TSTP Solution File: SWW469+1 by Twee---2.5.0
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% File : Twee---2.5.0
% Problem : SWW469+1 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n027.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 : Mon Jun 24 18:27:03 EDT 2024
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWW469+1 : TPTP v8.2.0. Released v5.3.0.
% 0.03/0.11 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jun 19 04:49:23 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.18/0.37 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.37
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 Take the following subset of the input axioms:
% 0.18/0.38 fof(conj_0, hypothesis, hoare_165779456gleton).
% 0.18/0.38 fof(conj_1, conjecture, ![T]: (is_state(T) => ~![S]: (is_state(S) => S=T))).
% 0.18/0.38 fof(fact_0_state__not__singleton__def, axiom, hoare_165779456gleton <=> ?[S2, T2]: (is_state(S2) & (is_state(T2) & S2!=T2))).
% 0.18/0.38
% 0.18/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.38 fresh(y, y, x1...xn) = u
% 0.18/0.38 C => fresh(s, t, x1...xn) = v
% 0.18/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.38 variables of u and v.
% 0.18/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.38 input problem has no model of domain size 1).
% 0.18/0.38
% 0.18/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.38
% 0.18/0.38 Axiom 1 (conj_0): hoare_165779456gleton = true.
% 0.18/0.38 Axiom 2 (fact_0_state__not__singleton__def_3): fresh(X, X) = true.
% 0.18/0.38 Axiom 3 (fact_0_state__not__singleton__def_3): fresh(hoare_165779456gleton, true) = is_state(s).
% 0.18/0.38 Axiom 4 (fact_0_state__not__singleton__def_2): fresh3(X, X) = true.
% 0.18/0.38 Axiom 5 (fact_0_state__not__singleton__def_2): fresh3(hoare_165779456gleton, true) = is_state(t2).
% 0.18/0.38 Axiom 6 (conj_1_1): fresh2(X, X, Y) = t.
% 0.18/0.38 Axiom 7 (conj_1_1): fresh2(is_state(X), true, X) = X.
% 0.18/0.38
% 0.18/0.38 Goal 1 (fact_0_state__not__singleton__def): tuple(s, hoare_165779456gleton) = tuple(t2, true).
% 0.18/0.38 Proof:
% 0.18/0.38 tuple(s, hoare_165779456gleton)
% 0.18/0.38 = { by axiom 1 (conj_0) }
% 0.18/0.38 tuple(s, true)
% 0.18/0.38 = { by axiom 7 (conj_1_1) R->L }
% 0.18/0.38 tuple(fresh2(is_state(s), true, s), true)
% 0.18/0.38 = { by axiom 3 (fact_0_state__not__singleton__def_3) R->L }
% 0.18/0.38 tuple(fresh2(fresh(hoare_165779456gleton, true), true, s), true)
% 0.18/0.38 = { by axiom 1 (conj_0) }
% 0.18/0.38 tuple(fresh2(fresh(true, true), true, s), true)
% 0.18/0.38 = { by axiom 2 (fact_0_state__not__singleton__def_3) }
% 0.18/0.38 tuple(fresh2(true, true, s), true)
% 0.18/0.38 = { by axiom 6 (conj_1_1) }
% 0.18/0.38 tuple(t, true)
% 0.18/0.38 = { by axiom 6 (conj_1_1) R->L }
% 0.18/0.38 tuple(fresh2(true, true, t2), true)
% 0.18/0.38 = { by axiom 4 (fact_0_state__not__singleton__def_2) R->L }
% 0.18/0.38 tuple(fresh2(fresh3(true, true), true, t2), true)
% 0.18/0.38 = { by axiom 1 (conj_0) R->L }
% 0.18/0.38 tuple(fresh2(fresh3(hoare_165779456gleton, true), true, t2), true)
% 0.18/0.38 = { by axiom 5 (fact_0_state__not__singleton__def_2) }
% 0.18/0.38 tuple(fresh2(is_state(t2), true, t2), true)
% 0.18/0.38 = { by axiom 7 (conj_1_1) }
% 0.18/0.38 tuple(t2, true)
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38
% 0.18/0.38 RESULT: Theorem (the conjecture is true).
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