TSTP Solution File: LCL106-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : LCL106-1 : 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 12:58:02 EDT 2022
% Result : Unsatisfiable 9.95s 10.04s
% Output : Proof 9.95s
% 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 : LCL106-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % 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 06:37:46 EDT 2022
% 0.14/0.34 % CPUTime :
% 9.95/10.04 % SZS status Unsatisfiable
% 9.95/10.04 % SZS output start Proof
% 9.95/10.04 The input problem is unsatisfiable because
% 9.95/10.04
% 9.95/10.04 [1] the following set of Horn clauses is unsatisfiable:
% 9.95/10.04
% 9.95/10.04 is_a_theorem(equivalent(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 9.95/10.04 is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, Y), X))))
% 9.95/10.04 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)))
% 9.95/10.04 is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))) ==> \bottom
% 9.95/10.04
% 9.95/10.04 This holds because
% 9.95/10.04
% 9.95/10.04 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 9.95/10.04
% 9.95/10.04 E:
% 9.95/10.04 f1(true__, Y) = is_a_theorem(Y)
% 9.95/10.04 f2(is_a_theorem(X), X, Y) = true__
% 9.95/10.04 f2(true__, X, Y) = f1(is_a_theorem(equivalent(X, Y)), Y)
% 9.95/10.04 f3(is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))) = true__
% 9.95/10.04 f3(true__) = false__
% 9.95/10.04 is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, Y), X)))) = true__
% 9.95/10.04 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))) = true__
% 9.95/10.04 G:
% 9.95/10.04 true__ = false__
% 9.95/10.04
% 9.95/10.04 This holds because
% 9.95/10.04
% 9.95/10.04 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 9.95/10.04
% 9.95/10.04
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X0))), Y1)), Y1) -> true__
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X1, X0), equivalent(X2, equivalent(equivalent(X3, X4), equivalent(equivalent(X4, X3), X2))))), Y1)), Y1) -> true__
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X1, X0), equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)))), Y1)), Y1) -> true__
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(X2, X1))), Y1)), Y1) -> true__
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X1, X2)), Y1)), Y1) -> true__
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(X2, X1))), equivalent(X3, equivalent(equivalent(X4, X5), equivalent(equivalent(X5, X4), X3)))), Y1)), Y1) -> true__
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(X2, X1))), equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), equivalent(X4, X5))), Y1)), Y1) -> true__
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X1, X0), X2)), X2), equivalent(X3, equivalent(equivalent(X4, X5), equivalent(equivalent(X5, X4), X3)))), Y1)), Y1) -> true__
% 9.95/10.04 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X1, X0), X2)), X2), equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), equivalent(X4, X5))), Y1)), Y1) -> true__
% 9.95/10.04 f1(true__, equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y0)))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y0)))))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(Y2, equivalent(equivalent(Y3, Y4), equivalent(equivalent(Y4, Y3), Y2)))))))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), equivalent(Y3, Y4))))))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2))))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(X2, Y0), equivalent(X2, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y0))))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(X2, equivalent(Y1, Y2)))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(Y4, Y1), equivalent(equivalent(Y5, Y4), equivalent(Y5, Y1)))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(X2, equivalent(equivalent(X3, X4), equivalent(equivalent(X4, X3), X2))))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(equivalent(Y2, equivalent(Y3, Y4)), equivalent(Y2, equivalent(Y3, Y5))), equivalent(Y4, Y5))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y0), equivalent(Y2, equivalent(equivalent(Y3, Y4), equivalent(equivalent(Y4, Y3), Y2)))), equivalent(Y0, Y1)), equivalent(X2, equivalent(equivalent(X3, X4), equivalent(equivalent(X4, X3), X2))))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y0)), Y0), equivalent(X2, equivalent(equivalent(X3, X4), equivalent(equivalent(X4, X3), X2))))) -> true__
% 9.95/10.04 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y0)), Y0), equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)))) -> true__
% 9.95/10.04 f2(f1(true__, Y0), Y0, Y1) -> true__
% 9.95/10.04 f2(true__, X, Y) -> f1(f1(true__, equivalent(X, Y)), Y)
% 9.95/10.04 f3(f1(true__, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))) -> true__
% 9.95/10.04 f3(true__) -> false__
% 9.95/10.04 false__ -> true__
% 9.95/10.04 is_a_theorem(Y) -> f1(true__, Y)
% 9.95/10.04 with the LPO induced by
% 9.95/10.04 c > b > a > f3 > f2 > equivalent > is_a_theorem > f1 > false__ > true__
% 9.95/10.04
% 9.95/10.04 % SZS output end Proof
% 9.95/10.04
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