TSTP Solution File: SET238-6 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET238-6 : 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 : n006.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 15:31:44 EDT 2023
% Result : Unsatisfiable 10.44s 1.72s
% Output : Proof 10.44s
% 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 : SET238-6 : 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
% 0.14/0.35 % Computer : n006.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 14:39:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 10.44/1.72 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 10.44/1.72
% 10.44/1.72 % SZS status Unsatisfiable
% 10.44/1.72
% 10.44/1.72 % SZS output start Proof
% 10.44/1.72 Take the following subset of the input axioms:
% 10.44/1.72 fof(cartesian_product4, axiom, ![X, Y, Z]: (~member(Z, cross_product(X, Y)) | ordered_pair(first(Z), second(Z))=Z)).
% 10.44/1.72 fof(intersection1, axiom, ![X2, Y2, Z2]: (~member(Z2, intersection(X2, Y2)) | member(Z2, X2))).
% 10.44/1.72 fof(prove_corollary_to_restriction_alternate_defn1_1, negated_conjecture, member(z, restrict(xr, x, y))).
% 10.44/1.72 fof(prove_corollary_to_restriction_alternate_defn1_2, negated_conjecture, ~member(ordered_pair(first(z), second(z)), restrict(xr, x, y))).
% 10.44/1.72 fof(restriction2, axiom, ![Xr, X2, Y2]: intersection(cross_product(X2, Y2), Xr)=restrict(Xr, X2, Y2)).
% 10.44/1.72
% 10.44/1.72 Now clausify the problem and encode Horn clauses using encoding 3 of
% 10.44/1.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 10.44/1.72 We repeatedly replace C & s=t => u=v by the two clauses:
% 10.44/1.72 fresh(y, y, x1...xn) = u
% 10.44/1.72 C => fresh(s, t, x1...xn) = v
% 10.44/1.72 where fresh is a fresh function symbol and x1..xn are the free
% 10.44/1.72 variables of u and v.
% 10.44/1.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 10.44/1.72 input problem has no model of domain size 1).
% 10.44/1.72
% 10.44/1.72 The encoding turns the above axioms into the following unit equations and goals:
% 10.44/1.72
% 10.44/1.72 Axiom 1 (cartesian_product4): fresh7(X, X, Y) = Y.
% 10.44/1.72 Axiom 2 (restriction2): intersection(cross_product(X, Y), Z) = restrict(Z, X, Y).
% 10.44/1.72 Axiom 3 (intersection1): fresh42(X, X, Y, Z) = true2.
% 10.44/1.72 Axiom 4 (prove_corollary_to_restriction_alternate_defn1_1): member(z, restrict(xr, x, y)) = true2.
% 10.44/1.72 Axiom 5 (cartesian_product4): fresh7(member(X, cross_product(Y, Z)), true2, X) = ordered_pair(first(X), second(X)).
% 10.44/1.72 Axiom 6 (intersection1): fresh42(member(X, intersection(Y, Z)), true2, X, Y) = member(X, Y).
% 10.44/1.72
% 10.44/1.72 Goal 1 (prove_corollary_to_restriction_alternate_defn1_2): member(ordered_pair(first(z), second(z)), restrict(xr, x, y)) = true2.
% 10.44/1.72 Proof:
% 10.44/1.72 member(ordered_pair(first(z), second(z)), restrict(xr, x, y))
% 10.44/1.72 = { by axiom 5 (cartesian_product4) R->L }
% 10.44/1.72 member(fresh7(member(z, cross_product(x, y)), true2, z), restrict(xr, x, y))
% 10.44/1.72 = { by axiom 6 (intersection1) R->L }
% 10.44/1.72 member(fresh7(fresh42(member(z, intersection(cross_product(x, y), xr)), true2, z, cross_product(x, y)), true2, z), restrict(xr, x, y))
% 10.44/1.72 = { by axiom 2 (restriction2) }
% 10.44/1.72 member(fresh7(fresh42(member(z, restrict(xr, x, y)), true2, z, cross_product(x, y)), true2, z), restrict(xr, x, y))
% 10.44/1.72 = { by axiom 4 (prove_corollary_to_restriction_alternate_defn1_1) }
% 10.44/1.72 member(fresh7(fresh42(true2, true2, z, cross_product(x, y)), true2, z), restrict(xr, x, y))
% 10.44/1.72 = { by axiom 3 (intersection1) }
% 10.44/1.72 member(fresh7(true2, true2, z), restrict(xr, x, y))
% 10.44/1.72 = { by axiom 1 (cartesian_product4) }
% 10.44/1.72 member(z, restrict(xr, x, y))
% 10.44/1.72 = { by axiom 4 (prove_corollary_to_restriction_alternate_defn1_1) }
% 10.44/1.72 true2
% 10.44/1.72 % SZS output end Proof
% 10.44/1.72
% 10.44/1.72 RESULT: Unsatisfiable (the axioms are contradictory).
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