TSTP Solution File: COL110-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL110-2 : 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 : n022.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL110-2 : 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
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 04:30:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.41 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Take the following subset of the input axioms:
% 0.20/0.42 fof(cls_Comb_Oparcontract_Ointros__4_0, axiom, ![V_z, V_w, V_x, V_y]: (~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)) | (~c_in(c_Pair(V_x, V_y, 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_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))).
% 0.20/0.42 fof(cls_conjecture_2, negated_conjecture, c_in(c_Pair(v_x, v_yb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.20/0.42 fof(cls_conjecture_3, negated_conjecture, c_in(c_Pair(v_z, v_wa, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.20/0.42 fof(cls_conjecture_4, negated_conjecture, ![V_U]: (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_yb, v_wa), 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(v_ya, v_w), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))).
% 0.20/0.42 fof(cls_conjecture_5, negated_conjecture, ![V_U2]: (c_in(c_Pair(v_ya, v_xb(V_U2), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | ~c_in(c_Pair(v_x, V_U2, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))).
% 0.20/0.42 fof(cls_conjecture_6, negated_conjecture, ![V_U2]: (c_in(c_Pair(V_U2, v_xb(V_U2), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | ~c_in(c_Pair(v_x, V_U2, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))).
% 0.20/0.42 fof(cls_conjecture_7, negated_conjecture, ![V_U2]: (c_in(c_Pair(v_w, v_xaa(V_U2), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | ~c_in(c_Pair(v_z, V_U2, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))).
% 0.20/0.42 fof(cls_conjecture_8, negated_conjecture, ![V_U2]: (c_in(c_Pair(V_U2, v_xaa(V_U2), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | ~c_in(c_Pair(v_z, V_U2, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))).
% 0.20/0.42
% 0.20/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.42 fresh(y, y, x1...xn) = u
% 0.20/0.42 C => fresh(s, t, x1...xn) = v
% 0.20/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.42 variables of u and v.
% 0.20/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.42 input problem has no model of domain size 1).
% 0.20/0.42
% 0.20/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.42
% 0.20/0.42 Axiom 1 (cls_conjecture_8): fresh(X, X, Y) = true2.
% 0.20/0.42 Axiom 2 (cls_conjecture_5): fresh4(X, X, Y) = true2.
% 0.20/0.42 Axiom 3 (cls_conjecture_6): fresh3(X, X, Y) = true2.
% 0.20/0.42 Axiom 4 (cls_conjecture_7): fresh2(X, X, Y) = true2.
% 0.20/0.42 Axiom 5 (cls_Comb_Oparcontract_Ointros__4_0): fresh6(X, X, Y, Z, W, V) = true2.
% 0.20/0.42 Axiom 6 (cls_conjecture_2): c_in(c_Pair(v_x, v_yb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 0.20/0.42 Axiom 7 (cls_conjecture_3): c_in(c_Pair(v_z, v_wa, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true2.
% 0.20/0.42 Axiom 8 (cls_conjecture_8): fresh(c_in(c_Pair(v_z, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, X) = c_in(c_Pair(X, v_xaa(X), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)).
% 0.20/0.42 Axiom 9 (cls_conjecture_5): fresh4(c_in(c_Pair(v_x, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, X) = c_in(c_Pair(v_ya, v_xb(X), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)).
% 0.20/0.42 Axiom 10 (cls_conjecture_6): fresh3(c_in(c_Pair(v_x, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, X) = c_in(c_Pair(X, v_xb(X), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)).
% 0.20/0.42 Axiom 11 (cls_conjecture_7): fresh2(c_in(c_Pair(v_z, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, X) = c_in(c_Pair(v_w, v_xaa(X), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)).
% 0.20/0.42 Axiom 12 (cls_Comb_Oparcontract_Ointros__4_0): fresh5(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)).
% 0.20/0.42 Axiom 13 (cls_Comb_Oparcontract_Ointros__4_0): fresh5(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) = fresh6(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).
% 0.20/0.43
% 0.20/0.43 Goal 1 (cls_conjecture_4): tuple(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_yb, v_wa), 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(v_ya, v_w), X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) = tuple(true2, true2).
% 0.20/0.43 The goal is true when:
% 0.20/0.43 X = c_Comb_Ocomb_Oop_A_D_D(v_xb(v_yb), v_xaa(v_wa))
% 0.20/0.43
% 0.20/0.43 Proof:
% 0.20/0.43 tuple(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_yb, v_wa), c_Comb_Ocomb_Oop_A_D_D(v_xb(v_yb), v_xaa(v_wa)), 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_ya, v_w), c_Comb_Ocomb_Oop_A_D_D(v_xb(v_yb), v_xaa(v_wa)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 0.20/0.43 = { by axiom 12 (cls_Comb_Oparcontract_Ointros__4_0) R->L }
% 0.20/0.43 tuple(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_yb, v_wa), c_Comb_Ocomb_Oop_A_D_D(v_xb(v_yb), v_xaa(v_wa)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), fresh5(true2, true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 12 (cls_Comb_Oparcontract_Ointros__4_0) R->L }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), fresh5(true2, true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 2 (cls_conjecture_5) R->L }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), fresh5(fresh4(true2, true2, v_yb), true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 6 (cls_conjecture_2) R->L }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), fresh5(fresh4(c_in(c_Pair(v_x, v_yb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_yb), true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 9 (cls_conjecture_5) }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), fresh5(c_in(c_Pair(v_ya, v_xb(v_yb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 13 (cls_Comb_Oparcontract_Ointros__4_0) }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), fresh6(c_in(c_Pair(v_w, v_xaa(v_wa), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 11 (cls_conjecture_7) R->L }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), fresh6(fresh2(c_in(c_Pair(v_z, v_wa, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_wa), true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 7 (cls_conjecture_3) }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), fresh6(fresh2(true2, true2, v_wa), true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 4 (cls_conjecture_7) }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), fresh6(true2, true2, v_w, v_xaa(v_wa), v_ya, v_xb(v_yb)))
% 0.20/0.43 = { by axiom 5 (cls_Comb_Oparcontract_Ointros__4_0) }
% 0.20/0.43 tuple(fresh5(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), true2)
% 0.20/0.43 = { by axiom 3 (cls_conjecture_6) R->L }
% 0.20/0.43 tuple(fresh5(fresh3(true2, true2, v_yb), true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), true2)
% 0.20/0.43 = { by axiom 6 (cls_conjecture_2) R->L }
% 0.20/0.43 tuple(fresh5(fresh3(c_in(c_Pair(v_x, v_yb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_yb), true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), true2)
% 0.20/0.43 = { by axiom 10 (cls_conjecture_6) }
% 0.20/0.43 tuple(fresh5(c_in(c_Pair(v_yb, v_xb(v_yb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), true2)
% 0.20/0.43 = { by axiom 13 (cls_Comb_Oparcontract_Ointros__4_0) }
% 0.20/0.43 tuple(fresh6(c_in(c_Pair(v_wa, v_xaa(v_wa), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), true2)
% 0.20/0.43 = { by axiom 8 (cls_conjecture_8) R->L }
% 0.20/0.43 tuple(fresh6(fresh(c_in(c_Pair(v_z, v_wa, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true2, v_wa), true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), true2)
% 0.20/0.43 = { by axiom 7 (cls_conjecture_3) }
% 0.20/0.43 tuple(fresh6(fresh(true2, true2, v_wa), true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), true2)
% 0.20/0.43 = { by axiom 1 (cls_conjecture_8) }
% 0.20/0.43 tuple(fresh6(true2, true2, v_wa, v_xaa(v_wa), v_yb, v_xb(v_yb)), true2)
% 0.20/0.43 = { by axiom 5 (cls_Comb_Oparcontract_Ointros__4_0) }
% 0.20/0.43 tuple(true2, true2)
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------