TSTP Solution File: LCL007-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n003.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 12:57:17 EDT 2022
% Result : Unsatisfiable 1.36s 1.48s
% Output : Proof 1.36s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n003.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 02:48:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.36/1.48 % SZS status Unsatisfiable
% 1.36/1.48 % SZS output start Proof
% 1.36/1.48 The input problem is unsatisfiable because
% 1.36/1.48
% 1.36/1.48 [1] the following set of Horn clauses is unsatisfiable:
% 1.36/1.48
% 1.36/1.48 is_a_theorem(equivalent(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 1.36/1.48 is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X)))
% 1.36/1.48 is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z))))
% 1.36/1.48 is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))) ==> \bottom
% 1.36/1.48
% 1.36/1.48 This holds because
% 1.36/1.48
% 1.36/1.48 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.36/1.48
% 1.36/1.48 E:
% 1.36/1.48 f1(true__, Y) = is_a_theorem(Y)
% 1.36/1.48 f2(is_a_theorem(X), X, Y) = true__
% 1.36/1.48 f2(true__, X, Y) = f1(is_a_theorem(equivalent(X, Y)), Y)
% 1.36/1.48 f3(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))) = true__
% 1.36/1.48 f3(true__) = false__
% 1.36/1.48 is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X))) = true__
% 1.36/1.48 is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))) = true__
% 1.36/1.48 G:
% 1.36/1.48 true__ = false__
% 1.36/1.48
% 1.36/1.48 This holds because
% 1.36/1.48
% 1.36/1.48 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.36/1.48
% 1.36/1.48
% 1.36/1.48 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(X1, X0)), Y1)), Y1) -> true__
% 1.36/1.48 f1(is_a_theorem(equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(equivalent(X0, X1), X2)), Y1)), Y1) -> true__
% 1.36/1.48 f1(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(X0, equivalent(X1, X2))), Y1)), Y1) -> true__
% 1.36/1.48 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(Y1, Y0))) -> true__
% 1.36/1.48 f1(true__, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(equivalent(Y0, Y1), Y2))) -> true__
% 1.36/1.48 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), Y2), equivalent(Y0, equivalent(Y1, Y2)))) -> true__
% 1.36/1.48 f2(f1(true__, Y0), Y0, Y1) -> true__
% 1.36/1.48 f2(true__, Y0, Y1) -> f1(f1(true__, equivalent(Y0, Y1)), Y1)
% 1.36/1.48 f3(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))) -> true__
% 1.36/1.48 f3(true__) -> false__
% 1.36/1.48 false__ -> true__
% 1.36/1.48 is_a_theorem(Y) -> f1(true__, Y)
% 1.36/1.48 with the LPO induced by
% 1.36/1.48 c > b > a > is_a_theorem > f2 > equivalent > f1 > f3 > false__ > true__
% 1.36/1.48
% 1.36/1.48 % SZS output end Proof
% 1.36/1.48
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