TSTP Solution File: SYO900_11 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYO900_11 : TPTP v8.2.0. Released v8.2.0.
% 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 : n007.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 04:59:25 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
% 0.07/0.12 % Problem : SYO900_11 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n007.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 05:28:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.37 Command-line arguments: --no-flatten-goal
% 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 tff(type, type, $ki_world: $tType).
% 0.12/0.38 tff(type, type, $ki_local_world: $i).
% 0.12/0.38 tff(type, type, $ki_accessible: ($i * $i) > $i).
% 0.12/0.38 tff(type, type, p: $i > $i).
% 0.12/0.38 tff(type, type, q: $i > $i).
% 0.12/0.38 tff(mrel_universal, axiom, ![W: $i, V: $i]: $ki_accessible(W, V)).
% 0.12/0.38 tff(verify, conjecture, ![W2: $ki_world]: ($ki_accessible($ki_local_world, W2) => (![W0: $i]: ($ki_accessible(W2, W0) => p(W0)) => ![W0_2: $ki_world]: ($ki_accessible(W2, W0_2) => q(W0_2)))) | ![W2: $ki_world]: ($ki_accessible($ki_local_world, W2) => (![W0_2: $i]: ($ki_accessible(W2, W0_2) => q(W0_2)) => ![W0_2: $ki_world]: ($ki_accessible(W2, W0_2) => p(W0_2))))).
% 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 (mrel_universal): $ki_accessible(X, Y) = true.
% 0.12/0.38 Axiom 2 (verify_4): fresh(X, X, Y) = true.
% 0.12/0.38 Axiom 3 (verify_5): fresh2(X, X, Y) = true.
% 0.12/0.38 Axiom 4 (verify_4): fresh($ki_accessible(w2, X), true, X) = p(X).
% 0.12/0.38 Axiom 5 (verify_5): fresh2($ki_accessible(w, X), true, X) = q(X).
% 0.12/0.38
% 0.12/0.38 Goal 1 (verify_7): q(w0_2) = true.
% 0.12/0.38 Proof:
% 0.12/0.38 q(w0_2)
% 0.12/0.38 = { by axiom 5 (verify_5) R->L }
% 0.12/0.38 fresh2($ki_accessible(w, w0_2), true, w0_2)
% 0.12/0.38 = { by axiom 1 (mrel_universal) }
% 0.12/0.38 fresh2(true, true, w0_2)
% 0.12/0.38 = { by axiom 3 (verify_5) }
% 0.12/0.38 true
% 0.12/0.38
% 0.12/0.38 Goal 2 (verify_6): p(w0) = true.
% 0.12/0.38 Proof:
% 0.12/0.38 p(w0)
% 0.12/0.38 = { by axiom 4 (verify_4) R->L }
% 0.12/0.38 fresh($ki_accessible(w2, w0), true, w0)
% 0.12/0.38 = { by axiom 1 (mrel_universal) }
% 0.12/0.38 fresh(true, true, w0)
% 0.12/0.38 = { by axiom 2 (verify_4) }
% 0.12/0.38 true
% 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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