TSTP Solution File: CAT011-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CAT011-3 : 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 : n019.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 18:18:54 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% 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 : CAT011-3 : 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
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun Aug 27 00:07:28 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.19/0.39 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Take the following subset of the input axioms:
% 0.19/0.39 fof(assume_domain_exists, hypothesis, there_exists(domain(a))).
% 0.19/0.39 fof(compose_codomain, axiom, ![X]: compose(codomain(X), X)=X).
% 0.19/0.39 fof(compose_domain, axiom, ![X2]: compose(X2, domain(X2))=X2).
% 0.19/0.39 fof(domain_codomain_composition1, axiom, ![Y, X2]: (~there_exists(compose(X2, Y)) | domain(X2)=codomain(Y))).
% 0.19/0.39 fof(domain_has_elements, axiom, ![X2]: (~there_exists(domain(X2)) | there_exists(X2))).
% 0.19/0.39 fof(prove_domain_is_idempotent, negated_conjecture, domain(domain(a))!=domain(a)).
% 0.19/0.39
% 0.19/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.39 fresh(y, y, x1...xn) = u
% 0.19/0.39 C => fresh(s, t, x1...xn) = v
% 0.19/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.39 variables of u and v.
% 0.19/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.39 input problem has no model of domain size 1).
% 0.19/0.39
% 0.19/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.39
% 0.19/0.39 Axiom 1 (assume_domain_exists): there_exists(domain(a)) = true.
% 0.19/0.39 Axiom 2 (compose_domain): compose(X, domain(X)) = X.
% 0.19/0.40 Axiom 3 (compose_codomain): compose(codomain(X), X) = X.
% 0.19/0.40 Axiom 4 (domain_has_elements): fresh8(X, X, Y) = true.
% 0.19/0.40 Axiom 5 (domain_codomain_composition1): fresh11(X, X, Y, Z) = codomain(Z).
% 0.19/0.40 Axiom 6 (domain_has_elements): fresh8(there_exists(domain(X)), true, X) = there_exists(X).
% 0.19/0.40 Axiom 7 (domain_codomain_composition1): fresh11(there_exists(compose(X, Y)), true, X, Y) = domain(X).
% 0.19/0.40
% 0.19/0.40 Lemma 8: codomain(domain(a)) = domain(a).
% 0.19/0.40 Proof:
% 0.19/0.40 codomain(domain(a))
% 0.19/0.40 = { by axiom 5 (domain_codomain_composition1) R->L }
% 0.19/0.40 fresh11(true, true, a, domain(a))
% 0.19/0.40 = { by axiom 4 (domain_has_elements) R->L }
% 0.19/0.40 fresh11(fresh8(true, true, a), true, a, domain(a))
% 0.19/0.40 = { by axiom 1 (assume_domain_exists) R->L }
% 0.19/0.40 fresh11(fresh8(there_exists(domain(a)), true, a), true, a, domain(a))
% 0.19/0.40 = { by axiom 6 (domain_has_elements) }
% 0.19/0.40 fresh11(there_exists(a), true, a, domain(a))
% 0.19/0.40 = { by axiom 2 (compose_domain) R->L }
% 0.19/0.40 fresh11(there_exists(compose(a, domain(a))), true, a, domain(a))
% 0.19/0.40 = { by axiom 7 (domain_codomain_composition1) }
% 0.19/0.40 domain(a)
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_domain_is_idempotent): domain(domain(a)) = domain(a).
% 0.19/0.40 Proof:
% 0.19/0.40 domain(domain(a))
% 0.19/0.40 = { by axiom 7 (domain_codomain_composition1) R->L }
% 0.19/0.40 fresh11(there_exists(compose(domain(a), domain(a))), true, domain(a), domain(a))
% 0.19/0.40 = { by lemma 8 R->L }
% 0.19/0.40 fresh11(there_exists(compose(codomain(domain(a)), domain(a))), true, domain(a), domain(a))
% 0.19/0.40 = { by axiom 3 (compose_codomain) }
% 0.19/0.40 fresh11(there_exists(domain(a)), true, domain(a), domain(a))
% 0.19/0.40 = { by axiom 1 (assume_domain_exists) }
% 0.19/0.40 fresh11(true, true, domain(a), domain(a))
% 0.19/0.40 = { by axiom 5 (domain_codomain_composition1) }
% 0.19/0.40 codomain(domain(a))
% 0.19/0.40 = { by lemma 8 }
% 0.19/0.40 domain(a)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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