TSTP Solution File: SET075-7 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET075-7 : 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 : n021.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 15:31:04 EDT 2023
% Result : Unsatisfiable 0.20s 0.56s
% 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
% 0.00/0.13 % Problem : SET075-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % 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 : n021.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
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 13:36:41 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.56 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.56
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56
% 0.20/0.56 % SZS output start Proof
% 0.20/0.56 Take the following subset of the input axioms:
% 0.20/0.57 fof(complement1, axiom, ![X, Z]: (~member(Z, complement(X)) | ~member(Z, X))).
% 0.20/0.57 fof(corollary_1_to_unordered_pair, axiom, ![Y, U, V, X2]: (~member(ordered_pair(X2, Y), cross_product(U, V)) | member(X2, unordered_pair(X2, Y)))).
% 0.20/0.57 fof(domain1, axiom, ![X2, Z2]: (restrict(X2, singleton(Z2), universal_class)!=null_class | ~member(Z2, domain_of(X2)))).
% 0.20/0.57 fof(existence_of_null_class, axiom, ![Z2]: ~member(Z2, null_class)).
% 0.20/0.57 fof(prove_corollary_to_unordered_pair_axiom3_1, negated_conjecture, member(ordered_pair(x, y), cross_product(u, v))).
% 0.20/0.57 fof(prove_corollary_to_unordered_pair_axiom3_2, negated_conjecture, unordered_pair(x, y)=null_class).
% 0.20/0.57 fof(special_classes_lemma, axiom, ![X2, Y2]: ~member(Y2, intersection(complement(X2), X2))).
% 0.20/0.57
% 0.20/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.57 fresh(y, y, x1...xn) = u
% 0.20/0.57 C => fresh(s, t, x1...xn) = v
% 0.20/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.57 variables of u and v.
% 0.20/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.57 input problem has no model of domain size 1).
% 0.20/0.57
% 0.20/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.57
% 0.20/0.57 Axiom 1 (prove_corollary_to_unordered_pair_axiom3_2): unordered_pair(x, y) = null_class.
% 0.20/0.57 Axiom 2 (corollary_1_to_unordered_pair): fresh65(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 3 (prove_corollary_to_unordered_pair_axiom3_1): member(ordered_pair(x, y), cross_product(u, v)) = true2.
% 0.20/0.57 Axiom 4 (corollary_1_to_unordered_pair): fresh65(member(ordered_pair(X, Y), cross_product(Z, W)), true2, X, Y) = member(X, unordered_pair(X, Y)).
% 0.20/0.57
% 0.20/0.57 Goal 1 (existence_of_null_class): member(X, null_class) = true2.
% 0.20/0.57 The goal is true when:
% 0.20/0.57 X = x
% 0.20/0.57
% 0.20/0.57 Proof:
% 0.20/0.57 member(x, null_class)
% 0.20/0.57 = { by axiom 1 (prove_corollary_to_unordered_pair_axiom3_2) R->L }
% 0.20/0.57 member(x, unordered_pair(x, y))
% 0.20/0.57 = { by axiom 4 (corollary_1_to_unordered_pair) R->L }
% 0.20/0.57 fresh65(member(ordered_pair(x, y), cross_product(u, v)), true2, x, y)
% 0.20/0.57 = { by axiom 3 (prove_corollary_to_unordered_pair_axiom3_1) }
% 0.20/0.57 fresh65(true2, true2, x, y)
% 0.20/0.57 = { by axiom 2 (corollary_1_to_unordered_pair) }
% 0.20/0.57 true2
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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