TSTP Solution File: NUM298+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM298+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 : n023.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 11:55:50 EDT 2023
% Result : Theorem 17.98s 2.67s
% Output : Proof 17.98s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM298+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13 % 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 : n023.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 18:15:12 EDT 2023
% 0.13/0.35 % CPUTime :
% 17.98/2.67 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 17.98/2.67
% 17.98/2.67 % SZS status Theorem
% 17.98/2.67
% 17.98/2.68 % SZS output start Proof
% 17.98/2.68 Take the following subset of the input axioms:
% 17.98/2.68 fof(less_entry_point_neg_pos, axiom, ![X, Y, RDN_X, RDN_Y]: ((rdn_translate(X, rdn_neg(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y))) => less(X, Y))).
% 17.98/2.68 fof(less_property, axiom, ![X2, Y2]: (less(X2, Y2) <=> (~less(Y2, X2) & Y2!=X2))).
% 17.98/2.68 fof(n2_not_less_nn2, conjecture, ~less(n2, nn2)).
% 17.98/2.68 fof(rdn2, axiom, rdn_translate(n2, rdn_pos(rdnn(n2)))).
% 17.98/2.68 fof(rdnn2, axiom, rdn_translate(nn2, rdn_neg(rdnn(n2)))).
% 17.98/2.68
% 17.98/2.68 Now clausify the problem and encode Horn clauses using encoding 3 of
% 17.98/2.68 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 17.98/2.68 We repeatedly replace C & s=t => u=v by the two clauses:
% 17.98/2.68 fresh(y, y, x1...xn) = u
% 17.98/2.68 C => fresh(s, t, x1...xn) = v
% 17.98/2.68 where fresh is a fresh function symbol and x1..xn are the free
% 17.98/2.68 variables of u and v.
% 17.98/2.68 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 17.98/2.68 input problem has no model of domain size 1).
% 17.98/2.68
% 17.98/2.68 The encoding turns the above axioms into the following unit equations and goals:
% 17.98/2.68
% 17.98/2.68 Axiom 1 (n2_not_less_nn2): less(n2, nn2) = true2.
% 17.98/2.68 Axiom 2 (rdn2): rdn_translate(n2, rdn_pos(rdnn(n2))) = true2.
% 17.98/2.68 Axiom 3 (rdnn2): rdn_translate(nn2, rdn_neg(rdnn(n2))) = true2.
% 17.98/2.68 Axiom 4 (less_entry_point_neg_pos): fresh24(X, X, Y, Z) = true2.
% 17.98/2.68 Axiom 5 (less_entry_point_neg_pos): fresh25(X, X, Y, Z, W) = less(Y, Z).
% 17.98/2.68 Axiom 6 (less_entry_point_neg_pos): fresh25(rdn_translate(X, rdn_pos(Y)), true2, Z, X, W) = fresh24(rdn_translate(Z, rdn_neg(W)), true2, Z, X).
% 17.98/2.68
% 17.98/2.68 Goal 1 (less_property_2): tuple(less(X, Y), less(Y, X)) = tuple(true2, true2).
% 17.98/2.68 The goal is true when:
% 17.98/2.68 X = nn2
% 17.98/2.68 Y = n2
% 17.98/2.68
% 17.98/2.68 Proof:
% 17.98/2.68 tuple(less(nn2, n2), less(n2, nn2))
% 17.98/2.68 = { by axiom 5 (less_entry_point_neg_pos) R->L }
% 17.98/2.68 tuple(fresh25(true2, true2, nn2, n2, rdnn(n2)), less(n2, nn2))
% 17.98/2.68 = { by axiom 2 (rdn2) R->L }
% 17.98/2.68 tuple(fresh25(rdn_translate(n2, rdn_pos(rdnn(n2))), true2, nn2, n2, rdnn(n2)), less(n2, nn2))
% 17.98/2.68 = { by axiom 6 (less_entry_point_neg_pos) }
% 17.98/2.68 tuple(fresh24(rdn_translate(nn2, rdn_neg(rdnn(n2))), true2, nn2, n2), less(n2, nn2))
% 17.98/2.68 = { by axiom 3 (rdnn2) }
% 17.98/2.68 tuple(fresh24(true2, true2, nn2, n2), less(n2, nn2))
% 17.98/2.68 = { by axiom 4 (less_entry_point_neg_pos) }
% 17.98/2.68 tuple(true2, less(n2, nn2))
% 17.98/2.68 = { by axiom 1 (n2_not_less_nn2) }
% 17.98/2.68 tuple(true2, true2)
% 17.98/2.68 % SZS output end Proof
% 17.98/2.68
% 17.98/2.68 RESULT: Theorem (the conjecture is true).
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