TSTP Solution File: RNG005-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG005-2 : 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 : n012.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 13:58:44 EDT 2023
% Result : Unsatisfiable 6.84s 1.24s
% Output : Proof 6.84s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG005-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n012.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 02:38:25 EDT 2023
% 0.15/0.34 % CPUTime :
% 6.84/1.24 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 6.84/1.24
% 6.84/1.24 % SZS status Unsatisfiable
% 6.84/1.24
% 6.84/1.24 % SZS output start Proof
% 6.84/1.24 Take the following subset of the input axioms:
% 6.84/1.24 fof(a_inverse_times_b, hypothesis, product(additive_inverse(a), b, c)).
% 6.84/1.24 fof(a_times_b, hypothesis, product(a, b, d)).
% 6.84/1.24 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)))))).
% 6.84/1.24 fof(left_inverse, axiom, ![X2]: sum(additive_inverse(X2), X2, additive_identity)).
% 6.84/1.24 fof(multiplicative_identity1, axiom, ![X2]: product(additive_identity, X2, additive_identity)).
% 6.84/1.24 fof(prove_sum_is_additive_identity, negated_conjecture, ~sum(c, d, additive_identity)).
% 6.84/1.24
% 6.84/1.24 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.84/1.24 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.84/1.24 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.84/1.24 fresh(y, y, x1...xn) = u
% 6.84/1.24 C => fresh(s, t, x1...xn) = v
% 6.84/1.24 where fresh is a fresh function symbol and x1..xn are the free
% 6.84/1.24 variables of u and v.
% 6.84/1.24 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.84/1.24 input problem has no model of domain size 1).
% 6.84/1.24
% 6.84/1.24 The encoding turns the above axioms into the following unit equations and goals:
% 6.84/1.24
% 6.84/1.24 Axiom 1 (multiplicative_identity1): product(additive_identity, X, additive_identity) = true.
% 6.84/1.24 Axiom 2 (a_times_b): product(a, b, d) = true.
% 6.84/1.24 Axiom 3 (left_inverse): sum(additive_inverse(X), X, additive_identity) = true.
% 6.84/1.24 Axiom 4 (a_inverse_times_b): product(additive_inverse(a), b, c) = true.
% 6.84/1.24 Axiom 5 (distributivity3): fresh32(X, X, Y, Z, W) = true.
% 6.84/1.24 Axiom 6 (distributivity3): fresh30(X, X, Y, Z, W, V, U, T) = sum(Z, V, T).
% 6.84/1.24 Axiom 7 (distributivity3): fresh31(X, X, Y, Z, W, V, U, T, S) = fresh32(sum(Y, V, T), true, W, U, S).
% 6.84/1.24 Axiom 8 (distributivity3): fresh29(X, X, Y, Z, W, V, U, T, S) = fresh30(product(Y, Z, W), true, Y, W, V, U, T, S).
% 6.84/1.24 Axiom 9 (distributivity3): fresh29(product(X, Y, Z), true, W, Y, V, U, T, X, Z) = fresh31(product(U, Y, T), true, W, Y, V, U, T, X, Z).
% 6.84/1.24
% 6.84/1.24 Goal 1 (prove_sum_is_additive_identity): sum(c, d, additive_identity) = true.
% 6.84/1.24 Proof:
% 6.84/1.24 sum(c, d, additive_identity)
% 6.84/1.24 = { by axiom 6 (distributivity3) R->L }
% 6.84/1.24 fresh30(true, true, additive_inverse(a), c, a, d, additive_identity, additive_identity)
% 6.84/1.24 = { by axiom 4 (a_inverse_times_b) R->L }
% 6.84/1.24 fresh30(product(additive_inverse(a), b, c), true, additive_inverse(a), c, a, d, additive_identity, additive_identity)
% 6.84/1.24 = { by axiom 8 (distributivity3) R->L }
% 6.84/1.24 fresh29(true, true, additive_inverse(a), b, c, a, d, additive_identity, additive_identity)
% 6.84/1.24 = { by axiom 1 (multiplicative_identity1) R->L }
% 6.84/1.24 fresh29(product(additive_identity, b, additive_identity), true, additive_inverse(a), b, c, a, d, additive_identity, additive_identity)
% 6.84/1.24 = { by axiom 9 (distributivity3) }
% 6.84/1.24 fresh31(product(a, b, d), true, additive_inverse(a), b, c, a, d, additive_identity, additive_identity)
% 6.84/1.24 = { by axiom 2 (a_times_b) }
% 6.84/1.24 fresh31(true, true, additive_inverse(a), b, c, a, d, additive_identity, additive_identity)
% 6.84/1.24 = { by axiom 7 (distributivity3) }
% 6.84/1.24 fresh32(sum(additive_inverse(a), a, additive_identity), true, c, d, additive_identity)
% 6.84/1.24 = { by axiom 3 (left_inverse) }
% 6.84/1.24 fresh32(true, true, c, d, additive_identity)
% 6.84/1.24 = { by axiom 5 (distributivity3) }
% 6.84/1.24 true
% 6.84/1.24 % SZS output end Proof
% 6.84/1.24
% 6.84/1.24 RESULT: Unsatisfiable (the axioms are contradictory).
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