TSTP Solution File: LAT162-1 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : LAT162-1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n025.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 : Mon Jun 24 10:31:33 EDT 2024
% Result : Unsatisfiable 177.91s 22.70s
% Output : Proof 178.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT162-1 : TPTP v8.2.0. Released v3.1.0.
% 0.03/0.11 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 21 23:15:09 EDT 2024
% 0.11/0.33 % CPUTime :
% 177.91/22.70 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 177.91/22.70
% 177.91/22.70 % SZS status Unsatisfiable
% 177.91/22.70
% 178.41/22.76 % SZS output start Proof
% 178.41/22.76 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 178.41/22.76 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 178.41/22.76 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 178.41/22.76 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 178.41/22.76 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 178.41/22.76 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 178.41/22.76 Axiom 7 (equation_H68): meet(X, join(Y, Z)) = meet(X, join(Y, meet(X, join(Z, meet(X, Y))))).
% 178.41/22.76
% 178.41/22.76 Lemma 8: meet(X, join(Y, X)) = X.
% 178.41/22.76 Proof:
% 178.41/22.76 meet(X, join(Y, X))
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.76 meet(X, join(X, Y))
% 178.41/22.76 = { by axiom 3 (absorption1) }
% 178.41/22.76 X
% 178.41/22.76
% 178.41/22.76 Lemma 9: meet(X, meet(X, Y)) = meet(X, Y).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(X, meet(X, Y))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 meet(meet(X, Y), X)
% 178.41/22.76 = { by axiom 5 (absorption2) R->L }
% 178.41/22.76 meet(meet(X, Y), join(X, meet(X, Y)))
% 178.41/22.76 = { by lemma 8 }
% 178.41/22.76 meet(X, Y)
% 178.41/22.76
% 178.41/22.76 Lemma 10: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(Y, meet(X, Z))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 meet(meet(X, Z), Y)
% 178.41/22.76 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.76 meet(X, meet(Z, Y))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.76 meet(X, meet(Y, Z))
% 178.41/22.76
% 178.41/22.76 Lemma 11: meet(Z, meet(X, Y)) = meet(X, meet(Y, Z)).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(Z, meet(X, Y))
% 178.41/22.76 = { by lemma 10 }
% 178.41/22.76 meet(X, meet(Z, Y))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.76 meet(X, meet(Y, Z))
% 178.41/22.76
% 178.41/22.76 Lemma 12: join(X, meet(Y, X)) = X.
% 178.41/22.76 Proof:
% 178.41/22.76 join(X, meet(Y, X))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 join(X, meet(X, Y))
% 178.41/22.76 = { by axiom 5 (absorption2) }
% 178.41/22.76 X
% 178.41/22.76
% 178.41/22.76 Lemma 13: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 178.41/22.76 Proof:
% 178.41/22.76 join(Y, join(X, Z))
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.76 join(join(X, Z), Y)
% 178.41/22.76 = { by axiom 6 (associativity_of_join) }
% 178.41/22.76 join(X, join(Z, Y))
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) }
% 178.41/22.76 join(X, join(Y, Z))
% 178.41/22.76
% 178.41/22.76 Lemma 14: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 178.41/22.76 Proof:
% 178.41/22.76 join(Z, join(X, Y))
% 178.41/22.76 = { by lemma 13 }
% 178.41/22.76 join(X, join(Z, Y))
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) }
% 178.41/22.76 join(X, join(Y, Z))
% 178.41/22.76
% 178.41/22.76 Lemma 15: join(meet(X, Y), Y) = Y.
% 178.41/22.76 Proof:
% 178.41/22.76 join(meet(X, Y), Y)
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.76 join(Y, meet(X, Y))
% 178.41/22.76 = { by lemma 12 }
% 178.41/22.76 Y
% 178.41/22.76
% 178.41/22.76 Lemma 16: meet(meet(X, meet(Y, Z)), Z) = meet(X, meet(Y, Z)).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(meet(X, meet(Y, Z)), Z)
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 meet(Z, meet(X, meet(Y, Z)))
% 178.41/22.76 = { by lemma 11 }
% 178.41/22.76 meet(X, meet(meet(Y, Z), Z))
% 178.41/22.76 = { by lemma 15 R->L }
% 178.41/22.76 meet(X, meet(meet(Y, Z), join(meet(Y, Z), Z)))
% 178.41/22.76 = { by axiom 3 (absorption1) }
% 178.41/22.76 meet(X, meet(Y, Z))
% 178.41/22.76
% 178.41/22.76 Lemma 17: join(X, join(Y, meet(Z, X))) = join(X, Y).
% 178.41/22.76 Proof:
% 178.41/22.76 join(X, join(Y, meet(Z, X)))
% 178.41/22.76 = { by lemma 13 }
% 178.41/22.76 join(Y, join(X, meet(Z, X)))
% 178.41/22.76 = { by lemma 12 }
% 178.41/22.76 join(Y, X)
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) }
% 178.41/22.76 join(X, Y)
% 178.41/22.76
% 178.41/22.76 Lemma 18: meet(X, meet(Y, join(Z, meet(X, Y)))) = meet(X, Y).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(X, meet(Y, join(Z, meet(X, Y))))
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.76 meet(X, meet(Y, join(meet(X, Y), Z)))
% 178.41/22.76 = { by axiom 4 (associativity_of_meet) R->L }
% 178.41/22.76 meet(meet(X, Y), join(meet(X, Y), Z))
% 178.41/22.76 = { by axiom 3 (absorption1) }
% 178.41/22.76 meet(X, Y)
% 178.41/22.76
% 178.41/22.76 Lemma 19: meet(Z, meet(X, meet(Y, join(Z, W)))) = meet(X, meet(Y, Z)).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(Z, meet(X, meet(Y, join(Z, W))))
% 178.41/22.76 = { by lemma 10 }
% 178.41/22.76 meet(X, meet(Z, meet(Y, join(Z, W))))
% 178.41/22.76 = { by lemma 10 }
% 178.41/22.76 meet(X, meet(Y, meet(Z, join(Z, W))))
% 178.41/22.76 = { by axiom 3 (absorption1) }
% 178.41/22.76 meet(X, meet(Y, Z))
% 178.41/22.76
% 178.41/22.76 Lemma 20: join(X, meet(Y, join(Z, meet(X, Y)))) = join(X, meet(Y, join(X, Z))).
% 178.41/22.76 Proof:
% 178.41/22.76 join(X, meet(Y, join(Z, meet(X, Y))))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 join(X, meet(Y, join(Z, meet(Y, X))))
% 178.41/22.76 = { by axiom 5 (absorption2) R->L }
% 178.41/22.76 join(join(X, meet(Y, join(Z, meet(Y, X)))), meet(join(X, meet(Y, join(Z, meet(Y, X)))), Y))
% 178.41/22.76 = { by axiom 6 (associativity_of_join) }
% 178.41/22.76 join(X, join(meet(Y, join(Z, meet(Y, X))), meet(join(X, meet(Y, join(Z, meet(Y, X)))), Y)))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.76 join(X, join(meet(Y, join(Z, meet(Y, X))), meet(Y, join(X, meet(Y, join(Z, meet(Y, X)))))))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 join(X, join(meet(join(Z, meet(Y, X)), Y), meet(Y, join(X, meet(Y, join(Z, meet(Y, X)))))))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 join(X, join(meet(join(Z, meet(Y, X)), Y), meet(Y, join(X, meet(join(Z, meet(Y, X)), Y)))))
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.76 join(X, join(meet(Y, join(X, meet(join(Z, meet(Y, X)), Y))), meet(join(Z, meet(Y, X)), Y)))
% 178.41/22.76 = { by lemma 18 R->L }
% 178.41/22.76 join(X, join(meet(Y, join(X, meet(join(Z, meet(Y, X)), Y))), meet(join(Z, meet(Y, X)), meet(Y, join(X, meet(join(Z, meet(Y, X)), Y))))))
% 178.41/22.76 = { by lemma 12 }
% 178.41/22.76 join(X, meet(Y, join(X, meet(join(Z, meet(Y, X)), Y))))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.76 join(X, meet(Y, join(X, meet(Y, join(Z, meet(Y, X))))))
% 178.41/22.76 = { by axiom 7 (equation_H68) R->L }
% 178.41/22.76 join(X, meet(Y, join(X, Z)))
% 178.41/22.76
% 178.41/22.76 Lemma 21: meet(meet(X, join(Y, meet(Z, W))), join(W, Y)) = meet(X, join(Y, meet(Z, W))).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(meet(X, join(Y, meet(Z, W))), join(W, Y))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 meet(join(W, Y), meet(X, join(Y, meet(Z, W))))
% 178.41/22.76 = { by lemma 10 }
% 178.41/22.76 meet(X, meet(join(W, Y), join(Y, meet(Z, W))))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 meet(X, meet(join(Y, meet(Z, W)), join(W, Y)))
% 178.41/22.76 = { by lemma 17 R->L }
% 178.41/22.76 meet(X, meet(join(Y, meet(Z, W)), join(W, join(Y, meet(Z, W)))))
% 178.41/22.76 = { by lemma 8 }
% 178.41/22.76 meet(X, join(Y, meet(Z, W)))
% 178.41/22.76
% 178.41/22.76 Lemma 22: meet(meet(X, meet(Y, join(Z, W))), join(W, meet(V, Z))) = meet(Y, meet(X, join(W, meet(V, Z)))).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(meet(X, meet(Y, join(Z, W))), join(W, meet(V, Z)))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 meet(join(W, meet(V, Z)), meet(X, meet(Y, join(Z, W))))
% 178.41/22.76 = { by lemma 11 }
% 178.41/22.76 meet(X, meet(meet(Y, join(Z, W)), join(W, meet(V, Z))))
% 178.41/22.76 = { by lemma 10 R->L }
% 178.41/22.76 meet(meet(Y, join(Z, W)), meet(X, join(W, meet(V, Z))))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.76 meet(meet(X, join(W, meet(V, Z))), meet(Y, join(Z, W)))
% 178.41/22.76 = { by lemma 10 }
% 178.41/22.76 meet(Y, meet(meet(X, join(W, meet(V, Z))), join(Z, W)))
% 178.41/22.76 = { by lemma 21 }
% 178.41/22.76 meet(Y, meet(X, join(W, meet(V, Z))))
% 178.41/22.76
% 178.41/22.76 Lemma 23: meet(meet(X, meet(Y, join(Z, W))), join(Z, meet(V, join(W, meet(U, Z))))) = meet(X, meet(Y, join(Z, meet(V, join(W, meet(U, Z)))))).
% 178.41/22.76 Proof:
% 178.41/22.76 meet(meet(X, meet(Y, join(Z, W))), join(Z, meet(V, join(W, meet(U, Z)))))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 meet(join(Z, meet(V, join(W, meet(U, Z)))), meet(X, meet(Y, join(Z, W))))
% 178.41/22.76 = { by lemma 11 }
% 178.41/22.76 meet(X, meet(meet(Y, join(Z, W)), join(Z, meet(V, join(W, meet(U, Z))))))
% 178.41/22.76 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.76 meet(X, meet(join(Z, meet(V, join(W, meet(U, Z)))), meet(Y, join(Z, W))))
% 178.41/22.76 = { by lemma 10 }
% 178.41/22.76 meet(X, meet(Y, meet(join(Z, meet(V, join(W, meet(U, Z)))), join(Z, W))))
% 178.41/22.76 = { by lemma 12 R->L }
% 178.41/22.76 meet(X, meet(Y, meet(join(Z, meet(V, join(W, meet(U, Z)))), join(join(Z, W), meet(meet(V, join(W, meet(U, Z))), join(Z, W))))))
% 178.41/22.76 = { by lemma 21 }
% 178.41/22.76 meet(X, meet(Y, meet(join(Z, meet(V, join(W, meet(U, Z)))), join(join(Z, W), meet(V, join(W, meet(U, Z)))))))
% 178.41/22.76 = { by axiom 2 (commutativity_of_join) }
% 178.41/22.76 meet(X, meet(Y, meet(join(Z, meet(V, join(W, meet(U, Z)))), join(meet(V, join(W, meet(U, Z))), join(Z, W)))))
% 178.41/22.76 = { by lemma 14 }
% 178.41/22.76 meet(X, meet(Y, meet(join(Z, meet(V, join(W, meet(U, Z)))), join(Z, join(W, meet(V, join(W, meet(U, Z))))))))
% 178.41/22.76 = { by lemma 13 R->L }
% 178.41/22.77 meet(X, meet(Y, meet(join(Z, meet(V, join(W, meet(U, Z)))), join(W, join(Z, meet(V, join(W, meet(U, Z))))))))
% 178.41/22.77 = { by lemma 8 }
% 178.41/22.77 meet(X, meet(Y, join(Z, meet(V, join(W, meet(U, Z))))))
% 178.41/22.77
% 178.41/22.77 Goal 1 (prove_H73): meet(a, meet(b, join(c, d))) = meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))).
% 178.41/22.77 Proof:
% 178.41/22.77 meet(a, meet(b, join(c, d)))
% 178.41/22.77 = { by lemma 9 R->L }
% 178.41/22.77 meet(a, meet(a, meet(b, join(c, d))))
% 178.41/22.77 = { by lemma 8 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(a, meet(b, join(c, d))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(b, join(c, d))), a)))
% 178.41/22.77 = { by lemma 16 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), join(c, d)), a)))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(b, join(c, d))), meet(join(c, d), a))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(b, join(c, d))), meet(a, join(c, d)))))
% 178.41/22.77 = { by lemma 17 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(b, join(c, d))), meet(a, join(c, join(d, meet(b, c)))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(c, join(d, meet(b, c))))))
% 178.41/22.77 = { by lemma 20 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(join(d, meet(b, c)), meet(c, meet(meet(a, meet(b, join(c, d))), a))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(join(d, meet(b, c)), meet(meet(c, meet(a, meet(b, join(c, d)))), a)))))
% 178.41/22.77 = { by lemma 19 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(join(d, meet(b, c)), meet(meet(a, meet(b, c)), a)))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(join(d, meet(b, c)), meet(a, meet(meet(b, c), a))))))
% 178.41/22.77 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(meet(a, meet(meet(b, c), a)), join(d, meet(b, c))))))
% 178.41/22.77 = { by lemma 14 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(d, join(meet(b, c), meet(a, meet(meet(b, c), a)))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(d, join(meet(b, c), meet(a, meet(a, meet(b, c))))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(d, join(meet(b, c), meet(meet(a, a), meet(b, c)))))))
% 178.41/22.77 = { by lemma 12 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), a), join(d, meet(b, c)))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(b, join(c, d))), meet(a, join(d, meet(b, c))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(b, join(c, d))), meet(join(d, meet(b, c)), a))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(meet(a, meet(b, join(c, d))), join(d, meet(b, c))), a)))
% 178.41/22.77 = { by lemma 22 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(b, meet(a, join(d, meet(b, c)))), a)))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(b, meet(meet(a, join(d, meet(b, c))), a))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(b, meet(a, meet(a, join(d, meet(b, c)))))))
% 178.41/22.77 = { by lemma 10 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(b, meet(a, join(d, meet(b, c)))))))
% 178.41/22.77 = { by lemma 22 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, meet(b, join(c, d))), join(d, meet(b, c))))))
% 178.41/22.77 = { by lemma 9 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, meet(a, meet(b, join(c, d)))), join(d, meet(b, c))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(a, meet(meet(a, meet(b, join(c, d))), join(d, meet(b, c)))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(a, meet(join(d, meet(b, c)), meet(a, meet(b, join(c, d))))))))
% 178.41/22.77 = { by lemma 11 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, meet(b, join(c, d))), meet(a, join(d, meet(b, c)))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, join(d, meet(b, c))), meet(a, meet(b, join(c, d)))))))
% 178.41/22.77 = { by lemma 8 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(meet(a, join(d, meet(b, c))), join(c, meet(a, join(d, meet(b, c))))), meet(a, meet(b, join(c, d)))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, join(d, meet(b, c))), meet(join(c, meet(a, join(d, meet(b, c)))), meet(a, meet(b, join(c, d))))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, join(d, meet(b, c))), meet(meet(a, meet(b, join(c, d))), join(c, meet(a, join(d, meet(b, c)))))))))
% 178.41/22.77 = { by lemma 23 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, join(d, meet(b, c))), meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), meet(a, join(d, meet(b, c)))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), meet(a, join(d, meet(b, c))))))
% 178.41/22.77 = { by axiom 5 (absorption2) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(meet(a, join(d, meet(b, c))), meet(a, meet(b, c)))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(meet(a, join(d, meet(b, c))), meet(meet(b, c), a))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(meet(meet(a, join(d, meet(b, c))), meet(b, c)), a)))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(meet(meet(b, c), meet(a, join(d, meet(b, c)))), a)))))
% 178.41/22.77 = { by lemma 10 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(meet(a, meet(meet(b, c), join(d, meet(b, c)))), a)))))
% 178.41/22.77 = { by lemma 8 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(meet(a, meet(b, c)), a)))))
% 178.41/22.77 = { by lemma 19 R->L }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(meet(c, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), a)))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(c, meet(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), a))))))
% 178.41/22.77 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, join(d, meet(b, c))), meet(c, meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))))
% 178.41/22.77 = { by lemma 20 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(c, meet(a, join(d, meet(b, c)))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), join(c, meet(a, join(d, meet(b, c))))))))
% 178.41/22.77 = { by lemma 16 }
% 178.41/22.77 meet(meet(a, meet(a, meet(b, join(c, d)))), join(c, meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))))))
% 178.41/22.77 = { by axiom 4 (associativity_of_meet) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), join(c, meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))
% 178.41/22.78 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c)))
% 178.41/22.78 = { by axiom 3 (absorption1) R->L }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), meet(a, join(d, meet(b, c))))))))
% 178.41/22.78 = { by axiom 6 (associativity_of_join) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(c, join(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), meet(a, join(d, meet(b, c)))))))))
% 178.41/22.78 = { by lemma 13 R->L }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), join(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), join(c, meet(a, join(d, meet(b, c)))))))))
% 178.41/22.78 = { by axiom 2 (commutativity_of_join) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), join(c, meet(a, join(d, meet(b, c))))), meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))))))))
% 178.41/22.78 = { by axiom 6 (associativity_of_join) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), join(join(c, meet(a, join(d, meet(b, c)))), meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))))
% 178.41/22.78 = { by axiom 2 (commutativity_of_join) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(join(c, meet(a, join(d, meet(b, c)))), meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))))), meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))
% 178.41/22.78 = { by axiom 6 (associativity_of_join) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(c, meet(a, join(d, meet(b, c)))), join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))))))))
% 178.41/22.78 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(c, meet(a, join(d, meet(b, c)))), join(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))))
% 178.41/22.78 = { by lemma 12 }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(c, meet(a, join(d, meet(b, c)))), meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))
% 178.41/22.78 = { by axiom 1 (commutativity_of_meet) R->L }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(c, meet(a, join(d, meet(b, c)))), meet(meet(b, join(c, meet(a, join(d, meet(b, c))))), a)))))
% 178.41/22.78 = { by lemma 15 R->L }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(meet(b, join(c, meet(a, join(d, meet(b, c))))), join(c, meet(a, join(d, meet(b, c))))), meet(meet(b, join(c, meet(a, join(d, meet(b, c))))), a)))))
% 178.41/22.78 = { by axiom 6 (associativity_of_join) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(meet(b, join(c, meet(a, join(d, meet(b, c))))), join(join(c, meet(a, join(d, meet(b, c)))), meet(meet(b, join(c, meet(a, join(d, meet(b, c))))), a))))))
% 178.41/22.78 = { by axiom 2 (commutativity_of_join) R->L }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(meet(b, join(c, meet(a, join(d, meet(b, c))))), join(meet(meet(b, join(c, meet(a, join(d, meet(b, c))))), a), join(c, meet(a, join(d, meet(b, c)))))))))
% 178.41/22.78 = { by axiom 6 (associativity_of_join) R->L }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(join(meet(b, join(c, meet(a, join(d, meet(b, c))))), meet(meet(b, join(c, meet(a, join(d, meet(b, c))))), a)), join(c, meet(a, join(d, meet(b, c))))))))
% 178.41/22.78 = { by axiom 5 (absorption2) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(meet(b, join(c, meet(a, join(d, meet(b, c))))), join(c, meet(a, join(d, meet(b, c))))))))
% 178.41/22.78 = { by lemma 15 }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c), join(c, meet(a, join(d, meet(b, c)))))))
% 178.41/22.78 = { by axiom 1 (commutativity_of_meet) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(c, meet(a, join(d, meet(b, c)))), join(meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))), c))))
% 178.41/22.78 = { by axiom 2 (commutativity_of_join) }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, d))), meet(join(c, meet(a, join(d, meet(b, c)))), join(c, meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))))))))
% 178.41/22.78 = { by axiom 4 (associativity_of_meet) R->L }
% 178.41/22.78 meet(a, meet(meet(meet(a, meet(b, join(c, d))), join(c, meet(a, join(d, meet(b, c))))), join(c, meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))
% 178.41/22.78 = { by lemma 23 }
% 178.41/22.78 meet(a, meet(meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))), join(c, meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))))))
% 178.41/22.78 = { by lemma 18 }
% 178.41/22.78 meet(a, meet(a, meet(b, join(c, meet(a, join(d, meet(b, c)))))))
% 178.41/22.78 = { by lemma 9 }
% 178.41/22.78 meet(a, meet(b, join(c, meet(a, join(d, meet(b, c))))))
% 178.41/22.78 % SZS output end Proof
% 178.41/22.78
% 178.41/22.78 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------