TSTP Solution File: NUM025-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM025-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n003.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 11:55:02 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% 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
% 0.00/0.13 % Problem : NUM025-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 09:25:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
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% 0.20/0.40 % SZS status Unsatisfiable
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% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Take the following subset of the input axioms:
% 0.20/0.40 fof(a_less_than_b, hypothesis, less(a, b)).
% 0.20/0.40 fof(no_number_less_than_itself, axiom, ![A]: ~less(A, A)).
% 0.20/0.40 fof(prove_b_not_less_than_a, negated_conjecture, less(b, a)).
% 0.20/0.40 fof(transitivity_of_less, axiom, ![B, C, A2]: (~less(A2, B) | (~less(C, A2) | less(C, B)))).
% 0.20/0.40 fof(zero_is_the_first_number, axiom, ![A3]: ~equalish(successor(A3), n0)).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
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% 0.20/0.40 Axiom 1 (a_less_than_b): less(a, b) = true2.
% 0.20/0.40 Axiom 2 (prove_b_not_less_than_a): less(b, a) = true2.
% 0.20/0.40 Axiom 3 (transitivity_of_less): fresh(X, X, Y, Z) = true2.
% 0.20/0.40 Axiom 4 (transitivity_of_less): fresh2(X, X, Y, Z, W) = less(W, Z).
% 0.20/0.40 Axiom 5 (transitivity_of_less): fresh2(less(X, Y), true2, Y, Z, X) = fresh(less(Y, Z), true2, Z, X).
% 0.20/0.40
% 0.20/0.40 Goal 1 (no_number_less_than_itself): less(X, X) = true2.
% 0.20/0.40 The goal is true when:
% 0.20/0.40 X = a
% 0.20/0.40
% 0.20/0.40 Proof:
% 0.20/0.40 less(a, a)
% 0.20/0.40 = { by axiom 4 (transitivity_of_less) R->L }
% 0.20/0.40 fresh2(true2, true2, b, a, a)
% 0.20/0.40 = { by axiom 1 (a_less_than_b) R->L }
% 0.20/0.40 fresh2(less(a, b), true2, b, a, a)
% 0.20/0.40 = { by axiom 5 (transitivity_of_less) }
% 0.20/0.40 fresh(less(b, a), true2, a, a)
% 0.20/0.40 = { by axiom 2 (prove_b_not_less_than_a) }
% 0.20/0.40 fresh(true2, true2, a, a)
% 0.20/0.40 = { by axiom 3 (transitivity_of_less) }
% 0.20/0.40 true2
% 0.20/0.40 % SZS output end Proof
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% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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