TSTP Solution File: LAT005-10 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT005-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n003.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 06:27:04 EDT 2023
% Result : Unsatisfiable 0.20s 0.76s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT005-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35 % CPULimit : 300
% 0.20/0.35 % WCLimit : 300
% 0.20/0.35 % DateTime : Thu Aug 24 05:30:07 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.76 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.76
% 0.20/0.76 % SZS status Unsatisfiable
% 0.20/0.76
% 0.20/0.78 % SZS output start Proof
% 0.20/0.78 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.20/0.78 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.20/0.78 Axiom 3 (x_join_0): join(X, n0) = X.
% 0.20/0.78 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 0.20/0.78 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.20/0.78 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 0.20/0.78 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.20/0.78 Axiom 8 (complement_of_a_meet_b): complement(r2, meet(a, b)) = true.
% 0.20/0.78 Axiom 9 (complement_of_a_join_b): complement(r1, join(a, b)) = true.
% 0.20/0.78 Axiom 10 (ifeq_axiom_002): ifeq(X, X, Y, Z) = Y.
% 0.20/0.78 Axiom 11 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.20/0.78 Axiom 12 (complement_meet): ifeq(complement(X, Y), true, meet(X, Y), n0) = n0.
% 0.20/0.78 Axiom 13 (modular): ifeq3(meet(X, Y), X, meet(Y, join(X, Z)), join(X, meet(Z, Y))) = join(X, meet(Z, Y)).
% 0.20/0.78
% 0.20/0.78 Lemma 14: meet(Y, meet(Z, X)) = meet(X, meet(Y, Z)).
% 0.20/0.78 Proof:
% 0.20/0.78 meet(Y, meet(Z, X))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.78 meet(meet(Z, X), Y)
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.78 meet(meet(X, Z), Y)
% 0.20/0.78 = { by axiom 5 (associativity_of_meet) }
% 0.20/0.78 meet(X, meet(Z, Y))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.78 meet(X, meet(Y, Z))
% 0.20/0.78
% 0.20/0.78 Lemma 15: join(X, meet(Y, X)) = X.
% 0.20/0.78 Proof:
% 0.20/0.78 join(X, meet(Y, X))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.78 join(X, meet(X, Y))
% 0.20/0.78 = { by axiom 6 (absorption2) }
% 0.20/0.78 X
% 0.20/0.78
% 0.20/0.78 Lemma 16: join(X, meet(Y, join(X, Z))) = meet(join(X, Y), join(X, Z)).
% 0.20/0.78 Proof:
% 0.20/0.78 join(X, meet(Y, join(X, Z)))
% 0.20/0.78 = { by axiom 13 (modular) R->L }
% 0.20/0.78 ifeq3(meet(X, join(X, Z)), X, meet(join(X, Z), join(X, Y)), join(X, meet(Y, join(X, Z))))
% 0.20/0.78 = { by axiom 4 (absorption1) }
% 0.20/0.78 ifeq3(X, X, meet(join(X, Z), join(X, Y)), join(X, meet(Y, join(X, Z))))
% 0.20/0.78 = { by axiom 11 (ifeq_axiom) }
% 0.20/0.78 meet(join(X, Z), join(X, Y))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.78 meet(join(X, Y), join(X, Z))
% 0.20/0.78
% 0.20/0.78 Lemma 17: join(X, join(Y, meet(Z, X))) = join(Y, X).
% 0.20/0.78 Proof:
% 0.20/0.78 join(X, join(Y, meet(Z, X)))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.78 join(X, join(meet(Z, X), Y))
% 0.20/0.78 = { by axiom 7 (associativity_of_join) R->L }
% 0.20/0.78 join(join(X, meet(Z, X)), Y)
% 0.20/0.78 = { by lemma 15 }
% 0.20/0.78 join(X, Y)
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) }
% 0.20/0.78 join(Y, X)
% 0.20/0.78
% 0.20/0.78 Lemma 18: meet(join(r1, meet(r2, b)), join(r1, a)) = r1.
% 0.20/0.78 Proof:
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(r1, a))
% 0.20/0.78 = { by lemma 16 R->L }
% 0.20/0.78 join(r1, meet(meet(r2, b), join(r1, a)))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.78 join(r1, meet(join(r1, a), meet(r2, b)))
% 0.20/0.78 = { by lemma 14 R->L }
% 0.20/0.78 join(r1, meet(r2, meet(b, join(r1, a))))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.78 join(r1, meet(r2, meet(join(r1, a), b)))
% 0.20/0.78 = { by axiom 4 (absorption1) R->L }
% 0.20/0.78 join(r1, meet(r2, meet(join(r1, a), meet(b, join(b, a)))))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) }
% 0.20/0.78 join(r1, meet(r2, meet(join(r1, a), meet(b, join(a, b)))))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.78 join(r1, meet(r2, meet(join(r1, a), meet(join(a, b), b))))
% 0.20/0.78 = { by axiom 5 (associativity_of_meet) R->L }
% 0.20/0.78 join(r1, meet(r2, meet(meet(join(r1, a), join(a, b)), b)))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.78 join(r1, meet(r2, meet(b, meet(join(r1, a), join(a, b)))))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.78 join(r1, meet(r2, meet(b, meet(join(a, r1), join(a, b)))))
% 0.20/0.78 = { by lemma 16 R->L }
% 0.20/0.78 join(r1, meet(r2, meet(b, join(a, meet(r1, join(a, b))))))
% 0.20/0.78 = { by axiom 10 (ifeq_axiom_002) R->L }
% 0.20/0.78 join(r1, meet(r2, meet(b, join(a, ifeq(true, true, meet(r1, join(a, b)), n0)))))
% 0.20/0.78 = { by axiom 9 (complement_of_a_join_b) R->L }
% 0.20/0.78 join(r1, meet(r2, meet(b, join(a, ifeq(complement(r1, join(a, b)), true, meet(r1, join(a, b)), n0)))))
% 0.20/0.78 = { by axiom 12 (complement_meet) }
% 0.20/0.78 join(r1, meet(r2, meet(b, join(a, n0))))
% 0.20/0.78 = { by axiom 3 (x_join_0) }
% 0.20/0.78 join(r1, meet(r2, meet(b, a)))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.78 join(r1, meet(r2, meet(a, b)))
% 0.20/0.78 = { by axiom 10 (ifeq_axiom_002) R->L }
% 0.20/0.78 join(r1, ifeq(true, true, meet(r2, meet(a, b)), n0))
% 0.20/0.78 = { by axiom 8 (complement_of_a_meet_b) R->L }
% 0.20/0.78 join(r1, ifeq(complement(r2, meet(a, b)), true, meet(r2, meet(a, b)), n0))
% 0.20/0.78 = { by axiom 12 (complement_meet) }
% 0.20/0.78 join(r1, n0)
% 0.20/0.78 = { by axiom 3 (x_join_0) }
% 0.20/0.78 r1
% 0.20/0.78
% 0.20/0.78 Lemma 19: join(X, meet(join(X, Y), join(X, Z))) = meet(join(X, Y), join(X, Z)).
% 0.20/0.78 Proof:
% 0.20/0.78 join(X, meet(join(X, Y), join(X, Z)))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.78 join(meet(join(X, Y), join(X, Z)), X)
% 0.20/0.78 = { by axiom 4 (absorption1) R->L }
% 0.20/0.78 join(meet(join(X, Y), join(X, Z)), meet(X, join(X, Z)))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.78 join(meet(join(X, Y), join(X, Z)), meet(join(X, Z), X))
% 0.20/0.78 = { by axiom 4 (absorption1) R->L }
% 0.20/0.78 join(meet(join(X, Y), join(X, Z)), meet(join(X, Z), meet(X, join(X, Y))))
% 0.20/0.78 = { by lemma 14 R->L }
% 0.20/0.78 join(meet(join(X, Y), join(X, Z)), meet(X, meet(join(X, Y), join(X, Z))))
% 0.20/0.78 = { by lemma 15 }
% 0.20/0.78 meet(join(X, Y), join(X, Z))
% 0.20/0.78
% 0.20/0.78 Lemma 20: join(X, join(Y, meet(join(X, Z), join(X, W)))) = join(Y, meet(join(X, Z), join(X, W))).
% 0.20/0.78 Proof:
% 0.20/0.78 join(X, join(Y, meet(join(X, Z), join(X, W))))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.78 join(X, join(meet(join(X, Z), join(X, W)), Y))
% 0.20/0.78 = { by axiom 7 (associativity_of_join) R->L }
% 0.20/0.78 join(join(X, meet(join(X, Z), join(X, W))), Y)
% 0.20/0.78 = { by lemma 19 }
% 0.20/0.78 join(meet(join(X, Z), join(X, W)), Y)
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) }
% 0.20/0.78 join(Y, meet(join(X, Z), join(X, W)))
% 0.20/0.78
% 0.20/0.78 Goal 1 (prove_lemma): r1 = meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))).
% 0.20/0.78 Proof:
% 0.20/0.78 r1
% 0.20/0.78 = { by lemma 18 R->L }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(r1, a))
% 0.20/0.78 = { by lemma 17 R->L }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(a, join(r1, meet(r2, a))))
% 0.20/0.78 = { by axiom 6 (absorption2) R->L }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(a, join(join(r1, meet(r2, a)), meet(join(r1, meet(r2, a)), join(r1, meet(r2, b))))))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(a, join(join(r1, meet(r2, a)), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))))
% 0.20/0.78 = { by axiom 7 (associativity_of_join) }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(a, join(r1, join(meet(r2, a), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a)))))))
% 0.20/0.78 = { by lemma 20 }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(a, join(meet(r2, a), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(a, join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(r2, a))))
% 0.20/0.78 = { by lemma 17 }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), a))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(a, meet(join(r1, meet(r2, b)), join(r1, meet(r2, a)))))
% 0.20/0.78 = { by lemma 20 R->L }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(r1, join(a, meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))))
% 0.20/0.78 = { by axiom 7 (associativity_of_join) R->L }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(join(r1, a), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a)))))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a)))
% 0.20/0.78 = { by axiom 11 (ifeq_axiom) R->L }
% 0.20/0.78 ifeq3(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 0.20/0.78 = { by axiom 4 (absorption1) R->L }
% 0.20/0.78 ifeq3(meet(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, meet(r2, b)))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) R->L }
% 0.20/0.78 ifeq3(meet(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(join(r1, meet(r2, b)), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.78 ifeq3(meet(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(join(r1, meet(r2, b)), meet(join(r1, meet(r2, a)), join(r1, meet(r2, b))))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 0.20/0.78 = { by lemma 15 }
% 0.20/0.78 ifeq3(meet(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, meet(r2, b))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 0.20/0.78 = { by axiom 13 (modular) }
% 0.20/0.78 join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b))))
% 0.20/0.78 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.78 join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(r1, a)))
% 0.20/0.78 = { by lemma 18 }
% 0.20/0.78 join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), r1)
% 0.20/0.78 = { by axiom 2 (commutativity_of_join) }
% 0.20/0.78 join(r1, meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))
% 0.20/0.78 = { by lemma 19 }
% 0.20/0.78 meet(join(r1, meet(r2, b)), join(r1, meet(r2, a)))
% 0.20/0.78 % SZS output end Proof
% 0.20/0.78
% 0.20/0.78 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------