TSTP Solution File: LCL013-1 by Moca---0.1
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% File : Moca---0.1
% Problem : LCL013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 12:57:19 EDT 2022
% Result : Unsatisfiable 0.76s 0.92s
% Output : Proof 0.76s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LCL013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n019.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 : 600
% 0.13/0.34 % DateTime : Sun Jul 3 21:13:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.76/0.92 % SZS status Unsatisfiable
% 0.76/0.92 % SZS output start Proof
% 0.76/0.92 The input problem is unsatisfiable because
% 0.76/0.92
% 0.76/0.92 [1] the following set of Horn clauses is unsatisfiable:
% 0.76/0.92
% 0.76/0.92 is_a_theorem(equivalent(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 0.76/0.92 is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(X, Z)), equivalent(Z, Y))))
% 0.76/0.92 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))) ==> \bottom
% 0.76/0.92
% 0.76/0.92 This holds because
% 0.76/0.92
% 0.76/0.92 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.76/0.92
% 0.76/0.92 E:
% 0.76/0.92 f1(true__, Y) = is_a_theorem(Y)
% 0.76/0.92 f2(is_a_theorem(X), X, Y) = true__
% 0.76/0.92 f2(true__, X, Y) = f1(is_a_theorem(equivalent(X, Y)), Y)
% 0.76/0.92 f3(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))) = true__
% 0.76/0.92 f3(true__) = false__
% 0.76/0.92 is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(X, Z)), equivalent(Z, Y)))) = true__
% 0.76/0.92 G:
% 0.76/0.92 true__ = false__
% 0.76/0.92
% 0.76/0.92 This holds because
% 0.76/0.92
% 0.76/0.92 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.76/0.92
% 0.76/0.92
% 0.76/0.92 f1(f1(true__, equivalent(equivalent(X0, equivalent(equivalent(X1, equivalent(X0, X2)), equivalent(X2, X1))), Y1)), Y1) -> true__
% 0.76/0.92 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, equivalent(equivalent(X2, equivalent(X1, X3)), equivalent(X3, X2))), X4)), equivalent(X4, X0)), Y1)), Y1) -> true__
% 0.76/0.92 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(X1, equivalent(X2, X0))), Y1)), Y1) -> true__
% 0.76/0.92 f1(true__, equivalent(X1, equivalent(equivalent(equivalent(Y1, equivalent(equivalent(X0, X1), Y2)), equivalent(Y2, Y1)), X0))) -> true__
% 0.76/0.92 f1(true__, equivalent(Y0, equivalent(Y0, equivalent(equivalent(Y1, equivalent(equivalent(Y2, equivalent(Y1, Y3)), equivalent(Y3, Y2))), equivalent(X1, equivalent(equivalent(X2, equivalent(X1, X3)), equivalent(X3, X2))))))) -> true__
% 0.76/0.92 f1(true__, equivalent(Y0, equivalent(equivalent(Y1, equivalent(Y0, Y2)), equivalent(Y2, Y1)))) -> true__
% 0.76/0.92 f1(true__, equivalent(equivalent(X1, equivalent(equivalent(Y0, equivalent(equivalent(Y1, equivalent(Y0, Y2)), equivalent(Y2, Y1))), X2)), equivalent(X2, X1))) -> true__
% 0.76/0.92 f1(true__, equivalent(equivalent(X1, equivalent(equivalent(equivalent(Y0, equivalent(equivalent(Y1, equivalent(equivalent(Y2, equivalent(Y1, Y3)), equivalent(Y3, Y2))), Y4)), equivalent(Y4, Y0)), X2)), equivalent(X2, X1))) -> true__
% 0.76/0.92 f1(true__, equivalent(equivalent(equivalent(X3, X2), Y1), equivalent(X2, equivalent(Y1, X3)))) -> true__
% 0.76/0.92 f1(true__, equivalent(equivalent(equivalent(Y1, equivalent(equivalent(Y2, equivalent(Y1, Y3)), equivalent(Y3, Y2))), Y4), equivalent(equivalent(Y4, Y0), Y0))) -> true__
% 0.76/0.92 f2(f1(true__, Y0), Y0, Y1) -> true__
% 0.76/0.92 f2(is_a_theorem(X), X, Y) -> true__
% 0.76/0.92 f2(true__, X, Y) -> f1(is_a_theorem(equivalent(X, Y)), Y)
% 0.76/0.92 f3(f1(true__, equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))) -> true__
% 0.76/0.92 f3(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))) -> true__
% 0.76/0.92 f3(true__) -> false__
% 0.76/0.92 false__ -> true__
% 0.76/0.92 is_a_theorem(Y) -> f1(true__, Y)
% 0.76/0.92 is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(X, Z)), equivalent(Z, Y)))) -> true__
% 0.76/0.92 with the LPO induced by
% 0.76/0.92 f2 > equivalent > is_a_theorem > f1 > c > b > a > f3 > false__ > true__
% 0.76/0.92
% 0.76/0.92 % SZS output end Proof
% 0.76/0.92
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