TSTP Solution File: LAT144-1 by Twee---2.5.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : LAT144-1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 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 : Mon Jun 24 10:31:30 EDT 2024
% Result : Unsatisfiable 174.69s 22.25s
% Output : Proof 174.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LAT144-1 : TPTP v8.2.0. Released v3.1.0.
% 0.00/0.09 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Fri Jun 21 23:12:23 EDT 2024
% 0.08/0.27 % CPUTime :
% 174.69/22.25 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 174.69/22.25
% 174.69/22.25 % SZS status Unsatisfiable
% 174.69/22.25
% 174.69/22.26 % SZS output start Proof
% 174.69/22.26 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 174.69/22.26 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 174.69/22.26 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 174.69/22.26 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 174.69/22.26 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 174.69/22.26 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 174.69/22.26 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))))).
% 174.69/22.26
% 174.69/22.26 Lemma 8: meet(X, join(Y, X)) = X.
% 174.69/22.26 Proof:
% 174.69/22.26 meet(X, join(Y, X))
% 174.69/22.26 = { by axiom 2 (commutativity_of_join) R->L }
% 174.69/22.26 meet(X, join(X, Y))
% 174.69/22.26 = { by axiom 3 (absorption1) }
% 174.69/22.26 X
% 174.69/22.26
% 174.69/22.26 Lemma 9: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 174.69/22.26 Proof:
% 174.69/22.26 meet(Y, meet(X, Z))
% 174.69/22.26 = { by axiom 1 (commutativity_of_meet) R->L }
% 174.69/22.26 meet(meet(X, Z), Y)
% 174.69/22.26 = { by axiom 4 (associativity_of_meet) }
% 174.69/22.26 meet(X, meet(Z, Y))
% 174.69/22.26 = { by axiom 1 (commutativity_of_meet) }
% 174.69/22.26 meet(X, meet(Y, Z))
% 174.69/22.26
% 174.69/22.26 Lemma 10: join(X, meet(Y, X)) = X.
% 174.69/22.26 Proof:
% 174.69/22.26 join(X, meet(Y, X))
% 174.69/22.26 = { by axiom 1 (commutativity_of_meet) R->L }
% 174.69/22.26 join(X, meet(X, Y))
% 174.69/22.26 = { by axiom 5 (absorption2) }
% 174.69/22.26 X
% 174.69/22.26
% 174.69/22.26 Lemma 11: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 174.69/22.26 Proof:
% 174.69/22.26 join(Y, join(X, Z))
% 174.69/22.26 = { by axiom 2 (commutativity_of_join) R->L }
% 174.69/22.26 join(join(X, Z), Y)
% 174.69/22.26 = { by axiom 6 (associativity_of_join) }
% 174.69/22.26 join(X, join(Z, Y))
% 174.69/22.26 = { by axiom 2 (commutativity_of_join) }
% 174.69/22.26 join(X, join(Y, Z))
% 174.69/22.26
% 174.69/22.26 Goal 1 (prove_H2): meet(a, join(b, meet(a, c))) = meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(b, c))))).
% 174.69/22.26 Proof:
% 174.69/22.26 meet(a, join(b, meet(a, c)))
% 174.69/22.26 = { by lemma 8 R->L }
% 174.69/22.26 meet(a, meet(join(b, meet(a, c)), join(c, join(b, meet(a, c)))))
% 174.69/22.26 = { by lemma 11 }
% 174.69/22.26 meet(a, meet(join(b, meet(a, c)), join(b, join(c, meet(a, c)))))
% 174.69/22.26 = { by lemma 10 }
% 174.69/22.26 meet(a, meet(join(b, meet(a, c)), join(b, c)))
% 174.69/22.26 = { by lemma 9 R->L }
% 174.69/22.26 meet(join(b, meet(a, c)), meet(a, join(b, c)))
% 174.69/22.26 = { by axiom 1 (commutativity_of_meet) }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(a, c)))
% 174.69/22.26 = { by lemma 8 R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(a, meet(c, join(b, c)))))
% 174.69/22.26 = { by lemma 9 R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(c, meet(a, join(b, c)))))
% 174.69/22.26 = { by axiom 3 (absorption1) R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(c, meet(meet(a, join(b, c)), join(meet(a, join(b, c)), meet(b, c))))))
% 174.69/22.26 = { by lemma 9 R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(a, join(b, c)), meet(c, join(meet(a, join(b, c)), meet(b, c))))))
% 174.69/22.26 = { by axiom 3 (absorption1) R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(meet(a, join(b, c)), join(meet(a, join(b, c)), b)), meet(c, join(meet(a, join(b, c)), meet(b, c))))))
% 174.69/22.26 = { by axiom 4 (associativity_of_meet) }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(a, join(b, c)), meet(join(meet(a, join(b, c)), b), meet(c, join(meet(a, join(b, c)), meet(b, c)))))))
% 174.69/22.26 = { by axiom 1 (commutativity_of_meet) }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(a, join(b, c)), meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(a, join(b, c)), b)))))
% 174.69/22.26 = { by axiom 7 (equation_H32) }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(meet(a, join(b, c)), join(meet(a, join(b, c)), b)), meet(b, join(meet(a, join(b, c)), b))))))
% 174.69/22.26 = { by axiom 3 (absorption1) }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(a, join(b, c)), meet(b, join(meet(a, join(b, c)), b))))))
% 174.69/22.26 = { by lemma 8 }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(a, join(b, c)), b))))
% 174.69/22.26 = { by axiom 5 (absorption2) R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(meet(a, join(b, c)), join(b, meet(b, c))))))
% 174.69/22.26 = { by lemma 11 R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(b, join(meet(a, join(b, c)), meet(b, c))))))
% 174.69/22.26 = { by lemma 10 R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(b, join(join(meet(a, join(b, c)), meet(b, c)), meet(c, join(meet(a, join(b, c)), meet(b, c))))))))
% 174.69/22.26 = { by axiom 6 (associativity_of_join) R->L }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(join(b, join(meet(a, join(b, c)), meet(b, c))), meet(c, join(meet(a, join(b, c)), meet(b, c)))))))
% 174.69/22.26 = { by lemma 8 }
% 174.69/22.26 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))))
% 174.69/22.26 = { by axiom 1 (commutativity_of_meet) R->L }
% 174.69/22.26 meet(join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))), meet(a, join(b, c)))
% 174.69/22.26 = { by lemma 9 }
% 174.69/22.26 meet(a, meet(join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))), join(b, c)))
% 174.69/22.26 = { by axiom 5 (absorption2) R->L }
% 174.69/22.26 meet(a, meet(join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))), join(b, join(c, meet(c, join(meet(a, join(b, c)), meet(b, c)))))))
% 174.69/22.26 = { by lemma 11 R->L }
% 174.69/22.26 meet(a, meet(join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))), join(c, join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))))))
% 174.69/22.26 = { by lemma 8 }
% 174.69/22.26 meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))))
% 174.69/22.26 % SZS output end Proof
% 174.69/22.26
% 174.69/22.26 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------