TSTP Solution File: LAT145-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT145-1 : 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 : n032.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 06:27:33 EDT 2023
% Result : Unsatisfiable 232.16s 30.08s
% Output : Proof 232.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT145-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Aug 24 04:16:41 EDT 2023
% 0.10/0.30 % CPUTime :
% 232.16/30.08 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 232.16/30.08
% 232.16/30.08 % SZS status Unsatisfiable
% 232.16/30.08
% 232.16/30.09 % SZS output start Proof
% 232.16/30.09 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 232.16/30.09 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 232.16/30.09 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 232.16/30.09 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 232.16/30.09 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 232.16/30.09 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 232.16/30.09 Axiom 7 (equation_H32): meet(X, join(Y, meet(X, meet(Z, W)))) = meet(X, join(Y, meet(Z, join(meet(X, W), meet(Y, W))))).
% 232.16/30.09
% 232.16/30.09 Lemma 8: join(X, meet(Y, X)) = X.
% 232.16/30.09 Proof:
% 232.16/30.09 join(X, meet(Y, X))
% 232.16/30.09 = { by axiom 1 (commutativity_of_meet) R->L }
% 232.16/30.09 join(X, meet(X, Y))
% 232.16/30.09 = { by axiom 5 (absorption2) }
% 232.16/30.09 X
% 232.16/30.09
% 232.16/30.09 Lemma 9: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 232.16/30.09 Proof:
% 232.16/30.09 join(Z, join(X, Y))
% 232.16/30.09 = { by axiom 2 (commutativity_of_join) R->L }
% 232.16/30.09 join(join(X, Y), Z)
% 232.16/30.09 = { by axiom 6 (associativity_of_join) }
% 232.16/30.09 join(X, join(Y, Z))
% 232.16/30.09
% 232.16/30.09 Lemma 10: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 232.16/30.09 Proof:
% 232.16/30.09 meet(X, meet(Y, join(X, Z)))
% 232.16/30.09 = { by axiom 1 (commutativity_of_meet) R->L }
% 232.16/30.09 meet(meet(Y, join(X, Z)), X)
% 232.16/30.09 = { by axiom 4 (associativity_of_meet) }
% 232.16/30.09 meet(Y, meet(join(X, Z), X))
% 232.16/30.09 = { by axiom 1 (commutativity_of_meet) }
% 232.16/30.09 meet(Y, meet(X, join(X, Z)))
% 232.16/30.09 = { by axiom 3 (absorption1) }
% 232.16/30.09 meet(Y, X)
% 232.16/30.09 = { by axiom 1 (commutativity_of_meet) }
% 232.16/30.09 meet(X, Y)
% 232.16/30.09
% 232.16/30.09 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)))).
% 232.16/30.09 Proof:
% 232.16/30.09 meet(a, join(b, meet(a, c)))
% 232.60/30.09 = { by axiom 3 (absorption1) R->L }
% 232.60/30.09 meet(meet(a, join(b, meet(a, c))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 232.60/30.09 = { by axiom 1 (commutativity_of_meet) R->L }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, c))))
% 232.60/30.09 = { by axiom 3 (absorption1) R->L }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(meet(a, join(a, b)), c))))
% 232.60/30.09 = { by axiom 4 (associativity_of_meet) }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, meet(join(a, b), c)))))
% 232.60/30.09 = { by axiom 1 (commutativity_of_meet) }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, meet(c, join(a, b))))))
% 232.60/30.09 = { by axiom 7 (equation_H32) }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(c, join(meet(a, join(a, b)), meet(b, join(a, b)))))))
% 232.60/30.09 = { by axiom 1 (commutativity_of_meet) }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(join(meet(a, join(a, b)), meet(b, join(a, b))), c))))
% 232.60/30.09 = { by axiom 3 (absorption1) }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(join(a, meet(b, join(a, b))), c))))
% 232.60/30.09 = { by axiom 1 (commutativity_of_meet) }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(c, join(a, meet(b, join(a, b)))))))
% 232.60/30.09 = { by axiom 2 (commutativity_of_join) R->L }
% 232.60/30.09 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(c, join(a, meet(b, join(b, a)))))))
% 232.60/30.10 = { by axiom 3 (absorption1) }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(c, join(a, b)))))
% 232.60/30.10 = { by lemma 8 R->L }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, join(meet(c, join(a, b)), meet(a, meet(c, join(a, b)))))))
% 232.60/30.10 = { by lemma 10 }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, join(meet(c, join(a, b)), meet(a, c)))))
% 232.60/30.10 = { by axiom 2 (commutativity_of_join) }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, join(meet(a, c), meet(c, join(a, b))))))
% 232.60/30.10 = { by lemma 9 R->L }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(meet(c, join(a, b)), join(b, meet(a, c)))))
% 232.60/30.10 = { by axiom 2 (commutativity_of_join) R->L }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(b, meet(a, c)), meet(c, join(a, b)))))
% 232.60/30.10 = { by lemma 8 R->L }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(join(b, meet(a, c)), meet(a, join(b, meet(a, c)))), meet(c, join(a, b)))))
% 232.60/30.10 = { by axiom 2 (commutativity_of_join) }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(meet(a, join(b, meet(a, c))), join(b, meet(a, c))), meet(c, join(a, b)))))
% 232.60/30.10 = { by axiom 6 (associativity_of_join) }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(meet(a, join(b, meet(a, c))), join(join(b, meet(a, c)), meet(c, join(a, b))))))
% 232.60/30.10 = { by axiom 2 (commutativity_of_join) }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(meet(a, join(b, meet(a, c))), join(meet(c, join(a, b)), join(b, meet(a, c))))))
% 232.60/30.10 = { by lemma 9 R->L }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 232.60/30.10 = { by axiom 2 (commutativity_of_join) }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))
% 232.60/30.10 = { by lemma 10 }
% 232.60/30.10 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), a)
% 232.60/30.10 = { by axiom 1 (commutativity_of_meet) }
% 232.60/30.10 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 232.60/30.10 % SZS output end Proof
% 232.60/30.10
% 232.60/30.10 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------