TSTP Solution File: SYN649-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN649-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n023.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 : Fri Sep 1 03:35:34 EDT 2023
% Result : Unsatisfiable 1.76s 0.58s
% Output : Proof 1.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN649-1 : TPTP v8.1.2. Released v2.5.0.
% 0.03/0.13 % 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 : n023.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 : Sat Aug 26 19:15:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 1.76/0.58 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 1.76/0.58
% 1.76/0.58 % SZS status Unsatisfiable
% 1.76/0.58
% 1.76/0.59 % SZS output start Proof
% 1.76/0.59 Take the following subset of the input axioms:
% 1.76/0.59 fof(not_p23_38, negated_conjecture, ![X87]: (~p23(f5(c24, c25), X87) | ~p23(f5(f7(f10(c26, f12(c27, c28)), c24), X87), c29))).
% 1.76/0.59 fof(p23_26, negated_conjecture, p23(f5(f7(f10(c26, f12(c27, f12(c27, c28))), c24), c25), c29)).
% 1.76/0.59 fof(p23_39, negated_conjecture, ![X49, X50]: (p23(f5(c24, X49), f14(f22(c33, X50), X49)) | ~p23(f5(f7(f10(c26, f12(c27, c28)), c24), X49), X50))).
% 1.76/0.59 fof(p23_40, negated_conjecture, ![X45, X46, X47, X48]: (p23(f5(X45, f14(f16(f18(f20(c30, X46), X47), X45), X48)), X48) | ~p23(f5(f7(f10(c26, f12(c27, X46)), X45), X47), X48))).
% 1.76/0.59 fof(p23_41, negated_conjecture, ![X49_2, X50_2]: (p23(f5(f7(f10(c26, c28), c24), f14(f22(c33, X50_2), X49_2)), X50_2) | ~p23(f5(f7(f10(c26, f12(c27, c28)), c24), X49_2), X50_2))).
% 1.76/0.59 fof(p23_42, negated_conjecture, ![X51, X45_2, X46_2, X47_2, X48_2]: (p23(f5(f7(f10(c26, f12(c27, X46_2)), X45_2), X47_2), X48_2) | (~p23(f5(X45_2, X51), X48_2) | ~p23(f5(f7(f10(c26, X46_2), X45_2), X47_2), X51)))).
% 1.76/0.59 fof(p23_44, negated_conjecture, ![X45_2, X46_2, X47_2, X48_2]: (p23(f5(f7(f10(c26, X46_2), X45_2), X47_2), f14(f16(f18(f20(c30, X46_2), X47_2), X45_2), X48_2)) | ~p23(f5(f7(f10(c26, f12(c27, X46_2)), X45_2), X47_2), X48_2))).
% 1.76/0.59
% 1.76/0.59 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.76/0.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.76/0.59 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.76/0.59 fresh(y, y, x1...xn) = u
% 1.76/0.59 C => fresh(s, t, x1...xn) = v
% 1.76/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 1.76/0.59 variables of u and v.
% 1.76/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.76/0.60 input problem has no model of domain size 1).
% 1.76/0.60
% 1.76/0.60 The encoding turns the above axioms into the following unit equations and goals:
% 1.76/0.60
% 1.76/0.60 Axiom 1 (p23_39): fresh31(X, X, Y, Z) = true2.
% 1.76/0.60 Axiom 2 (p23_41): fresh29(X, X, Y, Z) = true2.
% 1.76/0.60 Axiom 3 (p23_40): fresh30(X, X, Y, Z, W, V) = true2.
% 1.76/0.60 Axiom 4 (p23_42): fresh27(X, X, Y, Z, W, V) = true2.
% 1.76/0.60 Axiom 5 (p23_44): fresh24(X, X, Y, Z, W, V) = true2.
% 1.76/0.60 Axiom 6 (p23_42): fresh28(X, X, Y, Z, W, V, U) = p23(f5(f7(f10(c26, f12(c27, Y)), Z), W), V).
% 1.76/0.60 Axiom 7 (p23_26): p23(f5(f7(f10(c26, f12(c27, f12(c27, c28))), c24), c25), c29) = true2.
% 1.76/0.60 Axiom 8 (p23_39): fresh31(p23(f5(f7(f10(c26, f12(c27, c28)), c24), X), Y), true2, X, Y) = p23(f5(c24, X), f14(f22(c33, Y), X)).
% 1.76/0.60 Axiom 9 (p23_41): fresh29(p23(f5(f7(f10(c26, f12(c27, c28)), c24), X), Y), true2, Y, X) = p23(f5(f7(f10(c26, c28), c24), f14(f22(c33, Y), X)), Y).
% 1.76/0.60 Axiom 10 (p23_42): fresh28(p23(f5(f7(f10(c26, X), Y), Z), W), true2, X, Y, Z, V, W) = fresh27(p23(f5(Y, W), V), true2, X, Y, Z, V).
% 1.76/0.60 Axiom 11 (p23_40): fresh30(p23(f5(f7(f10(c26, f12(c27, X)), Y), Z), W), true2, Y, X, Z, W) = p23(f5(Y, f14(f16(f18(f20(c30, X), Z), Y), W)), W).
% 1.76/0.60 Axiom 12 (p23_44): fresh24(p23(f5(f7(f10(c26, f12(c27, X)), Y), Z), W), true2, X, Y, Z, W) = p23(f5(f7(f10(c26, X), Y), Z), f14(f16(f18(f20(c30, X), Z), Y), W)).
% 1.76/0.60
% 1.76/0.60 Lemma 13: fresh28(X, X, f12(c27, c28), c24, c25, c29, Y) = true2.
% 1.76/0.60 Proof:
% 1.76/0.60 fresh28(X, X, f12(c27, c28), c24, c25, c29, Y)
% 1.76/0.60 = { by axiom 6 (p23_42) }
% 1.76/0.60 p23(f5(f7(f10(c26, f12(c27, f12(c27, c28))), c24), c25), c29)
% 1.76/0.60 = { by axiom 7 (p23_26) }
% 1.76/0.60 true2
% 1.76/0.60
% 1.76/0.60 Lemma 14: p23(f5(f7(f10(c26, f12(c27, c28)), c24), c25), f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)) = true2.
% 1.76/0.60 Proof:
% 1.76/0.60 p23(f5(f7(f10(c26, f12(c27, c28)), c24), c25), f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29))
% 1.76/0.60 = { by axiom 12 (p23_44) R->L }
% 1.76/0.60 fresh24(p23(f5(f7(f10(c26, f12(c27, f12(c27, c28))), c24), c25), c29), true2, f12(c27, c28), c24, c25, c29)
% 1.76/0.60 = { by axiom 6 (p23_42) R->L }
% 1.76/0.60 fresh24(fresh28(X, X, f12(c27, c28), c24, c25, c29, Y), true2, f12(c27, c28), c24, c25, c29)
% 1.76/0.60 = { by lemma 13 }
% 1.76/0.60 fresh24(true2, true2, f12(c27, c28), c24, c25, c29)
% 1.76/0.60 = { by axiom 5 (p23_44) }
% 1.76/0.60 true2
% 1.76/0.60
% 1.76/0.60 Goal 1 (not_p23_38): tuple(p23(f5(f7(f10(c26, f12(c27, c28)), c24), X), c29), p23(f5(c24, c25), X)) = tuple(true2, true2).
% 1.76/0.60 The goal is true when:
% 1.76/0.60 X = f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)
% 1.76/0.60
% 1.76/0.60 Proof:
% 1.76/0.60 tuple(p23(f5(f7(f10(c26, f12(c27, c28)), c24), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)), c29), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 6 (p23_42) R->L }
% 1.76/0.60 tuple(fresh28(true2, true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 2 (p23_41) R->L }
% 1.76/0.60 tuple(fresh28(fresh29(true2, true2, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29), c25), true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by lemma 14 R->L }
% 1.76/0.60 tuple(fresh28(fresh29(p23(f5(f7(f10(c26, f12(c27, c28)), c24), c25), f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), true2, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29), c25), true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 9 (p23_41) }
% 1.76/0.60 tuple(fresh28(p23(f5(f7(f10(c26, c28), c24), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)), f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 10 (p23_42) }
% 1.76/0.60 tuple(fresh27(p23(f5(c24, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c29), true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 11 (p23_40) R->L }
% 1.76/0.60 tuple(fresh27(fresh30(p23(f5(f7(f10(c26, f12(c27, f12(c27, c28))), c24), c25), c29), true2, c24, f12(c27, c28), c25, c29), true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 6 (p23_42) R->L }
% 1.76/0.60 tuple(fresh27(fresh30(fresh28(X, X, f12(c27, c28), c24, c25, c29, Y), true2, c24, f12(c27, c28), c25, c29), true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by lemma 13 }
% 1.76/0.60 tuple(fresh27(fresh30(true2, true2, c24, f12(c27, c28), c25, c29), true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 3 (p23_40) }
% 1.76/0.60 tuple(fresh27(true2, true2, c28, c24, f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25), c29), p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 4 (p23_42) }
% 1.76/0.60 tuple(true2, p23(f5(c24, c25), f14(f22(c33, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), c25)))
% 1.76/0.60 = { by axiom 8 (p23_39) R->L }
% 1.76/0.60 tuple(true2, fresh31(p23(f5(f7(f10(c26, f12(c27, c28)), c24), c25), f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)), true2, c25, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)))
% 1.76/0.60 = { by lemma 14 }
% 1.76/0.60 tuple(true2, fresh31(true2, true2, c25, f14(f16(f18(f20(c30, f12(c27, c28)), c25), c24), c29)))
% 1.76/0.60 = { by axiom 1 (p23_39) }
% 1.76/0.60 tuple(true2, true2)
% 1.76/0.60 % SZS output end Proof
% 1.76/0.60
% 1.76/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------