TSTP Solution File: LAT138-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT138-1 : 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 : n007.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 06:27:32 EDT 2023
% Result : Unsatisfiable 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT138-1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 05:39:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.21/0.55 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.55
% 0.21/0.55 % SZS status Unsatisfiable
% 0.21/0.55
% 0.21/0.55 % SZS output start Proof
% 0.21/0.55 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.21/0.55 Axiom 2 (idempotence_of_join): join(X, X) = X.
% 0.21/0.55 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.21/0.55 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 0.21/0.55 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.21/0.55 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 0.21/0.55 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.21/0.55 Axiom 8 (equation_H7): meet(X, join(Y, meet(X, Z))) = meet(X, join(Y, meet(X, join(meet(X, Y), meet(Z, join(X, Y)))))).
% 0.21/0.55
% 0.21/0.55 Lemma 9: meet(X, meet(X, Y)) = meet(X, Y).
% 0.21/0.55 Proof:
% 0.21/0.55 meet(X, meet(X, Y))
% 0.21/0.55 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.21/0.55 meet(meet(X, Y), X)
% 0.21/0.55 = { by axiom 6 (absorption2) R->L }
% 0.21/0.55 meet(meet(X, Y), join(X, meet(X, Y)))
% 0.21/0.55 = { by axiom 3 (commutativity_of_join) R->L }
% 0.21/0.55 meet(meet(X, Y), join(meet(X, Y), X))
% 0.21/0.55 = { by axiom 4 (absorption1) }
% 0.21/0.55 meet(X, Y)
% 0.21/0.55
% 0.21/0.55 Lemma 10: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 0.21/0.55 Proof:
% 0.21/0.55 join(Y, join(X, Z))
% 0.21/0.55 = { by axiom 3 (commutativity_of_join) R->L }
% 0.21/0.55 join(join(X, Z), Y)
% 0.21/0.55 = { by axiom 7 (associativity_of_join) }
% 0.21/0.55 join(X, join(Z, Y))
% 0.21/0.55 = { by axiom 3 (commutativity_of_join) }
% 0.21/0.55 join(X, join(Y, Z))
% 0.21/0.55
% 0.21/0.55 Goal 1 (prove_H6): meet(a, join(b, meet(a, c))) = meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))).
% 0.21/0.55 Proof:
% 0.21/0.55 meet(a, join(b, meet(a, c)))
% 0.21/0.55 = { by lemma 9 R->L }
% 0.21/0.55 meet(a, meet(a, join(b, meet(a, c))))
% 0.21/0.55 = { by axiom 4 (absorption1) R->L }
% 0.21/0.55 meet(a, meet(meet(a, join(b, meet(a, c))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 0.21/0.55 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.21/0.56 meet(a, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, c)))))
% 0.21/0.56 = { by axiom 5 (associativity_of_meet) R->L }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(b, meet(a, c))))
% 0.21/0.56 = { by axiom 2 (idempotence_of_join) R->L }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(b, join(meet(a, c), meet(a, c)))))
% 0.21/0.56 = { by lemma 10 R->L }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(meet(a, c), join(b, meet(a, c)))))
% 0.21/0.56 = { by axiom 3 (commutativity_of_join) R->L }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(join(b, meet(a, c)), meet(a, c))))
% 0.21/0.56 = { by axiom 8 (equation_H7) }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(join(b, meet(a, c)), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, join(b, meet(a, c)))))))))
% 0.21/0.56 = { by lemma 10 }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(join(b, meet(a, c)), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(b, join(a, meet(a, c)))))))))
% 0.21/0.56 = { by axiom 6 (absorption2) }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(join(b, meet(a, c)), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(b, a)))))))
% 0.21/0.56 = { by axiom 3 (commutativity_of_join) }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(join(b, meet(a, c)), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))))
% 0.21/0.56 = { by axiom 3 (commutativity_of_join) }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))))
% 0.21/0.56 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(join(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), a))
% 0.21/0.56 = { by axiom 5 (associativity_of_meet) R->L }
% 0.21/0.56 meet(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))), a)
% 0.21/0.56 = { by axiom 4 (absorption1) }
% 0.21/0.56 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), a)
% 0.21/0.56 = { by axiom 1 (commutativity_of_meet) }
% 0.21/0.56 meet(a, meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 0.21/0.56 = { by lemma 9 }
% 0.21/0.56 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 0.21/0.56 % SZS output end Proof
% 0.21/0.56
% 0.21/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
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