TSTP Solution File: SYN365+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN365+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n032.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 03:34:19 EDT 2023
% Result : Theorem 0.09s 0.31s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SYN365+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Sat Aug 26 18:09:59 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.09/0.31 Command-line arguments: --no-flatten-goal
% 0.09/0.31
% 0.09/0.31 % SZS status Theorem
% 0.09/0.31
% 0.09/0.31 % SZS output start Proof
% 0.09/0.31 Take the following subset of the input axioms:
% 0.09/0.31 fof(x2116, conjecture, (![X]: ?[Y]: (big_p(X) => (big_r(X, g(h(Y))) & big_p(Y))) & ![W]: (big_p(W) => (big_p(g(W)) & big_p(h(W))))) => ![X2]: (big_p(X2) => ?[Y2]: (big_r(X2, Y2) & big_p(Y2)))).
% 0.09/0.31
% 0.09/0.31 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.09/0.31 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.09/0.31 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.09/0.31 fresh(y, y, x1...xn) = u
% 0.09/0.31 C => fresh(s, t, x1...xn) = v
% 0.09/0.31 where fresh is a fresh function symbol and x1..xn are the free
% 0.09/0.31 variables of u and v.
% 0.09/0.31 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.09/0.31 input problem has no model of domain size 1).
% 0.09/0.31
% 0.09/0.31 The encoding turns the above axioms into the following unit equations and goals:
% 0.09/0.31
% 0.09/0.31 Axiom 1 (x2116): big_p(x) = true2.
% 0.09/0.31 Axiom 2 (x2116_4): fresh(X, X, Y) = true2.
% 0.09/0.31 Axiom 3 (x2116_2): fresh4(X, X, Y) = true2.
% 0.09/0.31 Axiom 4 (x2116_1): fresh3(X, X, Y) = true2.
% 0.09/0.31 Axiom 5 (x2116_3): fresh2(X, X, Y) = true2.
% 0.09/0.31 Axiom 6 (x2116_4): fresh(big_p(X), true2, X) = big_p(h(X)).
% 0.09/0.31 Axiom 7 (x2116_1): fresh3(big_p(X), true2, X) = big_p(y(X)).
% 0.09/0.31 Axiom 8 (x2116_3): fresh2(big_p(X), true2, X) = big_p(g(X)).
% 0.09/0.31 Axiom 9 (x2116_2): fresh4(big_p(X), true2, X) = big_r(X, g(h(y(X)))).
% 0.09/0.31
% 0.09/0.31 Goal 1 (x2116_5): tuple(big_p(X), big_r(x, X)) = tuple(true2, true2).
% 0.09/0.31 The goal is true when:
% 0.09/0.31 X = g(h(y(x)))
% 0.09/0.31
% 0.09/0.31 Proof:
% 0.09/0.31 tuple(big_p(g(h(y(x)))), big_r(x, g(h(y(x)))))
% 0.09/0.31 = { by axiom 8 (x2116_3) R->L }
% 0.09/0.31 tuple(fresh2(big_p(h(y(x))), true2, h(y(x))), big_r(x, g(h(y(x)))))
% 0.09/0.31 = { by axiom 6 (x2116_4) R->L }
% 0.09/0.31 tuple(fresh2(fresh(big_p(y(x)), true2, y(x)), true2, h(y(x))), big_r(x, g(h(y(x)))))
% 0.09/0.31 = { by axiom 7 (x2116_1) R->L }
% 0.09/0.31 tuple(fresh2(fresh(fresh3(big_p(x), true2, x), true2, y(x)), true2, h(y(x))), big_r(x, g(h(y(x)))))
% 0.09/0.32 = { by axiom 1 (x2116) }
% 0.09/0.32 tuple(fresh2(fresh(fresh3(true2, true2, x), true2, y(x)), true2, h(y(x))), big_r(x, g(h(y(x)))))
% 0.09/0.32 = { by axiom 4 (x2116_1) }
% 0.09/0.32 tuple(fresh2(fresh(true2, true2, y(x)), true2, h(y(x))), big_r(x, g(h(y(x)))))
% 0.09/0.32 = { by axiom 2 (x2116_4) }
% 0.09/0.32 tuple(fresh2(true2, true2, h(y(x))), big_r(x, g(h(y(x)))))
% 0.09/0.32 = { by axiom 5 (x2116_3) }
% 0.09/0.32 tuple(true2, big_r(x, g(h(y(x)))))
% 0.09/0.32 = { by axiom 9 (x2116_2) R->L }
% 0.09/0.32 tuple(true2, fresh4(big_p(x), true2, x))
% 0.09/0.32 = { by axiom 1 (x2116) }
% 0.09/0.32 tuple(true2, fresh4(true2, true2, x))
% 0.09/0.32 = { by axiom 3 (x2116_2) }
% 0.09/0.32 tuple(true2, true2)
% 0.09/0.32 % SZS output end Proof
% 0.09/0.32
% 0.09/0.32 RESULT: Theorem (the conjecture is true).
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