TSTP Solution File: SET025-8 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET025-8 : TPTP v8.1.2. Released v1.0.0.
% 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 : n029.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 0.21s 0.77s
% 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
% 0.00/0.13 % Problem : SET025-8 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 15:55:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.77 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.77
% 0.21/0.77 % SZS status Unsatisfiable
% 0.21/0.77
% 0.21/0.77 % SZS output start Proof
% 0.21/0.77 Take the following subset of the input axioms:
% 0.21/0.77 fof(an_ordered_pair_predicate, hypothesis, ordered_pair_predicate(a)).
% 0.21/0.77 fof(ordered_pair_predicate3, axiom, ![X]: (~ordered_pair_predicate(X) | X=ordered_pair(f2(X), f3(X)))).
% 0.21/0.77 fof(ordered_pairs_are_small1, axiom, ![Y, X2]: little_set(ordered_pair(X2, Y))).
% 0.21/0.77 fof(prove_predicate_is_small, negated_conjecture, ~little_set(a)).
% 0.21/0.77
% 0.21/0.77 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.77 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.77 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.77 fresh(y, y, x1...xn) = u
% 0.21/0.77 C => fresh(s, t, x1...xn) = v
% 0.21/0.77 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.77 variables of u and v.
% 0.21/0.77 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.77 input problem has no model of domain size 1).
% 0.21/0.77
% 0.21/0.77 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.77
% 0.21/0.77 Axiom 1 (an_ordered_pair_predicate): ordered_pair_predicate(a) = true2.
% 0.21/0.77 Axiom 2 (ordered_pairs_are_small1): little_set(ordered_pair(X, Y)) = true2.
% 0.21/0.77 Axiom 3 (ordered_pair_predicate3): fresh19(X, X, Y) = Y.
% 0.21/0.77 Axiom 4 (ordered_pair_predicate3): fresh19(ordered_pair_predicate(X), true2, X) = ordered_pair(f2(X), f3(X)).
% 0.21/0.77
% 0.21/0.77 Goal 1 (prove_predicate_is_small): little_set(a) = true2.
% 0.21/0.77 Proof:
% 0.21/0.77 little_set(a)
% 0.21/0.77 = { by axiom 3 (ordered_pair_predicate3) R->L }
% 0.21/0.77 little_set(fresh19(true2, true2, a))
% 0.21/0.77 = { by axiom 1 (an_ordered_pair_predicate) R->L }
% 0.21/0.77 little_set(fresh19(ordered_pair_predicate(a), true2, a))
% 0.21/0.77 = { by axiom 4 (ordered_pair_predicate3) }
% 0.21/0.77 little_set(ordered_pair(f2(a), f3(a)))
% 0.21/0.77 = { by axiom 2 (ordered_pairs_are_small1) }
% 0.21/0.77 true2
% 0.21/0.77 % SZS output end Proof
% 0.21/0.77
% 0.21/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
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