TSTP Solution File: SET025-9 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET025-9 : 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 : n013.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 0.20s 0.70s
% 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
% 0.13/0.13 % Problem : SET025-9 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 13:05:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.70 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.70
% 0.20/0.70 % SZS status Unsatisfiable
% 0.20/0.70
% 0.20/0.70 % SZS output start Proof
% 0.20/0.70 Take the following subset of the input axioms:
% 0.20/0.70 fof(an_ordered_pair_predicate, hypothesis, ordered_pair_predicate(a)).
% 0.20/0.70 fof(non_ordered_pair4, axiom, ![X, Y]: little_set(non_ordered_pair(X, Y))).
% 0.20/0.70 fof(ordered_pair, axiom, ![X2, Y2]: ordered_pair(X2, Y2)=non_ordered_pair(singleton_set(X2), non_ordered_pair(X2, Y2))).
% 0.20/0.70 fof(ordered_pair_predicate3, axiom, ![X2]: (~ordered_pair_predicate(X2) | X2=ordered_pair(f2(X2), f3(X2)))).
% 0.20/0.70 fof(prove_predicate_is_small, negated_conjecture, ~little_set(a)).
% 0.20/0.70
% 0.20/0.70 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.70 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.70 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.70 fresh(y, y, x1...xn) = u
% 0.20/0.70 C => fresh(s, t, x1...xn) = v
% 0.20/0.70 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.70 variables of u and v.
% 0.20/0.70 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.70 input problem has no model of domain size 1).
% 0.20/0.70
% 0.20/0.70 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.70
% 0.20/0.70 Axiom 1 (an_ordered_pair_predicate): ordered_pair_predicate(a) = true2.
% 0.20/0.70 Axiom 2 (non_ordered_pair4): little_set(non_ordered_pair(X, Y)) = true2.
% 0.20/0.70 Axiom 3 (ordered_pair_predicate3): fresh12(X, X, Y) = Y.
% 0.20/0.70 Axiom 4 (ordered_pair_predicate3): fresh12(ordered_pair_predicate(X), true2, X) = ordered_pair(f2(X), f3(X)).
% 0.20/0.70 Axiom 5 (ordered_pair): ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)).
% 0.20/0.70
% 0.20/0.70 Goal 1 (prove_predicate_is_small): little_set(a) = true2.
% 0.20/0.70 Proof:
% 0.20/0.70 little_set(a)
% 0.20/0.70 = { by axiom 3 (ordered_pair_predicate3) R->L }
% 0.20/0.70 little_set(fresh12(true2, true2, a))
% 0.20/0.70 = { by axiom 1 (an_ordered_pair_predicate) R->L }
% 0.20/0.70 little_set(fresh12(ordered_pair_predicate(a), true2, a))
% 0.20/0.70 = { by axiom 4 (ordered_pair_predicate3) }
% 0.20/0.70 little_set(ordered_pair(f2(a), f3(a)))
% 0.20/0.70 = { by axiom 5 (ordered_pair) }
% 0.20/0.70 little_set(non_ordered_pair(singleton_set(f2(a)), non_ordered_pair(f2(a), f3(a))))
% 0.20/0.70 = { by axiom 2 (non_ordered_pair4) }
% 0.20/0.70 true2
% 0.20/0.70 % SZS output end Proof
% 0.20/0.70
% 0.20/0.70 RESULT: Unsatisfiable (the axioms are contradictory).
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