TSTP Solution File: LAT011-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LAT011-1 : 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 : 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 06:27:06 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% 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 : LAT011-1 : 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
% 0.14/0.34 % Computer : n026.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 05:09:01 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.20/0.40 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.20/0.40 Axiom 3 (commutativity_of_meet2): meet2(X, Y) = meet2(Y, X).
% 0.20/0.40 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 0.20/0.40 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.20/0.40 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 0.20/0.40 Axiom 7 (absorption2_2): join(X, meet2(X, Y)) = X.
% 0.20/0.40 Axiom 8 (absorption1_2): meet2(X, join(X, Y)) = X.
% 0.20/0.40 Axiom 9 (associativity_of_meet2): meet2(meet2(X, Y), Z) = meet2(X, meet2(Y, Z)).
% 0.20/0.40
% 0.20/0.40 Lemma 10: join(X, meet2(Y, X)) = X.
% 0.20/0.40 Proof:
% 0.20/0.40 join(X, meet2(Y, X))
% 0.20/0.40 = { by axiom 3 (commutativity_of_meet2) R->L }
% 0.20/0.40 join(X, meet2(X, Y))
% 0.20/0.40 = { by axiom 7 (absorption2_2) }
% 0.20/0.40 X
% 0.20/0.40
% 0.20/0.40 Goal 1 (prove_meets_are_same): meet(a, b) = meet2(a, b).
% 0.20/0.40 Proof:
% 0.20/0.40 meet(a, b)
% 0.20/0.40 = { by axiom 6 (absorption2) R->L }
% 0.20/0.40 join(meet(a, b), meet(meet(a, b), meet2(a, b)))
% 0.20/0.40 = { by axiom 5 (associativity_of_meet) }
% 0.20/0.40 join(meet(a, b), meet(a, meet(b, meet2(a, b))))
% 0.20/0.40 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.40 join(meet(a, b), meet(a, meet(meet2(a, b), b)))
% 0.20/0.40 = { by lemma 10 R->L }
% 0.20/0.40 join(meet(a, b), meet(a, meet(meet2(a, b), join(b, meet2(a, b)))))
% 0.20/0.40 = { by axiom 2 (commutativity_of_join) }
% 0.20/0.40 join(meet(a, b), meet(a, meet(meet2(a, b), join(meet2(a, b), b))))
% 0.20/0.40 = { by axiom 4 (absorption1) }
% 0.20/0.40 join(meet(a, b), meet(a, meet2(a, b)))
% 0.20/0.40 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.40 join(meet(a, b), meet(meet2(a, b), a))
% 0.20/0.40 = { by axiom 7 (absorption2_2) R->L }
% 0.20/0.40 join(meet(a, b), meet(meet2(a, b), join(a, meet2(a, b))))
% 0.20/0.40 = { by axiom 2 (commutativity_of_join) }
% 0.20/0.40 join(meet(a, b), meet(meet2(a, b), join(meet2(a, b), a)))
% 0.20/0.40 = { by axiom 4 (absorption1) }
% 0.20/0.40 join(meet(a, b), meet2(a, b))
% 0.20/0.40 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.40 join(meet2(a, b), meet(a, b))
% 0.20/0.40 = { by axiom 8 (absorption1_2) R->L }
% 0.20/0.40 join(meet2(a, b), meet2(meet(a, b), join(meet(a, b), a)))
% 0.20/0.40 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.40 join(meet2(a, b), meet2(meet(a, b), join(a, meet(a, b))))
% 0.20/0.40 = { by axiom 6 (absorption2) }
% 0.20/0.40 join(meet2(a, b), meet2(meet(a, b), a))
% 0.20/0.40 = { by axiom 3 (commutativity_of_meet2) R->L }
% 0.20/0.40 join(meet2(a, b), meet2(a, meet(a, b)))
% 0.20/0.40 = { by axiom 8 (absorption1_2) R->L }
% 0.20/0.40 join(meet2(a, b), meet2(a, meet2(meet(a, b), join(meet(a, b), b))))
% 0.20/0.41 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.41 join(meet2(a, b), meet2(a, meet2(meet(a, b), join(b, meet(a, b)))))
% 0.20/0.41 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.41 join(meet2(a, b), meet2(a, meet2(meet(a, b), join(b, meet(b, a)))))
% 0.20/0.41 = { by axiom 6 (absorption2) }
% 0.20/0.41 join(meet2(a, b), meet2(a, meet2(meet(a, b), b)))
% 0.20/0.41 = { by axiom 3 (commutativity_of_meet2) R->L }
% 0.20/0.41 join(meet2(a, b), meet2(a, meet2(b, meet(a, b))))
% 0.20/0.41 = { by axiom 9 (associativity_of_meet2) R->L }
% 0.20/0.41 join(meet2(a, b), meet2(meet2(a, b), meet(a, b)))
% 0.20/0.41 = { by axiom 3 (commutativity_of_meet2) }
% 0.20/0.41 join(meet2(a, b), meet2(meet(a, b), meet2(a, b)))
% 0.20/0.41 = { by lemma 10 }
% 0.20/0.41 meet2(a, b)
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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