TSTP Solution File: LAT146-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT146-1 : 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 : n018.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 177.16s 23.05s
% Output : Proof 177.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT146-1 : 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
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 09:37:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 177.16/23.05 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 177.16/23.05
% 177.16/23.05 % SZS status Unsatisfiable
% 177.16/23.05
% 177.16/23.06 % SZS output start Proof
% 177.16/23.06 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 177.16/23.06 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 177.16/23.06 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 177.16/23.06 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 177.16/23.06 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 177.16/23.06 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 177.16/23.06 Axiom 7 (equation_H34): meet(X, join(Y, meet(Z, W))) = meet(X, join(Y, meet(Z, join(Y, meet(W, join(Y, Z)))))).
% 177.16/23.06
% 177.16/23.06 Lemma 8: meet(Z, meet(X, Y)) = meet(X, meet(Y, Z)).
% 177.16/23.06 Proof:
% 177.16/23.06 meet(Z, meet(X, Y))
% 177.16/23.06 = { by axiom 1 (commutativity_of_meet) R->L }
% 177.16/23.06 meet(meet(X, Y), Z)
% 177.16/23.06 = { by axiom 4 (associativity_of_meet) }
% 177.16/23.06 meet(X, meet(Y, Z))
% 177.16/23.06
% 177.16/23.06 Goal 1 (prove_H28): meet(a, join(b, meet(a, meet(c, d)))) = meet(a, join(b, meet(c, meet(d, join(a, meet(b, d)))))).
% 177.16/23.06 Proof:
% 177.16/23.06 meet(a, join(b, meet(a, meet(c, d))))
% 177.16/23.06 = { by axiom 3 (absorption1) R->L }
% 177.16/23.06 meet(a, join(b, meet(meet(a, join(a, meet(b, d))), meet(c, d))))
% 177.16/23.06 = { by axiom 4 (associativity_of_meet) }
% 177.16/23.06 meet(a, join(b, meet(a, meet(join(a, meet(b, d)), meet(c, d)))))
% 177.16/23.06 = { by axiom 1 (commutativity_of_meet) }
% 177.16/23.06 meet(a, join(b, meet(a, meet(meet(c, d), join(a, meet(b, d))))))
% 177.16/23.06 = { by axiom 4 (associativity_of_meet) }
% 177.16/23.06 meet(a, join(b, meet(a, meet(c, meet(d, join(a, meet(b, d)))))))
% 177.16/23.06 = { by axiom 7 (equation_H34) }
% 177.16/23.06 meet(a, join(b, meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a))))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) R->L }
% 177.16/23.06 meet(a, join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b))))
% 177.16/23.06 = { by axiom 3 (absorption1) R->L }
% 177.16/23.06 meet(a, meet(join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b))), join(join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b))), meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) }
% 177.16/23.06 meet(a, meet(join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b))), join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b))))))
% 177.16/23.06 = { by axiom 1 (commutativity_of_meet) R->L }
% 177.16/23.06 meet(a, meet(join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b))), join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), join(b, meet(join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b), a)))))
% 177.16/23.06 = { by axiom 6 (associativity_of_join) R->L }
% 177.16/23.06 meet(a, meet(join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b))), join(join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b), meet(join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b), a))))
% 177.16/23.06 = { by axiom 5 (absorption2) }
% 177.16/23.06 meet(a, meet(join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b))), join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b)))
% 177.16/23.06 = { by axiom 1 (commutativity_of_meet) }
% 177.16/23.06 meet(a, meet(join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b), join(b, meet(a, join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b)))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) }
% 177.16/23.06 meet(a, meet(join(meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)), b), join(b, meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)))))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) }
% 177.16/23.06 meet(a, meet(join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a))), join(b, meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)))))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) R->L }
% 177.16/23.06 meet(a, meet(join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a))), join(meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)))), b)))
% 177.16/23.06 = { by axiom 4 (associativity_of_meet) R->L }
% 177.16/23.06 meet(meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)))), join(meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a)))), b))
% 177.16/23.06 = { by axiom 3 (absorption1) }
% 177.16/23.06 meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, a))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) }
% 177.16/23.06 meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(a, b))))
% 177.16/23.06 = { by axiom 5 (absorption2) R->L }
% 177.16/23.06 meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(a, join(b, meet(b, d))))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) R->L }
% 177.16/23.06 meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(a, join(meet(b, d), b)))))
% 177.16/23.06 = { by axiom 6 (associativity_of_join) R->L }
% 177.16/23.06 meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(join(a, meet(b, d)), b))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) }
% 177.16/23.06 meet(a, join(b, meet(meet(c, meet(d, join(a, meet(b, d)))), join(b, join(a, meet(b, d))))))
% 177.16/23.06 = { by axiom 1 (commutativity_of_meet) R->L }
% 177.16/23.06 meet(a, join(b, meet(join(b, join(a, meet(b, d))), meet(c, meet(d, join(a, meet(b, d)))))))
% 177.16/23.06 = { by lemma 8 }
% 177.16/23.06 meet(a, join(b, meet(c, meet(meet(d, join(a, meet(b, d))), join(b, join(a, meet(b, d)))))))
% 177.16/23.06 = { by axiom 2 (commutativity_of_join) R->L }
% 177.16/23.06 meet(a, join(b, meet(c, meet(meet(d, join(a, meet(b, d))), join(join(a, meet(b, d)), b)))))
% 177.16/23.06 = { by axiom 1 (commutativity_of_meet) R->L }
% 177.16/23.06 meet(a, join(b, meet(c, meet(join(join(a, meet(b, d)), b), meet(d, join(a, meet(b, d)))))))
% 177.16/23.07 = { by lemma 8 }
% 177.16/23.07 meet(a, join(b, meet(c, meet(d, meet(join(a, meet(b, d)), join(join(a, meet(b, d)), b))))))
% 177.16/23.07 = { by axiom 3 (absorption1) }
% 177.16/23.07 meet(a, join(b, meet(c, meet(d, join(a, meet(b, d))))))
% 177.16/23.07 % SZS output end Proof
% 177.16/23.07
% 177.16/23.07 RESULT: Unsatisfiable (the axioms are contradictory).
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