TSTP Solution File: SET024-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET024-3 : 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 : n011.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 2.37s 0.77s
% Output : Proof 2.37s
% 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 : SET024-3 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:48:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.37/0.77 Command-line arguments: --no-flatten-goal
% 2.37/0.77
% 2.37/0.77 % SZS status Unsatisfiable
% 2.37/0.77
% 2.37/0.77 % SZS output start Proof
% 2.37/0.77 Take the following subset of the input axioms:
% 2.37/0.77 fof(a_little_set, hypothesis, little_set(a)).
% 2.37/0.77 fof(non_ordered_pair2, axiom, ![X, Y, U]: (member(U, non_ordered_pair(X, Y)) | (~little_set(U) | U!=X))).
% 2.37/0.77 fof(prove_membership_of_singleton_set, negated_conjecture, ~member(a, singleton_set(a))).
% 2.37/0.77 fof(singleton_set, axiom, ![X2]: singleton_set(X2)=non_ordered_pair(X2, X2)).
% 2.37/0.77
% 2.37/0.77 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.37/0.77 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.37/0.77 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.37/0.77 fresh(y, y, x1...xn) = u
% 2.37/0.77 C => fresh(s, t, x1...xn) = v
% 2.37/0.77 where fresh is a fresh function symbol and x1..xn are the free
% 2.37/0.77 variables of u and v.
% 2.37/0.77 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.37/0.77 input problem has no model of domain size 1).
% 2.37/0.77
% 2.37/0.77 The encoding turns the above axioms into the following unit equations and goals:
% 2.37/0.77
% 2.37/0.77 Axiom 1 (a_little_set): little_set(a) = true2.
% 2.37/0.77 Axiom 2 (singleton_set): singleton_set(X) = non_ordered_pair(X, X).
% 2.37/0.77 Axiom 3 (non_ordered_pair2): fresh63(X, X, Y, Z) = true2.
% 2.37/0.77 Axiom 4 (non_ordered_pair2): fresh63(little_set(X), true2, X, Y) = member(X, non_ordered_pair(X, Y)).
% 2.37/0.77
% 2.37/0.77 Goal 1 (prove_membership_of_singleton_set): member(a, singleton_set(a)) = true2.
% 2.37/0.77 Proof:
% 2.37/0.77 member(a, singleton_set(a))
% 2.37/0.77 = { by axiom 2 (singleton_set) }
% 2.37/0.77 member(a, non_ordered_pair(a, a))
% 2.37/0.77 = { by axiom 4 (non_ordered_pair2) R->L }
% 2.37/0.77 fresh63(little_set(a), true2, a, a)
% 2.37/0.77 = { by axiom 1 (a_little_set) }
% 2.37/0.77 fresh63(true2, true2, a, a)
% 2.37/0.77 = { by axiom 3 (non_ordered_pair2) }
% 2.37/0.77 true2
% 2.37/0.77 % SZS output end Proof
% 2.37/0.77
% 2.37/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
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