TSTP Solution File: SET558-6 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET558-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n005.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 : Thu Aug 31 15:32:26 EDT 2023
% Result : Unsatisfiable 0.20s 0.57s
% 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
% 0.07/0.13 % Problem : SET558-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 13:36:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.57
% 0.20/0.57 % SZS status Unsatisfiable
% 0.20/0.57
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Take the following subset of the input axioms:
% 0.20/0.57 fof(compatible2, axiom, ![Xh, Xf1, Xf2]: (~compatible(Xh, Xf1, Xf2) | domain_of(domain_of(Xf1))=domain_of(Xh))).
% 0.20/0.57 fof(operation2, axiom, ![Xf]: (~operation(Xf) | cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf)))=domain_of(Xf))).
% 0.20/0.57 fof(prove_compatible_functions_alternate_defn1_1, negated_conjecture, operation(xf1)).
% 0.20/0.57 fof(prove_compatible_functions_alternate_defn1_2, negated_conjecture, compatible(xh, xf1, xf2)).
% 0.20/0.57 fof(prove_compatible_functions_alternate_defn1_3, negated_conjecture, cross_product(domain_of(xh), domain_of(xh))!=domain_of(xf1)).
% 0.20/0.57
% 0.20/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.57 fresh(y, y, x1...xn) = u
% 0.20/0.57 C => fresh(s, t, x1...xn) = v
% 0.20/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.57 variables of u and v.
% 0.20/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.57 input problem has no model of domain size 1).
% 0.20/0.57
% 0.20/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.57
% 0.20/0.57 Axiom 1 (prove_compatible_functions_alternate_defn1_1): operation(xf1) = true2.
% 0.20/0.57 Axiom 2 (prove_compatible_functions_alternate_defn1_2): compatible(xh, xf1, xf2) = true2.
% 0.20/0.57 Axiom 3 (operation2): fresh27(X, X, Y) = domain_of(Y).
% 0.20/0.57 Axiom 4 (compatible2): fresh72(X, X, Y, Z) = domain_of(Y).
% 0.20/0.57 Axiom 5 (operation2): fresh27(operation(X), true2, X) = cross_product(domain_of(domain_of(X)), domain_of(domain_of(X))).
% 0.20/0.57 Axiom 6 (compatible2): fresh72(compatible(X, Y, Z), true2, X, Y) = domain_of(domain_of(Y)).
% 0.20/0.57
% 0.20/0.57 Lemma 7: domain_of(domain_of(xf1)) = domain_of(xh).
% 0.20/0.57 Proof:
% 0.20/0.57 domain_of(domain_of(xf1))
% 0.20/0.57 = { by axiom 6 (compatible2) R->L }
% 0.20/0.57 fresh72(compatible(xh, xf1, xf2), true2, xh, xf1)
% 0.20/0.57 = { by axiom 2 (prove_compatible_functions_alternate_defn1_2) }
% 0.20/0.57 fresh72(true2, true2, xh, xf1)
% 0.20/0.57 = { by axiom 4 (compatible2) }
% 0.20/0.57 domain_of(xh)
% 0.20/0.57
% 0.20/0.57 Goal 1 (prove_compatible_functions_alternate_defn1_3): cross_product(domain_of(xh), domain_of(xh)) = domain_of(xf1).
% 0.20/0.57 Proof:
% 0.20/0.57 cross_product(domain_of(xh), domain_of(xh))
% 0.20/0.57 = { by lemma 7 R->L }
% 0.20/0.57 cross_product(domain_of(xh), domain_of(domain_of(xf1)))
% 0.20/0.57 = { by lemma 7 R->L }
% 0.20/0.57 cross_product(domain_of(domain_of(xf1)), domain_of(domain_of(xf1)))
% 0.20/0.57 = { by axiom 5 (operation2) R->L }
% 0.20/0.57 fresh27(operation(xf1), true2, xf1)
% 0.20/0.57 = { by axiom 1 (prove_compatible_functions_alternate_defn1_1) }
% 0.20/0.57 fresh27(true2, true2, xf1)
% 0.20/0.57 = { by axiom 3 (operation2) }
% 0.20/0.57 domain_of(xf1)
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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