TSTP Solution File: LAT021-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT021-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n014.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 06:27:09 EDT 2023
% Result : Unsatisfiable 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT021-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 08:30:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 Command-line arguments: --no-flatten-goal
% 0.20/0.56
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56
% 0.20/0.56 % SZS output start Proof
% 0.20/0.56 Axiom 1 (idempotence_of_meet): meet(X, X) = X.
% 0.20/0.56 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.20/0.56 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.20/0.56 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.20/0.57 Axiom 5 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.20/0.57 Axiom 6 (quasi_lattice1): join(meet(X, join(Y, Z)), meet(X, Y)) = meet(X, join(Y, Z)).
% 0.20/0.57 Axiom 7 (bowden): join(join(X, meet(Y, Z)), meet(join(X, Y), Z)) = join(X, meet(Y, Z)).
% 0.20/0.57
% 0.20/0.57 Lemma 8: join(meet(X, Y), meet(X, join(Y, Z))) = meet(X, join(Y, Z)).
% 0.20/0.57 Proof:
% 0.20/0.57 join(meet(X, Y), meet(X, join(Y, Z)))
% 0.20/0.57 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.57 join(meet(X, join(Y, Z)), meet(X, Y))
% 0.20/0.57 = { by axiom 6 (quasi_lattice1) }
% 0.20/0.57 meet(X, join(Y, Z))
% 0.20/0.57
% 0.20/0.57 Lemma 9: join(meet(X, Y), meet(join(X, Z), Y)) = meet(Y, join(X, Z)).
% 0.20/0.57 Proof:
% 0.20/0.57 join(meet(X, Y), meet(join(X, Z), Y))
% 0.20/0.57 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.57 join(meet(X, Y), meet(Y, join(X, Z)))
% 0.20/0.57 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.57 join(meet(Y, X), meet(Y, join(X, Z)))
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 meet(Y, join(X, Z))
% 0.20/0.57
% 0.20/0.57 Lemma 10: join(X, meet(Y, join(X, Z))) = join(X, meet(Z, Y)).
% 0.20/0.57 Proof:
% 0.20/0.57 join(X, meet(Y, join(X, Z)))
% 0.20/0.57 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.57 join(X, meet(Y, join(Z, X)))
% 0.20/0.57 = { by lemma 9 R->L }
% 0.20/0.57 join(X, join(meet(Z, Y), meet(join(Z, X), Y)))
% 0.20/0.57 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.57 join(X, join(meet(Z, Y), meet(join(X, Z), Y)))
% 0.20/0.57 = { by axiom 5 (associativity_of_join) R->L }
% 0.20/0.57 join(join(X, meet(Z, Y)), meet(join(X, Z), Y))
% 0.20/0.57 = { by axiom 7 (bowden) }
% 0.20/0.57 join(X, meet(Z, Y))
% 0.20/0.57
% 0.20/0.57 Lemma 11: join(meet(X, Y), meet(X, Z)) = meet(X, join(Z, meet(X, Y))).
% 0.20/0.57 Proof:
% 0.20/0.57 join(meet(X, Y), meet(X, Z))
% 0.20/0.57 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.57 join(meet(X, Y), meet(Z, X))
% 0.20/0.57 = { by lemma 10 R->L }
% 0.20/0.57 join(meet(X, Y), meet(X, join(meet(X, Y), Z)))
% 0.20/0.57 = { by axiom 1 (idempotence_of_meet) R->L }
% 0.20/0.57 join(meet(meet(X, X), Y), meet(X, join(meet(X, Y), Z)))
% 0.20/0.57 = { by axiom 4 (associativity_of_meet) }
% 0.20/0.57 join(meet(X, meet(X, Y)), meet(X, join(meet(X, Y), Z)))
% 0.20/0.57 = { by lemma 8 }
% 0.20/0.57 meet(X, join(meet(X, Y), Z))
% 0.20/0.57 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.57 meet(X, join(Z, meet(X, Y)))
% 0.20/0.57
% 0.20/0.57 Lemma 12: join(meet(X, Y), meet(Y, Z)) = meet(Y, join(Z, meet(X, Y))).
% 0.20/0.57 Proof:
% 0.20/0.57 join(meet(X, Y), meet(Y, Z))
% 0.20/0.57 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.57 join(meet(Y, X), meet(Y, Z))
% 0.20/0.57 = { by lemma 11 }
% 0.20/0.57 meet(Y, join(Z, meet(Y, X)))
% 0.20/0.57 = { by axiom 2 (commutativity_of_meet) }
% 0.20/0.57 meet(Y, join(Z, meet(X, Y)))
% 0.20/0.57
% 0.20/0.57 Goal 1 (prove_distributivity): meet(a, join(b, c)) = join(meet(a, b), meet(a, c)).
% 0.20/0.57 Proof:
% 0.20/0.57 meet(a, join(b, c))
% 0.20/0.57 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.57 meet(a, join(c, b))
% 0.20/0.57 = { by lemma 9 R->L }
% 0.20/0.57 join(meet(c, a), meet(join(c, b), a))
% 0.20/0.57 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.57 join(meet(c, a), meet(a, join(c, b)))
% 0.20/0.57 = { by lemma 12 }
% 0.20/0.57 meet(a, join(join(c, b), meet(c, a)))
% 0.20/0.57 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.57 meet(a, join(join(c, b), meet(a, c)))
% 0.20/0.57 = { by lemma 11 R->L }
% 0.20/0.57 join(meet(a, c), meet(a, join(c, b)))
% 0.20/0.57 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.57 join(meet(a, join(c, b)), meet(a, c))
% 0.20/0.57 = { by lemma 11 }
% 0.20/0.57 meet(a, join(c, meet(a, join(c, b))))
% 0.20/0.57 = { by lemma 10 }
% 0.20/0.57 meet(a, join(c, meet(b, a)))
% 0.20/0.57 = { by lemma 12 R->L }
% 0.20/0.57 join(meet(b, a), meet(a, c))
% 0.20/0.57 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.57 join(meet(a, b), meet(a, c))
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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