TSTP Solution File: LAT175-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT175-1 : 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 : n011.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 06:27:39 EDT 2023
% Result : Timeout 286.61s 37.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT175-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 09:43:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 286.61/37.48 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 286.61/37.48
% 286.61/37.48 % SZS status Unsatisfiable
% 286.61/37.48
% 286.61/37.50 % SZS output start Proof
% 286.61/37.50 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 286.61/37.50 Axiom 2 (idempotence_of_join): join(X, X) = X.
% 286.61/37.50 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 286.61/37.50 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 286.61/37.50 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 286.61/37.50 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 286.61/37.50 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 286.61/37.50 Axiom 8 (equation_H79_dual): join(X, meet(Y, join(Z, meet(X, W)))) = join(X, meet(join(X, meet(Y, join(X, Z))), join(Z, W))).
% 286.61/37.50
% 286.61/37.50 Lemma 9: meet(X, join(Y, X)) = X.
% 286.61/37.50 Proof:
% 286.61/37.50 meet(X, join(Y, X))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.50 meet(X, join(X, Y))
% 286.61/37.50 = { by axiom 4 (absorption1) }
% 286.61/37.50 X
% 286.61/37.50
% 286.61/37.50 Lemma 10: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 286.61/37.50 Proof:
% 286.61/37.50 meet(Y, meet(X, Z))
% 286.61/37.50 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.50 meet(meet(X, Z), Y)
% 286.61/37.50 = { by axiom 5 (associativity_of_meet) }
% 286.61/37.50 meet(X, meet(Z, Y))
% 286.61/37.50 = { by axiom 1 (commutativity_of_meet) }
% 286.61/37.50 meet(X, meet(Y, Z))
% 286.61/37.50
% 286.61/37.50 Lemma 11: meet(Z, meet(X, Y)) = meet(X, meet(Y, Z)).
% 286.61/37.50 Proof:
% 286.61/37.50 meet(Z, meet(X, Y))
% 286.61/37.50 = { by lemma 10 }
% 286.61/37.50 meet(X, meet(Z, Y))
% 286.61/37.50 = { by axiom 1 (commutativity_of_meet) }
% 286.61/37.50 meet(X, meet(Y, Z))
% 286.61/37.50
% 286.61/37.50 Lemma 12: meet(Z, meet(Y, X)) = meet(X, meet(Y, Z)).
% 286.61/37.50 Proof:
% 286.61/37.50 meet(Z, meet(Y, X))
% 286.61/37.50 = { by lemma 11 R->L }
% 286.61/37.50 meet(X, meet(Z, Y))
% 286.61/37.50 = { by axiom 1 (commutativity_of_meet) }
% 286.61/37.50 meet(X, meet(Y, Z))
% 286.61/37.50
% 286.61/37.50 Lemma 13: join(X, meet(Y, X)) = X.
% 286.61/37.50 Proof:
% 286.61/37.50 join(X, meet(Y, X))
% 286.61/37.50 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.50 join(X, meet(X, Y))
% 286.61/37.50 = { by axiom 6 (absorption2) }
% 286.61/37.50 X
% 286.61/37.50
% 286.61/37.50 Lemma 14: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 286.61/37.50 Proof:
% 286.61/37.50 join(Y, join(X, Z))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.50 join(join(X, Z), Y)
% 286.61/37.50 = { by axiom 7 (associativity_of_join) }
% 286.61/37.50 join(X, join(Z, Y))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) }
% 286.61/37.50 join(X, join(Y, Z))
% 286.61/37.50
% 286.61/37.50 Lemma 15: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 286.61/37.50 Proof:
% 286.61/37.50 join(Z, join(X, Y))
% 286.61/37.50 = { by lemma 14 }
% 286.61/37.50 join(X, join(Z, Y))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) }
% 286.61/37.50 join(X, join(Y, Z))
% 286.61/37.50
% 286.61/37.50 Lemma 16: join(X, join(Y, meet(X, Z))) = join(X, Y).
% 286.61/37.50 Proof:
% 286.61/37.50 join(X, join(Y, meet(X, Z)))
% 286.61/37.50 = { by lemma 14 }
% 286.61/37.50 join(Y, join(X, meet(X, Z)))
% 286.61/37.50 = { by axiom 6 (absorption2) }
% 286.61/37.50 join(Y, X)
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) }
% 286.61/37.50 join(X, Y)
% 286.61/37.50
% 286.61/37.50 Lemma 17: meet(meet(X, Y), join(Z, join(W, Y))) = meet(X, Y).
% 286.61/37.50 Proof:
% 286.61/37.50 meet(meet(X, Y), join(Z, join(W, Y)))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.50 meet(meet(X, Y), join(Z, join(Y, W)))
% 286.61/37.50 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.50 meet(join(Z, join(Y, W)), meet(X, Y))
% 286.61/37.50 = { by lemma 11 }
% 286.61/37.50 meet(X, meet(Y, join(Z, join(Y, W))))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.50 meet(X, meet(Y, join(Z, join(W, Y))))
% 286.61/37.50 = { by axiom 7 (associativity_of_join) R->L }
% 286.61/37.50 meet(X, meet(Y, join(join(Z, W), Y)))
% 286.61/37.50 = { by lemma 9 }
% 286.61/37.50 meet(X, Y)
% 286.61/37.50
% 286.61/37.50 Goal 1 (prove_H32): meet(a, join(b, meet(a, meet(c, d)))) = meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))).
% 286.61/37.50 Proof:
% 286.61/37.50 meet(a, join(b, meet(a, meet(c, d))))
% 286.61/37.50 = { by lemma 17 R->L }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(b, join(meet(c, join(meet(a, d), meet(b, d))), join(b, meet(a, meet(c, d))))))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(b, join(join(b, meet(a, meet(c, d))), meet(c, join(meet(a, d), meet(b, d))))))
% 286.61/37.50 = { by axiom 7 (associativity_of_join) R->L }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(join(b, join(b, meet(a, meet(c, d)))), meet(c, join(meet(a, d), meet(b, d)))))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(join(join(b, meet(a, meet(c, d))), b), meet(c, join(meet(a, d), meet(b, d)))))
% 286.61/37.50 = { by axiom 4 (absorption1) R->L }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(join(join(b, meet(a, meet(c, d))), meet(b, join(b, meet(a, meet(c, d))))), meet(c, join(meet(a, d), meet(b, d)))))
% 286.61/37.50 = { by lemma 13 }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(join(b, meet(a, meet(c, d))), meet(c, join(meet(a, d), meet(b, d)))))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(meet(c, join(meet(a, d), meet(b, d))), join(b, meet(a, meet(c, d)))))
% 286.61/37.50 = { by lemma 15 }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(b, join(meet(a, meet(c, d)), meet(c, join(meet(a, d), meet(b, d))))))
% 286.61/37.50 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(b, join(meet(c, join(meet(a, d), meet(b, d))), meet(a, meet(c, d)))))
% 286.61/37.50 = { by lemma 10 }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(b, join(meet(c, join(meet(a, d), meet(b, d))), meet(c, meet(a, d)))))
% 286.61/37.50 = { by axiom 4 (absorption1) R->L }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(b, join(meet(c, join(meet(a, d), meet(b, d))), meet(c, meet(meet(a, d), join(meet(a, d), meet(b, d)))))))
% 286.61/37.50 = { by lemma 10 R->L }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(b, join(meet(c, join(meet(a, d), meet(b, d))), meet(meet(a, d), meet(c, join(meet(a, d), meet(b, d)))))))
% 286.61/37.50 = { by lemma 13 }
% 286.61/37.50 meet(meet(a, join(b, meet(a, meet(c, d)))), join(b, meet(c, join(meet(a, d), meet(b, d)))))
% 286.61/37.50 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.50 meet(join(b, meet(c, join(meet(a, d), meet(b, d)))), meet(a, join(b, meet(a, meet(c, d)))))
% 286.61/37.50 = { by lemma 11 }
% 286.61/37.50 meet(a, meet(join(b, meet(a, meet(c, d))), join(b, meet(c, join(meet(a, d), meet(b, d))))))
% 286.61/37.50 = { by lemma 10 R->L }
% 286.61/37.50 meet(join(b, meet(a, meet(c, d))), meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(c, d))))
% 286.61/37.51 = { by axiom 4 (absorption1) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(meet(a, meet(c, d)), join(meet(a, d), meet(b, d))))))
% 286.61/37.51 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(a, meet(c, d))))))
% 286.61/37.51 = { by lemma 9 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(a, meet(meet(c, d), join(d, meet(c, d))))))))
% 286.61/37.51 = { by lemma 13 }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(a, meet(meet(c, d), d))))))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(a, meet(d, meet(c, d)))))))
% 286.61/37.51 = { by lemma 10 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(d, meet(a, meet(c, d)))))))
% 286.61/37.51 = { by lemma 9 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(d, meet(meet(a, meet(c, d)), join(a, meet(a, meet(c, d)))))))))
% 286.61/37.51 = { by axiom 6 (absorption2) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(d, meet(meet(a, meet(c, d)), a))))))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(d, meet(a, meet(a, meet(c, d))))))))
% 286.61/37.51 = { by lemma 12 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(meet(a, meet(c, d)), meet(a, d))))))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(meet(a, d), meet(a, meet(c, d)))))))
% 286.61/37.51 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(meet(meet(a, d), meet(a, meet(c, d))), join(meet(a, d), meet(b, d))))))
% 286.61/37.51 = { by lemma 15 }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(meet(a, d), join(meet(b, d), meet(meet(a, d), meet(a, meet(c, d))))))))
% 286.61/37.51 = { by lemma 16 }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(a, meet(c, d)), join(meet(a, d), meet(b, d)))))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(join(meet(a, d), meet(b, d)), meet(a, meet(c, d)))))
% 286.61/37.51 = { by lemma 11 }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(meet(c, d), join(meet(a, d), meet(b, d))))))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(join(meet(a, d), meet(b, d)), meet(c, d)))))
% 286.61/37.51 = { by lemma 12 }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(d, meet(c, join(meet(a, d), meet(b, d)))))))
% 286.61/37.51 = { by lemma 10 }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(c, meet(d, join(meet(a, d), meet(b, d)))))))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), d)))))
% 286.61/37.51 = { by lemma 13 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), join(d, meet(a, d)))))))
% 286.61/37.51 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), join(meet(a, d), d))))))
% 286.61/37.51 = { by lemma 13 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), join(meet(a, d), join(d, meet(b, d))))))))
% 286.61/37.51 = { by lemma 14 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), join(d, join(meet(a, d), meet(b, d))))))))
% 286.61/37.51 = { by lemma 9 }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, meet(c, join(meet(a, d), meet(b, d))))))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(c, join(meet(a, d), meet(b, d))), a)))
% 286.61/37.51 = { by lemma 13 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, meet(b, a)))))
% 286.61/37.51 = { by axiom 8 (equation_H79_dual) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(b, a))), join(a, a))))
% 286.61/37.51 = { by axiom 2 (idempotence_of_join) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(b, a))), a)))
% 286.61/37.51 = { by axiom 1 (commutativity_of_meet) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(b, a))))))
% 286.61/37.51 = { by axiom 3 (commutativity_of_join) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, b))))))
% 286.61/37.51 = { by axiom 6 (absorption2) R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(join(a, meet(a, d)), b))))))
% 286.61/37.51 = { by axiom 7 (associativity_of_join) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, join(meet(a, d), b)))))))
% 286.61/37.51 = { by axiom 3 (commutativity_of_join) }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, join(b, meet(a, d))))))))
% 286.61/37.51 = { by lemma 16 R->L }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, join(b, join(meet(a, d), meet(b, d)))))))))
% 286.61/37.51 = { by lemma 17 }
% 286.61/37.51 meet(meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))), join(b, meet(a, join(b, meet(c, join(meet(a, d), meet(b, d)))))))
% 286.61/37.51 = { by lemma 9 }
% 286.61/37.51 meet(a, join(b, meet(c, join(meet(a, d), meet(b, d)))))
% 286.61/37.51 % SZS output end Proof
% 286.61/37.51
% 286.61/37.51 RESULT: Unsatisfiable (the axioms are contradictory).
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