TSTP Solution File: CAT004-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CAT004-2 : 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 : n024.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 18:18:49 EDT 2023
% Result : Unsatisfiable 5.55s 1.22s
% Output : Proof 5.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : CAT004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 00:04:23 EDT 2023
% 0.11/0.32 % CPUTime :
% 5.55/1.22 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 5.55/1.22
% 5.55/1.22 % SZS status Unsatisfiable
% 5.55/1.22
% 5.55/1.24 % SZS output start Proof
% 5.55/1.24 Take the following subset of the input axioms:
% 5.55/1.24 fof(ab_h_equals_ab_g, hypothesis, compose(compose(a, b), h)=compose(compose(a, b), g)).
% 5.55/1.24 fof(codomain_domain1, axiom, ![X, Y]: (codomain(X)!=domain(Y) | domain(compose(X, Y))=domain(X))).
% 5.55/1.24 fof(codomain_domain2, axiom, ![X2, Y2]: (codomain(X2)!=domain(Y2) | codomain(compose(X2, Y2))=codomain(Y2))).
% 5.55/1.24 fof(codomain_of_a_equals_domain_of_b, hypothesis, codomain(a)=domain(b)).
% 5.55/1.24 fof(codomain_of_ab_equals_domain_of_g, hypothesis, codomain(compose(a, b))=domain(g)).
% 5.55/1.24 fof(codomain_of_ab_equals_domain_of_h, hypothesis, codomain(compose(a, b))=domain(h)).
% 5.55/1.24 fof(epimorphism1, hypothesis, ![Z, X2, Y2]: (codomain(a)!=domain(X2) | (compose(a, X2)!=Y2 | (codomain(a)!=domain(Z) | (compose(a, Z)!=Y2 | X2=Z))))).
% 5.55/1.24 fof(epimorphism2, hypothesis, ![X2, Y2, Z2]: (codomain(b)!=domain(X2) | (compose(b, X2)!=Y2 | (codomain(b)!=domain(Z2) | (compose(b, Z2)!=Y2 | X2=Z2))))).
% 5.55/1.24 fof(prove_h_equals_g, negated_conjecture, h!=g).
% 5.55/1.24 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)))).
% 5.55/1.24
% 5.55/1.24 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.55/1.24 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.55/1.24 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.55/1.24 fresh(y, y, x1...xn) = u
% 5.55/1.24 C => fresh(s, t, x1...xn) = v
% 5.55/1.24 where fresh is a fresh function symbol and x1..xn are the free
% 5.55/1.24 variables of u and v.
% 5.55/1.24 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.55/1.24 input problem has no model of domain size 1).
% 5.55/1.24
% 5.55/1.24 The encoding turns the above axioms into the following unit equations and goals:
% 5.55/1.24
% 5.55/1.24 Axiom 1 (codomain_of_a_equals_domain_of_b): codomain(a) = domain(b).
% 5.55/1.24 Axiom 2 (codomain_of_ab_equals_domain_of_h): codomain(compose(a, b)) = domain(h).
% 5.55/1.24 Axiom 3 (codomain_of_ab_equals_domain_of_g): codomain(compose(a, b)) = domain(g).
% 5.55/1.24 Axiom 4 (epimorphism1): fresh12(X, X, Y, Z) = Z.
% 5.55/1.24 Axiom 5 (epimorphism2): fresh8(X, X, Y, Z) = Z.
% 5.55/1.24 Axiom 6 (codomain_domain2): fresh4(X, X, Y, Z) = codomain(Z).
% 5.55/1.24 Axiom 7 (codomain_domain1): fresh3(X, X, Y, Z) = domain(Y).
% 5.55/1.24 Axiom 8 (ab_h_equals_ab_g): compose(compose(a, b), h) = compose(compose(a, b), g).
% 5.55/1.24 Axiom 9 (star_property): fresh(X, X, Y, Z, W) = compose(compose(Y, Z), W).
% 5.55/1.24 Axiom 10 (epimorphism1): fresh10(X, X, Y, Z, W) = Y.
% 5.55/1.24 Axiom 11 (epimorphism2): fresh6(X, X, Y, Z, W) = Y.
% 5.55/1.24 Axiom 12 (star_property): fresh2(X, X, Y, Z, W) = compose(Y, compose(Z, W)).
% 5.55/1.24 Axiom 13 (epimorphism1): fresh11(X, X, Y, Z, W) = fresh12(compose(a, Y), Z, Y, W).
% 5.55/1.24 Axiom 14 (epimorphism2): fresh7(X, X, Y, Z, W) = fresh8(compose(b, Y), Z, Y, W).
% 5.55/1.24 Axiom 15 (codomain_domain2): fresh4(codomain(X), domain(Y), X, Y) = codomain(compose(X, Y)).
% 5.55/1.24 Axiom 16 (codomain_domain1): fresh3(codomain(X), domain(Y), X, Y) = domain(compose(X, Y)).
% 5.55/1.24 Axiom 17 (epimorphism1): fresh9(X, X, Y, Z, W) = fresh10(compose(a, W), Z, Y, Z, W).
% 5.55/1.24 Axiom 18 (epimorphism1): fresh9(codomain(a), domain(X), Y, Z, X) = fresh11(codomain(a), domain(Y), Y, Z, X).
% 5.55/1.24 Axiom 19 (epimorphism2): fresh5(X, X, Y, Z, W) = fresh6(compose(b, W), Z, Y, Z, W).
% 5.55/1.24 Axiom 20 (epimorphism2): fresh5(codomain(b), domain(X), Y, Z, X) = fresh7(codomain(b), domain(Y), Y, Z, X).
% 5.55/1.24 Axiom 21 (star_property): fresh2(codomain(X), domain(Y), Z, X, Y) = fresh(codomain(Z), domain(X), Z, X, Y).
% 5.55/1.24
% 5.55/1.24 Lemma 22: domain(h) = codomain(b).
% 5.55/1.24 Proof:
% 5.55/1.24 domain(h)
% 5.55/1.24 = { by axiom 2 (codomain_of_ab_equals_domain_of_h) R->L }
% 5.55/1.24 codomain(compose(a, b))
% 5.55/1.24 = { by axiom 15 (codomain_domain2) R->L }
% 5.55/1.24 fresh4(codomain(a), domain(b), a, b)
% 5.55/1.24 = { by axiom 1 (codomain_of_a_equals_domain_of_b) R->L }
% 5.55/1.24 fresh4(codomain(a), codomain(a), a, b)
% 5.55/1.24 = { by axiom 6 (codomain_domain2) }
% 5.55/1.24 codomain(b)
% 5.55/1.24
% 5.55/1.24 Lemma 23: domain(g) = domain(h).
% 5.55/1.24 Proof:
% 5.55/1.24 domain(g)
% 5.55/1.24 = { by axiom 3 (codomain_of_ab_equals_domain_of_g) R->L }
% 5.55/1.24 codomain(compose(a, b))
% 5.55/1.24 = { by axiom 2 (codomain_of_ab_equals_domain_of_h) }
% 5.55/1.24 domain(h)
% 5.55/1.24
% 5.55/1.24 Lemma 24: fresh2(codomain(b), domain(X), Y, b, X) = fresh(codomain(Y), codomain(a), Y, b, X).
% 5.55/1.24 Proof:
% 5.55/1.24 fresh2(codomain(b), domain(X), Y, b, X)
% 5.55/1.24 = { by axiom 21 (star_property) }
% 5.55/1.24 fresh(codomain(Y), domain(b), Y, b, X)
% 5.55/1.24 = { by axiom 1 (codomain_of_a_equals_domain_of_b) R->L }
% 5.55/1.24 fresh(codomain(Y), codomain(a), Y, b, X)
% 5.55/1.24
% 5.55/1.24 Goal 1 (prove_h_equals_g): h = g.
% 5.55/1.24 Proof:
% 5.55/1.24 h
% 5.55/1.24 = { by axiom 11 (epimorphism2) R->L }
% 5.55/1.24 fresh6(compose(b, g), compose(b, g), h, compose(b, g), g)
% 5.55/1.24 = { by axiom 19 (epimorphism2) R->L }
% 5.55/1.24 fresh5(codomain(b), codomain(b), h, compose(b, g), g)
% 5.55/1.24 = { by lemma 22 R->L }
% 5.55/1.24 fresh5(codomain(b), domain(h), h, compose(b, g), g)
% 5.55/1.24 = { by lemma 23 R->L }
% 5.55/1.24 fresh5(codomain(b), domain(g), h, compose(b, g), g)
% 5.55/1.24 = { by axiom 20 (epimorphism2) }
% 5.55/1.24 fresh7(codomain(b), domain(h), h, compose(b, g), g)
% 5.55/1.24 = { by lemma 22 }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, compose(b, g), g)
% 5.55/1.24 = { by axiom 4 (epimorphism1) R->L }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh12(compose(a, compose(b, h)), compose(a, compose(b, h)), compose(b, h), compose(b, g)), g)
% 5.55/1.24 = { by axiom 13 (epimorphism1) R->L }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), compose(a, compose(b, h)), compose(b, g)), g)
% 5.55/1.24 = { by axiom 12 (star_property) R->L }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), fresh2(codomain(b), codomain(b), a, b, h), compose(b, g)), g)
% 5.55/1.24 = { by lemma 22 R->L }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), fresh2(codomain(b), domain(h), a, b, h), compose(b, g)), g)
% 5.55/1.24 = { by lemma 24 }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), fresh(codomain(a), codomain(a), a, b, h), compose(b, g)), g)
% 5.55/1.24 = { by axiom 9 (star_property) }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), compose(compose(a, b), h), compose(b, g)), g)
% 5.55/1.24 = { by axiom 8 (ab_h_equals_ab_g) }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), compose(compose(a, b), g), compose(b, g)), g)
% 5.55/1.24 = { by axiom 9 (star_property) R->L }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), fresh(codomain(a), codomain(a), a, b, g), compose(b, g)), g)
% 5.55/1.24 = { by lemma 24 R->L }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), fresh2(codomain(b), domain(g), a, b, g), compose(b, g)), g)
% 5.55/1.24 = { by lemma 23 }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), fresh2(codomain(b), domain(h), a, b, g), compose(b, g)), g)
% 5.55/1.24 = { by lemma 22 }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), fresh2(codomain(b), codomain(b), a, b, g), compose(b, g)), g)
% 5.55/1.24 = { by axiom 12 (star_property) }
% 5.55/1.24 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), codomain(a), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 1 (codomain_of_a_equals_domain_of_b) }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), domain(b), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 7 (codomain_domain1) R->L }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), fresh3(codomain(b), codomain(b), b, h), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by lemma 22 R->L }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), fresh3(codomain(b), domain(h), b, h), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 16 (codomain_domain1) }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh11(codomain(a), domain(compose(b, h)), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 18 (epimorphism1) R->L }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh9(codomain(a), domain(compose(b, g)), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 16 (codomain_domain1) R->L }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh9(codomain(a), fresh3(codomain(b), domain(g), b, g), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by lemma 23 }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh9(codomain(a), fresh3(codomain(b), domain(h), b, g), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by lemma 22 }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh9(codomain(a), fresh3(codomain(b), codomain(b), b, g), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 7 (codomain_domain1) }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh9(codomain(a), domain(b), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 1 (codomain_of_a_equals_domain_of_b) R->L }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh9(codomain(a), codomain(a), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 17 (epimorphism1) }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, fresh10(compose(a, compose(b, g)), compose(a, compose(b, g)), compose(b, h), compose(a, compose(b, g)), compose(b, g)), g)
% 5.55/1.25 = { by axiom 10 (epimorphism1) }
% 5.55/1.25 fresh7(codomain(b), codomain(b), h, compose(b, h), g)
% 5.55/1.25 = { by axiom 14 (epimorphism2) }
% 5.55/1.25 fresh8(compose(b, h), compose(b, h), h, g)
% 5.55/1.25 = { by axiom 5 (epimorphism2) }
% 5.55/1.25 g
% 5.55/1.25 % SZS output end Proof
% 5.55/1.25
% 5.55/1.25 RESULT: Unsatisfiable (the axioms are contradictory).
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