TSTP Solution File: SET083-7 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET083-7 : 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 : n031.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 15:31:08 EDT 2023
% Result : Unsatisfiable 0.20s 0.56s
% 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
% 0.08/0.12 % Problem : SET083-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.13 % 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 : n031.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 13:28:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --no-flatten-goal
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% 0.20/0.56 % SZS status Unsatisfiable
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% 0.20/0.56 % SZS output start Proof
% 0.20/0.56 Take the following subset of the input axioms:
% 0.20/0.56 fof(only_member_in_singleton, axiom, ![X, Y]: (~member(Y, singleton(X)) | Y=X)).
% 0.20/0.56 fof(prove_singleton_identified_by_element1_1, negated_conjecture, singleton(x)=singleton(y)).
% 0.20/0.56 fof(prove_singleton_identified_by_element1_2, negated_conjecture, member(x, universal_class)).
% 0.20/0.56 fof(prove_singleton_identified_by_element1_3, negated_conjecture, x!=y).
% 0.20/0.56 fof(set_in_its_singleton, axiom, ![X2]: (~member(X2, universal_class) | member(X2, singleton(X2)))).
% 0.20/0.56
% 0.20/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.56 fresh(y, y, x1...xn) = u
% 0.20/0.56 C => fresh(s, t, x1...xn) = v
% 0.20/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.56 variables of u and v.
% 0.20/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.56 input problem has no model of domain size 1).
% 0.20/0.56
% 0.20/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.56
% 0.20/0.56 Axiom 1 (prove_singleton_identified_by_element1_1): singleton(x) = singleton(y).
% 0.20/0.56 Axiom 2 (prove_singleton_identified_by_element1_2): member(x, universal_class) = true2.
% 0.20/0.56 Axiom 3 (set_in_its_singleton): fresh25(X, X, Y) = true2.
% 0.20/0.56 Axiom 4 (only_member_in_singleton): fresh(X, X, Y, Z) = Z.
% 0.20/0.56 Axiom 5 (set_in_its_singleton): fresh25(member(X, universal_class), true2, X) = member(X, singleton(X)).
% 0.20/0.56 Axiom 6 (only_member_in_singleton): fresh(member(X, singleton(Y)), true2, X, Y) = X.
% 0.20/0.56
% 0.20/0.56 Goal 1 (prove_singleton_identified_by_element1_3): x = y.
% 0.20/0.56 Proof:
% 0.20/0.56 x
% 0.20/0.56 = { by axiom 6 (only_member_in_singleton) R->L }
% 0.20/0.56 fresh(member(x, singleton(y)), true2, x, y)
% 0.20/0.56 = { by axiom 1 (prove_singleton_identified_by_element1_1) R->L }
% 0.20/0.56 fresh(member(x, singleton(x)), true2, x, y)
% 0.20/0.56 = { by axiom 5 (set_in_its_singleton) R->L }
% 0.20/0.56 fresh(fresh25(member(x, universal_class), true2, x), true2, x, y)
% 0.20/0.56 = { by axiom 2 (prove_singleton_identified_by_element1_2) }
% 0.20/0.56 fresh(fresh25(true2, true2, x), true2, x, y)
% 0.20/0.56 = { by axiom 3 (set_in_its_singleton) }
% 0.20/0.56 fresh(true2, true2, x, y)
% 0.20/0.56 = { by axiom 4 (only_member_in_singleton) }
% 0.20/0.56 y
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56
% 0.20/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
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