TSTP Solution File: SET242-6 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET242-6 : 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 : n005.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 0.61s
% 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
% 0.12/0.13 % Problem : SET242-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 08:33:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.61
% 0.20/0.61 % SZS status Unsatisfiable
% 0.20/0.61
% 0.20/0.61 % SZS output start Proof
% 0.20/0.61 Take the following subset of the input axioms:
% 0.20/0.61 fof(intersection3, axiom, ![X, Y, Z]: (~member(Z, X) | (~member(Z, Y) | member(Z, intersection(X, Y))))).
% 0.20/0.61 fof(prove_restriction_alternate_defn5_1, negated_conjecture, member(z, xr)).
% 0.20/0.61 fof(prove_restriction_alternate_defn5_2, negated_conjecture, member(z, cross_product(x, y))).
% 0.20/0.61 fof(prove_restriction_alternate_defn5_3, negated_conjecture, ~member(z, restrict(xr, x, y))).
% 0.20/0.61 fof(restriction1, axiom, ![Xr, X2, Y2]: intersection(Xr, cross_product(X2, Y2))=restrict(Xr, X2, Y2)).
% 0.20/0.61
% 0.20/0.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.61 fresh(y, y, x1...xn) = u
% 0.20/0.61 C => fresh(s, t, x1...xn) = v
% 0.20/0.61 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.61 variables of u and v.
% 0.20/0.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.61 input problem has no model of domain size 1).
% 0.20/0.61
% 0.20/0.61 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.61
% 0.20/0.61 Axiom 1 (prove_restriction_alternate_defn5_1): member(z, xr) = true2.
% 0.20/0.61 Axiom 2 (prove_restriction_alternate_defn5_2): member(z, cross_product(x, y)) = true2.
% 0.20/0.61 Axiom 3 (restriction1): intersection(X, cross_product(Y, Z)) = restrict(X, Y, Z).
% 0.20/0.61 Axiom 4 (intersection3): fresh40(X, X, Y, Z, W) = member(Y, intersection(Z, W)).
% 0.20/0.61 Axiom 5 (intersection3): fresh39(X, X, Y, Z, W) = true2.
% 0.20/0.61 Axiom 6 (intersection3): fresh40(member(X, Y), true2, X, Z, Y) = fresh39(member(X, Z), true2, X, Z, Y).
% 0.20/0.61
% 0.20/0.61 Goal 1 (prove_restriction_alternate_defn5_3): member(z, restrict(xr, x, y)) = true2.
% 0.20/0.61 Proof:
% 0.20/0.61 member(z, restrict(xr, x, y))
% 0.20/0.61 = { by axiom 3 (restriction1) R->L }
% 0.20/0.61 member(z, intersection(xr, cross_product(x, y)))
% 0.20/0.61 = { by axiom 4 (intersection3) R->L }
% 0.20/0.61 fresh40(true2, true2, z, xr, cross_product(x, y))
% 0.20/0.61 = { by axiom 2 (prove_restriction_alternate_defn5_2) R->L }
% 0.20/0.61 fresh40(member(z, cross_product(x, y)), true2, z, xr, cross_product(x, y))
% 0.20/0.61 = { by axiom 6 (intersection3) }
% 0.20/0.61 fresh39(member(z, xr), true2, z, xr, cross_product(x, y))
% 0.20/0.61 = { by axiom 1 (prove_restriction_alternate_defn5_1) }
% 0.20/0.61 fresh39(true2, true2, z, xr, cross_product(x, y))
% 0.20/0.61 = { by axiom 5 (intersection3) }
% 0.20/0.61 true2
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61
% 0.20/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
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