TSTP Solution File: SET018-7 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET018-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 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 : n003.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 15:30:37 EDT 2023
% Result : Unsatisfiable 0.17s 0.75s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16 % Problem : SET018-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.07/0.16 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.36 % Computer : n003.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Aug 26 12:21:24 EDT 2023
% 0.12/0.36 % CPUTime :
% 0.17/0.75 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.17/0.75
% 0.17/0.75 % SZS status Unsatisfiable
% 0.17/0.75
% 0.17/0.76 % SZS output start Proof
% 0.17/0.76 Take the following subset of the input axioms:
% 0.17/0.76 fof(ordered_pair_determines_components2, axiom, ![X, Y, Z, W]: (ordered_pair(W, X)!=ordered_pair(Y, Z) | (~member(X, universal_class) | X=Z))).
% 0.17/0.76 fof(prove_ordered_pair_determines_components2_1, negated_conjecture, ordered_pair(w, x)=ordered_pair(y, z)).
% 0.17/0.76 fof(prove_ordered_pair_determines_components2_2, negated_conjecture, member(x, universal_class)).
% 0.17/0.76 fof(prove_ordered_pair_determines_components2_3, negated_conjecture, x!=z).
% 0.17/0.76
% 0.17/0.76 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.76 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.76 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.76 fresh(y, y, x1...xn) = u
% 0.17/0.76 C => fresh(s, t, x1...xn) = v
% 0.17/0.76 where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.76 variables of u and v.
% 0.17/0.76 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.76 input problem has no model of domain size 1).
% 0.17/0.76
% 0.17/0.76 The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.76
% 0.17/0.76 Axiom 1 (prove_ordered_pair_determines_components2_2): member(x, universal_class) = true2.
% 0.17/0.76 Axiom 2 (prove_ordered_pair_determines_components2_1): ordered_pair(w, x) = ordered_pair(y, z).
% 0.17/0.76 Axiom 3 (ordered_pair_determines_components2): fresh4(X, X, Y, Z) = Z.
% 0.17/0.76 Axiom 4 (ordered_pair_determines_components2): fresh5(X, X, Y, Z, W, V) = Z.
% 0.17/0.76 Axiom 5 (ordered_pair_determines_components2): fresh5(member(X, universal_class), true2, Y, X, Z, W) = fresh4(ordered_pair(Y, X), ordered_pair(W, Z), X, Z).
% 0.17/0.76
% 0.17/0.76 Goal 1 (prove_ordered_pair_determines_components2_3): x = z.
% 0.17/0.76 Proof:
% 0.17/0.76 x
% 0.17/0.76 = { by axiom 4 (ordered_pair_determines_components2) R->L }
% 0.17/0.76 fresh5(true2, true2, w, x, z, y)
% 0.17/0.76 = { by axiom 1 (prove_ordered_pair_determines_components2_2) R->L }
% 0.17/0.76 fresh5(member(x, universal_class), true2, w, x, z, y)
% 0.17/0.76 = { by axiom 5 (ordered_pair_determines_components2) }
% 0.17/0.76 fresh4(ordered_pair(w, x), ordered_pair(y, z), x, z)
% 0.17/0.76 = { by axiom 2 (prove_ordered_pair_determines_components2_1) R->L }
% 0.17/0.76 fresh4(ordered_pair(w, x), ordered_pair(w, x), x, z)
% 0.17/0.76 = { by axiom 3 (ordered_pair_determines_components2) }
% 0.17/0.76 z
% 0.17/0.76 % SZS output end Proof
% 0.17/0.76
% 0.17/0.76 RESULT: Unsatisfiable (the axioms are contradictory).
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