TSTP Solution File: SET079-7 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET079-7 : 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 15:31:06 EDT 2023
% Result : Unsatisfiable 1.35s 0.53s
% Output : Proof 1.35s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET079-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % 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 : n009.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 08:25:35 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.35/0.53 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 1.35/0.53
% 1.35/0.53 % SZS status Unsatisfiable
% 1.35/0.53
% 1.35/0.53 % SZS output start Proof
% 1.35/0.53 Take the following subset of the input axioms:
% 1.35/0.54 fof(complement1, axiom, ![X, Z]: (~member(Z, complement(X)) | ~member(Z, X))).
% 1.35/0.54 fof(corollary_to_unordered_pair_axiom1, axiom, ![Y, X2]: (~member(X2, universal_class) | unordered_pair(X2, Y)!=null_class)).
% 1.35/0.54 fof(corollary_to_unordered_pair_axiom2, axiom, ![X2, Y2]: (~member(Y2, universal_class) | unordered_pair(X2, Y2)!=null_class)).
% 1.35/0.54 fof(corollary_to_unordered_pair_axiom3, axiom, ![U, V, X2, Y2]: (~member(ordered_pair(X2, Y2), cross_product(U, V)) | unordered_pair(X2, Y2)!=null_class)).
% 1.35/0.54 fof(domain1, axiom, ![X2, Z2]: (restrict(X2, singleton(Z2), universal_class)!=null_class | ~member(Z2, domain_of(X2)))).
% 1.35/0.54 fof(existence_of_null_class, axiom, ![Z2]: ~member(Z2, null_class)).
% 1.35/0.54 fof(prove_corollary_to_set_in_its_singleton_1, negated_conjecture, member(x, universal_class)).
% 1.35/0.54 fof(prove_corollary_to_set_in_its_singleton_2, negated_conjecture, singleton(x)=null_class).
% 1.35/0.54 fof(singleton_set, axiom, ![X2]: unordered_pair(X2, X2)=singleton(X2)).
% 1.35/0.54 fof(special_classes_lemma, axiom, ![X2, Y2]: ~member(Y2, intersection(complement(X2), X2))).
% 1.35/0.54
% 1.35/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.35/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.35/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.35/0.54 fresh(y, y, x1...xn) = u
% 1.35/0.54 C => fresh(s, t, x1...xn) = v
% 1.35/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 1.35/0.54 variables of u and v.
% 1.35/0.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.35/0.54 input problem has no model of domain size 1).
% 1.35/0.54
% 1.35/0.54 The encoding turns the above axioms into the following unit equations and goals:
% 1.35/0.54
% 1.35/0.54 Axiom 1 (prove_corollary_to_set_in_its_singleton_1): member(x, universal_class) = true2.
% 1.35/0.54 Axiom 2 (singleton_set): unordered_pair(X, X) = singleton(X).
% 1.35/0.54 Axiom 3 (prove_corollary_to_set_in_its_singleton_2): singleton(x) = null_class.
% 1.35/0.54
% 1.35/0.54 Goal 1 (corollary_to_unordered_pair_axiom1): tuple2(unordered_pair(X, Y), member(X, universal_class)) = tuple2(null_class, true2).
% 1.35/0.54 The goal is true when:
% 1.35/0.54 X = x
% 1.35/0.54 Y = x
% 1.35/0.54
% 1.35/0.54 Proof:
% 1.35/0.54 tuple2(unordered_pair(x, x), member(x, universal_class))
% 1.35/0.54 = { by axiom 2 (singleton_set) }
% 1.35/0.54 tuple2(singleton(x), member(x, universal_class))
% 1.35/0.54 = { by axiom 3 (prove_corollary_to_set_in_its_singleton_2) }
% 1.35/0.54 tuple2(null_class, member(x, universal_class))
% 1.35/0.54 = { by axiom 1 (prove_corollary_to_set_in_its_singleton_1) }
% 1.35/0.54 tuple2(null_class, true2)
% 1.35/0.54 % SZS output end Proof
% 1.35/0.54
% 1.35/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
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