TSTP Solution File: RNG040-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG040-1 : 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 : n024.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 2.23s 0.72s
% Output : Proof 2.23s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG040-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 02:15:23 EDT 2023
% 0.20/0.35 % CPUTime :
% 2.23/0.72 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 2.23/0.72
% 2.23/0.72 % SZS status Unsatisfiable
% 2.23/0.72
% 2.23/0.72 % SZS output start Proof
% 2.23/0.72 Take the following subset of the input axioms:
% 2.23/0.73 fof(b_plus_a, negated_conjecture, product(b, a, l)).
% 2.23/0.73 fof(b_plus_c, negated_conjecture, sum(b, c, d)).
% 2.23/0.73 fof(c_plus_a, negated_conjecture, product(c, a, n)).
% 2.23/0.73 fof(d_plus_a, negated_conjecture, product(d, a, additive_identity)).
% 2.23/0.73 fof(distributivity3, axiom, ![X, Y, Z, V1, V2, V3, V4]: (~product(Y, X, V1) | (~product(Z, X, V2) | (~sum(Y, Z, V3) | (~product(V3, X, V4) | sum(V1, V2, V4)))))).
% 2.23/0.73 fof(prove_equation, negated_conjecture, ~sum(l, n, additive_identity)).
% 2.23/0.73
% 2.23/0.73 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.23/0.73 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.23/0.73 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.23/0.73 fresh(y, y, x1...xn) = u
% 2.23/0.73 C => fresh(s, t, x1...xn) = v
% 2.23/0.73 where fresh is a fresh function symbol and x1..xn are the free
% 2.23/0.73 variables of u and v.
% 2.23/0.73 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.23/0.73 input problem has no model of domain size 1).
% 2.23/0.73
% 2.23/0.73 The encoding turns the above axioms into the following unit equations and goals:
% 2.23/0.73
% 2.23/0.73 Axiom 1 (b_plus_a): product(b, a, l) = true.
% 2.23/0.73 Axiom 2 (c_plus_a): product(c, a, n) = true.
% 2.23/0.73 Axiom 3 (d_plus_a): product(d, a, additive_identity) = true.
% 2.23/0.73 Axiom 4 (b_plus_c): sum(b, c, d) = true.
% 2.23/0.73 Axiom 5 (distributivity3): fresh18(X, X, Y, Z, W) = true.
% 2.23/0.73 Axiom 6 (distributivity3): fresh16(X, X, Y, Z, W, V, U, T) = sum(Z, V, T).
% 2.23/0.73 Axiom 7 (distributivity3): fresh17(X, X, Y, Z, W, V, U, T, S) = fresh18(sum(Y, V, T), true, W, U, S).
% 2.23/0.73 Axiom 8 (distributivity3): fresh15(X, X, Y, Z, W, V, U, T, S) = fresh16(product(Y, Z, W), true, Y, W, V, U, T, S).
% 2.23/0.73 Axiom 9 (distributivity3): fresh15(product(X, Y, Z), true, W, Y, V, U, T, X, Z) = fresh17(product(U, Y, T), true, W, Y, V, U, T, X, Z).
% 2.23/0.73
% 2.23/0.73 Goal 1 (prove_equation): sum(l, n, additive_identity) = true.
% 2.23/0.73 Proof:
% 2.23/0.73 sum(l, n, additive_identity)
% 2.23/0.73 = { by axiom 6 (distributivity3) R->L }
% 2.23/0.73 fresh16(true, true, b, l, c, n, d, additive_identity)
% 2.23/0.73 = { by axiom 1 (b_plus_a) R->L }
% 2.23/0.73 fresh16(product(b, a, l), true, b, l, c, n, d, additive_identity)
% 2.23/0.73 = { by axiom 8 (distributivity3) R->L }
% 2.23/0.73 fresh15(true, true, b, a, l, c, n, d, additive_identity)
% 2.23/0.73 = { by axiom 3 (d_plus_a) R->L }
% 2.23/0.73 fresh15(product(d, a, additive_identity), true, b, a, l, c, n, d, additive_identity)
% 2.23/0.73 = { by axiom 9 (distributivity3) }
% 2.23/0.73 fresh17(product(c, a, n), true, b, a, l, c, n, d, additive_identity)
% 2.23/0.73 = { by axiom 2 (c_plus_a) }
% 2.23/0.73 fresh17(true, true, b, a, l, c, n, d, additive_identity)
% 2.23/0.73 = { by axiom 7 (distributivity3) }
% 2.23/0.73 fresh18(sum(b, c, d), true, l, n, additive_identity)
% 2.23/0.73 = { by axiom 4 (b_plus_c) }
% 2.23/0.73 fresh18(true, true, l, n, additive_identity)
% 2.23/0.73 = { by axiom 5 (distributivity3) }
% 2.23/0.73 true
% 2.23/0.73 % SZS output end Proof
% 2.23/0.73
% 2.23/0.73 RESULT: Unsatisfiable (the axioms are contradictory).
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