TSTP Solution File: LAT153-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT153-1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n001.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 06:27:35 EDT 2023
% Result : Unsatisfiable 29.26s 4.16s
% Output : Proof 29.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT153-1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n001.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 : Thu Aug 24 05:17:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 29.26/4.16 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 29.26/4.16
% 29.26/4.16 % SZS status Unsatisfiable
% 29.26/4.16
% 29.26/4.17 % SZS output start Proof
% 29.26/4.17 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 29.26/4.17 Axiom 2 (idempotence_of_meet): meet(X, X) = X.
% 29.26/4.17 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 29.26/4.17 Axiom 4 (absorption2): join(X, meet(X, Y)) = X.
% 29.26/4.17 Axiom 5 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 29.26/4.17 Axiom 6 (absorption1): meet(X, join(X, Y)) = X.
% 29.26/4.17 Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 29.26/4.17 Axiom 8 (equation_H40): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(W, meet(Z, join(X, Y)))))).
% 29.26/4.17
% 29.26/4.17 Lemma 9: meet(X, meet(X, Y)) = meet(X, Y).
% 29.26/4.17 Proof:
% 29.26/4.17 meet(X, meet(X, Y))
% 29.26/4.17 = { by axiom 7 (associativity_of_meet) R->L }
% 29.26/4.17 meet(meet(X, X), Y)
% 29.26/4.17 = { by axiom 2 (idempotence_of_meet) }
% 29.26/4.17 meet(X, Y)
% 29.26/4.17
% 29.26/4.17 Lemma 10: join(X, meet(Y, X)) = X.
% 29.26/4.17 Proof:
% 29.26/4.17 join(X, meet(Y, X))
% 29.26/4.17 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.26/4.17 join(X, meet(X, Y))
% 29.26/4.17 = { by axiom 4 (absorption2) }
% 29.26/4.17 X
% 29.26/4.17
% 29.26/4.17 Lemma 11: join(X, join(meet(X, Y), Z)) = join(X, Z).
% 29.26/4.17 Proof:
% 29.26/4.17 join(X, join(meet(X, Y), Z))
% 29.26/4.17 = { by axiom 5 (associativity_of_join) R->L }
% 29.26/4.17 join(join(X, meet(X, Y)), Z)
% 29.26/4.17 = { by axiom 4 (absorption2) }
% 29.26/4.17 join(X, Z)
% 29.26/4.17
% 29.26/4.17 Lemma 12: join(meet(X, Y), meet(X, join(Y, Z))) = meet(X, join(Y, Z)).
% 29.26/4.17 Proof:
% 29.26/4.17 join(meet(X, Y), meet(X, join(Y, Z)))
% 29.26/4.17 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.26/4.17 join(meet(Y, X), meet(X, join(Y, Z)))
% 29.26/4.17 = { by axiom 1 (commutativity_of_join) R->L }
% 29.26/4.17 join(meet(X, join(Y, Z)), meet(Y, X))
% 29.26/4.17 = { by axiom 6 (absorption1) R->L }
% 29.26/4.17 join(meet(X, join(Y, Z)), meet(meet(Y, join(Y, Z)), X))
% 29.26/4.17 = { by axiom 7 (associativity_of_meet) }
% 29.26/4.17 join(meet(X, join(Y, Z)), meet(Y, meet(join(Y, Z), X)))
% 29.26/4.17 = { by axiom 3 (commutativity_of_meet) }
% 29.26/4.17 join(meet(X, join(Y, Z)), meet(Y, meet(X, join(Y, Z))))
% 29.26/4.17 = { by lemma 10 }
% 29.26/4.17 meet(X, join(Y, Z))
% 29.26/4.17
% 29.26/4.17 Lemma 13: meet(X, join(Y, meet(join(X, Y), Z))) = meet(X, join(Y, meet(X, Z))).
% 29.26/4.17 Proof:
% 29.26/4.17 meet(X, join(Y, meet(join(X, Y), Z)))
% 29.26/4.17 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.26/4.17 meet(X, join(Y, meet(Z, join(X, Y))))
% 29.26/4.17 = { by lemma 9 R->L }
% 29.26/4.17 meet(X, join(Y, meet(Z, meet(Z, join(X, Y)))))
% 29.26/4.17 = { by lemma 12 R->L }
% 29.26/4.17 meet(X, join(Y, meet(Z, join(meet(Z, X), meet(Z, join(X, Y))))))
% 29.26/4.17 = { by axiom 8 (equation_H40) R->L }
% 29.26/4.17 meet(X, join(Y, meet(Z, join(X, meet(Z, X)))))
% 29.26/4.17 = { by lemma 10 }
% 29.26/4.17 meet(X, join(Y, meet(Z, X)))
% 29.26/4.17 = { by axiom 3 (commutativity_of_meet) }
% 29.26/4.17 meet(X, join(Y, meet(X, Z)))
% 29.26/4.17
% 29.26/4.17 Goal 1 (prove_H7): meet(a, join(b, meet(a, c))) = meet(a, join(b, meet(a, join(meet(a, b), meet(c, join(a, b)))))).
% 29.26/4.17 Proof:
% 29.26/4.17 meet(a, join(b, meet(a, c)))
% 29.26/4.17 = { by lemma 13 R->L }
% 29.26/4.17 meet(a, join(b, meet(join(a, b), c)))
% 29.26/4.17 = { by lemma 11 R->L }
% 29.26/4.17 meet(a, join(b, join(meet(b, a), meet(join(a, b), c))))
% 29.26/4.17 = { by axiom 4 (absorption2) R->L }
% 29.26/4.17 meet(a, join(b, join(join(meet(b, a), meet(join(a, b), c)), meet(join(meet(b, a), meet(join(a, b), c)), join(a, b)))))
% 29.26/4.17 = { by axiom 5 (associativity_of_join) }
% 29.26/4.17 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), c), meet(join(meet(b, a), meet(join(a, b), c)), join(a, b))))))
% 29.26/4.17 = { by axiom 3 (commutativity_of_meet) }
% 29.26/4.17 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), c), meet(join(a, b), join(meet(b, a), meet(join(a, b), c)))))))
% 29.26/4.17 = { by axiom 1 (commutativity_of_join) R->L }
% 29.26/4.17 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), c), meet(join(a, b), join(meet(join(a, b), c), meet(b, a)))))))
% 29.26/4.17 = { by lemma 9 R->L }
% 29.26/4.17 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), meet(join(a, b), c)), meet(join(a, b), join(meet(join(a, b), c), meet(b, a)))))))
% 29.26/4.17 = { by lemma 12 }
% 29.26/4.17 meet(a, join(b, join(meet(b, a), meet(join(a, b), join(meet(join(a, b), c), meet(b, a))))))
% 29.26/4.18 = { by axiom 1 (commutativity_of_join) }
% 29.26/4.18 meet(a, join(b, join(meet(b, a), meet(join(a, b), join(meet(b, a), meet(join(a, b), c))))))
% 29.26/4.18 = { by lemma 11 }
% 29.26/4.18 meet(a, join(b, meet(join(a, b), join(meet(b, a), meet(join(a, b), c)))))
% 29.26/4.18 = { by axiom 1 (commutativity_of_join) }
% 29.26/4.18 meet(a, join(b, meet(join(a, b), join(meet(join(a, b), c), meet(b, a)))))
% 29.26/4.18 = { by lemma 13 }
% 29.26/4.18 meet(a, join(b, meet(a, join(meet(join(a, b), c), meet(b, a)))))
% 29.26/4.18 = { by axiom 1 (commutativity_of_join) }
% 29.26/4.18 meet(a, join(b, meet(a, join(meet(b, a), meet(join(a, b), c)))))
% 29.26/4.18 = { by axiom 3 (commutativity_of_meet) }
% 29.26/4.18 meet(a, join(b, meet(a, join(meet(b, a), meet(c, join(a, b))))))
% 29.26/4.18 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.26/4.18 meet(a, join(b, meet(a, join(meet(a, b), meet(c, join(a, b))))))
% 29.26/4.18 % SZS output end Proof
% 29.26/4.18
% 29.26/4.18 RESULT: Unsatisfiable (the axioms are contradictory).
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