TSTP Solution File: LAT038-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LAT038-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n022.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 06:27:13 EDT 2023
% Result : Unsatisfiable 0.19s 0.52s
% Output : Proof 0.19s
% 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 : LAT038-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n022.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 07:00:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.52 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.52
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.19/0.52 Axiom 2 (idempotence_of_meet): meet(X, X) = X.
% 0.19/0.52 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.19/0.52 Axiom 4 (absorption2): join(X, meet(X, Y)) = X.
% 0.19/0.52 Axiom 5 (lhs1): f(join(aa, bb), dd) = f(join(cc, bb), dd).
% 0.19/0.52 Axiom 6 (absorption1): meet(X, join(X, Y)) = X.
% 0.19/0.52 Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.19/0.53 Axiom 8 (f_on_left_join): f(join(X, Y), Z) = join(f(X, Z), f(Y, Z)).
% 0.19/0.53 Axiom 9 (dist_meet): meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)).
% 0.19/0.53 Axiom 10 (lhs2): meet(f(aa, dd), f(bb, dd)) = meet(f(cc, dd), f(bb, dd)).
% 0.19/0.53
% 0.19/0.53 Lemma 11: join(f(cc, dd), f(bb, dd)) = join(f(aa, dd), f(bb, dd)).
% 0.19/0.53 Proof:
% 0.19/0.53 join(f(cc, dd), f(bb, dd))
% 0.19/0.53 = { by axiom 8 (f_on_left_join) R->L }
% 0.19/0.53 f(join(cc, bb), dd)
% 0.19/0.53 = { by axiom 5 (lhs1) R->L }
% 0.19/0.53 f(join(aa, bb), dd)
% 0.19/0.53 = { by axiom 8 (f_on_left_join) }
% 0.19/0.53 join(f(aa, dd), f(bb, dd))
% 0.19/0.53
% 0.19/0.53 Goal 1 (rhs): f(aa, dd) = f(cc, dd).
% 0.19/0.53 Proof:
% 0.19/0.53 f(aa, dd)
% 0.19/0.53 = { by axiom 4 (absorption2) R->L }
% 0.19/0.53 join(f(aa, dd), meet(f(aa, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 10 (lhs2) }
% 0.19/0.53 join(f(aa, dd), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 6 (absorption1) R->L }
% 0.19/0.53 join(meet(f(aa, dd), join(f(aa, dd), f(bb, dd))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by lemma 11 R->L }
% 0.19/0.53 join(meet(f(aa, dd), join(f(cc, dd), f(bb, dd))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 1 (commutativity_of_join) R->L }
% 0.19/0.53 join(meet(f(aa, dd), join(f(bb, dd), f(cc, dd))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 9 (dist_meet) }
% 0.19/0.53 join(join(meet(f(aa, dd), f(bb, dd)), meet(f(aa, dd), f(cc, dd))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 2 (idempotence_of_meet) R->L }
% 0.19/0.53 join(join(meet(meet(f(aa, dd), f(aa, dd)), f(bb, dd)), meet(f(aa, dd), f(cc, dd))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 7 (associativity_of_meet) }
% 0.19/0.53 join(join(meet(f(aa, dd), meet(f(aa, dd), f(bb, dd))), meet(f(aa, dd), f(cc, dd))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 9 (dist_meet) R->L }
% 0.19/0.53 join(meet(f(aa, dd), join(meet(f(aa, dd), f(bb, dd)), f(cc, dd))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 1 (commutativity_of_join) }
% 0.19/0.53 join(meet(f(aa, dd), join(f(cc, dd), meet(f(aa, dd), f(bb, dd)))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 10 (lhs2) }
% 0.19/0.53 join(meet(f(aa, dd), join(f(cc, dd), meet(f(cc, dd), f(bb, dd)))), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 4 (absorption2) }
% 0.19/0.53 join(meet(f(aa, dd), f(cc, dd)), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 3 (commutativity_of_meet) R->L }
% 0.19/0.53 join(meet(f(cc, dd), f(aa, dd)), meet(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 9 (dist_meet) R->L }
% 0.19/0.53 meet(f(cc, dd), join(f(aa, dd), f(bb, dd)))
% 0.19/0.53 = { by lemma 11 R->L }
% 0.19/0.53 meet(f(cc, dd), join(f(cc, dd), f(bb, dd)))
% 0.19/0.53 = { by axiom 6 (absorption1) }
% 0.19/0.53 f(cc, dd)
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53
% 0.19/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
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