TSTP Solution File: NUM343+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM343+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n018.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 11:55:57 EDT 2023
% Result : Theorem 2.63s 0.83s
% Output : Proof 2.63s
% 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 : NUM343+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 11:54:29 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.63/0.83 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.63/0.83
% 2.63/0.83 % SZS status Theorem
% 2.63/0.83
% 2.63/0.83 % SZS output start Proof
% 2.63/0.83 Take the following subset of the input axioms:
% 2.63/0.83 fof(less_property, axiom, ![X, Y]: (less(X, Y) <=> (~less(Y, X) & Y!=X))).
% 2.63/0.83 fof(sum_something_n0_samething, conjecture, ?[X2]: ((less(nn1, X2) & less(X2, n1)) => sum(n21, X2, n21))).
% 2.63/0.83
% 2.63/0.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.63/0.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.63/0.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.63/0.83 fresh(y, y, x1...xn) = u
% 2.63/0.83 C => fresh(s, t, x1...xn) = v
% 2.63/0.83 where fresh is a fresh function symbol and x1..xn are the free
% 2.63/0.83 variables of u and v.
% 2.63/0.83 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.63/0.83 input problem has no model of domain size 1).
% 2.63/0.83
% 2.63/0.83 The encoding turns the above axioms into the following unit equations and goals:
% 2.63/0.83
% 2.63/0.83 Axiom 1 (sum_something_n0_samething): less(X, n1) = true2.
% 2.63/0.83
% 2.63/0.83 Goal 1 (less_property_1): less(X, X) = true2.
% 2.63/0.83 The goal is true when:
% 2.63/0.83 X = n1
% 2.63/0.83
% 2.63/0.83 Proof:
% 2.63/0.83 less(n1, n1)
% 2.63/0.83 = { by axiom 1 (sum_something_n0_samething) }
% 2.63/0.83 true2
% 2.63/0.83 % SZS output end Proof
% 2.63/0.83
% 2.63/0.83 RESULT: Theorem (the conjecture is true).
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