TSTP Solution File: CAT017-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CAT017-3 : 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 : 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 : Wed Aug 30 18:18:58 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% 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 : CAT017-3 : 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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 00:36:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.40 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.20/0.40 % SZS status Unsatisfiable
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% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Take the following subset of the input axioms:
% 0.20/0.40 fof(assume_a_exists, hypothesis, there_exists(a)).
% 0.20/0.40 fof(codomain_has_elements, axiom, ![X]: (~there_exists(codomain(X)) | there_exists(X))).
% 0.20/0.40 fof(compose_codomain, axiom, ![X2]: compose(codomain(X2), X2)=X2).
% 0.20/0.40 fof(composition_implies_codomain, axiom, ![Y, X2]: (~there_exists(compose(X2, Y)) | there_exists(codomain(X2)))).
% 0.20/0.40 fof(prove_codomain_of_a_exists, negated_conjecture, ~there_exists(codomain(a))).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (assume_a_exists): there_exists(a) = true.
% 0.20/0.40 Axiom 2 (compose_codomain): compose(codomain(X), X) = X.
% 0.20/0.40 Axiom 3 (composition_implies_codomain): fresh14(X, X, Y) = true.
% 0.20/0.40 Axiom 4 (codomain_has_elements): fresh13(X, X, Y) = true.
% 0.20/0.40 Axiom 5 (composition_implies_codomain): fresh14(there_exists(compose(X, Y)), true, X) = there_exists(codomain(X)).
% 0.20/0.40 Axiom 6 (codomain_has_elements): fresh13(there_exists(codomain(X)), true, X) = there_exists(X).
% 0.20/0.40
% 0.20/0.40 Goal 1 (prove_codomain_of_a_exists): there_exists(codomain(a)) = true.
% 0.20/0.40 Proof:
% 0.20/0.40 there_exists(codomain(a))
% 0.20/0.40 = { by axiom 6 (codomain_has_elements) R->L }
% 0.20/0.40 fresh13(there_exists(codomain(codomain(a))), true, codomain(a))
% 0.20/0.40 = { by axiom 5 (composition_implies_codomain) R->L }
% 0.20/0.40 fresh13(fresh14(there_exists(compose(codomain(a), a)), true, codomain(a)), true, codomain(a))
% 0.20/0.40 = { by axiom 2 (compose_codomain) }
% 0.20/0.40 fresh13(fresh14(there_exists(a), true, codomain(a)), true, codomain(a))
% 0.20/0.40 = { by axiom 1 (assume_a_exists) }
% 0.20/0.40 fresh13(fresh14(true, true, codomain(a)), true, codomain(a))
% 0.20/0.40 = { by axiom 3 (composition_implies_codomain) }
% 0.20/0.40 fresh13(true, true, codomain(a))
% 0.20/0.40 = { by axiom 4 (codomain_has_elements) }
% 0.20/0.40 true
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40
% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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