TSTP Solution File: SET024-7 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET024-7 : 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 : n016.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 15:30:41 EDT 2023
% Result : Unsatisfiable 0.20s 0.58s
% 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
% 0.00/0.12 % Problem : SET024-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 11:56:12 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.58 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.20/0.58 % SZS status Unsatisfiable
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% 0.20/0.58 % SZS output start Proof
% 0.20/0.58 Take the following subset of the input axioms:
% 0.20/0.58 fof(prove_set_in_its_singleton_1, negated_conjecture, member(x, universal_class)).
% 0.20/0.58 fof(prove_set_in_its_singleton_2, negated_conjecture, ~member(x, singleton(x))).
% 0.20/0.58 fof(singleton_set, axiom, ![X]: unordered_pair(X, X)=singleton(X)).
% 0.20/0.58 fof(unordered_pair2, axiom, ![Y, X2]: (~member(X2, universal_class) | member(X2, unordered_pair(X2, Y)))).
% 0.20/0.58
% 0.20/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.58 fresh(y, y, x1...xn) = u
% 0.20/0.58 C => fresh(s, t, x1...xn) = v
% 0.20/0.58 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.58 variables of u and v.
% 0.20/0.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.58 input problem has no model of domain size 1).
% 0.20/0.58
% 0.20/0.58 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.58
% 0.20/0.58 Axiom 1 (singleton_set): unordered_pair(X, X) = singleton(X).
% 0.20/0.58 Axiom 2 (prove_set_in_its_singleton_1): member(x, universal_class) = true2.
% 0.20/0.58 Axiom 3 (unordered_pair2): fresh14(X, X, Y, Z) = true2.
% 0.20/0.58 Axiom 4 (unordered_pair2): fresh14(member(X, universal_class), true2, X, Y) = member(X, unordered_pair(X, Y)).
% 0.20/0.58
% 0.20/0.58 Goal 1 (prove_set_in_its_singleton_2): member(x, singleton(x)) = true2.
% 0.20/0.58 Proof:
% 0.20/0.58 member(x, singleton(x))
% 0.20/0.58 = { by axiom 1 (singleton_set) R->L }
% 0.20/0.58 member(x, unordered_pair(x, x))
% 0.20/0.58 = { by axiom 4 (unordered_pair2) R->L }
% 0.20/0.58 fresh14(member(x, universal_class), true2, x, x)
% 0.20/0.58 = { by axiom 2 (prove_set_in_its_singleton_1) }
% 0.20/0.58 fresh14(true2, true2, x, x)
% 0.20/0.58 = { by axiom 3 (unordered_pair2) }
% 0.20/0.58 true2
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58
% 0.20/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
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