TSTP Solution File: LCL130-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL130-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n015.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 : 600s
% DateTime : Sun Jul 17 12:58:21 EDT 2022
% Result : Unsatisfiable 4.07s 4.12s
% Output : Proof 4.07s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL130-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 04:46:31 EDT 2022
% 0.14/0.35 % CPUTime :
% 4.07/4.12 % SZS status Unsatisfiable
% 4.07/4.12 % SZS output start Proof
% 4.07/4.12 The input problem is unsatisfiable because
% 4.07/4.12
% 4.07/4.12 [1] the following set of Horn clauses is unsatisfiable:
% 4.07/4.12
% 4.07/4.12 is_a_theorem(equivalent(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 4.07/4.12 is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, U), equivalent(Z, U)))), X))
% 4.07/4.12 is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))) ==> \bottom
% 4.07/4.12
% 4.07/4.12 This holds because
% 4.07/4.12
% 4.07/4.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 4.07/4.12
% 4.07/4.12 E:
% 4.07/4.12 f1(true__, Y) = is_a_theorem(Y)
% 4.07/4.12 f2(is_a_theorem(X), X, Y) = true__
% 4.07/4.12 f2(true__, X, Y) = f1(is_a_theorem(equivalent(X, Y)), Y)
% 4.07/4.12 f3(is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))) = true__
% 4.07/4.12 f3(true__) = false__
% 4.07/4.12 is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, U), equivalent(Z, U)))), X)) = true__
% 4.07/4.12 G:
% 4.07/4.12 true__ = false__
% 4.07/4.12
% 4.07/4.12 This holds because
% 4.07/4.12
% 4.07/4.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 4.07/4.12
% 4.07/4.12
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(X0, X0), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(X0, equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3))))), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(X0, equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X2, X4), equivalent(X3, X4))), X1))), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(X0, X0), equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3)))), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X0, X2), equivalent(X1, X2))), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X0, X2), X3), equivalent(equivalent(X1, X2), X3))), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3)))), X0), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X0), X1), equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X2, X4), equivalent(X3, X4))), X1)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(equivalent(X0, X3), equivalent(X1, X3)), X2)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X2, X1)), equivalent(X0, X2)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X2, X1)), equivalent(equivalent(X0, X3), equivalent(X2, X3))), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X0, X2), equivalent(X1, X2))), equivalent(X3, X3)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X0, X2), equivalent(X1, X2))), equivalent(equivalent(X3, X4), equivalent(equivalent(X3, X5), equivalent(X4, X5)))), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X0, X2), equivalent(X1, X2))), equivalent(equivalent(equivalent(X3, X4), X5), equivalent(equivalent(equivalent(X3, X6), equivalent(X4, X6)), X5))), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X2, X4), equivalent(X3, X4))), X1)), X0), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3)))), X4), equivalent(X0, X4)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), X3), equivalent(equivalent(equivalent(equivalent(X0, X4), equivalent(X1, X4)), X2), X3)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(X3, X1), X2)), equivalent(X0, X3)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X2, X1)), X3), equivalent(equivalent(X0, X2), X3)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X2, X1)), X3), equivalent(equivalent(equivalent(X0, X4), equivalent(X2, X4)), X3)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X0, X2), equivalent(X1, X2))), X3), equivalent(equivalent(equivalent(X4, X5), equivalent(equivalent(X4, X6), equivalent(X5, X6))), X3)), Y1)), Y1) -> true__
% 4.07/4.12 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3)))), X4), X5), equivalent(equivalent(X0, X4), X5)), Y1)), Y1) -> true__
% 4.07/4.12 f1(true__, equivalent(X0, equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3)))))) -> true__
% 4.07/4.12 f1(true__, equivalent(Y0, Y0)) -> true__
% 4.07/4.12 f1(true__, equivalent(Y0, equivalent(equivalent(Y0, Y2), equivalent(equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3))), Y2)))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(Y0, X2), equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y1, Y3), equivalent(Y2, Y3)))), X2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(Y0, Y0), equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3))))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y0, Y2), equivalent(Y1, Y2)))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(equivalent(Y0, Y3), X3), equivalent(equivalent(Y1, Y3), X3)))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y1, Y3), equivalent(Y2, Y3)))), Y0)) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(X0, X3), equivalent(X1, X3)), equivalent(X0, X1))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3))), equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y1, Y3), equivalent(Y2, Y3))))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X2, X4), equivalent(X3, X4))), equivalent(X0, X0))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(X4, X5), equivalent(equivalent(X4, X6), equivalent(X5, X6))), equivalent(equivalent(equivalent(X0, X1), Y2), equivalent(equivalent(equivalent(X0, X2), equivalent(X1, X2)), Y2)))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(Y0, X3), equivalent(Y1, X3)), equivalent(equivalent(Y0, Y2), equivalent(Y1, Y2)))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(Y0, X3), equivalent(equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y1, Y3), equivalent(Y2, Y3))), X3)), Y0)) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(Y0, Y0), X1), equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X2, X4), equivalent(X3, X4))), X1))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), X2), equivalent(equivalent(equivalent(Y0, Y2), equivalent(Y1, Y2)), X2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y1, Y3), equivalent(Y2, Y3)))), X2), equivalent(Y0, X2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y1, Y3), equivalent(Y2, Y3)))), Y0), equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3))))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), X3), equivalent(equivalent(Y2, Y1), X3)), equivalent(Y0, Y2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), Y2), X2), equivalent(equivalent(equivalent(equivalent(Y0, Y3), equivalent(Y1, Y3)), Y2), X2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y2, Y1)), X2), equivalent(equivalent(Y0, Y2), X2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y2, Y1)), X2), equivalent(equivalent(equivalent(Y0, Y3), equivalent(Y2, Y3)), X2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y2, Y1)), equivalent(Y0, Y2)), equivalent(equivalent(X1, X2), equivalent(equivalent(X1, X3), equivalent(X2, X3))))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y0, Y2), equivalent(Y1, Y2))), X2), equivalent(equivalent(equivalent(Y3, Y4), equivalent(equivalent(Y3, Y5), equivalent(Y4, Y5))), X2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y1, Y3), equivalent(Y2, Y3)))), Y4), X2), equivalent(equivalent(Y0, Y4), X2))) -> true__
% 4.07/4.12 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y2, Y1)), X2), X3), equivalent(equivalent(equivalent(Y0, Y2), X2), X3))) -> true__
% 4.07/4.12 f2(f1(true__, Y0), Y0, Y1) -> true__
% 4.07/4.12 f2(is_a_theorem(X), X, Y) -> true__
% 4.07/4.12 f2(true__, X, Y) -> f1(is_a_theorem(equivalent(X, Y)), Y)
% 4.07/4.12 f3(f1(true__, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))) -> true__
% 4.07/4.12 f3(is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))) -> true__
% 4.07/4.12 f3(true__) -> false__
% 4.07/4.12 is_a_theorem(Y) -> f1(true__, Y)
% 4.07/4.12 is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, U), equivalent(Z, U)))), X)) -> true__
% 4.07/4.12 true__ -> false__
% 4.07/4.12 with the LPO induced by
% 4.07/4.12 e > c > b > a > f2 > equivalent > f3 > is_a_theorem > f1 > true__ > false__
% 4.07/4.12
% 4.07/4.12 % SZS output end Proof
% 4.07/4.12
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