TSTP Solution File: LAT023-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT023-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n016.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 06:27:09 EDT 2023
% Result : Unsatisfiable 0.19s 0.63s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT023-1 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n016.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 09:10:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.63 Command-line arguments: --no-flatten-goal
% 0.19/0.63
% 0.19/0.63 % SZS status Unsatisfiable
% 0.19/0.63
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 Axiom 1 (idempotence_of_meet): meet(X, X) = X.
% 0.19/0.64 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.19/0.64 Axiom 3 (idempotence_of_join): join(X, X) = X.
% 0.19/0.64 Axiom 4 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.19/0.64 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.19/0.64 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.19/0.64 Axiom 7 (modularity_axiom): join(meet(join(X, Y), Z), Y) = join(meet(join(Z, Y), X), Y).
% 0.19/0.64 Axiom 8 (quasi_lattice2): meet(join(X, meet(Y, Z)), join(X, Y)) = join(X, meet(Y, Z)).
% 0.19/0.64 Axiom 9 (quasi_lattice1): join(meet(X, join(Y, Z)), meet(X, Y)) = meet(X, join(Y, Z)).
% 0.19/0.64
% 0.19/0.64 Lemma 10: meet(X, meet(X, Y)) = meet(X, Y).
% 0.19/0.64 Proof:
% 0.19/0.64 meet(X, meet(X, Y))
% 0.19/0.64 = { by axiom 5 (associativity_of_meet) R->L }
% 0.19/0.65 meet(meet(X, X), Y)
% 0.19/0.65 = { by axiom 1 (idempotence_of_meet) }
% 0.19/0.65 meet(X, Y)
% 0.19/0.65
% 0.19/0.65 Lemma 11: join(X, join(X, Y)) = join(X, Y).
% 0.19/0.65 Proof:
% 0.19/0.65 join(X, join(X, Y))
% 0.19/0.65 = { by axiom 6 (associativity_of_join) R->L }
% 0.19/0.65 join(join(X, X), Y)
% 0.19/0.65 = { by axiom 3 (idempotence_of_join) }
% 0.19/0.65 join(X, Y)
% 0.19/0.65
% 0.19/0.65 Lemma 12: join(X, meet(join(Z, X), Y)) = join(X, meet(join(Y, X), Z)).
% 0.19/0.65 Proof:
% 0.19/0.65 join(X, meet(join(Z, X), Y))
% 0.19/0.65 = { by axiom 4 (commutativity_of_join) R->L }
% 0.19/0.65 join(meet(join(Z, X), Y), X)
% 0.19/0.65 = { by axiom 7 (modularity_axiom) R->L }
% 0.19/0.65 join(meet(join(Y, X), Z), X)
% 0.19/0.65 = { by axiom 4 (commutativity_of_join) }
% 0.19/0.65 join(X, meet(join(Y, X), Z))
% 0.19/0.65
% 0.19/0.65 Lemma 13: join(X, meet(Z, join(Y, X))) = join(X, meet(Y, join(X, Z))).
% 0.19/0.65 Proof:
% 0.19/0.65 join(X, meet(Z, join(Y, X)))
% 0.19/0.65 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.19/0.65 join(X, meet(join(Y, X), Z))
% 0.19/0.65 = { by lemma 12 R->L }
% 0.19/0.65 join(X, meet(join(Z, X), Y))
% 0.19/0.65 = { by axiom 2 (commutativity_of_meet) }
% 0.19/0.65 join(X, meet(Y, join(Z, X)))
% 0.19/0.65 = { by axiom 4 (commutativity_of_join) }
% 0.19/0.65 join(X, meet(Y, join(X, Z)))
% 0.19/0.65
% 0.19/0.65 Lemma 14: join(meet(X, Y), meet(X, join(Y, Z))) = meet(X, join(Y, Z)).
% 0.19/0.65 Proof:
% 0.19/0.65 join(meet(X, Y), meet(X, join(Y, Z)))
% 0.19/0.65 = { by axiom 4 (commutativity_of_join) R->L }
% 0.19/0.65 join(meet(X, join(Y, Z)), meet(X, Y))
% 0.19/0.65 = { by axiom 9 (quasi_lattice1) }
% 0.19/0.65 meet(X, join(Y, Z))
% 0.19/0.65
% 0.19/0.65 Goal 1 (prove_modularity): meet(a, join(b, meet(a, c))) = join(meet(a, b), meet(a, c)).
% 0.19/0.65 Proof:
% 0.19/0.65 meet(a, join(b, meet(a, c)))
% 0.19/0.65 = { by lemma 10 R->L }
% 0.19/0.65 meet(a, join(b, meet(a, meet(a, c))))
% 0.19/0.65 = { by axiom 4 (commutativity_of_join) R->L }
% 0.19/0.65 meet(a, join(meet(a, meet(a, c)), b))
% 0.19/0.65 = { by lemma 14 R->L }
% 0.19/0.65 join(meet(a, meet(a, meet(a, c))), meet(a, join(meet(a, meet(a, c)), b)))
% 0.19/0.65 = { by axiom 2 (commutativity_of_meet) }
% 0.19/0.65 join(meet(a, meet(a, meet(a, c))), meet(join(meet(a, meet(a, c)), b), a))
% 0.19/0.65 = { by lemma 10 }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(join(meet(a, meet(a, c)), b), a))
% 0.19/0.65 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(a, join(meet(a, meet(a, c)), b)))
% 0.19/0.65 = { by lemma 13 R->L }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(b, join(a, meet(a, meet(a, c)))))
% 0.19/0.65 = { by axiom 3 (idempotence_of_join) R->L }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(b, join(a, meet(join(a, a), meet(a, c)))))
% 0.19/0.65 = { by lemma 12 R->L }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(b, join(a, meet(join(meet(a, c), a), a))))
% 0.19/0.65 = { by axiom 2 (commutativity_of_meet) }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(b, join(a, meet(a, join(meet(a, c), a)))))
% 0.19/0.65 = { by axiom 4 (commutativity_of_join) }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(b, join(a, meet(a, join(a, meet(a, c))))))
% 0.19/0.65 = { by axiom 1 (idempotence_of_meet) R->L }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(b, join(meet(a, a), meet(a, join(a, meet(a, c))))))
% 0.19/0.65 = { by lemma 14 }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(b, meet(a, join(a, meet(a, c)))))
% 0.19/0.65 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.19/0.65 join(meet(a, meet(a, c)), meet(b, meet(join(a, meet(a, c)), a)))
% 0.19/0.65 = { by axiom 5 (associativity_of_meet) R->L }
% 0.19/0.66 join(meet(a, meet(a, c)), meet(meet(b, join(a, meet(a, c))), a))
% 0.19/0.66 = { by axiom 2 (commutativity_of_meet) }
% 0.19/0.66 join(meet(a, meet(a, c)), meet(a, meet(b, join(a, meet(a, c)))))
% 0.19/0.66 = { by lemma 10 }
% 0.19/0.66 join(meet(a, c), meet(a, meet(b, join(a, meet(a, c)))))
% 0.19/0.66 = { by axiom 4 (commutativity_of_join) R->L }
% 0.19/0.66 join(meet(a, c), meet(a, meet(b, join(meet(a, c), a))))
% 0.19/0.66 = { by lemma 11 R->L }
% 0.19/0.66 join(meet(a, c), meet(a, meet(b, join(meet(a, c), join(meet(a, c), a)))))
% 0.19/0.66 = { by axiom 4 (commutativity_of_join) }
% 0.19/0.66 join(meet(a, c), meet(a, meet(b, join(meet(a, c), join(a, meet(a, c))))))
% 0.19/0.66 = { by axiom 6 (associativity_of_join) R->L }
% 0.19/0.66 join(meet(a, c), meet(a, meet(b, join(join(meet(a, c), a), meet(a, c)))))
% 0.19/0.66 = { by axiom 5 (associativity_of_meet) R->L }
% 0.19/0.66 join(meet(a, c), meet(meet(a, b), join(join(meet(a, c), a), meet(a, c))))
% 0.19/0.66 = { by lemma 13 }
% 0.19/0.66 join(meet(a, c), meet(join(meet(a, c), a), join(meet(a, c), meet(a, b))))
% 0.19/0.66 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.19/0.66 join(meet(a, c), meet(join(meet(a, c), meet(a, b)), join(meet(a, c), a)))
% 0.19/0.66 = { by axiom 8 (quasi_lattice2) }
% 0.19/0.66 join(meet(a, c), join(meet(a, c), meet(a, b)))
% 0.19/0.66 = { by lemma 11 }
% 0.19/0.66 join(meet(a, c), meet(a, b))
% 0.19/0.66 = { by axiom 4 (commutativity_of_join) }
% 0.19/0.66 join(meet(a, b), meet(a, c))
% 0.19/0.66 % SZS output end Proof
% 0.19/0.66
% 0.19/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------