TSTP Solution File: SET095-7 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET095-7 : 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 : n028.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 15:31:14 EDT 2023
% Result : Unsatisfiable 0.16s 0.61s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET095-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31 % Computer : n028.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 11:05:22 EDT 2023
% 0.16/0.32 % CPUTime :
% 0.16/0.61 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.16/0.61
% 0.16/0.61 % SZS status Unsatisfiable
% 0.16/0.61
% 0.16/0.61 % SZS output start Proof
% 0.16/0.61 Take the following subset of the input axioms:
% 0.16/0.61 fof(prove_property_of_singletons2_1, negated_conjecture, member(x, y)).
% 0.16/0.61 fof(prove_property_of_singletons2_2, negated_conjecture, ~subclass(singleton(x), y)).
% 0.16/0.61 fof(singleton_set, axiom, ![X]: unordered_pair(X, X)=singleton(X)).
% 0.16/0.61 fof(unordered_pair_is_subset, axiom, ![Y, Z, X2]: (~member(X2, Z) | (~member(Y, Z) | subclass(unordered_pair(X2, Y), Z)))).
% 0.16/0.61
% 0.16/0.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.61 fresh(y, y, x1...xn) = u
% 0.16/0.61 C => fresh(s, t, x1...xn) = v
% 0.16/0.61 where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.61 variables of u and v.
% 0.16/0.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.61 input problem has no model of domain size 1).
% 0.16/0.61
% 0.16/0.61 The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.61
% 0.16/0.61 Axiom 1 (singleton_set): unordered_pair(X, X) = singleton(X).
% 0.16/0.61 Axiom 2 (prove_property_of_singletons2_1): member(x, y) = true2.
% 0.16/0.61 Axiom 3 (unordered_pair_is_subset): fresh19(X, X, Y, Z, W) = subclass(unordered_pair(Y, W), Z).
% 0.16/0.61 Axiom 4 (unordered_pair_is_subset): fresh18(X, X, Y, Z, W) = true2.
% 0.16/0.61 Axiom 5 (unordered_pair_is_subset): fresh19(member(X, Y), true2, Z, Y, X) = fresh18(member(Z, Y), true2, Z, Y, X).
% 0.16/0.61
% 0.16/0.61 Goal 1 (prove_property_of_singletons2_2): subclass(singleton(x), y) = true2.
% 0.16/0.61 Proof:
% 0.16/0.61 subclass(singleton(x), y)
% 0.16/0.61 = { by axiom 1 (singleton_set) R->L }
% 0.16/0.61 subclass(unordered_pair(x, x), y)
% 0.16/0.61 = { by axiom 3 (unordered_pair_is_subset) R->L }
% 0.16/0.61 fresh19(true2, true2, x, y, x)
% 0.16/0.61 = { by axiom 2 (prove_property_of_singletons2_1) R->L }
% 0.16/0.61 fresh19(member(x, y), true2, x, y, x)
% 0.16/0.61 = { by axiom 5 (unordered_pair_is_subset) }
% 0.16/0.61 fresh18(member(x, y), true2, x, y, x)
% 0.16/0.61 = { by axiom 2 (prove_property_of_singletons2_1) }
% 0.16/0.61 fresh18(true2, true2, x, y, x)
% 0.16/0.61 = { by axiom 4 (unordered_pair_is_subset) }
% 0.16/0.61 true2
% 0.16/0.61 % SZS output end Proof
% 0.16/0.61
% 0.16/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
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