TSTP Solution File: CAT014-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CAT014-1 : 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 18:18:56 EDT 2023
% Result : Unsatisfiable 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : CAT014-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 00:24:38 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.43 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.43
% 0.22/0.43 % SZS status Unsatisfiable
% 0.22/0.43
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 Take the following subset of the input axioms:
% 0.22/0.43 fof(codomain_is_an_identity_map, axiom, ![X]: identity_map(codomain(X))).
% 0.22/0.43 fof(composition_is_well_defined, axiom, ![Y, Z, W, X2]: (~product(X2, Y, Z) | (~product(X2, Y, W) | Z=W))).
% 0.22/0.43 fof(identity2, axiom, ![X2, Y2]: (~defined(X2, Y2) | (~identity_map(Y2) | product(X2, Y2, X2)))).
% 0.22/0.43 fof(mapping_from_codomain_of_x_to_x, axiom, ![X2]: defined(codomain(X2), X2)).
% 0.22/0.43 fof(product_on_codomain, axiom, ![X2]: product(codomain(X2), X2, X2)).
% 0.22/0.43 fof(prove_codomain_is_idempotent, negated_conjecture, codomain(codomain(a))!=codomain(a)).
% 0.22/0.43
% 0.22/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.43 fresh(y, y, x1...xn) = u
% 0.22/0.43 C => fresh(s, t, x1...xn) = v
% 0.22/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.43 variables of u and v.
% 0.22/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.43 input problem has no model of domain size 1).
% 0.22/0.43
% 0.22/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.43
% 0.22/0.43 Axiom 1 (codomain_is_an_identity_map): identity_map(codomain(X)) = true.
% 0.22/0.43 Axiom 2 (mapping_from_codomain_of_x_to_x): defined(codomain(X), X) = true.
% 0.22/0.43 Axiom 3 (product_on_codomain): product(codomain(X), X, X) = true.
% 0.22/0.43 Axiom 4 (composition_is_well_defined): fresh(X, X, Y, Z) = Z.
% 0.22/0.43 Axiom 5 (identity2): fresh4(X, X, Y, Z) = product(Y, Z, Y).
% 0.22/0.43 Axiom 6 (identity2): fresh3(X, X, Y, Z) = true.
% 0.22/0.43 Axiom 7 (identity2): fresh4(identity_map(X), true, Y, X) = fresh3(defined(Y, X), true, Y, X).
% 0.22/0.43 Axiom 8 (composition_is_well_defined): fresh2(X, X, Y, Z, W, V) = W.
% 0.22/0.43 Axiom 9 (composition_is_well_defined): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.22/0.43
% 0.22/0.43 Goal 1 (prove_codomain_is_idempotent): codomain(codomain(a)) = codomain(a).
% 0.22/0.43 Proof:
% 0.22/0.43 codomain(codomain(a))
% 0.22/0.43 = { by axiom 8 (composition_is_well_defined) R->L }
% 0.22/0.43 fresh2(true, true, codomain(codomain(a)), codomain(a), codomain(codomain(a)), codomain(a))
% 0.22/0.43 = { by axiom 3 (product_on_codomain) R->L }
% 0.22/0.43 fresh2(product(codomain(codomain(a)), codomain(a), codomain(a)), true, codomain(codomain(a)), codomain(a), codomain(codomain(a)), codomain(a))
% 0.22/0.43 = { by axiom 9 (composition_is_well_defined) }
% 0.22/0.43 fresh(product(codomain(codomain(a)), codomain(a), codomain(codomain(a))), true, codomain(codomain(a)), codomain(a))
% 0.22/0.43 = { by axiom 5 (identity2) R->L }
% 0.22/0.43 fresh(fresh4(true, true, codomain(codomain(a)), codomain(a)), true, codomain(codomain(a)), codomain(a))
% 0.22/0.43 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 0.22/0.43 fresh(fresh4(identity_map(codomain(a)), true, codomain(codomain(a)), codomain(a)), true, codomain(codomain(a)), codomain(a))
% 0.22/0.43 = { by axiom 7 (identity2) }
% 0.22/0.43 fresh(fresh3(defined(codomain(codomain(a)), codomain(a)), true, codomain(codomain(a)), codomain(a)), true, codomain(codomain(a)), codomain(a))
% 0.22/0.43 = { by axiom 2 (mapping_from_codomain_of_x_to_x) }
% 0.22/0.43 fresh(fresh3(true, true, codomain(codomain(a)), codomain(a)), true, codomain(codomain(a)), codomain(a))
% 0.22/0.43 = { by axiom 6 (identity2) }
% 0.22/0.43 fresh(true, true, codomain(codomain(a)), codomain(a))
% 0.22/0.43 = { by axiom 4 (composition_is_well_defined) }
% 0.22/0.43 codomain(a)
% 0.22/0.43 % SZS output end Proof
% 0.22/0.43
% 0.22/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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