TSTP Solution File: COL052-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL052-2 : 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 : n009.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 0.12s 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
% 0.07/0.11 % Problem : COL052-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 05:14:20 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.37 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37
% 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(agreeable1, axiom, ![X, Y]: (~agreeable(X) | response(X, common_bird(Y))=response(Y, common_bird(Y)))).
% 0.18/0.38 fof(agreeable2, axiom, ![Z, X2]: (response(X2, Z)!=response(compatible(X2), Z) | agreeable(X2))).
% 0.18/0.38 fof(c_composes_a_with_b, hypothesis, c=compose(a, b)).
% 0.18/0.38 fof(c_is_agreeable, hypothesis, agreeable(c)).
% 0.18/0.38 fof(composer_exists, axiom, ![W, X2, Y2]: response(compose(X2, Y2), W)=response(X2, response(Y2, W))).
% 0.18/0.38 fof(prove_a_is_agreeable, negated_conjecture, ~agreeable(a)).
% 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 (c_is_agreeable): agreeable(c) = true.
% 0.18/0.38 Axiom 2 (c_composes_a_with_b): c = compose(a, b).
% 0.18/0.38 Axiom 3 (agreeable2): fresh2(X, X, Y) = true.
% 0.18/0.38 Axiom 4 (agreeable1): fresh(X, X, Y, Z) = response(Z, common_bird(Z)).
% 0.18/0.38 Axiom 5 (composer_exists): response(compose(X, Y), Z) = response(X, response(Y, Z)).
% 0.18/0.38 Axiom 6 (agreeable1): fresh(agreeable(X), true, X, Y) = response(X, common_bird(Y)).
% 0.18/0.38 Axiom 7 (agreeable2): fresh2(response(X, Y), response(compatible(X), Y), X) = agreeable(X).
% 0.18/0.38
% 0.18/0.38 Goal 1 (prove_a_is_agreeable): agreeable(a) = true.
% 0.18/0.38 Proof:
% 0.18/0.38 agreeable(a)
% 0.18/0.38 = { by axiom 7 (agreeable2) R->L }
% 0.18/0.38 fresh2(response(a, response(b, common_bird(compose(compatible(a), b)))), response(compatible(a), response(b, common_bird(compose(compatible(a), b)))), a)
% 0.18/0.38 = { by axiom 5 (composer_exists) R->L }
% 0.18/0.38 fresh2(response(compose(a, b), common_bird(compose(compatible(a), b))), response(compatible(a), response(b, common_bird(compose(compatible(a), b)))), a)
% 0.18/0.38 = { by axiom 2 (c_composes_a_with_b) R->L }
% 0.18/0.38 fresh2(response(c, common_bird(compose(compatible(a), b))), response(compatible(a), response(b, common_bird(compose(compatible(a), b)))), a)
% 0.18/0.38 = { by axiom 5 (composer_exists) R->L }
% 0.18/0.38 fresh2(response(c, common_bird(compose(compatible(a), b))), response(compose(compatible(a), b), common_bird(compose(compatible(a), b))), a)
% 0.18/0.38 = { by axiom 4 (agreeable1) R->L }
% 0.18/0.38 fresh2(response(c, common_bird(compose(compatible(a), b))), fresh(true, true, c, compose(compatible(a), b)), a)
% 0.18/0.38 = { by axiom 1 (c_is_agreeable) R->L }
% 0.18/0.38 fresh2(response(c, common_bird(compose(compatible(a), b))), fresh(agreeable(c), true, c, compose(compatible(a), b)), a)
% 0.18/0.38 = { by axiom 6 (agreeable1) }
% 0.18/0.38 fresh2(response(c, common_bird(compose(compatible(a), b))), response(c, common_bird(compose(compatible(a), b))), a)
% 0.18/0.38 = { by axiom 3 (agreeable2) }
% 0.18/0.38 true
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38
% 0.18/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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