TSTP Solution File: RNG001-4 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG001-4 : 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 : n020.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 13:58:42 EDT 2023
% Result : Unsatisfiable 10.29s 2.77s
% Output : Proof 10.29s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.17 % Problem : RNG001-4 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.18 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8042.1875MB
% 0.13/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Aug 27 02:51:29 EDT 2023
% 0.13/0.39 % CPUTime :
% 10.29/2.77 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 10.29/2.77
% 10.29/2.77 % SZS status Unsatisfiable
% 10.29/2.78
% 10.29/2.79 % SZS output start Proof
% 10.29/2.79 Take the following subset of the input axioms:
% 10.29/2.79 fof(additive_identity2, axiom, ![X]: sum(X, additive_identity, X)).
% 10.29/2.79 fof(cancellation1, axiom, ![Y, Z, W, X2]: (~sum(X2, Y, Z) | (~sum(X2, W, Z) | Y=W))).
% 10.29/2.79 fof(closure_of_multiplication, axiom, ![X2, Y2]: product(X2, Y2, multiply(X2, Y2))).
% 10.29/2.79 fof(distributivity1, axiom, ![V1, V2, V3, V4, X2, Y2, Z2]: (~product(X2, Y2, V1) | (~product(X2, Z2, V2) | (~sum(Y2, Z2, V3) | (~product(X2, V3, V4) | sum(V1, V2, V4)))))).
% 10.29/2.79 fof(prove_a_times_additive_id_is_additive_id, negated_conjecture, ~product(a, additive_identity, additive_identity)).
% 10.29/2.79
% 10.29/2.79 Now clausify the problem and encode Horn clauses using encoding 3 of
% 10.29/2.79 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 10.29/2.79 We repeatedly replace C & s=t => u=v by the two clauses:
% 10.29/2.79 fresh(y, y, x1...xn) = u
% 10.29/2.79 C => fresh(s, t, x1...xn) = v
% 10.29/2.79 where fresh is a fresh function symbol and x1..xn are the free
% 10.29/2.79 variables of u and v.
% 10.29/2.79 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 10.29/2.79 input problem has no model of domain size 1).
% 10.29/2.79
% 10.29/2.79 The encoding turns the above axioms into the following unit equations and goals:
% 10.29/2.79
% 10.29/2.80 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 10.29/2.80 Axiom 2 (cancellation1): fresh3(X, X, Y, Z) = Z.
% 10.29/2.80 Axiom 3 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 10.29/2.80 Axiom 4 (distributivity1): fresh29(X, X, Y, Z, W) = true.
% 10.29/2.80 Axiom 5 (cancellation1): fresh4(X, X, Y, Z, W, V) = Z.
% 10.29/2.80 Axiom 6 (distributivity1): fresh27(X, X, Y, Z, W, V, U, T) = sum(Z, V, T).
% 10.29/2.80 Axiom 7 (distributivity1): fresh28(X, X, Y, Z, W, V, U, T, S) = fresh29(sum(Z, V, T), true, W, U, S).
% 10.29/2.80 Axiom 8 (cancellation1): fresh4(sum(X, Y, Z), true, X, W, Z, Y) = fresh3(sum(X, W, Z), true, W, Y).
% 10.29/2.80 Axiom 9 (distributivity1): fresh26(X, X, Y, Z, W, V, U, T, S) = fresh27(product(Y, Z, W), true, Z, W, V, U, T, S).
% 10.29/2.80 Axiom 10 (distributivity1): fresh26(product(X, Y, Z), true, X, W, V, U, T, Y, Z) = fresh28(product(X, U, T), true, X, W, V, U, T, Y, Z).
% 10.29/2.80
% 10.29/2.80 Goal 1 (prove_a_times_additive_id_is_additive_id): product(a, additive_identity, additive_identity) = true.
% 10.29/2.80 Proof:
% 10.29/2.80 product(a, additive_identity, additive_identity)
% 10.29/2.80 = { by axiom 2 (cancellation1) R->L }
% 10.29/2.80 product(a, additive_identity, fresh3(true, true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 4 (distributivity1) R->L }
% 10.29/2.80 product(a, additive_identity, fresh3(fresh29(true, true, multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 1 (additive_identity2) R->L }
% 10.29/2.80 product(a, additive_identity, fresh3(fresh29(sum(X, additive_identity, X), true, multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 7 (distributivity1) R->L }
% 10.29/2.80 product(a, additive_identity, fresh3(fresh28(true, true, a, X, multiply(a, X), additive_identity, multiply(a, additive_identity), X, multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 3 (closure_of_multiplication) R->L }
% 10.29/2.80 product(a, additive_identity, fresh3(fresh28(product(a, additive_identity, multiply(a, additive_identity)), true, a, X, multiply(a, X), additive_identity, multiply(a, additive_identity), X, multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 10 (distributivity1) R->L }
% 10.29/2.80 product(a, additive_identity, fresh3(fresh26(product(a, X, multiply(a, X)), true, a, X, multiply(a, X), additive_identity, multiply(a, additive_identity), X, multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 3 (closure_of_multiplication) }
% 10.29/2.80 product(a, additive_identity, fresh3(fresh26(true, true, a, X, multiply(a, X), additive_identity, multiply(a, additive_identity), X, multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 9 (distributivity1) }
% 10.29/2.80 product(a, additive_identity, fresh3(fresh27(product(a, X, multiply(a, X)), true, X, multiply(a, X), additive_identity, multiply(a, additive_identity), X, multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 3 (closure_of_multiplication) }
% 10.29/2.80 product(a, additive_identity, fresh3(fresh27(true, true, X, multiply(a, X), additive_identity, multiply(a, additive_identity), X, multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 6 (distributivity1) }
% 10.29/2.80 product(a, additive_identity, fresh3(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, multiply(a, additive_identity), additive_identity))
% 10.29/2.80 = { by axiom 8 (cancellation1) R->L }
% 10.29/2.80 product(a, additive_identity, fresh4(sum(multiply(a, X), additive_identity, multiply(a, X)), true, multiply(a, X), multiply(a, additive_identity), multiply(a, X), additive_identity))
% 10.29/2.80 = { by axiom 1 (additive_identity2) }
% 10.29/2.80 product(a, additive_identity, fresh4(true, true, multiply(a, X), multiply(a, additive_identity), multiply(a, X), additive_identity))
% 10.29/2.80 = { by axiom 5 (cancellation1) }
% 10.29/2.80 product(a, additive_identity, multiply(a, additive_identity))
% 10.29/2.80 = { by axiom 3 (closure_of_multiplication) }
% 10.29/2.80 true
% 10.29/2.80 % SZS output end Proof
% 10.29/2.80
% 10.29/2.80 RESULT: Unsatisfiable (the axioms are contradictory).
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