TSTP Solution File: COL054-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL054-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n015.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 : Wed Aug 30 18:31:50 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% 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
% 0.00/0.12 % Problem : COL054-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % 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 : n015.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 : Sun Aug 27 05:05:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.39 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
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% 0.21/0.39 % SZS status Unsatisfiable
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% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 Take the following subset of the input axioms:
% 0.21/0.39 fof(composer_exists, hypothesis, ![Y, X, W]: response(compose(X, Y), W)=response(X, response(Y, W))).
% 0.21/0.39 fof(mocking_bird_exists, axiom, ![Y2]: response(mocking_bird, Y2)=response(Y2, Y2)).
% 0.21/0.39 fof(prove_birds_are_compatible, negated_conjecture, ![Y2, X2]: (response(a, X2)!=Y2 | response(b, Y2)!=X2)).
% 0.21/0.39
% 0.21/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.39 fresh(y, y, x1...xn) = u
% 0.21/0.39 C => fresh(s, t, x1...xn) = v
% 0.21/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.39 variables of u and v.
% 0.21/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.39 input problem has no model of domain size 1).
% 0.21/0.39
% 0.21/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.39
% 0.21/0.39 Axiom 1 (mocking_bird_exists): response(mocking_bird, X) = response(X, X).
% 0.21/0.39 Axiom 2 (composer_exists): response(compose(X, Y), Z) = response(X, response(Y, Z)).
% 0.21/0.39
% 0.21/0.39 Goal 1 (prove_birds_are_compatible): tuple(response(b, X), response(a, Y)) = tuple(Y, X).
% 0.21/0.39 The goal is true when:
% 0.21/0.39 X = response(compose(a, mocking_bird), compose(b, compose(a, mocking_bird)))
% 0.21/0.39 Y = response(mocking_bird, compose(b, compose(a, mocking_bird)))
% 0.21/0.39
% 0.21/0.39 Proof:
% 0.21/0.39 tuple(response(b, response(compose(a, mocking_bird), compose(b, compose(a, mocking_bird)))), response(a, response(mocking_bird, compose(b, compose(a, mocking_bird)))))
% 0.21/0.39 = { by axiom 2 (composer_exists) R->L }
% 0.21/0.39 tuple(response(compose(b, compose(a, mocking_bird)), compose(b, compose(a, mocking_bird))), response(a, response(mocking_bird, compose(b, compose(a, mocking_bird)))))
% 0.21/0.39 = { by axiom 1 (mocking_bird_exists) R->L }
% 0.21/0.39 tuple(response(mocking_bird, compose(b, compose(a, mocking_bird))), response(a, response(mocking_bird, compose(b, compose(a, mocking_bird)))))
% 0.21/0.39 = { by axiom 2 (composer_exists) R->L }
% 0.21/0.39 tuple(response(mocking_bird, compose(b, compose(a, mocking_bird))), response(compose(a, mocking_bird), compose(b, compose(a, mocking_bird))))
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39
% 0.21/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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