 31.21/4.40 fresh2(c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_z, v_w, X, Y)
% 31.21/4.40 = { by axiom 2 (cls_conjecture_0) }
% 31.21/4.40 fresh2(true2, true2, v_z, v_w, X, Y)
% 31.21/4.40 = { by axiom 1 (cls_Comb_Oparcontract_Ointros__4_0) }
% 31.21/4.40 true2
% 31.21/4.40
% 31.21/4.40 Goal 1 (cls_conjecture_3): tuple(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)), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) = tuple(true2, true2).
% 31.21/4.40 The goal is true when:
% 31.21/4.40 X = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w))
% 31.21/4.40
% 31.21/4.40 Proof:
% 31.21/4.40 tuple(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_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 31.21/4.40 = { by axiom 5 (cls_Comb_Oparcontract_Ointros__4_0) R->L }
% 31.21/4.40 tuple(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_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by axiom 5 (cls_Comb_Oparcontract_Ointros__4_0) R->L }
% 31.21/4.40 tuple(fresh(true2, true2, c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by lemma 8 R->L }
% 31.21/4.40 tuple(fresh(fresh(c_in(c_Pair(v_xb, v_x_H, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_z, v_w, v_xb, v_x_H), true2, c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by axiom 3 (cls_conjecture_1) }
% 31.21/4.40 tuple(fresh(fresh(true2, true2, v_z, v_w, v_xb, v_x_H), true2, c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by axiom 5 (cls_Comb_Oparcontract_Ointros__4_0) }
% 31.21/4.40 tuple(fresh(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by axiom 6 (cls_Comb_Oparcontract_Ointros__4_0) }
% 31.21/4.40 tuple(fresh2(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by axiom 5 (cls_Comb_Oparcontract_Ointros__4_0) R->L }
% 31.21/4.40 tuple(fresh2(fresh(true2, true2, v_z, v_w, v_yb, v_y_Ha), true2, c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by axiom 4 (cls_conjecture_2) R->L }
% 31.21/4.40 tuple(fresh2(fresh(c_in(c_Pair(v_yb, v_y_Ha, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_z, v_w, v_yb, v_y_Ha), true2, c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by lemma 8 }
% 31.21/4.40 tuple(fresh2(true2, true2, c_Comb_Ocomb_Oop_A_D_D(v_yb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)), fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by axiom 1 (cls_Comb_Oparcontract_Ointros__4_0) }
% 31.21/4.40 tuple(true2, fresh(X, X, v_w, c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w)))
% 31.21/4.40 = { by axiom 5 (cls_Comb_Oparcontract_Ointros__4_0) }
% 31.21/4.40 tuple(true2, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 31.21/4.40 = { by axiom 7 (cls_Comb_Oparcontract_Ointros__3_0) }
% 31.21/4.40 tuple(true2, true2)
% 31.21/4.40 % SZS output end Proof
% 31.21/4.40
% 31.21/4.40 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------