TSTP Solution File: RNG040-2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG040-2 : TPTP v8.1.2. Released v1.0.0.
% 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 : Thu Aug 31 13:58:59 EDT 2023
% Result : Unsatisfiable 5.57s 1.08s
% Output : Proof 5.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG040-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 01:57:26 EDT 2023
% 0.12/0.34 % CPUTime :
% 5.57/1.08 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 5.57/1.08
% 5.57/1.08 % SZS status Unsatisfiable
% 5.57/1.08
% 5.57/1.09 % SZS output start Proof
% 5.57/1.09 Take the following subset of the input axioms:
% 5.57/1.09 fof(b_plus_a, negated_conjecture, product(b, a, l)).
% 5.57/1.09 fof(b_plus_c, negated_conjecture, sum(b, c, d)).
% 5.57/1.09 fof(c_plus_a, negated_conjecture, product(c, a, n)).
% 5.57/1.09 fof(closure_of_multiplication, axiom, ![X, Y]: product(X, Y, multiply(X, Y))).
% 5.57/1.09 fof(d_plus_a, negated_conjecture, product(d, a, additive_identity)).
% 5.57/1.09 fof(distributivity1, axiom, ![Z, V1, V2, V3, V4, X2, Y2]: (~product(X2, Y2, V1) | (~product(X2, Z, V2) | (~sum(Y2, Z, V3) | (~product(X2, V3, V4) | sum(V1, V2, V4)))))).
% 5.57/1.09 fof(multiplication_is_well_defined, axiom, ![U, V, X2, Y2]: (~product(X2, Y2, U) | (~product(X2, Y2, V) | U=V))).
% 5.57/1.09 fof(product_symmetry, hypothesis, ![B, C, A2]: (~product(A2, B, C) | product(B, A2, C))).
% 5.57/1.09 fof(prove_equation, negated_conjecture, ~sum(l, n, additive_identity)).
% 5.57/1.09
% 5.57/1.09 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.57/1.09 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.57/1.09 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.57/1.09 fresh(y, y, x1...xn) = u
% 5.57/1.09 C => fresh(s, t, x1...xn) = v
% 5.57/1.09 where fresh is a fresh function symbol and x1..xn are the free
% 5.57/1.09 variables of u and v.
% 5.57/1.09 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.57/1.09 input problem has no model of domain size 1).
% 5.57/1.09
% 5.57/1.09 The encoding turns the above axioms into the following unit equations and goals:
% 5.57/1.09
% 5.57/1.09 Axiom 1 (b_plus_c): sum(b, c, d) = true.
% 5.57/1.09 Axiom 2 (b_plus_a): product(b, a, l) = true.
% 5.57/1.09 Axiom 3 (c_plus_a): product(c, a, n) = true.
% 5.57/1.09 Axiom 4 (d_plus_a): product(d, a, additive_identity) = true.
% 5.57/1.09 Axiom 5 (multiplication_is_well_defined): fresh(X, X, Y, Z) = Z.
% 5.57/1.09 Axiom 6 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 5.57/1.09 Axiom 7 (distributivity1): fresh18(X, X, Y, Z, W) = true.
% 5.57/1.09 Axiom 8 (product_symmetry): fresh5(X, X, Y, Z, W) = true.
% 5.57/1.09 Axiom 9 (multiplication_is_well_defined): fresh2(X, X, Y, Z, W, V) = W.
% 5.57/1.09 Axiom 10 (distributivity1): fresh16(X, X, Y, Z, W, V, U, T) = sum(Z, V, T).
% 5.57/1.09 Axiom 11 (product_symmetry): fresh5(product(X, Y, Z), true, X, Y, Z) = product(Y, X, Z).
% 5.57/1.09 Axiom 12 (distributivity1): fresh17(X, X, Y, Z, W, V, U, T, S) = fresh18(sum(Z, V, T), true, W, U, S).
% 5.57/1.09 Axiom 13 (multiplication_is_well_defined): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 5.57/1.09 Axiom 14 (distributivity1): fresh15(X, X, Y, Z, W, V, U, T, S) = fresh16(product(Y, Z, W), true, Z, W, V, U, T, S).
% 5.57/1.09 Axiom 15 (distributivity1): fresh15(product(X, Y, Z), true, X, W, V, U, T, Y, Z) = fresh17(product(X, U, T), true, X, W, V, U, T, Y, Z).
% 5.57/1.09
% 5.57/1.09 Lemma 16: multiply(X, Y) = multiply(Y, X).
% 5.57/1.09 Proof:
% 5.57/1.09 multiply(X, Y)
% 5.57/1.09 = { by axiom 9 (multiplication_is_well_defined) R->L }
% 5.57/1.09 fresh2(true, true, Y, X, multiply(X, Y), multiply(Y, X))
% 5.57/1.09 = { by axiom 6 (closure_of_multiplication) R->L }
% 5.57/1.09 fresh2(product(Y, X, multiply(Y, X)), true, Y, X, multiply(X, Y), multiply(Y, X))
% 5.57/1.09 = { by axiom 13 (multiplication_is_well_defined) }
% 5.57/1.09 fresh(product(Y, X, multiply(X, Y)), true, multiply(X, Y), multiply(Y, X))
% 5.57/1.09 = { by axiom 11 (product_symmetry) R->L }
% 5.57/1.09 fresh(fresh5(product(X, Y, multiply(X, Y)), true, X, Y, multiply(X, Y)), true, multiply(X, Y), multiply(Y, X))
% 5.57/1.09 = { by axiom 6 (closure_of_multiplication) }
% 5.57/1.09 fresh(fresh5(true, true, X, Y, multiply(X, Y)), true, multiply(X, Y), multiply(Y, X))
% 5.57/1.09 = { by axiom 8 (product_symmetry) }
% 5.57/1.09 fresh(true, true, multiply(X, Y), multiply(Y, X))
% 5.57/1.09 = { by axiom 5 (multiplication_is_well_defined) }
% 5.57/1.09 multiply(Y, X)
% 5.57/1.09
% 5.57/1.09 Goal 1 (prove_equation): sum(l, n, additive_identity) = true.
% 5.57/1.09 Proof:
% 5.57/1.09 sum(l, n, additive_identity)
% 5.57/1.09 = { by axiom 5 (multiplication_is_well_defined) R->L }
% 5.57/1.09 sum(l, fresh(true, true, multiply(c, a), n), additive_identity)
% 5.57/1.09 = { by axiom 6 (closure_of_multiplication) R->L }
% 5.57/1.09 sum(l, fresh(product(c, a, multiply(c, a)), true, multiply(c, a), n), additive_identity)
% 5.57/1.09 = { by axiom 13 (multiplication_is_well_defined) R->L }
% 5.57/1.09 sum(l, fresh2(product(c, a, n), true, c, a, multiply(c, a), n), additive_identity)
% 5.57/1.09 = { by axiom 3 (c_plus_a) }
% 5.57/1.09 sum(l, fresh2(true, true, c, a, multiply(c, a), n), additive_identity)
% 5.57/1.09 = { by axiom 9 (multiplication_is_well_defined) }
% 5.57/1.09 sum(l, multiply(c, a), additive_identity)
% 5.57/1.09 = { by axiom 10 (distributivity1) R->L }
% 5.57/1.09 fresh16(true, true, b, l, c, multiply(c, a), d, additive_identity)
% 5.57/1.09 = { by axiom 8 (product_symmetry) R->L }
% 5.57/1.09 fresh16(fresh5(true, true, b, a, l), true, b, l, c, multiply(c, a), d, additive_identity)
% 5.57/1.09 = { by axiom 2 (b_plus_a) R->L }
% 5.57/1.09 fresh16(fresh5(product(b, a, l), true, b, a, l), true, b, l, c, multiply(c, a), d, additive_identity)
% 5.57/1.09 = { by axiom 11 (product_symmetry) }
% 5.57/1.09 fresh16(product(a, b, l), true, b, l, c, multiply(c, a), d, additive_identity)
% 5.57/1.09 = { by axiom 14 (distributivity1) R->L }
% 5.57/1.09 fresh15(true, true, a, b, l, c, multiply(c, a), d, additive_identity)
% 5.57/1.09 = { by lemma 16 R->L }
% 5.57/1.09 fresh15(true, true, a, b, l, c, multiply(a, c), d, additive_identity)
% 5.57/1.09 = { by axiom 8 (product_symmetry) R->L }
% 5.57/1.09 fresh15(fresh5(true, true, d, a, additive_identity), true, a, b, l, c, multiply(a, c), d, additive_identity)
% 5.57/1.09 = { by axiom 4 (d_plus_a) R->L }
% 5.57/1.09 fresh15(fresh5(product(d, a, additive_identity), true, d, a, additive_identity), true, a, b, l, c, multiply(a, c), d, additive_identity)
% 5.57/1.09 = { by axiom 11 (product_symmetry) }
% 5.57/1.09 fresh15(product(a, d, additive_identity), true, a, b, l, c, multiply(a, c), d, additive_identity)
% 5.57/1.09 = { by axiom 15 (distributivity1) }
% 5.57/1.09 fresh17(product(a, c, multiply(a, c)), true, a, b, l, c, multiply(a, c), d, additive_identity)
% 5.57/1.09 = { by axiom 6 (closure_of_multiplication) }
% 5.57/1.09 fresh17(true, true, a, b, l, c, multiply(a, c), d, additive_identity)
% 5.57/1.09 = { by axiom 12 (distributivity1) }
% 5.57/1.09 fresh18(sum(b, c, d), true, l, multiply(a, c), additive_identity)
% 5.57/1.09 = { by lemma 16 }
% 5.57/1.09 fresh18(sum(b, c, d), true, l, multiply(c, a), additive_identity)
% 5.57/1.09 = { by axiom 1 (b_plus_c) }
% 5.57/1.09 fresh18(true, true, l, multiply(c, a), additive_identity)
% 5.57/1.09 = { by axiom 7 (distributivity1) }
% 5.57/1.09 true
% 5.57/1.09 % SZS output end Proof
% 5.57/1.09
% 5.57/1.09 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------