TSTP Solution File: SYN066+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN066+1 : TPTP v8.1.2. Bugfixed v3.0.0.
% 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 : n001.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 : Fri Sep 1 03:33:00 EDT 2023
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% 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 : SYN066+1 : TPTP v8.1.2. Bugfixed v3.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 22:28:16 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.37 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 Take the following subset of the input axioms:
% 0.12/0.38 fof(pel37, conjecture, ![X]: ?[Y]: big_r(X, Y)).
% 0.12/0.38 fof(pel37_1, axiom, ![Z]: ?[W]: ![X2]: ?[Y2]: ((big_p(X2, Z) => big_p(Y2, W)) & (big_p(Y2, Z) & (big_p(Y2, W) => ?[U]: big_q(U, W))))).
% 0.12/0.38 fof(pel37_3, axiom, ?[X2, Y2]: big_q(X2, Y2) => ![Z2]: big_r(Z2, Z2)).
% 0.12/0.38
% 0.12/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.12/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.12/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.12/0.38 fresh(y, y, x1...xn) = u
% 0.12/0.38 C => fresh(s, t, x1...xn) = v
% 0.12/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.12/0.38 variables of u and v.
% 0.12/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.12/0.38 input problem has no model of domain size 1).
% 0.12/0.38
% 0.12/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.12/0.38
% 0.12/0.38 Axiom 1 (pel37_3): fresh(X, X, Y) = true2.
% 0.12/0.38 Axiom 2 (pel37_1_2): fresh3(X, X, Y) = true2.
% 0.12/0.38 Axiom 3 (pel37_1): big_p(y(X, Y), X) = true2.
% 0.12/0.38 Axiom 4 (pel37_1_1): fresh2(X, X, Y, Z) = true2.
% 0.12/0.38 Axiom 5 (pel37_3): fresh(big_q(X, Y), true2, Z) = big_r(Z, Z).
% 0.12/0.38 Axiom 6 (pel37_1_1): fresh2(big_p(X, Y), true2, Y, X) = big_p(y(Y, X), w(Y)).
% 0.12/0.38 Axiom 7 (pel37_1_2): fresh3(big_p(y(X, Y), w(X)), true2, X) = big_q(u(X), w(X)).
% 0.12/0.38
% 0.12/0.38 Goal 1 (pel37): big_r(x, X) = true2.
% 0.12/0.38 The goal is true when:
% 0.12/0.38 X = x
% 0.12/0.38
% 0.12/0.38 Proof:
% 0.12/0.38 big_r(x, x)
% 0.12/0.38 = { by axiom 5 (pel37_3) R->L }
% 0.12/0.38 fresh(big_q(u(X), w(X)), true2, x)
% 0.12/0.38 = { by axiom 7 (pel37_1_2) R->L }
% 0.12/0.38 fresh(fresh3(big_p(y(X, y(X, Y)), w(X)), true2, X), true2, x)
% 0.12/0.38 = { by axiom 6 (pel37_1_1) R->L }
% 0.12/0.38 fresh(fresh3(fresh2(big_p(y(X, Y), X), true2, X, y(X, Y)), true2, X), true2, x)
% 0.12/0.38 = { by axiom 3 (pel37_1) }
% 0.12/0.38 fresh(fresh3(fresh2(true2, true2, X, y(X, Y)), true2, X), true2, x)
% 0.12/0.38 = { by axiom 4 (pel37_1_1) }
% 0.12/0.38 fresh(fresh3(true2, true2, X), true2, x)
% 0.12/0.38 = { by axiom 2 (pel37_1_2) }
% 0.12/0.38 fresh(true2, true2, x)
% 0.12/0.38 = { by axiom 1 (pel37_3) }
% 0.12/0.38 true2
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38
% 0.12/0.38 RESULT: Theorem (the conjecture is true).
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