TSTP Solution File: SET102-6 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET102-6 : 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 : n024.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 15:31:16 EDT 2023
% Result : Unsatisfiable 0.21s 0.57s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET102-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % 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 : n024.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 09:50:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.57 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.57
% 0.21/0.57 % SZS status Unsatisfiable
% 0.21/0.57
% 0.21/0.57 % SZS output start Proof
% 0.21/0.57 Take the following subset of the input axioms:
% 0.21/0.57 fof(ordered_pair, axiom, ![X, Y]: unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))=ordered_pair(X, Y)).
% 0.21/0.57 fof(prove_unordered_pair_member_of_ordered_pair_1, negated_conjecture, ~member(unordered_pair(x, singleton(y)), ordered_pair(x, y))).
% 0.21/0.57 fof(unordered_pair3, axiom, ![X2, Y2]: (~member(Y2, universal_class) | member(Y2, unordered_pair(X2, Y2)))).
% 0.21/0.57 fof(unordered_pairs_in_universal, axiom, ![X2, Y2]: member(unordered_pair(X2, Y2), universal_class)).
% 0.21/0.57
% 0.21/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.57 fresh(y, y, x1...xn) = u
% 0.21/0.57 C => fresh(s, t, x1...xn) = v
% 0.21/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.57 variables of u and v.
% 0.21/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.57 input problem has no model of domain size 1).
% 0.21/0.57
% 0.21/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.57
% 0.21/0.57 Axiom 1 (unordered_pairs_in_universal): member(unordered_pair(X, Y), universal_class) = true2.
% 0.21/0.57 Axiom 2 (unordered_pair3): fresh5(X, X, Y, Z) = true2.
% 0.21/0.57 Axiom 3 (ordered_pair): unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y).
% 0.21/0.57 Axiom 4 (unordered_pair3): fresh5(member(X, universal_class), true2, X, Y) = member(X, unordered_pair(Y, X)).
% 0.21/0.57
% 0.21/0.57 Goal 1 (prove_unordered_pair_member_of_ordered_pair_1): member(unordered_pair(x, singleton(y)), ordered_pair(x, y)) = true2.
% 0.21/0.57 Proof:
% 0.21/0.57 member(unordered_pair(x, singleton(y)), ordered_pair(x, y))
% 0.21/0.57 = { by axiom 3 (ordered_pair) R->L }
% 0.21/0.57 member(unordered_pair(x, singleton(y)), unordered_pair(singleton(x), unordered_pair(x, singleton(y))))
% 0.21/0.57 = { by axiom 4 (unordered_pair3) R->L }
% 0.21/0.57 fresh5(member(unordered_pair(x, singleton(y)), universal_class), true2, unordered_pair(x, singleton(y)), singleton(x))
% 0.21/0.57 = { by axiom 1 (unordered_pairs_in_universal) }
% 0.21/0.57 fresh5(true2, true2, unordered_pair(x, singleton(y)), singleton(x))
% 0.21/0.57 = { by axiom 2 (unordered_pair3) }
% 0.21/0.57 true2
% 0.21/0.57 % SZS output end Proof
% 0.21/0.57
% 0.21/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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