TSTP Solution File: LCL107-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL107-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n008.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 12:58:02 EDT 2022
% Result : Unsatisfiable 5.06s 5.11s
% Output : Proof 5.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL107-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n008.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 : 600
% 0.12/0.34 % DateTime : Sun Jul 3 22:01:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 5.06/5.11 % SZS status Unsatisfiable
% 5.06/5.11 % SZS output start Proof
% 5.06/5.11 The input problem is unsatisfiable because
% 5.06/5.11
% 5.06/5.11 [1] the following set of Horn clauses is unsatisfiable:
% 5.06/5.11
% 5.06/5.11 is_a_theorem(equivalent(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 5.06/5.11 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(U, V), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), V6))), equivalent(Z, equivalent(equivalent(Y, X), V6))))
% 5.06/5.11 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) ==> \bottom
% 5.06/5.11
% 5.06/5.11 This holds because
% 5.06/5.11
% 5.06/5.11 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.06/5.11
% 5.06/5.11 E:
% 5.06/5.11 f1(true__, Y) = is_a_theorem(Y)
% 5.06/5.11 f2(is_a_theorem(X), X, Y) = true__
% 5.06/5.11 f2(true__, X, Y) = f1(is_a_theorem(equivalent(X, Y)), Y)
% 5.06/5.11 f3(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))) = true__
% 5.06/5.11 f3(true__) = false__
% 5.06/5.11 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(U, V), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), V6))), equivalent(Z, equivalent(equivalent(Y, X), V6)))) = true__
% 5.06/5.11 G:
% 5.06/5.11 true__ = false__
% 5.06/5.11
% 5.06/5.11 This holds because
% 5.06/5.11
% 5.06/5.11 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.06/5.11
% 5.06/5.11
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X0)), equivalent(X3, X1))), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), X4)), equivalent(X0, equivalent(equivalent(X2, X3), X4))), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(X3, X1), equivalent(equivalent(X0, X3), X2))), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(equivalent(X3, X0), equivalent(X3, X1)), X2)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X1), equivalent(X2, X0)), X3)), equivalent(equivalent(equivalent(X4, X5), equivalent(equivalent(X6, X4), equivalent(X6, X5))), X3)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(X0, X3)), equivalent(equivalent(equivalent(X4, X1), equivalent(X4, X2)), X3)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, equivalent(X1, equivalent(equivalent(X2, X3), equivalent(X2, X4)))), equivalent(X0, equivalent(X1, X5))), equivalent(equivalent(X3, X4), X5)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(X1, X3))), equivalent(X0, X4)), equivalent(equivalent(X2, X3), X4)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(X3, X4), equivalent(equivalent(equivalent(X5, X4), equivalent(X5, X3)), X6))), equivalent(X2, equivalent(equivalent(X1, X0), X6))), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3), equivalent(equivalent(X1, X2), X3)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(equivalent(equivalent(X3, equivalent(equivalent(X4, X5), equivalent(X4, X6))), equivalent(X3, equivalent(X5, X6))), X7)), equivalent(equivalent(X1, X2), X7)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(X0, equivalent(X1, X3))), X4), equivalent(equivalent(X2, X3), X4)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(X1, X3))), equivalent(X0, equivalent(X2, X3))), equivalent(equivalent(equivalent(X4, X5), equivalent(X4, X6)), X7)), equivalent(equivalent(X5, X6), X7)), Y1)), Y1) -> true__
% 5.06/5.11 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, equivalent(X2, X3)), equivalent(X1, equivalent(X2, X4)))), equivalent(X0, equivalent(X3, X4))), X5), X5), Y1)), Y1) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(X3, Y3), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), X3), equivalent(equivalent(Y1, Y2), Y3)))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(Y1, X2), equivalent(equivalent(equivalent(Y3, Y0), equivalent(Y3, Y1)), equivalent(Y0, X2)))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(Y2, equivalent(equivalent(equivalent(Y5, Y4), equivalent(Y5, Y3)), Y6)), equivalent(Y2, equivalent(equivalent(Y4, Y3), Y6)))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(X1, equivalent(X2, equivalent(equivalent(Y5, Y4), equivalent(Y5, Y3)))), equivalent(X1, equivalent(X2, Y6))), equivalent(equivalent(Y4, Y3), Y6))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(X3, equivalent(Y0, Y1)), equivalent(X3, Y2)), equivalent(equivalent(equivalent(Y3, Y0), equivalent(Y3, Y1)), Y2))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(X3, equivalent(Y0, Y1)), equivalent(X3, equivalent(equivalent(equivalent(Y2, Y1), equivalent(Y2, Y0)), Y3))), equivalent(equivalent(equivalent(Y4, Y5), equivalent(equivalent(Y6, Y4), equivalent(Y6, Y5))), Y3))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(X3, equivalent(equivalent(Y0, Y1), Y2)), equivalent(X3, equivalent(equivalent(Y3, Y4), equivalent(equivalent(equivalent(Y5, Y4), equivalent(Y5, Y3)), Y6)))), equivalent(Y2, equivalent(equivalent(Y1, Y0), Y6)))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(X3, equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(X3, Y3)), equivalent(equivalent(Y1, Y2), Y3))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(Y0, Y2), X2), equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, Y1), X2)))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(Y3, Y4), equivalent(equivalent(equivalent(Y5, Y4), equivalent(Y5, Y3)), Y6)), equivalent(equivalent(equivalent(X3, X4), equivalent(equivalent(X5, X3), equivalent(X5, X4))), Y6))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(Y5, Y6), X3), equivalent(equivalent(equivalent(Y4, Y5), equivalent(Y4, Y6)), X3))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(equivalent(X3, equivalent(equivalent(X4, X5), equivalent(X4, X6))), equivalent(X3, equivalent(X5, X6))), equivalent(equivalent(equivalent(Y5, Y4), equivalent(Y5, Y3)), Y6)), equivalent(equivalent(Y4, Y3), Y6))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), Y2), equivalent(equivalent(Y3, Y4), equivalent(equivalent(equivalent(Y5, Y4), equivalent(Y5, Y3)), Y6))), equivalent(Y2, equivalent(equivalent(Y1, Y0), Y6)))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, equivalent(X1, X2)), equivalent(Y0, equivalent(X1, X3))), Y3), equivalent(equivalent(X2, X3), Y3))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(equivalent(Y2, Y1), equivalent(Y2, Y0)), equivalent(equivalent(equivalent(X5, equivalent(equivalent(Y6, Y4), equivalent(Y6, Y5))), equivalent(X5, equivalent(Y4, Y5))), X6)), equivalent(equivalent(Y1, Y0), X6))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(equivalent(Y3, equivalent(equivalent(Y4, Y5), equivalent(Y4, Y6))), equivalent(Y3, equivalent(Y5, Y6))), equivalent(equivalent(equivalent(X5, Y2), equivalent(X5, Y1)), X6)), equivalent(equivalent(equivalent(Y0, Y2), equivalent(Y0, Y1)), X6))) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(equivalent(Y3, equivalent(equivalent(Y4, equivalent(X4, X5)), equivalent(Y4, equivalent(X4, X6)))), equivalent(Y3, equivalent(X5, X6))), Y7), Y7)) -> true__
% 5.06/5.11 f1(true__, equivalent(equivalent(equivalent(equivalent(Y5, Y4), equivalent(Y5, Y3)), Y6), equivalent(equivalent(Y4, Y3), Y6))) -> true__
% 5.06/5.11 f2(f1(true__, Y0), Y0, Y1) -> true__
% 5.06/5.11 f2(is_a_theorem(X), X, Y) -> true__
% 5.06/5.11 f2(true__, X, Y) -> f1(is_a_theorem(equivalent(X, Y)), Y)
% 5.06/5.11 f3(f1(true__, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))) -> true__
% 5.06/5.11 f3(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))) -> true__
% 5.06/5.11 f3(true__) -> false__
% 5.06/5.11 is_a_theorem(Y) -> f1(true__, Y)
% 5.06/5.11 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(U, V), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), V6))), equivalent(Z, equivalent(equivalent(Y, X), V6)))) -> true__
% 5.06/5.11 true__ -> false__
% 5.06/5.11 with the LPO induced by
% 5.06/5.11 e > c > b > a > f2 > equivalent > f3 > is_a_theorem > f1 > true__ > false__
% 5.06/5.11
% 5.06/5.11 % SZS output end Proof
% 5.06/5.11
%------------------------------------------------------------------------------