TSTP Solution File: SET241-6 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET241-6 : 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 : n027.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 15:31:45 EDT 2023
% Result : Unsatisfiable 0.20s 0.58s
% 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
% 0.00/0.12 % Problem : SET241-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 16:59:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.20/0.58 % SZS status Unsatisfiable
% 0.20/0.58
% 0.20/0.58 % SZS output start Proof
% 0.20/0.58 Take the following subset of the input axioms:
% 0.20/0.58 fof(cartesian_product2, axiom, ![X, Y, U, V]: (~member(ordered_pair(U, V), cross_product(X, Y)) | member(V, Y))).
% 0.20/0.58 fof(intersection2, axiom, ![Z, X2, Y2]: (~member(Z, intersection(X2, Y2)) | member(Z, Y2))).
% 0.20/0.58 fof(prove_restriction_alternate_defn4_1, negated_conjecture, member(ordered_pair(u, v), restrict(xr, x, y))).
% 0.20/0.58 fof(prove_restriction_alternate_defn4_2, negated_conjecture, ~member(v, y)).
% 0.20/0.58 fof(restriction1, axiom, ![Xr, X2, Y2]: intersection(Xr, cross_product(X2, Y2))=restrict(Xr, X2, Y2)).
% 0.20/0.58
% 0.20/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.59 fresh(y, y, x1...xn) = u
% 0.20/0.59 C => fresh(s, t, x1...xn) = v
% 0.20/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.59 variables of u and v.
% 0.20/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.59 input problem has no model of domain size 1).
% 0.20/0.59
% 0.20/0.59 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.59
% 0.20/0.59 Axiom 1 (restriction1): intersection(X, cross_product(Y, Z)) = restrict(X, Y, Z).
% 0.20/0.59 Axiom 2 (cartesian_product2): fresh76(X, X, Y, Z) = true2.
% 0.20/0.59 Axiom 3 (intersection2): fresh41(X, X, Y, Z) = true2.
% 0.20/0.59 Axiom 4 (prove_restriction_alternate_defn4_1): member(ordered_pair(u, v), restrict(xr, x, y)) = true2.
% 0.20/0.59 Axiom 5 (intersection2): fresh41(member(X, intersection(Y, Z)), true2, X, Z) = member(X, Z).
% 0.20/0.59 Axiom 6 (cartesian_product2): fresh76(member(ordered_pair(X, Y), cross_product(Z, W)), true2, Y, W) = member(Y, W).
% 0.20/0.59
% 0.20/0.59 Goal 1 (prove_restriction_alternate_defn4_2): member(v, y) = true2.
% 0.20/0.59 Proof:
% 0.20/0.59 member(v, y)
% 0.20/0.59 = { by axiom 6 (cartesian_product2) R->L }
% 0.20/0.59 fresh76(member(ordered_pair(u, v), cross_product(x, y)), true2, v, y)
% 0.20/0.59 = { by axiom 5 (intersection2) R->L }
% 0.20/0.59 fresh76(fresh41(member(ordered_pair(u, v), intersection(xr, cross_product(x, y))), true2, ordered_pair(u, v), cross_product(x, y)), true2, v, y)
% 0.20/0.59 = { by axiom 1 (restriction1) }
% 0.20/0.59 fresh76(fresh41(member(ordered_pair(u, v), restrict(xr, x, y)), true2, ordered_pair(u, v), cross_product(x, y)), true2, v, y)
% 0.20/0.59 = { by axiom 4 (prove_restriction_alternate_defn4_1) }
% 0.20/0.59 fresh76(fresh41(true2, true2, ordered_pair(u, v), cross_product(x, y)), true2, v, y)
% 0.20/0.59 = { by axiom 3 (intersection2) }
% 0.20/0.59 fresh76(true2, true2, v, y)
% 0.20/0.59 = { by axiom 2 (cartesian_product2) }
% 0.20/0.59 true2
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59
% 0.20/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
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