TSTP Solution File: NUM295+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM295+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 : n027.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 4.48s 0.98s
% Output : Proof 4.48s
% 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 : NUM295+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % 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 : n027.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 : Fri Aug 25 15:29:19 EDT 2023
% 0.20/0.35 % CPUTime :
% 4.48/0.98 Command-line arguments: --no-flatten-goal
% 4.48/0.98
% 4.48/0.98 % SZS status Theorem
% 4.48/0.98
% 4.48/0.98 % SZS output start Proof
% 4.48/0.98 Take the following subset of the input axioms:
% 4.48/0.99 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))).
% 4.48/0.99 fof(less_property, axiom, ![X2, Y2]: (less(X2, Y2) <=> (~less(Y2, X2) & Y2!=X2))).
% 4.48/0.99 fof(rdn9, axiom, rdn_translate(n9, rdn_pos(rdnn(n9)))).
% 4.48/0.99 fof(rdnn1, axiom, rdn_translate(nn1, rdn_neg(rdnn(n1)))).
% 4.48/0.99 fof(something_less_something, conjecture, ?[X2, Y2]: less(X2, Y2)).
% 4.48/0.99
% 4.48/0.99 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.48/0.99 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.48/0.99 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.48/0.99 fresh(y, y, x1...xn) = u
% 4.48/0.99 C => fresh(s, t, x1...xn) = v
% 4.48/0.99 where fresh is a fresh function symbol and x1..xn are the free
% 4.48/0.99 variables of u and v.
% 4.48/0.99 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.48/0.99 input problem has no model of domain size 1).
% 4.48/0.99
% 4.48/0.99 The encoding turns the above axioms into the following unit equations and goals:
% 4.48/0.99
% 4.48/0.99 Axiom 1 (less_entry_point_neg_pos): fresh24(X, X, Y, Z) = true2.
% 4.48/0.99 Axiom 2 (rdnn1): rdn_translate(nn1, rdn_neg(rdnn(n1))) = true2.
% 4.48/0.99 Axiom 3 (rdn9): rdn_translate(n9, rdn_pos(rdnn(n9))) = true2.
% 4.48/0.99 Axiom 4 (less_entry_point_neg_pos): fresh25(X, X, Y, Z, W) = less(Y, Z).
% 4.48/0.99 Axiom 5 (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).
% 4.48/0.99
% 4.48/0.99 Goal 1 (something_less_something): less(X, Y) = true2.
% 4.48/0.99 The goal is true when:
% 4.48/0.99 X = nn1
% 4.48/0.99 Y = n9
% 4.48/0.99
% 4.48/0.99 Proof:
% 4.48/0.99 less(nn1, n9)
% 4.48/0.99 = { by axiom 4 (less_entry_point_neg_pos) R->L }
% 4.48/0.99 fresh25(true2, true2, nn1, n9, rdnn(n1))
% 4.48/0.99 = { by axiom 3 (rdn9) R->L }
% 4.48/0.99 fresh25(rdn_translate(n9, rdn_pos(rdnn(n9))), true2, nn1, n9, rdnn(n1))
% 4.48/0.99 = { by axiom 5 (less_entry_point_neg_pos) }
% 4.48/0.99 fresh24(rdn_translate(nn1, rdn_neg(rdnn(n1))), true2, nn1, n9)
% 4.48/0.99 = { by axiom 2 (rdnn1) }
% 4.48/0.99 fresh24(true2, true2, nn1, n9)
% 4.48/0.99 = { by axiom 1 (less_entry_point_neg_pos) }
% 4.48/0.99 true2
% 4.48/0.99 % SZS output end Proof
% 4.48/0.99
% 4.48/0.99 RESULT: Theorem (the conjecture is true).
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