TSTP Solution File: SET001-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET001-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n029.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 15:30:27 EDT 2023
% Result : Unsatisfiable 0.15s 0.41s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n029.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 15:20:25 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.15/0.41
% 0.15/0.41 % SZS status Unsatisfiable
% 0.15/0.41
% 0.15/0.41 % SZS output start Proof
% 0.15/0.41 Take the following subset of the input axioms:
% 0.15/0.41 fof(b_equals_bb, hypothesis, equal_sets(b, bb)).
% 0.15/0.41 fof(element_of_b, hypothesis, member(element_of_b, b)).
% 0.15/0.41 fof(membership_in_subsets, axiom, ![Element, Subset, Superset]: (~member(Element, Subset) | (~subset(Subset, Superset) | member(Element, Superset)))).
% 0.15/0.41 fof(prove_element_of_bb, negated_conjecture, ~member(element_of_b, bb)).
% 0.15/0.41 fof(set_equal_sets_are_subsets1, axiom, ![Subset2, Superset2]: (~equal_sets(Subset2, Superset2) | subset(Subset2, Superset2))).
% 0.15/0.41
% 0.15/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.15/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.15/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.15/0.41 fresh(y, y, x1...xn) = u
% 0.15/0.41 C => fresh(s, t, x1...xn) = v
% 0.15/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.15/0.41 variables of u and v.
% 0.15/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.15/0.41 input problem has no model of domain size 1).
% 0.15/0.41
% 0.15/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.15/0.41
% 0.15/0.41 Axiom 1 (b_equals_bb): equal_sets(b, bb) = true.
% 0.15/0.41 Axiom 2 (element_of_b): member(element_of_b, b) = true.
% 0.15/0.41 Axiom 3 (membership_in_subsets): fresh7(X, X, Y, Z) = true.
% 0.15/0.41 Axiom 4 (set_equal_sets_are_subsets1): fresh5(X, X, Y, Z) = true.
% 0.15/0.41 Axiom 5 (membership_in_subsets): fresh6(X, X, Y, Z, W) = member(Y, W).
% 0.15/0.41 Axiom 6 (set_equal_sets_are_subsets1): fresh5(equal_sets(X, Y), true, X, Y) = subset(X, Y).
% 0.15/0.41 Axiom 7 (membership_in_subsets): fresh6(subset(X, Y), true, Z, X, Y) = fresh7(member(Z, X), true, Z, Y).
% 0.15/0.41
% 0.15/0.41 Goal 1 (prove_element_of_bb): member(element_of_b, bb) = true.
% 0.15/0.41 Proof:
% 0.15/0.41 member(element_of_b, bb)
% 0.15/0.41 = { by axiom 5 (membership_in_subsets) R->L }
% 0.15/0.41 fresh6(true, true, element_of_b, b, bb)
% 0.15/0.41 = { by axiom 4 (set_equal_sets_are_subsets1) R->L }
% 0.15/0.41 fresh6(fresh5(true, true, b, bb), true, element_of_b, b, bb)
% 0.15/0.41 = { by axiom 1 (b_equals_bb) R->L }
% 0.15/0.41 fresh6(fresh5(equal_sets(b, bb), true, b, bb), true, element_of_b, b, bb)
% 0.15/0.41 = { by axiom 6 (set_equal_sets_are_subsets1) }
% 0.15/0.41 fresh6(subset(b, bb), true, element_of_b, b, bb)
% 0.15/0.41 = { by axiom 7 (membership_in_subsets) }
% 0.15/0.41 fresh7(member(element_of_b, b), true, element_of_b, bb)
% 0.15/0.41 = { by axiom 2 (element_of_b) }
% 0.15/0.41 fresh7(true, true, element_of_b, bb)
% 0.15/0.41 = { by axiom 3 (membership_in_subsets) }
% 0.15/0.41 true
% 0.15/0.41 % SZS output end Proof
% 0.15/0.41
% 0.15/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------