TSTP Solution File: LAT168-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LAT168-1 : 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 : n010.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 06:27:38 EDT 2023
% Result : Unsatisfiable 6.89s 1.44s
% Output : Proof 6.89s
% 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 : LAT168-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 06:50:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 6.89/1.44 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 6.89/1.44
% 6.89/1.44 % SZS status Unsatisfiable
% 6.89/1.44
% 6.89/1.45 % SZS output start Proof
% 6.89/1.45 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 6.89/1.45 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 6.89/1.45 Axiom 3 (absorption2): join(X, meet(X, Y)) = X.
% 6.89/1.45 Axiom 4 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 6.89/1.45 Axiom 5 (absorption1): meet(X, join(X, Y)) = X.
% 6.89/1.45 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 6.89/1.45 Axiom 7 (equation_H18_dual): meet(join(X, Y), join(X, Z)) = join(X, meet(join(X, Y), meet(join(X, Z), join(Y, meet(X, Z))))).
% 6.89/1.45
% 6.89/1.45 Lemma 8: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 6.89/1.45 Proof:
% 6.89/1.45 meet(Y, meet(X, Z))
% 6.89/1.45 = { by axiom 2 (commutativity_of_meet) R->L }
% 6.89/1.45 meet(meet(X, Z), Y)
% 6.89/1.45 = { by axiom 6 (associativity_of_meet) }
% 6.89/1.45 meet(X, meet(Z, Y))
% 6.89/1.45 = { by axiom 2 (commutativity_of_meet) }
% 6.89/1.45 meet(X, meet(Y, Z))
% 6.89/1.45
% 6.89/1.45 Goal 1 (prove_H58): meet(a, join(b, c)) = meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))).
% 6.89/1.45 Proof:
% 6.89/1.45 meet(a, join(b, c))
% 6.89/1.45 = { by axiom 5 (absorption1) R->L }
% 6.89/1.45 meet(meet(a, join(b, c)), join(meet(a, join(b, c)), join(a, b)))
% 6.89/1.45 = { by axiom 1 (commutativity_of_join) R->L }
% 6.89/1.45 meet(meet(a, join(b, c)), join(join(a, b), meet(a, join(b, c))))
% 6.89/1.45 = { by axiom 1 (commutativity_of_join) }
% 6.89/1.45 meet(meet(a, join(b, c)), join(join(b, a), meet(a, join(b, c))))
% 6.89/1.45 = { by axiom 4 (associativity_of_join) }
% 6.89/1.45 meet(meet(a, join(b, c)), join(b, join(a, meet(a, join(b, c)))))
% 6.89/1.45 = { by axiom 3 (absorption2) }
% 6.89/1.45 meet(meet(a, join(b, c)), join(b, a))
% 6.89/1.45 = { by axiom 1 (commutativity_of_join) R->L }
% 6.89/1.45 meet(meet(a, join(b, c)), join(a, b))
% 6.89/1.45 = { by axiom 2 (commutativity_of_meet) R->L }
% 6.89/1.45 meet(join(a, b), meet(a, join(b, c)))
% 6.89/1.45 = { by lemma 8 }
% 6.89/1.45 meet(a, meet(join(a, b), join(b, c)))
% 6.89/1.45 = { by axiom 2 (commutativity_of_meet) R->L }
% 6.89/1.45 meet(a, meet(join(b, c), join(a, b)))
% 6.89/1.45 = { by axiom 1 (commutativity_of_join) }
% 6.89/1.45 meet(a, meet(join(b, c), join(b, a)))
% 6.89/1.45 = { by axiom 7 (equation_H18_dual) }
% 6.89/1.45 meet(a, join(b, meet(join(b, c), meet(join(b, a), join(c, meet(b, a))))))
% 6.89/1.45 = { by axiom 1 (commutativity_of_join) R->L }
% 6.89/1.45 meet(a, join(b, meet(join(b, c), meet(join(a, b), join(c, meet(b, a))))))
% 6.89/1.45 = { by axiom 2 (commutativity_of_meet) R->L }
% 6.89/1.45 meet(a, join(b, meet(join(b, c), meet(join(a, b), join(c, meet(a, b))))))
% 6.89/1.45 = { by lemma 8 R->L }
% 6.89/1.45 meet(a, join(b, meet(join(a, b), meet(join(b, c), join(c, meet(a, b))))))
% 6.89/1.45 = { by axiom 2 (commutativity_of_meet) }
% 6.89/1.45 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(b, c)))))
% 6.89/1.45 = { by axiom 3 (absorption2) R->L }
% 6.89/1.45 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(join(b, meet(b, a)), c)))))
% 6.89/1.45 = { by axiom 2 (commutativity_of_meet) R->L }
% 6.89/1.45 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(join(b, meet(a, b)), c)))))
% 6.89/1.45 = { by axiom 4 (associativity_of_join) }
% 6.89/1.45 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(b, join(meet(a, b), c))))))
% 6.89/1.45 = { by axiom 1 (commutativity_of_join) }
% 6.89/1.45 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(b, join(c, meet(a, b)))))))
% 6.89/1.45 = { by axiom 1 (commutativity_of_join) R->L }
% 6.89/1.45 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(join(c, meet(a, b)), b)))))
% 6.89/1.45 = { by axiom 5 (absorption1) }
% 6.89/1.45 meet(a, join(b, meet(join(a, b), join(c, meet(a, b)))))
% 6.89/1.45 % SZS output end Proof
% 6.89/1.45
% 6.89/1.45 RESULT: Unsatisfiable (the axioms are contradictory).
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