TSTP Solution File: NUM290+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM290+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 11:55:49 EDT 2023
% Result : Theorem 50.97s 6.78s
% Output : Proof 50.97s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM290+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 11:45:42 EDT 2023
% 0.12/0.33 % CPUTime :
% 50.97/6.78 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 50.97/6.78
% 50.97/6.78 % SZS status Theorem
% 50.97/6.78
% 50.97/6.78 % SZS output start Proof
% 50.97/6.78 Take the following subset of the input axioms:
% 50.97/6.78 fof(less_entry_point_pos_pos, axiom, ![X, Y, RDN_X, RDN_Y]: ((rdn_translate(X, rdn_pos(RDN_X)) & (rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) => less(X, Y))).
% 50.97/6.78 fof(n2_less_n3, conjecture, less(n2, n3)).
% 50.97/6.78 fof(rdn2, axiom, rdn_translate(n2, rdn_pos(rdnn(n2)))).
% 50.97/6.78 fof(rdn3, axiom, rdn_translate(n3, rdn_pos(rdnn(n3)))).
% 50.97/6.78 fof(rdn_positive_less23, axiom, rdn_positive_less(rdnn(n2), rdnn(n3))).
% 50.97/6.78
% 50.97/6.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 50.97/6.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 50.97/6.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 50.97/6.78 fresh(y, y, x1...xn) = u
% 50.97/6.78 C => fresh(s, t, x1...xn) = v
% 50.97/6.78 where fresh is a fresh function symbol and x1..xn are the free
% 50.97/6.78 variables of u and v.
% 50.97/6.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 50.97/6.78 input problem has no model of domain size 1).
% 50.97/6.78
% 50.97/6.78 The encoding turns the above axioms into the following unit equations and goals:
% 50.97/6.78
% 50.97/6.78 Axiom 1 (rdn2): rdn_translate(n2, rdn_pos(rdnn(n2))) = true2.
% 50.97/6.78 Axiom 2 (rdn3): rdn_translate(n3, rdn_pos(rdnn(n3))) = true2.
% 50.97/6.78 Axiom 3 (rdn_positive_less23): rdn_positive_less(rdnn(n2), rdnn(n3)) = true2.
% 50.97/6.78 Axiom 4 (less_entry_point_pos_pos): fresh69(X, X, Y, Z) = true2.
% 50.97/6.78 Axiom 5 (less_entry_point_pos_pos): fresh23(X, X, Y, Z, W) = less(Y, Z).
% 50.97/6.78 Axiom 6 (less_entry_point_pos_pos): fresh68(X, X, Y, Z, W, V) = fresh69(rdn_translate(Y, rdn_pos(W)), true2, Y, Z).
% 50.97/6.78 Axiom 7 (less_entry_point_pos_pos): fresh68(rdn_positive_less(X, Y), true2, Z, W, X, Y) = fresh23(rdn_translate(W, rdn_pos(Y)), true2, Z, W, X).
% 50.97/6.78
% 50.97/6.78 Goal 1 (n2_less_n3): less(n2, n3) = true2.
% 50.97/6.78 Proof:
% 50.97/6.78 less(n2, n3)
% 50.97/6.79 = { by axiom 5 (less_entry_point_pos_pos) R->L }
% 50.97/6.79 fresh23(true2, true2, n2, n3, rdnn(n2))
% 50.97/6.79 = { by axiom 2 (rdn3) R->L }
% 50.97/6.79 fresh23(rdn_translate(n3, rdn_pos(rdnn(n3))), true2, n2, n3, rdnn(n2))
% 50.97/6.79 = { by axiom 7 (less_entry_point_pos_pos) R->L }
% 50.97/6.79 fresh68(rdn_positive_less(rdnn(n2), rdnn(n3)), true2, n2, n3, rdnn(n2), rdnn(n3))
% 50.97/6.79 = { by axiom 3 (rdn_positive_less23) }
% 50.97/6.79 fresh68(true2, true2, n2, n3, rdnn(n2), rdnn(n3))
% 50.97/6.79 = { by axiom 6 (less_entry_point_pos_pos) }
% 50.97/6.79 fresh69(rdn_translate(n2, rdn_pos(rdnn(n2))), true2, n2, n3)
% 50.97/6.79 = { by axiom 1 (rdn2) }
% 50.97/6.79 fresh69(true2, true2, n2, n3)
% 50.97/6.79 = { by axiom 4 (less_entry_point_pos_pos) }
% 50.97/6.79 true2
% 50.97/6.79 % SZS output end Proof
% 50.97/6.79
% 50.97/6.79 RESULT: Theorem (the conjecture is true).
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