TSTP Solution File: SYN969+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN969+1 : TPTP v8.1.2. Released v3.1.0.
% 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 03:36:41 EDT 2023
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SYN969+1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 17:08:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.40 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.40
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Take the following subset of the input axioms:
% 0.21/0.40 fof(prove_this, conjecture, ![B]: ((![X]: (p(X) => q(X)) & r(B)) => (![Y]: (r(Y) => p(Y)) => q(B)))).
% 0.21/0.40
% 0.21/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.40 fresh(y, y, x1...xn) = u
% 0.21/0.40 C => fresh(s, t, x1...xn) = v
% 0.21/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.40 variables of u and v.
% 0.21/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.40 input problem has no model of domain size 1).
% 0.21/0.40
% 0.21/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.40
% 0.21/0.40 Axiom 1 (prove_this): r(b) = true.
% 0.21/0.40 Axiom 2 (prove_this_1): fresh(X, X, Y) = true.
% 0.21/0.40 Axiom 3 (prove_this_3): fresh2(X, X, Y) = true.
% 0.21/0.40 Axiom 4 (prove_this_1): fresh(p(X), true, X) = q(X).
% 0.21/0.40 Axiom 5 (prove_this_3): fresh2(r(X), true, X) = p(X).
% 0.21/0.40
% 0.21/0.40 Goal 1 (prove_this_2): q(b) = true.
% 0.21/0.40 Proof:
% 0.21/0.40 q(b)
% 0.21/0.40 = { by axiom 4 (prove_this_1) R->L }
% 0.21/0.40 fresh(p(b), true, b)
% 0.21/0.40 = { by axiom 5 (prove_this_3) R->L }
% 0.21/0.40 fresh(fresh2(r(b), true, b), true, b)
% 0.21/0.40 = { by axiom 1 (prove_this) }
% 0.21/0.40 fresh(fresh2(true, true, b), true, b)
% 0.21/0.40 = { by axiom 3 (prove_this_3) }
% 0.21/0.40 fresh(true, true, b)
% 0.21/0.40 = { by axiom 2 (prove_this_1) }
% 0.21/0.40 true
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40
% 0.21/0.40 RESULT: Theorem (the conjecture is true).
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