TSTP Solution File: SET072-7 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET072-7 : 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 : n026.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 15:31:03 EDT 2023
% Result : Unsatisfiable 0.20s 0.60s
% 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 : SET072-7 : 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
% 0.14/0.35 % Computer : n026.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 13:42:33 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.60 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.60
% 0.20/0.60 % SZS status Unsatisfiable
% 0.20/0.60
% 0.20/0.60 % SZS output start Proof
% 0.20/0.60 Take the following subset of the input axioms:
% 0.20/0.60 fof(commutativity_of_unordered_pair, axiom, ![X, Y]: unordered_pair(X, Y)=unordered_pair(Y, X)).
% 0.20/0.60 fof(left_cancellation, axiom, ![Z, X2, Y2]: (unordered_pair(X2, Y2)!=unordered_pair(X2, Z) | (~member(ordered_pair(Y2, Z), cross_product(universal_class, universal_class)) | Y2=Z))).
% 0.20/0.60 fof(prove_right_cancellation_1, negated_conjecture, unordered_pair(x, z)=unordered_pair(y, z)).
% 0.20/0.60 fof(prove_right_cancellation_2, negated_conjecture, member(ordered_pair(x, y), cross_product(universal_class, universal_class))).
% 0.20/0.60 fof(prove_right_cancellation_3, negated_conjecture, x!=y).
% 0.20/0.60
% 0.20/0.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.60 fresh(y, y, x1...xn) = u
% 0.20/0.60 C => fresh(s, t, x1...xn) = v
% 0.20/0.60 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.60 variables of u and v.
% 0.20/0.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.60 input problem has no model of domain size 1).
% 0.20/0.60
% 0.20/0.60 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.60
% 0.20/0.60 Axiom 1 (commutativity_of_unordered_pair): unordered_pair(X, Y) = unordered_pair(Y, X).
% 0.20/0.60 Axiom 2 (prove_right_cancellation_1): unordered_pair(x, z) = unordered_pair(y, z).
% 0.20/0.60 Axiom 3 (prove_right_cancellation_2): member(ordered_pair(x, y), cross_product(universal_class, universal_class)) = true2.
% 0.20/0.60 Axiom 4 (left_cancellation): fresh(X, X, Y, Z) = Z.
% 0.20/0.60 Axiom 5 (left_cancellation): fresh2(X, X, Y, Z, W) = Z.
% 0.20/0.60 Axiom 6 (left_cancellation): fresh2(member(ordered_pair(X, Y), cross_product(universal_class, universal_class)), true2, Z, X, Y) = fresh(unordered_pair(Z, X), unordered_pair(Z, Y), X, Y).
% 0.20/0.60
% 0.20/0.60 Goal 1 (prove_right_cancellation_3): x = y.
% 0.20/0.60 Proof:
% 0.20/0.60 x
% 0.20/0.60 = { by axiom 5 (left_cancellation) R->L }
% 0.20/0.60 fresh2(true2, true2, z, x, y)
% 0.20/0.60 = { by axiom 3 (prove_right_cancellation_2) R->L }
% 0.20/0.60 fresh2(member(ordered_pair(x, y), cross_product(universal_class, universal_class)), true2, z, x, y)
% 0.20/0.60 = { by axiom 6 (left_cancellation) }
% 0.20/0.60 fresh(unordered_pair(z, x), unordered_pair(z, y), x, y)
% 0.20/0.60 = { by axiom 1 (commutativity_of_unordered_pair) }
% 0.20/0.60 fresh(unordered_pair(x, z), unordered_pair(z, y), x, y)
% 0.20/0.60 = { by axiom 1 (commutativity_of_unordered_pair) }
% 0.20/0.60 fresh(unordered_pair(x, z), unordered_pair(y, z), x, y)
% 0.20/0.60 = { by axiom 2 (prove_right_cancellation_1) R->L }
% 0.20/0.60 fresh(unordered_pair(x, z), unordered_pair(x, z), x, y)
% 0.20/0.60 = { by axiom 4 (left_cancellation) }
% 0.20/0.60 y
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60
% 0.20/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
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