TSTP Solution File: SYO895_9 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYO895_9 : 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 : n011.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 04:59:24 EDT 2023
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO895_9 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 06:38:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.39 Command-line arguments: --no-flatten-goal
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 Take the following subset of the input axioms:
% 0.14/0.39 tff(type, type, $ki_world: $tType).
% 0.14/0.39 tff(type, type, $ki_local_world: $i).
% 0.14/0.39 tff(type, type, $ki_accessible: ($i * $i) > $i).
% 0.14/0.39 tff(type, type, p: $i > $i).
% 0.14/0.39 tff(type, type, q: $i > $i).
% 0.14/0.39 tff(verify, conjecture, (![W: $i]: ($ki_accessible($ki_local_world, W) => p(W)) & ![W2: $i]: ($ki_accessible($ki_local_world, W2) => q(W2))) => ![W2: $ki_world]: ($ki_accessible($ki_local_world, W2) => (p(W2) & q(W2)))).
% 0.14/0.39
% 0.14/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.39 fresh(y, y, x1...xn) = u
% 0.14/0.39 C => fresh(s, t, x1...xn) = v
% 0.14/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.39 variables of u and v.
% 0.14/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.39 input problem has no model of domain size 1).
% 0.14/0.39
% 0.14/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.39
% 0.14/0.39 Axiom 1 (verify): $ki_accessible($ki_local_world, w) = true.
% 0.14/0.39 Axiom 2 (verify_1): fresh(X, X, Y) = true.
% 0.14/0.40 Axiom 3 (verify_2): fresh2(X, X, Y) = true.
% 0.14/0.40 Axiom 4 (verify_1): fresh($ki_accessible($ki_local_world, X), true, X) = p(X).
% 0.14/0.40 Axiom 5 (verify_2): fresh2($ki_accessible($ki_local_world, X), true, X) = q(X).
% 0.14/0.40
% 0.14/0.40 Goal 1 (verify_3): tuple(p(w), q(w)) = tuple(true, true).
% 0.14/0.40 Proof:
% 0.14/0.40 tuple(p(w), q(w))
% 0.14/0.40 = { by axiom 4 (verify_1) R->L }
% 0.14/0.40 tuple(fresh($ki_accessible($ki_local_world, w), true, w), q(w))
% 0.14/0.40 = { by axiom 1 (verify) }
% 0.14/0.40 tuple(fresh(true, true, w), q(w))
% 0.14/0.40 = { by axiom 2 (verify_1) }
% 0.14/0.40 tuple(true, q(w))
% 0.14/0.40 = { by axiom 5 (verify_2) R->L }
% 0.14/0.40 tuple(true, fresh2($ki_accessible($ki_local_world, w), true, w))
% 0.14/0.40 = { by axiom 1 (verify) }
% 0.14/0.40 tuple(true, fresh2(true, true, w))
% 0.14/0.40 = { by axiom 3 (verify_2) }
% 0.14/0.40 tuple(true, true)
% 0.14/0.40 % SZS output end Proof
% 0.14/0.40
% 0.14/0.40 RESULT: Theorem (the conjecture is true).
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