TSTP Solution File: LAT165-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT165-1 : 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 : n019.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 06:27:37 EDT 2023
% Result : Timeout 298.86s 38.96s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT165-1 : 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
% 0.18/0.35 % Computer : n019.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 24 10:19:13 EDT 2023
% 0.18/0.35 % CPUTime :
% 298.86/38.96 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 298.86/38.96
% 298.86/38.96 % SZS status Unsatisfiable
% 298.86/38.96
% 298.86/38.97 % SZS output start Proof
% 298.86/38.97 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 298.86/38.97 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 298.86/38.97 Axiom 3 (absorption2): join(X, meet(X, Y)) = X.
% 298.86/38.97 Axiom 4 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 298.86/38.97 Axiom 5 (absorption1): meet(X, join(X, Y)) = X.
% 298.86/38.97 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 298.86/38.97 Axiom 7 (equation_H76): meet(X, join(Y, meet(Z, join(Y, W)))) = meet(X, join(Y, meet(Z, join(W, meet(X, Y))))).
% 298.86/38.97
% 298.86/38.97 Lemma 8: meet(X, meet(Y, join(Z, meet(X, Y)))) = meet(X, Y).
% 298.86/38.97 Proof:
% 298.86/38.97 meet(X, meet(Y, join(Z, meet(X, Y))))
% 298.86/38.97 = { by axiom 1 (commutativity_of_join) R->L }
% 298.86/38.97 meet(X, meet(Y, join(meet(X, Y), Z)))
% 298.86/38.97 = { by axiom 6 (associativity_of_meet) R->L }
% 298.86/38.97 meet(meet(X, Y), join(meet(X, Y), Z))
% 298.86/38.97 = { by axiom 5 (absorption1) }
% 298.86/38.97 meet(X, Y)
% 298.86/38.97
% 298.86/38.97 Lemma 9: meet(join(X, Y), join(meet(X, Z), Y)) = join(Y, meet(X, Z)).
% 298.86/38.97 Proof:
% 298.86/38.97 meet(join(X, Y), join(meet(X, Z), Y))
% 298.86/38.97 = { by axiom 1 (commutativity_of_join) R->L }
% 298.86/38.97 meet(join(X, Y), join(Y, meet(X, Z)))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.97 meet(join(Y, meet(X, Z)), join(X, Y))
% 298.86/38.97 = { by axiom 3 (absorption2) R->L }
% 298.86/38.97 meet(join(Y, meet(X, Z)), join(join(X, meet(X, Z)), Y))
% 298.86/38.97 = { by axiom 4 (associativity_of_join) }
% 298.86/38.97 meet(join(Y, meet(X, Z)), join(X, join(meet(X, Z), Y)))
% 298.86/38.97 = { by axiom 1 (commutativity_of_join) }
% 298.86/38.97 meet(join(Y, meet(X, Z)), join(X, join(Y, meet(X, Z))))
% 298.86/38.97 = { by axiom 1 (commutativity_of_join) R->L }
% 298.86/38.97 meet(join(Y, meet(X, Z)), join(join(Y, meet(X, Z)), X))
% 298.86/38.97 = { by axiom 5 (absorption1) }
% 298.86/38.97 join(Y, meet(X, Z))
% 298.86/38.97
% 298.86/38.97 Lemma 10: join(meet(X, Y), meet(X, join(Z, meet(X, Y)))) = meet(X, join(Z, meet(X, Y))).
% 298.86/38.97 Proof:
% 298.86/38.97 join(meet(X, Y), meet(X, join(Z, meet(X, Y))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.97 join(meet(Y, X), meet(X, join(Z, meet(X, Y))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.97 join(meet(Y, X), meet(X, join(Z, meet(Y, X))))
% 298.86/38.97 = { by axiom 1 (commutativity_of_join) R->L }
% 298.86/38.97 join(meet(X, join(Z, meet(Y, X))), meet(Y, X))
% 298.86/38.97 = { by lemma 8 R->L }
% 298.86/38.97 join(meet(X, join(Z, meet(Y, X))), meet(Y, meet(X, join(Z, meet(Y, X)))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.97 join(meet(X, join(Z, meet(Y, X))), meet(meet(X, join(Z, meet(Y, X))), Y))
% 298.86/38.97 = { by axiom 3 (absorption2) }
% 298.86/38.97 meet(X, join(Z, meet(Y, X)))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.97 meet(X, join(Z, meet(X, Y)))
% 298.86/38.97
% 298.86/38.97 Lemma 11: join(X, meet(Y, join(X, meet(Z, Y)))) = join(X, meet(Z, Y)).
% 298.86/38.97 Proof:
% 298.86/38.97 join(X, meet(Y, join(X, meet(Z, Y))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.97 join(X, meet(Y, join(X, meet(Y, Z))))
% 298.86/38.97 = { by lemma 10 R->L }
% 298.86/38.97 join(X, join(meet(Y, Z), meet(Y, join(X, meet(Y, Z)))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.97 join(X, join(meet(Z, Y), meet(Y, join(X, meet(Y, Z)))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.97 join(X, join(meet(Z, Y), meet(Y, join(X, meet(Z, Y)))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.97 join(X, join(meet(Z, Y), meet(join(X, meet(Z, Y)), Y)))
% 298.86/38.97 = { by axiom 4 (associativity_of_join) R->L }
% 298.86/38.97 join(join(X, meet(Z, Y)), meet(join(X, meet(Z, Y)), Y))
% 298.86/38.97 = { by axiom 3 (absorption2) }
% 298.86/38.97 join(X, meet(Z, Y))
% 298.86/38.97
% 298.86/38.97 Goal 1 (prove_H77): meet(a, join(b, meet(c, join(b, d)))) = meet(a, join(b, meet(c, join(d, meet(a, meet(b, c)))))).
% 298.86/38.97 Proof:
% 298.86/38.97 meet(a, join(b, meet(c, join(b, d))))
% 298.86/38.97 = { by axiom 7 (equation_H76) }
% 298.86/38.97 meet(a, join(b, meet(c, join(d, meet(a, b)))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.97 meet(a, join(b, meet(c, join(d, meet(b, a)))))
% 298.86/38.97 = { by axiom 1 (commutativity_of_join) R->L }
% 298.86/38.97 meet(a, join(b, meet(c, join(meet(b, a), d))))
% 298.86/38.97 = { by axiom 5 (absorption1) R->L }
% 298.86/38.97 meet(a, join(b, meet(meet(c, join(meet(b, a), d)), join(meet(c, join(meet(b, a), d)), meet(c, join(meet(c, join(meet(b, a), d)), meet(b, a)))))))
% 298.86/38.97 = { by lemma 11 R->L }
% 298.86/38.97 meet(a, join(b, meet(join(meet(c, join(meet(b, a), d)), meet(c, join(meet(c, join(meet(b, a), d)), meet(b, a)))), join(b, meet(meet(c, join(meet(b, a), d)), join(meet(c, join(meet(b, a), d)), meet(c, join(meet(c, join(meet(b, a), d)), meet(b, a)))))))))
% 298.86/38.97 = { by axiom 5 (absorption1) }
% 298.86/38.97 meet(a, join(b, meet(join(meet(c, join(meet(b, a), d)), meet(c, join(meet(c, join(meet(b, a), d)), meet(b, a)))), join(b, meet(c, join(meet(b, a), d))))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.97 meet(a, join(b, meet(join(b, meet(c, join(meet(b, a), d))), join(meet(c, join(meet(b, a), d)), meet(c, join(meet(c, join(meet(b, a), d)), meet(b, a)))))))
% 298.86/38.97 = { by axiom 1 (commutativity_of_join) R->L }
% 298.86/38.97 meet(a, join(b, meet(join(b, meet(c, join(meet(b, a), d))), join(meet(c, join(meet(b, a), d)), meet(c, join(meet(b, a), meet(c, join(meet(b, a), d))))))))
% 298.86/38.97 = { by lemma 10 }
% 298.86/38.97 meet(a, join(b, meet(join(b, meet(c, join(meet(b, a), d))), meet(c, join(meet(b, a), meet(c, join(meet(b, a), d)))))))
% 298.86/38.97 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.97 meet(a, join(b, meet(meet(c, join(meet(b, a), meet(c, join(meet(b, a), d)))), join(b, meet(c, join(meet(b, a), d))))))
% 298.86/38.98 = { by axiom 6 (associativity_of_meet) }
% 298.86/38.98 meet(a, join(b, meet(c, meet(join(meet(b, a), meet(c, join(meet(b, a), d))), join(b, meet(c, join(meet(b, a), d)))))))
% 298.86/38.98 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.98 meet(a, join(b, meet(c, meet(join(b, meet(c, join(meet(b, a), d))), join(meet(b, a), meet(c, join(meet(b, a), d)))))))
% 298.86/38.98 = { by lemma 9 }
% 298.86/38.98 meet(a, join(b, meet(c, join(meet(c, join(meet(b, a), d)), meet(b, a)))))
% 298.86/38.98 = { by axiom 1 (commutativity_of_join) }
% 298.86/38.98 meet(a, join(b, meet(c, join(meet(b, a), meet(c, join(meet(b, a), d))))))
% 298.86/38.98 = { by axiom 7 (equation_H76) }
% 298.86/38.98 meet(a, join(b, meet(c, join(meet(b, a), meet(c, join(d, meet(c, meet(b, a))))))))
% 298.86/38.98 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.98 meet(a, join(b, meet(c, join(meet(b, a), meet(join(d, meet(c, meet(b, a))), c)))))
% 298.86/38.98 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.98 meet(a, join(b, meet(c, join(meet(b, a), meet(join(d, meet(meet(b, a), c)), c)))))
% 298.86/38.98 = { by axiom 1 (commutativity_of_join) R->L }
% 298.86/38.98 meet(a, join(b, meet(c, join(meet(join(d, meet(meet(b, a), c)), c), meet(b, a)))))
% 298.86/38.98 = { by lemma 9 R->L }
% 298.86/38.98 meet(a, join(b, meet(c, meet(join(b, meet(join(d, meet(meet(b, a), c)), c)), join(meet(b, a), meet(join(d, meet(meet(b, a), c)), c))))))
% 298.86/38.98 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.98 meet(a, join(b, meet(c, meet(join(meet(b, a), meet(join(d, meet(meet(b, a), c)), c)), join(b, meet(join(d, meet(meet(b, a), c)), c))))))
% 298.86/38.98 = { by axiom 6 (associativity_of_meet) R->L }
% 298.86/38.98 meet(a, join(b, meet(meet(c, join(meet(b, a), meet(join(d, meet(meet(b, a), c)), c))), join(b, meet(join(d, meet(meet(b, a), c)), c)))))
% 298.86/38.98 = { by lemma 8 R->L }
% 298.86/38.98 meet(a, join(b, meet(meet(c, join(meet(b, a), meet(join(d, meet(meet(b, a), c)), c))), join(b, meet(join(d, meet(meet(b, a), c)), meet(c, join(meet(b, a), meet(join(d, meet(meet(b, a), c)), c))))))))
% 298.86/38.98 = { by lemma 11 }
% 298.86/38.98 meet(a, join(b, meet(join(d, meet(meet(b, a), c)), meet(c, join(meet(b, a), meet(join(d, meet(meet(b, a), c)), c))))))
% 298.86/38.98 = { by lemma 8 }
% 298.86/38.98 meet(a, join(b, meet(join(d, meet(meet(b, a), c)), c)))
% 298.86/38.98 = { by axiom 6 (associativity_of_meet) }
% 298.86/38.98 meet(a, join(b, meet(join(d, meet(b, meet(a, c))), c)))
% 298.86/38.98 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.98 meet(a, join(b, meet(c, join(d, meet(b, meet(a, c))))))
% 298.86/38.98 = { by axiom 2 (commutativity_of_meet) }
% 298.86/38.98 meet(a, join(b, meet(c, join(d, meet(meet(a, c), b)))))
% 298.86/38.98 = { by axiom 6 (associativity_of_meet) }
% 298.86/38.98 meet(a, join(b, meet(c, join(d, meet(a, meet(c, b))))))
% 298.86/38.98 = { by axiom 2 (commutativity_of_meet) R->L }
% 298.86/38.98 meet(a, join(b, meet(c, join(d, meet(a, meet(b, c))))))
% 298.86/38.98 % SZS output end Proof
% 298.86/38.98
% 298.86/38.98 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------