TSTP Solution File: FLD070-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD070-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n016.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 : Wed Aug 30 22:37:12 EDT 2023
% Result : Unsatisfiable 0.19s 0.53s
% Output : Proof 0.19s
% 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 : FLD070-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n016.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 : Mon Aug 28 00:52:14 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.53 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.53
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53
% 0.19/0.53 % SZS output start Proof
% 0.19/0.53 Take the following subset of the input axioms:
% 0.19/0.53 fof(a_is_defined, hypothesis, defined(a)).
% 0.19/0.53 fof(b_is_defined, hypothesis, defined(b)).
% 0.19/0.53 fof(compatibility_of_order_relation_and_addition, axiom, ![X, V, Y, U, Z]: (less_or_equal(U, V) | (~less_or_equal(X, Y) | (~sum(X, Z, U) | ~sum(Y, Z, V))))).
% 0.19/0.53 fof(existence_of_identity_addition, axiom, ![X2]: (sum(additive_identity, X2, X2) | ~defined(X2))).
% 0.19/0.53 fof(less_or_equal_3, negated_conjecture, less_or_equal(additive_identity, a)).
% 0.19/0.53 fof(less_or_equal_4, negated_conjecture, less_or_equal(additive_identity, b)).
% 0.19/0.53 fof(not_less_or_equal_5, negated_conjecture, ~less_or_equal(additive_identity, add(a, b))).
% 0.19/0.53 fof(totality_of_addition, axiom, ![X2, Y2]: (sum(X2, Y2, add(X2, Y2)) | (~defined(X2) | ~defined(Y2)))).
% 0.19/0.53 fof(transitivity_of_order_relation, axiom, ![X2, Y2, Z2]: (less_or_equal(X2, Z2) | (~less_or_equal(X2, Y2) | ~less_or_equal(Y2, Z2)))).
% 0.19/0.53
% 0.19/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.53 fresh(y, y, x1...xn) = u
% 0.19/0.53 C => fresh(s, t, x1...xn) = v
% 0.19/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.53 variables of u and v.
% 0.19/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.53 input problem has no model of domain size 1).
% 0.19/0.53
% 0.19/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.53
% 0.19/0.53 Axiom 1 (a_is_defined): defined(a) = true.
% 0.19/0.53 Axiom 2 (b_is_defined): defined(b) = true.
% 0.19/0.53 Axiom 3 (less_or_equal_3): less_or_equal(additive_identity, a) = true.
% 0.19/0.53 Axiom 4 (less_or_equal_4): less_or_equal(additive_identity, b) = true.
% 0.19/0.53 Axiom 5 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 0.19/0.53 Axiom 6 (compatibility_of_order_relation_and_addition): fresh28(X, X, Y, Z) = true.
% 0.19/0.53 Axiom 7 (existence_of_identity_addition): fresh14(defined(X), true, X) = sum(additive_identity, X, X).
% 0.19/0.53 Axiom 8 (totality_of_addition): fresh11(X, X, Y, Z) = sum(Y, Z, add(Y, Z)).
% 0.19/0.53 Axiom 9 (totality_of_addition): fresh10(X, X, Y, Z) = true.
% 0.19/0.53 Axiom 10 (transitivity_of_order_relation): fresh6(X, X, Y, Z) = true.
% 0.19/0.53 Axiom 11 (totality_of_addition): fresh11(defined(X), true, Y, X) = fresh10(defined(Y), true, Y, X).
% 0.19/0.53 Axiom 12 (transitivity_of_order_relation): fresh7(X, X, Y, Z, W) = less_or_equal(Y, Z).
% 0.19/0.53 Axiom 13 (compatibility_of_order_relation_and_addition): fresh16(X, X, Y, Z, W, V) = less_or_equal(Y, Z).
% 0.19/0.53 Axiom 14 (transitivity_of_order_relation): fresh7(less_or_equal(X, Y), true, Z, Y, X) = fresh6(less_or_equal(Z, X), true, Z, Y).
% 0.19/0.53 Axiom 15 (compatibility_of_order_relation_and_addition): fresh27(X, X, Y, Z, W, V, U) = fresh28(sum(W, U, Y), true, Y, Z).
% 0.19/0.53 Axiom 16 (compatibility_of_order_relation_and_addition): fresh27(less_or_equal(X, Y), true, Z, W, X, Y, V) = fresh16(sum(Y, V, W), true, Z, W, X, V).
% 0.19/0.53
% 0.19/0.53 Goal 1 (not_less_or_equal_5): less_or_equal(additive_identity, add(a, b)) = true.
% 0.19/0.53 Proof:
% 0.19/0.53 less_or_equal(additive_identity, add(a, b))
% 0.19/0.53 = { by axiom 12 (transitivity_of_order_relation) R->L }
% 0.19/0.53 fresh7(true, true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 6 (compatibility_of_order_relation_and_addition) R->L }
% 0.19/0.53 fresh7(fresh28(true, true, b, add(a, b)), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 5 (existence_of_identity_addition) R->L }
% 0.19/0.53 fresh7(fresh28(fresh14(true, true, b), true, b, add(a, b)), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 2 (b_is_defined) R->L }
% 0.19/0.53 fresh7(fresh28(fresh14(defined(b), true, b), true, b, add(a, b)), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 7 (existence_of_identity_addition) }
% 0.19/0.53 fresh7(fresh28(sum(additive_identity, b, b), true, b, add(a, b)), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 15 (compatibility_of_order_relation_and_addition) R->L }
% 0.19/0.53 fresh7(fresh27(true, true, b, add(a, b), additive_identity, a, b), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 3 (less_or_equal_3) R->L }
% 0.19/0.53 fresh7(fresh27(less_or_equal(additive_identity, a), true, b, add(a, b), additive_identity, a, b), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 16 (compatibility_of_order_relation_and_addition) }
% 0.19/0.53 fresh7(fresh16(sum(a, b, add(a, b)), true, b, add(a, b), additive_identity, b), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 8 (totality_of_addition) R->L }
% 0.19/0.53 fresh7(fresh16(fresh11(true, true, a, b), true, b, add(a, b), additive_identity, b), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 2 (b_is_defined) R->L }
% 0.19/0.53 fresh7(fresh16(fresh11(defined(b), true, a, b), true, b, add(a, b), additive_identity, b), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 11 (totality_of_addition) }
% 0.19/0.53 fresh7(fresh16(fresh10(defined(a), true, a, b), true, b, add(a, b), additive_identity, b), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 1 (a_is_defined) }
% 0.19/0.53 fresh7(fresh16(fresh10(true, true, a, b), true, b, add(a, b), additive_identity, b), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 9 (totality_of_addition) }
% 0.19/0.53 fresh7(fresh16(true, true, b, add(a, b), additive_identity, b), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 13 (compatibility_of_order_relation_and_addition) }
% 0.19/0.53 fresh7(less_or_equal(b, add(a, b)), true, additive_identity, add(a, b), b)
% 0.19/0.53 = { by axiom 14 (transitivity_of_order_relation) }
% 0.19/0.53 fresh6(less_or_equal(additive_identity, b), true, additive_identity, add(a, b))
% 0.19/0.53 = { by axiom 4 (less_or_equal_4) }
% 0.19/0.53 fresh6(true, true, additive_identity, add(a, b))
% 0.19/0.53 = { by axiom 10 (transitivity_of_order_relation) }
% 0.19/0.53 true
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53
% 0.19/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
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