TSTP Solution File: LAT142-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT142-1 : 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 : n026.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 13.66s 2.25s
% Output : Proof 13.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT142-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 07:20:46 EDT 2023
% 0.13/0.35 % CPUTime :
% 13.66/2.25 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 13.66/2.25
% 13.66/2.25 % SZS status Unsatisfiable
% 13.66/2.25
% 13.66/2.29 % SZS output start Proof
% 13.66/2.29 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 13.66/2.29 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 13.66/2.29 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 13.66/2.29 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 13.66/2.29 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 13.66/2.29 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 13.66/2.29 Axiom 7 (equation_H22): join(meet(X, Y), meet(X, Z)) = meet(X, join(meet(Y, join(Z, meet(X, Y))), meet(Z, join(X, Y)))).
% 13.66/2.29
% 13.66/2.29 Lemma 8: meet(X, join(Y, X)) = X.
% 13.66/2.29 Proof:
% 13.66/2.29 meet(X, join(Y, X))
% 13.66/2.29 = { by axiom 2 (commutativity_of_join) R->L }
% 13.66/2.29 meet(X, join(X, Y))
% 13.66/2.29 = { by axiom 3 (absorption1) }
% 13.66/2.29 X
% 13.66/2.29
% 13.66/2.29 Lemma 9: meet(X, meet(X, Y)) = meet(X, Y).
% 13.66/2.29 Proof:
% 13.66/2.29 meet(X, meet(X, Y))
% 13.66/2.29 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.29 meet(meet(X, Y), X)
% 13.66/2.29 = { by axiom 5 (absorption2) R->L }
% 13.66/2.29 meet(meet(X, Y), join(X, meet(X, Y)))
% 13.66/2.29 = { by lemma 8 }
% 13.66/2.29 meet(X, Y)
% 13.66/2.29
% 13.66/2.29 Lemma 10: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 13.66/2.29 Proof:
% 13.66/2.29 meet(Y, meet(X, Z))
% 13.66/2.29 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.29 meet(meet(X, Z), Y)
% 13.66/2.29 = { by axiom 4 (associativity_of_meet) }
% 13.66/2.29 meet(X, meet(Z, Y))
% 13.66/2.29 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.29 meet(X, meet(Y, Z))
% 13.66/2.29
% 13.66/2.29 Lemma 11: join(X, meet(Y, X)) = X.
% 13.66/2.29 Proof:
% 13.66/2.29 join(X, meet(Y, X))
% 13.66/2.29 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.29 join(X, meet(X, Y))
% 13.66/2.29 = { by axiom 5 (absorption2) }
% 13.66/2.29 X
% 13.66/2.29
% 13.66/2.29 Lemma 12: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 13.66/2.29 Proof:
% 13.66/2.29 join(Y, join(X, Z))
% 13.66/2.29 = { by axiom 2 (commutativity_of_join) R->L }
% 13.66/2.29 join(join(X, Z), Y)
% 13.66/2.29 = { by axiom 6 (associativity_of_join) }
% 13.66/2.29 join(X, join(Z, Y))
% 13.66/2.29 = { by axiom 2 (commutativity_of_join) }
% 13.66/2.29 join(X, join(Y, Z))
% 13.66/2.29
% 13.66/2.29 Lemma 13: meet(X, join(meet(Y, join(X, Z)), meet(Z, join(Y, meet(X, Z))))) = join(meet(X, Z), meet(X, Y)).
% 13.66/2.29 Proof:
% 13.66/2.29 meet(X, join(meet(Y, join(X, Z)), meet(Z, join(Y, meet(X, Z)))))
% 13.66/2.29 = { by axiom 2 (commutativity_of_join) R->L }
% 13.66/2.29 meet(X, join(meet(Z, join(Y, meet(X, Z))), meet(Y, join(X, Z))))
% 13.66/2.29 = { by axiom 7 (equation_H22) R->L }
% 13.66/2.29 join(meet(X, Z), meet(X, Y))
% 13.66/2.29
% 13.66/2.29 Lemma 14: meet(join(X, Y), join(Y, meet(join(X, Y), Z))) = join(Y, meet(Z, join(X, Y))).
% 13.66/2.29 Proof:
% 13.66/2.29 meet(join(X, Y), join(Y, meet(join(X, Y), Z)))
% 13.66/2.29 = { by lemma 8 R->L }
% 13.66/2.29 meet(join(X, Y), join(meet(Y, join(X, Y)), meet(join(X, Y), Z)))
% 13.66/2.29 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.29 meet(join(X, Y), join(meet(join(X, Y), Y), meet(join(X, Y), Z)))
% 13.66/2.29 = { by axiom 2 (commutativity_of_join) R->L }
% 13.66/2.29 meet(join(X, Y), join(meet(join(X, Y), Z), meet(join(X, Y), Y)))
% 13.66/2.29 = { by lemma 13 R->L }
% 13.66/2.29 meet(join(X, Y), meet(join(X, Y), join(meet(Y, join(join(X, Y), Z)), meet(Z, join(Y, meet(join(X, Y), Z))))))
% 13.66/2.29 = { by lemma 9 }
% 13.66/2.29 meet(join(X, Y), join(meet(Y, join(join(X, Y), Z)), meet(Z, join(Y, meet(join(X, Y), Z)))))
% 13.66/2.29 = { by lemma 13 }
% 13.66/2.29 join(meet(join(X, Y), Z), meet(join(X, Y), Y))
% 13.66/2.29 = { by axiom 2 (commutativity_of_join) }
% 13.66/2.29 join(meet(join(X, Y), Y), meet(join(X, Y), Z))
% 13.66/2.29 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.29 join(meet(Y, join(X, Y)), meet(join(X, Y), Z))
% 13.66/2.29 = { by lemma 8 }
% 13.66/2.29 join(Y, meet(join(X, Y), Z))
% 13.66/2.29 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.29 join(Y, meet(Z, join(X, Y)))
% 13.66/2.29
% 13.66/2.29 Lemma 15: meet(X, join(meet(Y, join(X, Z)), meet(join(meet(X, join(Z, meet(X, Y))), meet(Y, join(X, Z))), join(Z, meet(X, Y))))) = meet(X, join(Z, meet(X, Y))).
% 13.66/2.29 Proof:
% 13.66/2.29 meet(X, join(meet(Y, join(X, Z)), meet(join(meet(X, join(Z, meet(X, Y))), meet(Y, join(X, Z))), join(Z, meet(X, Y)))))
% 13.66/2.29 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.29 meet(X, join(meet(Y, join(X, Z)), meet(join(Z, meet(X, Y)), join(meet(X, join(Z, meet(X, Y))), meet(Y, join(X, Z))))))
% 13.66/2.29 = { by axiom 2 (commutativity_of_join) R->L }
% 13.66/2.29 meet(X, join(meet(Y, join(X, Z)), meet(join(Z, meet(X, Y)), join(meet(Y, join(X, Z)), meet(X, join(Z, meet(X, Y)))))))
% 13.66/2.29 = { by axiom 3 (absorption1) R->L }
% 13.66/2.30 meet(X, join(meet(meet(Y, join(X, Z)), join(meet(Y, join(X, Z)), join(X, Z))), meet(join(Z, meet(X, Y)), join(meet(Y, join(X, Z)), meet(X, join(Z, meet(X, Y)))))))
% 13.66/2.30 = { by axiom 2 (commutativity_of_join) R->L }
% 13.66/2.30 meet(X, join(meet(meet(Y, join(X, Z)), join(join(X, Z), meet(Y, join(X, Z)))), meet(join(Z, meet(X, Y)), join(meet(Y, join(X, Z)), meet(X, join(Z, meet(X, Y)))))))
% 13.66/2.30 = { by lemma 11 }
% 13.66/2.30 meet(X, join(meet(meet(Y, join(X, Z)), join(X, Z)), meet(join(Z, meet(X, Y)), join(meet(Y, join(X, Z)), meet(X, join(Z, meet(X, Y)))))))
% 13.66/2.30 = { by axiom 2 (commutativity_of_join) R->L }
% 13.66/2.30 meet(X, join(meet(meet(Y, join(X, Z)), join(Z, X)), meet(join(Z, meet(X, Y)), join(meet(Y, join(X, Z)), meet(X, join(Z, meet(X, Y)))))))
% 13.66/2.30 = { by axiom 5 (absorption2) R->L }
% 13.66/2.30 meet(X, join(meet(meet(Y, join(X, Z)), join(Z, join(X, meet(X, Y)))), meet(join(Z, meet(X, Y)), join(meet(Y, join(X, Z)), meet(X, join(Z, meet(X, Y)))))))
% 13.66/2.30 = { by lemma 12 R->L }
% 13.66/2.30 meet(X, join(meet(meet(Y, join(X, Z)), join(X, join(Z, meet(X, Y)))), meet(join(Z, meet(X, Y)), join(meet(Y, join(X, Z)), meet(X, join(Z, meet(X, Y)))))))
% 13.66/2.30 = { by lemma 13 }
% 13.66/2.30 join(meet(X, join(Z, meet(X, Y))), meet(X, meet(Y, join(X, Z))))
% 13.66/2.30 = { by lemma 10 }
% 13.66/2.30 join(meet(X, join(Z, meet(X, Y))), meet(Y, meet(X, join(X, Z))))
% 13.66/2.30 = { by axiom 3 (absorption1) }
% 13.66/2.30 join(meet(X, join(Z, meet(X, Y))), meet(Y, X))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.30 join(meet(X, join(Z, meet(X, Y))), meet(X, Y))
% 13.66/2.30 = { by lemma 9 R->L }
% 13.66/2.30 join(meet(X, join(Z, meet(X, Y))), meet(X, meet(X, Y)))
% 13.66/2.30 = { by lemma 8 R->L }
% 13.66/2.30 join(meet(X, join(Z, meet(X, Y))), meet(X, meet(meet(X, Y), join(Z, meet(X, Y)))))
% 13.66/2.30 = { by lemma 10 R->L }
% 13.66/2.30 join(meet(X, join(Z, meet(X, Y))), meet(meet(X, Y), meet(X, join(Z, meet(X, Y)))))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.30 join(meet(X, join(Z, meet(X, Y))), meet(meet(X, join(Z, meet(X, Y))), meet(X, Y)))
% 13.66/2.30 = { by axiom 5 (absorption2) }
% 13.66/2.30 meet(X, join(Z, meet(X, Y)))
% 13.66/2.30
% 13.66/2.30 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)))).
% 13.66/2.30 Proof:
% 13.66/2.30 meet(a, join(b, meet(a, c)))
% 13.66/2.30 = { by lemma 15 R->L }
% 13.66/2.30 meet(a, join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.30 meet(a, join(meet(c, join(a, b)), meet(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 13.66/2.30 = { by lemma 14 R->L }
% 13.66/2.30 meet(a, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c))))))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.30 meet(a, meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 13.66/2.30 = { by lemma 11 R->L }
% 13.66/2.30 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(meet(a, join(b, meet(a, c))), meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.30 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(meet(a, join(b, meet(a, c))), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c))))))))
% 13.66/2.30 = { by axiom 4 (associativity_of_meet) R->L }
% 13.66/2.30 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(meet(meet(a, join(b, meet(a, c))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.30 = { by axiom 3 (absorption1) }
% 13.66/2.30 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(meet(a, join(b, meet(a, c))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.30 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), meet(a, join(b, meet(a, c))))))
% 13.66/2.30 = { by axiom 2 (commutativity_of_join) }
% 13.66/2.30 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), meet(a, join(b, meet(a, c)))), meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.30 meet(a, join(meet(meet(a, join(b, meet(a, c))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c))))), meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.30 meet(a, join(meet(meet(a, join(b, meet(a, c))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c))))), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.30 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.31 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), meet(a, join(b, meet(a, c)))), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.31 = { by lemma 15 R->L }
% 13.66/2.31 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), meet(a, join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.31 = { by axiom 1 (commutativity_of_meet) R->L }
% 13.66/2.31 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), a)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.31 = { by lemma 9 }
% 13.66/2.31 meet(a, join(meet(join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))), a), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.31 = { by axiom 1 (commutativity_of_meet) }
% 13.66/2.31 meet(a, join(meet(a, join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c))))), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.31 = { by lemma 15 }
% 13.66/2.31 meet(a, join(meet(a, join(b, meet(a, c))), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))))
% 13.66/2.31 = { by lemma 14 }
% 13.66/2.31 meet(a, join(meet(a, join(b, meet(a, c))), join(meet(c, join(a, b)), meet(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))))
% 13.66/2.31 = { by axiom 2 (commutativity_of_join) R->L }
% 13.66/2.31 meet(a, join(meet(a, join(b, meet(a, c))), join(meet(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(c, join(a, b)))))
% 13.66/2.31 = { by lemma 12 R->L }
% 13.66/2.31 meet(a, join(meet(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 13.66/2.31 = { by axiom 2 (commutativity_of_join) }
% 13.66/2.31 meet(a, join(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 13.66/2.31 = { by lemma 11 }
% 13.66/2.31 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 13.66/2.31 % SZS output end Proof
% 13.66/2.31
% 13.66/2.31 RESULT: Unsatisfiable (the axioms are contradictory).
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