TSTP Solution File: SET093-7 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET093-7 : 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 : n002.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 15:31:12 EDT 2023
% Result : Unsatisfiable 0.20s 0.54s
% 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
% 0.06/0.12 % Problem : SET093-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.13 % 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 : n002.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 15:09:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.54 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.54
% 0.20/0.54 % SZS status Unsatisfiable
% 0.20/0.54
% 0.20/0.54 % SZS output start Proof
% 0.20/0.54 Take the following subset of the input axioms:
% 0.20/0.54 fof(prove_corollary_2_to_singletons_are_sets_1, negated_conjecture, singleton(member_of(x))=x).
% 0.20/0.54 fof(prove_corollary_2_to_singletons_are_sets_2, negated_conjecture, ~member(x, universal_class)).
% 0.20/0.54 fof(singletons_are_sets, axiom, ![X]: member(singleton(X), universal_class)).
% 0.20/0.54
% 0.20/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.54 fresh(y, y, x1...xn) = u
% 0.20/0.54 C => fresh(s, t, x1...xn) = v
% 0.20/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.54 variables of u and v.
% 0.20/0.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.54 input problem has no model of domain size 1).
% 0.20/0.54
% 0.20/0.54 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.54
% 0.20/0.54 Axiom 1 (singletons_are_sets): member(singleton(X), universal_class) = true2.
% 0.20/0.54 Axiom 2 (prove_corollary_2_to_singletons_are_sets_1): singleton(member_of(x)) = x.
% 0.20/0.54
% 0.20/0.54 Goal 1 (prove_corollary_2_to_singletons_are_sets_2): member(x, universal_class) = true2.
% 0.20/0.54 Proof:
% 0.20/0.54 member(x, universal_class)
% 0.20/0.54 = { by axiom 2 (prove_corollary_2_to_singletons_are_sets_1) R->L }
% 0.20/0.54 member(singleton(member_of(x)), universal_class)
% 0.20/0.54 = { by axiom 1 (singletons_are_sets) }
% 0.20/0.54 true2
% 0.20/0.54 % SZS output end Proof
% 0.20/0.54
% 0.20/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
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