TSTP Solution File: SYO888_10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYO888_10 : 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 : n028.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 04:59:22 EDT 2023
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 07:48:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.39 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.39
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Take the following subset of the input axioms:
% 0.19/0.39 tff(type, type, $ki_world: $tType).
% 0.19/0.39 tff(type, type, $ki_local_world: $i).
% 0.19/0.39 tff(type, type, $ki_accessible: ($i * $i) > $i).
% 0.19/0.39 tff(type, type, f: ($i * $i) > $i).
% 0.19/0.39 tff(type, type, g: ($i * $i) > $i).
% 0.19/0.39 tff(type, type, h: ($i * $i) > $i).
% 0.19/0.39 tff(type, type, '$ki_exists_in_world_$i': ($i * $i) > $i).
% 0.19/0.39 tff(mrel_reflexive, axiom, ![W: $i]: $ki_accessible(W, W)).
% 0.19/0.39 tff(verify, conjecture, (![X: $i]: ('$ki_exists_in_world_$i'($ki_local_world, X) => (f($ki_local_world, X) => ![W2: $i]: ($ki_accessible($ki_local_world, W2) => g(W2, X)))) & ![X2: $i]: ('$ki_exists_in_world_$i'($ki_local_world, X2) => (g($ki_local_world, X2) => ![W2: $i]: ($ki_accessible($ki_local_world, W2) => h(W2, X2))))) => ![X2: $i]: ('$ki_exists_in_world_$i'($ki_local_world, X2) => (f($ki_local_world, X2) => ![W2: $ki_world]: ($ki_accessible($ki_local_world, W2) => h(W2, X2))))).
% 0.19/0.39
% 0.19/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.39 fresh(y, y, x1...xn) = u
% 0.19/0.39 C => fresh(s, t, x1...xn) = v
% 0.19/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.39 variables of u and v.
% 0.19/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.39 input problem has no model of domain size 1).
% 0.19/0.39
% 0.19/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.39
% 0.19/0.39 Axiom 1 (mrel_reflexive): $ki_accessible(X, X) = true.
% 0.19/0.39 Axiom 2 (verify): $ki_accessible($ki_local_world, w) = true.
% 0.19/0.39 Axiom 3 (verify_2): $ki_exists_in_world_$i($ki_local_world, x) = true.
% 0.19/0.39 Axiom 4 (verify_1): f($ki_local_world, x) = true.
% 0.19/0.39 Axiom 5 (verify_4): fresh(X, X, Y, Z) = h(Z, Y).
% 0.19/0.39 Axiom 6 (verify_3): fresh8(X, X, Y, Z) = true.
% 0.19/0.39 Axiom 7 (verify_4): fresh6(X, X, Y, Z) = true.
% 0.19/0.39 Axiom 8 (verify_3): fresh2(X, X, Y, Z) = g(Z, Y).
% 0.19/0.39 Axiom 9 (verify_3): fresh7(X, X, Y, Z) = fresh8($ki_accessible($ki_local_world, Z), true, Y, Z).
% 0.19/0.39 Axiom 10 (verify_4): fresh5(X, X, Y, Z) = fresh6($ki_accessible($ki_local_world, Z), true, Y, Z).
% 0.19/0.39 Axiom 11 (verify_4): fresh5($ki_exists_in_world_$i($ki_local_world, X), true, X, Y) = fresh(g($ki_local_world, X), true, X, Y).
% 0.19/0.39 Axiom 12 (verify_3): fresh7($ki_exists_in_world_$i($ki_local_world, X), true, X, Y) = fresh2(f($ki_local_world, X), true, X, Y).
% 0.19/0.39
% 0.19/0.39 Goal 1 (verify_5): h(w, x) = true.
% 0.19/0.39 Proof:
% 0.19/0.39 h(w, x)
% 0.19/0.39 = { by axiom 5 (verify_4) R->L }
% 0.19/0.39 fresh(true, true, x, w)
% 0.19/0.39 = { by axiom 6 (verify_3) R->L }
% 0.19/0.39 fresh(fresh8(true, true, x, $ki_local_world), true, x, w)
% 0.19/0.39 = { by axiom 1 (mrel_reflexive) R->L }
% 0.19/0.39 fresh(fresh8($ki_accessible($ki_local_world, $ki_local_world), true, x, $ki_local_world), true, x, w)
% 0.19/0.39 = { by axiom 9 (verify_3) R->L }
% 0.19/0.39 fresh(fresh7(true, true, x, $ki_local_world), true, x, w)
% 0.19/0.39 = { by axiom 3 (verify_2) R->L }
% 0.19/0.39 fresh(fresh7($ki_exists_in_world_$i($ki_local_world, x), true, x, $ki_local_world), true, x, w)
% 0.19/0.39 = { by axiom 12 (verify_3) }
% 0.19/0.39 fresh(fresh2(f($ki_local_world, x), true, x, $ki_local_world), true, x, w)
% 0.19/0.39 = { by axiom 4 (verify_1) }
% 0.19/0.39 fresh(fresh2(true, true, x, $ki_local_world), true, x, w)
% 0.19/0.39 = { by axiom 8 (verify_3) }
% 0.19/0.39 fresh(g($ki_local_world, x), true, x, w)
% 0.19/0.39 = { by axiom 11 (verify_4) R->L }
% 0.19/0.39 fresh5($ki_exists_in_world_$i($ki_local_world, x), true, x, w)
% 0.19/0.39 = { by axiom 3 (verify_2) }
% 0.19/0.39 fresh5(true, true, x, w)
% 0.19/0.39 = { by axiom 10 (verify_4) }
% 0.19/0.40 fresh6($ki_accessible($ki_local_world, w), true, x, w)
% 0.19/0.40 = { by axiom 2 (verify) }
% 0.19/0.40 fresh6(true, true, x, w)
% 0.19/0.40 = { by axiom 7 (verify_4) }
% 0.19/0.40 true
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Theorem (the conjecture is true).
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