TSTP Solution File: SYN978+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : SYN978+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 : n032.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 03:36:44 EDT 2023
% Result : Theorem 0.14s 0.31s
% 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
% 0.00/0.09 % Problem : SYN978+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sat Aug 26 19:43:59 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.31 Command-line arguments: --no-flatten-goal
% 0.14/0.31
% 0.14/0.31 % SZS status Theorem
% 0.14/0.31
% 0.14/0.31 % SZS output start Proof
% 0.14/0.31 Take the following subset of the input axioms:
% 0.14/0.31 fof(prove_this, conjecture, (a & b) => (a <=> b)).
% 0.14/0.31
% 0.14/0.31 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.31 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.31 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.31 fresh(y, y, x1...xn) = u
% 0.14/0.31 C => fresh(s, t, x1...xn) = v
% 0.14/0.31 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.31 variables of u and v.
% 0.14/0.31 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.31 input problem has no model of domain size 1).
% 0.14/0.31
% 0.14/0.31 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.31
% 0.14/0.31 Axiom 1 (prove_this): a = true.
% 0.14/0.31 Axiom 2 (prove_this_2): b = true.
% 0.14/0.31
% 0.14/0.31 Goal 1 (prove_this_3): tuple(a, b) = tuple(true, true).
% 0.14/0.31 Proof:
% 0.14/0.31 tuple(a, b)
% 0.14/0.31 = { by axiom 2 (prove_this_2) }
% 0.14/0.31 tuple(a, true)
% 0.14/0.31 = { by axiom 1 (prove_this) R->L }
% 0.14/0.31 tuple(a, a)
% 0.14/0.31 = { by axiom 1 (prove_this) }
% 0.14/0.31 tuple(true, a)
% 0.14/0.31 = { by axiom 1 (prove_this) }
% 0.14/0.31 tuple(true, true)
% 0.14/0.31 % SZS output end Proof
% 0.14/0.31
% 0.14/0.31 RESULT: Theorem (the conjecture is true).
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