TSTP Solution File: CAT003-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CAT003-2 : 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 18:18:48 EDT 2023
% Result : Unsatisfiable 0.21s 0.49s
% Output : Proof 0.21s
% 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 : CAT003-2 : 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
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 00:17:13 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.49
% 0.21/0.49 % SZS status Unsatisfiable
% 0.21/0.49
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Take the following subset of the input axioms:
% 0.21/0.49 fof(bh_equals_bg, hypothesis, compose(b, h)=compose(b, g)).
% 0.21/0.49 fof(codomain_domain2, axiom, ![X, Y]: (codomain(X)!=domain(Y) | codomain(compose(X, Y))=codomain(Y))).
% 0.21/0.49 fof(codomain_of_a_equals_domain_of_b, hypothesis, codomain(a)=domain(b)).
% 0.21/0.49 fof(codomain_of_b_equals_domain_of_g, hypothesis, codomain(b)=domain(g)).
% 0.21/0.49 fof(codomain_of_b_equals_domain_of_h, hypothesis, codomain(b)=domain(h)).
% 0.21/0.49 fof(endomorphism, hypothesis, ![Z, X2, Y2]: (codomain(compose(a, b))!=domain(X2) | (compose(compose(a, b), X2)!=Y2 | (codomain(compose(a, b))!=domain(Z) | (compose(compose(a, b), Z)!=Y2 | X2=Z))))).
% 0.21/0.49 fof(prove_g_equals_h, negated_conjecture, g!=h).
% 0.21/0.49 fof(star_property, axiom, ![X2, Y2, Z2]: (codomain(X2)!=domain(Y2) | (codomain(Y2)!=domain(Z2) | compose(X2, compose(Y2, Z2))=compose(compose(X2, Y2), Z2)))).
% 0.21/0.49
% 0.21/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.49 fresh(y, y, x1...xn) = u
% 0.21/0.49 C => fresh(s, t, x1...xn) = v
% 0.21/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.49 variables of u and v.
% 0.21/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.49 input problem has no model of domain size 1).
% 0.21/0.49
% 0.21/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.49
% 0.21/0.49 Axiom 1 (codomain_of_b_equals_domain_of_h): codomain(b) = domain(h).
% 0.21/0.49 Axiom 2 (codomain_of_b_equals_domain_of_g): codomain(b) = domain(g).
% 0.21/0.49 Axiom 3 (codomain_of_a_equals_domain_of_b): codomain(a) = domain(b).
% 0.21/0.49 Axiom 4 (bh_equals_bg): compose(b, h) = compose(b, g).
% 0.21/0.49 Axiom 5 (endomorphism): fresh8(X, X, Y, Z) = Z.
% 0.21/0.49 Axiom 6 (codomain_domain2): fresh4(X, X, Y, Z) = codomain(Z).
% 0.21/0.49 Axiom 7 (star_property): fresh(X, X, Y, Z, W) = compose(compose(Y, Z), W).
% 0.21/0.49 Axiom 8 (endomorphism): fresh6(X, X, Y, Z, W) = Y.
% 0.21/0.49 Axiom 9 (star_property): fresh2(X, X, Y, Z, W) = compose(Y, compose(Z, W)).
% 0.21/0.49 Axiom 10 (codomain_domain2): fresh4(codomain(X), domain(Y), X, Y) = codomain(compose(X, Y)).
% 0.21/0.49 Axiom 11 (star_property): fresh2(codomain(X), domain(Y), Z, X, Y) = fresh(codomain(Z), domain(X), Z, X, Y).
% 0.21/0.49 Axiom 12 (endomorphism): fresh7(X, X, Y, Z, W) = fresh8(compose(compose(a, b), Y), Z, Y, W).
% 0.21/0.49 Axiom 13 (endomorphism): fresh5(X, X, Y, Z, W) = fresh6(compose(compose(a, b), W), Z, Y, Z, W).
% 0.21/0.49 Axiom 14 (endomorphism): fresh5(codomain(compose(a, b)), domain(X), Y, Z, X) = fresh7(codomain(compose(a, b)), domain(Y), Y, Z, X).
% 0.21/0.49
% 0.21/0.49 Lemma 15: codomain(compose(a, b)) = codomain(b).
% 0.21/0.49 Proof:
% 0.21/0.49 codomain(compose(a, b))
% 0.21/0.49 = { by axiom 10 (codomain_domain2) R->L }
% 0.21/0.49 fresh4(codomain(a), domain(b), a, b)
% 0.21/0.49 = { by axiom 3 (codomain_of_a_equals_domain_of_b) R->L }
% 0.21/0.49 fresh4(codomain(a), codomain(a), a, b)
% 0.21/0.49 = { by axiom 6 (codomain_domain2) }
% 0.21/0.49 codomain(b)
% 0.21/0.49
% 0.21/0.49 Goal 1 (prove_g_equals_h): g = h.
% 0.21/0.49 Proof:
% 0.21/0.49 g
% 0.21/0.49 = { by axiom 8 (endomorphism) R->L }
% 0.21/0.49 fresh6(compose(compose(a, b), h), compose(compose(a, b), h), g, compose(compose(a, b), h), h)
% 0.21/0.49 = { by axiom 13 (endomorphism) R->L }
% 0.21/0.49 fresh5(codomain(b), codomain(b), g, compose(compose(a, b), h), h)
% 0.21/0.49 = { by axiom 1 (codomain_of_b_equals_domain_of_h) }
% 0.21/0.49 fresh5(codomain(b), domain(h), g, compose(compose(a, b), h), h)
% 0.21/0.49 = { by lemma 15 R->L }
% 0.21/0.49 fresh5(codomain(compose(a, b)), domain(h), g, compose(compose(a, b), h), h)
% 0.21/0.49 = { by axiom 14 (endomorphism) }
% 0.21/0.49 fresh7(codomain(compose(a, b)), domain(g), g, compose(compose(a, b), h), h)
% 0.21/0.49 = { by lemma 15 }
% 0.21/0.49 fresh7(codomain(b), domain(g), g, compose(compose(a, b), h), h)
% 0.21/0.49 = { by axiom 2 (codomain_of_b_equals_domain_of_g) R->L }
% 0.21/0.49 fresh7(codomain(b), codomain(b), g, compose(compose(a, b), h), h)
% 0.21/0.50 = { by axiom 7 (star_property) R->L }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, fresh(codomain(a), codomain(a), a, b, h), h)
% 0.21/0.50 = { by axiom 3 (codomain_of_a_equals_domain_of_b) }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, fresh(codomain(a), domain(b), a, b, h), h)
% 0.21/0.50 = { by axiom 11 (star_property) R->L }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, fresh2(codomain(b), domain(h), a, b, h), h)
% 0.21/0.50 = { by axiom 1 (codomain_of_b_equals_domain_of_h) R->L }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, fresh2(codomain(b), codomain(b), a, b, h), h)
% 0.21/0.50 = { by axiom 9 (star_property) }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, compose(a, compose(b, h)), h)
% 0.21/0.50 = { by axiom 4 (bh_equals_bg) }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, compose(a, compose(b, g)), h)
% 0.21/0.50 = { by axiom 9 (star_property) R->L }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, fresh2(codomain(b), codomain(b), a, b, g), h)
% 0.21/0.50 = { by axiom 2 (codomain_of_b_equals_domain_of_g) }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, fresh2(codomain(b), domain(g), a, b, g), h)
% 0.21/0.50 = { by axiom 11 (star_property) }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, fresh(codomain(a), domain(b), a, b, g), h)
% 0.21/0.50 = { by axiom 3 (codomain_of_a_equals_domain_of_b) R->L }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, fresh(codomain(a), codomain(a), a, b, g), h)
% 0.21/0.50 = { by axiom 7 (star_property) }
% 0.21/0.50 fresh7(codomain(b), codomain(b), g, compose(compose(a, b), g), h)
% 0.21/0.50 = { by axiom 12 (endomorphism) }
% 0.21/0.50 fresh8(compose(compose(a, b), g), compose(compose(a, b), g), g, h)
% 0.21/0.50 = { by axiom 5 (endomorphism) }
% 0.21/0.50 h
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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