TSTP Solution File: CAT007-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CAT007-3 : 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 18:18:52 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% 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 : CAT007-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 00:31:50 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.38 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.19/0.38 % SZS status Unsatisfiable
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% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 Take the following subset of the input axioms:
% 0.19/0.38 fof(domain_codomain_composition2, axiom, ![X, Y]: (~there_exists(domain(X)) | (~equalish(domain(X), codomain(Y)) | there_exists(compose(X, Y))))).
% 0.19/0.38 fof(domain_of_c2_equals_codomain_of_c1, hypothesis, equalish(domain(c2), codomain(c1))).
% 0.19/0.38 fof(domain_of_c2_exists, hypothesis, there_exists(domain(c2))).
% 0.19/0.38 fof(prove_c1_c2_is_defined, negated_conjecture, ~there_exists(compose(c2, c1))).
% 0.19/0.38
% 0.19/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.38 fresh(y, y, x1...xn) = u
% 0.19/0.38 C => fresh(s, t, x1...xn) = v
% 0.19/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.38 variables of u and v.
% 0.19/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.38 input problem has no model of domain size 1).
% 0.19/0.38
% 0.19/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.38
% 0.19/0.38 Axiom 1 (domain_of_c2_exists): there_exists(domain(c2)) = true.
% 0.19/0.38 Axiom 2 (domain_codomain_composition2): fresh8(X, X, Y, Z) = true.
% 0.19/0.38 Axiom 3 (domain_codomain_composition2): fresh7(X, X, Y, Z) = there_exists(compose(Y, Z)).
% 0.19/0.38 Axiom 4 (domain_of_c2_equals_codomain_of_c1): equalish(domain(c2), codomain(c1)) = true.
% 0.19/0.38 Axiom 5 (domain_codomain_composition2): fresh7(there_exists(domain(X)), true, X, Y) = fresh8(equalish(domain(X), codomain(Y)), true, X, Y).
% 0.19/0.38
% 0.19/0.38 Goal 1 (prove_c1_c2_is_defined): there_exists(compose(c2, c1)) = true.
% 0.19/0.38 Proof:
% 0.19/0.38 there_exists(compose(c2, c1))
% 0.19/0.38 = { by axiom 3 (domain_codomain_composition2) R->L }
% 0.19/0.38 fresh7(true, true, c2, c1)
% 0.19/0.38 = { by axiom 1 (domain_of_c2_exists) R->L }
% 0.19/0.38 fresh7(there_exists(domain(c2)), true, c2, c1)
% 0.19/0.38 = { by axiom 5 (domain_codomain_composition2) }
% 0.19/0.38 fresh8(equalish(domain(c2), codomain(c1)), true, c2, c1)
% 0.19/0.38 = { by axiom 4 (domain_of_c2_equals_codomain_of_c1) }
% 0.19/0.38 fresh8(true, true, c2, c1)
% 0.19/0.38 = { by axiom 2 (domain_codomain_composition2) }
% 0.19/0.38 true
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38
% 0.19/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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