TSTP Solution File: CAT011-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CAT011-1 : 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 : n027.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 0.20s 0.42s
% 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 : CAT011-1 : 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
% 0.16/0.35 % Computer : n027.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 01:10:21 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.42 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Take the following subset of the input axioms:
% 0.20/0.42 fof(composition_is_well_defined, axiom, ![X, Y, Z, W]: (~product(X, Y, Z) | (~product(X, Y, W) | Z=W))).
% 0.20/0.42 fof(domain_is_an_identity_map, axiom, ![X2]: identity_map(domain(X2))).
% 0.20/0.42 fof(identity1, axiom, ![X2, Y2]: (~defined(X2, Y2) | (~identity_map(X2) | product(X2, Y2, Y2)))).
% 0.20/0.42 fof(mapping_from_x_to_its_domain, axiom, ![X2]: defined(X2, domain(X2))).
% 0.20/0.42 fof(product_on_domain, axiom, ![X2]: product(X2, domain(X2), X2)).
% 0.20/0.42 fof(prove_domain_is_idempotent, negated_conjecture, domain(domain(a))!=domain(a)).
% 0.20/0.42
% 0.20/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.42 fresh(y, y, x1...xn) = u
% 0.20/0.42 C => fresh(s, t, x1...xn) = v
% 0.20/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.42 variables of u and v.
% 0.20/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.42 input problem has no model of domain size 1).
% 0.20/0.42
% 0.20/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.42
% 0.20/0.42 Axiom 1 (mapping_from_x_to_its_domain): defined(X, domain(X)) = true.
% 0.20/0.42 Axiom 2 (domain_is_an_identity_map): identity_map(domain(X)) = true.
% 0.20/0.42 Axiom 3 (product_on_domain): product(X, domain(X), X) = true.
% 0.20/0.42 Axiom 4 (composition_is_well_defined): fresh(X, X, Y, Z) = Z.
% 0.20/0.42 Axiom 5 (identity1): fresh6(X, X, Y, Z) = product(Y, Z, Z).
% 0.20/0.42 Axiom 6 (identity1): fresh5(X, X, Y, Z) = true.
% 0.20/0.42 Axiom 7 (identity1): fresh6(identity_map(X), true, X, Y) = fresh5(defined(X, Y), true, X, Y).
% 0.20/0.42 Axiom 8 (composition_is_well_defined): fresh2(X, X, Y, Z, W, V) = W.
% 0.20/0.42 Axiom 9 (composition_is_well_defined): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.20/0.42
% 0.20/0.42 Goal 1 (prove_domain_is_idempotent): domain(domain(a)) = domain(a).
% 0.20/0.42 Proof:
% 0.20/0.42 domain(domain(a))
% 0.20/0.42 = { by axiom 8 (composition_is_well_defined) R->L }
% 0.20/0.42 fresh2(true, true, domain(a), domain(domain(a)), domain(domain(a)), domain(a))
% 0.20/0.42 = { by axiom 3 (product_on_domain) R->L }
% 0.20/0.42 fresh2(product(domain(a), domain(domain(a)), domain(a)), true, domain(a), domain(domain(a)), domain(domain(a)), domain(a))
% 0.20/0.42 = { by axiom 9 (composition_is_well_defined) }
% 0.20/0.42 fresh(product(domain(a), domain(domain(a)), domain(domain(a))), true, domain(domain(a)), domain(a))
% 0.20/0.42 = { by axiom 5 (identity1) R->L }
% 0.20/0.42 fresh(fresh6(true, true, domain(a), domain(domain(a))), true, domain(domain(a)), domain(a))
% 0.20/0.42 = { by axiom 2 (domain_is_an_identity_map) R->L }
% 0.20/0.42 fresh(fresh6(identity_map(domain(a)), true, domain(a), domain(domain(a))), true, domain(domain(a)), domain(a))
% 0.20/0.42 = { by axiom 7 (identity1) }
% 0.20/0.42 fresh(fresh5(defined(domain(a), domain(domain(a))), true, domain(a), domain(domain(a))), true, domain(domain(a)), domain(a))
% 0.20/0.42 = { by axiom 1 (mapping_from_x_to_its_domain) }
% 0.20/0.42 fresh(fresh5(true, true, domain(a), domain(domain(a))), true, domain(domain(a)), domain(a))
% 0.20/0.42 = { by axiom 6 (identity1) }
% 0.20/0.42 fresh(true, true, domain(domain(a)), domain(a))
% 0.20/0.42 = { by axiom 4 (composition_is_well_defined) }
% 0.20/0.42 domain(a)
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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