TSTP Solution File: SET025-7 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET025-7 : 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 : n009.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 15:30:43 EDT 2023
% Result : Unsatisfiable 1.79s 0.62s
% Output : Proof 1.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET025-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.14 % 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 : n009.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 10:32:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.79/0.62 Command-line arguments: --no-flatten-goal
% 1.79/0.62
% 1.79/0.62 % SZS status Unsatisfiable
% 1.79/0.62
% 1.79/0.62 % SZS output start Proof
% 1.79/0.62 Take the following subset of the input axioms:
% 1.79/0.62 fof(ordered_pair, axiom, ![X, Y]: unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))=ordered_pair(X, Y)).
% 1.79/0.62 fof(prove_ordered_pair_is_set_1, negated_conjecture, ~member(ordered_pair(x, y), universal_class)).
% 1.79/0.62 fof(unordered_pairs_in_universal, axiom, ![X2, Y2]: member(unordered_pair(X2, Y2), universal_class)).
% 1.79/0.62
% 1.79/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.79/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.79/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.79/0.62 fresh(y, y, x1...xn) = u
% 1.79/0.62 C => fresh(s, t, x1...xn) = v
% 1.79/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 1.79/0.62 variables of u and v.
% 1.79/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.79/0.62 input problem has no model of domain size 1).
% 1.79/0.62
% 1.79/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 1.79/0.62
% 1.79/0.62 Axiom 1 (unordered_pairs_in_universal): member(unordered_pair(X, Y), universal_class) = true2.
% 1.79/0.62 Axiom 2 (ordered_pair): unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y).
% 1.79/0.62
% 1.79/0.62 Goal 1 (prove_ordered_pair_is_set_1): member(ordered_pair(x, y), universal_class) = true2.
% 1.79/0.62 Proof:
% 1.79/0.62 member(ordered_pair(x, y), universal_class)
% 1.79/0.62 = { by axiom 2 (ordered_pair) R->L }
% 1.79/0.62 member(unordered_pair(singleton(x), unordered_pair(x, singleton(y))), universal_class)
% 1.79/0.62 = { by axiom 1 (unordered_pairs_in_universal) }
% 1.79/0.62 true2
% 1.79/0.62 % SZS output end Proof
% 1.79/0.62
% 1.79/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
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