TSTP Solution File: FLD070-4 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : FLD070-4 : 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 : n001.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 0.20s 0.47s
% Output : Proof 0.20s
% 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 : FLD070-4 : 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
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 00:48:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 Take the following subset of the input axioms:
% 0.20/0.47 fof(b_is_defined, hypothesis, defined(b)).
% 0.20/0.47 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))))).
% 0.20/0.47 fof(existence_of_identity_addition, axiom, ![X2]: (sum(additive_identity, X2, X2) | ~defined(X2))).
% 0.20/0.47 fof(less_or_equal_4, negated_conjecture, less_or_equal(additive_identity, a)).
% 0.20/0.47 fof(less_or_equal_5, negated_conjecture, less_or_equal(additive_identity, b)).
% 0.20/0.47 fof(not_less_or_equal_7, negated_conjecture, ~less_or_equal(additive_identity, c)).
% 0.20/0.47 fof(sum_6, negated_conjecture, sum(a, b, c)).
% 0.20/0.47 fof(transitivity_of_order_relation, axiom, ![X2, Y2, Z2]: (less_or_equal(X2, Z2) | (~less_or_equal(X2, Y2) | ~less_or_equal(Y2, Z2)))).
% 0.20/0.47
% 0.20/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.47 fresh(y, y, x1...xn) = u
% 0.20/0.47 C => fresh(s, t, x1...xn) = v
% 0.20/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.47 variables of u and v.
% 0.20/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.47 input problem has no model of domain size 1).
% 0.20/0.47
% 0.20/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.47
% 0.20/0.47 Axiom 1 (b_is_defined): defined(b) = true.
% 0.20/0.47 Axiom 2 (less_or_equal_4): less_or_equal(additive_identity, a) = true.
% 0.20/0.47 Axiom 3 (less_or_equal_5): less_or_equal(additive_identity, b) = true.
% 0.20/0.47 Axiom 4 (sum_6): sum(a, b, c) = true.
% 0.20/0.47 Axiom 5 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 0.20/0.47 Axiom 6 (compatibility_of_order_relation_and_addition): fresh28(X, X, Y, Z) = true.
% 0.20/0.47 Axiom 7 (existence_of_identity_addition): fresh14(defined(X), true, X) = sum(additive_identity, X, X).
% 0.20/0.47 Axiom 8 (transitivity_of_order_relation): fresh6(X, X, Y, Z) = true.
% 0.20/0.47 Axiom 9 (transitivity_of_order_relation): fresh7(X, X, Y, Z, W) = less_or_equal(Y, Z).
% 0.20/0.47 Axiom 10 (compatibility_of_order_relation_and_addition): fresh16(X, X, Y, Z, W, V) = less_or_equal(Y, Z).
% 0.20/0.47 Axiom 11 (transitivity_of_order_relation): fresh7(less_or_equal(X, Y), true, Z, Y, X) = fresh6(less_or_equal(Z, X), true, Z, Y).
% 0.20/0.47 Axiom 12 (compatibility_of_order_relation_and_addition): fresh27(X, X, Y, Z, W, V, U) = fresh28(sum(W, U, Y), true, Y, Z).
% 0.20/0.47 Axiom 13 (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).
% 0.20/0.47
% 0.20/0.47 Goal 1 (not_less_or_equal_7): less_or_equal(additive_identity, c) = true.
% 0.20/0.47 Proof:
% 0.20/0.47 less_or_equal(additive_identity, c)
% 0.20/0.47 = { by axiom 9 (transitivity_of_order_relation) R->L }
% 0.20/0.47 fresh7(true, true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 6 (compatibility_of_order_relation_and_addition) R->L }
% 0.20/0.47 fresh7(fresh28(true, true, b, c), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 5 (existence_of_identity_addition) R->L }
% 0.20/0.47 fresh7(fresh28(fresh14(true, true, b), true, b, c), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 1 (b_is_defined) R->L }
% 0.20/0.47 fresh7(fresh28(fresh14(defined(b), true, b), true, b, c), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 7 (existence_of_identity_addition) }
% 0.20/0.47 fresh7(fresh28(sum(additive_identity, b, b), true, b, c), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 12 (compatibility_of_order_relation_and_addition) R->L }
% 0.20/0.47 fresh7(fresh27(true, true, b, c, additive_identity, a, b), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 2 (less_or_equal_4) R->L }
% 0.20/0.47 fresh7(fresh27(less_or_equal(additive_identity, a), true, b, c, additive_identity, a, b), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 13 (compatibility_of_order_relation_and_addition) }
% 0.20/0.47 fresh7(fresh16(sum(a, b, c), true, b, c, additive_identity, b), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 4 (sum_6) }
% 0.20/0.47 fresh7(fresh16(true, true, b, c, additive_identity, b), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 10 (compatibility_of_order_relation_and_addition) }
% 0.20/0.47 fresh7(less_or_equal(b, c), true, additive_identity, c, b)
% 0.20/0.47 = { by axiom 11 (transitivity_of_order_relation) }
% 0.20/0.47 fresh6(less_or_equal(additive_identity, b), true, additive_identity, c)
% 0.20/0.47 = { by axiom 3 (less_or_equal_5) }
% 0.20/0.47 fresh6(true, true, additive_identity, c)
% 0.20/0.47 = { by axiom 8 (transitivity_of_order_relation) }
% 0.20/0.47 true
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47
% 0.20/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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