TSTP Solution File: LCL414-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL414-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n023.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 13:01:04 EDT 2022
% Result : Unsatisfiable 3.46s 3.57s
% Output : Proof 3.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : LCL414-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.12 % Command : moca.sh %s
% 0.13/0.31 % Computer : n023.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 600
% 0.13/0.31 % DateTime : Sat Jul 2 21:12:28 EDT 2022
% 0.18/0.31 % CPUTime :
% 3.46/3.57 % SZS status Unsatisfiable
% 3.46/3.57 % SZS output start Proof
% 3.46/3.57 The input problem is unsatisfiable because
% 3.46/3.57
% 3.46/3.57 [1] the following set of Horn clauses is unsatisfiable:
% 3.46/3.57
% 3.46/3.57 a_truth(A) & a_truth(implies(A, B)) ==> a_truth(B)
% 3.46/3.57 a_truth(implies(A, implies(B, A)))
% 3.46/3.57 a_truth(implies(implies(A, implies(B, C)), implies(implies(A, B), implies(A, C))))
% 3.46/3.57 a_truth(implies(implies(not(A), not(B)), implies(B, A)))
% 3.46/3.57 a_truth(implies(sk1, sk1)) ==> \bottom
% 3.46/3.57
% 3.46/3.57 This holds because
% 3.46/3.57
% 3.46/3.57 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.46/3.57
% 3.46/3.57 E:
% 3.46/3.57 a_truth(implies(A, implies(B, A))) = true__
% 3.46/3.57 a_truth(implies(implies(A, implies(B, C)), implies(implies(A, B), implies(A, C)))) = true__
% 3.46/3.57 a_truth(implies(implies(not(A), not(B)), implies(B, A))) = true__
% 3.46/3.57 f1(true__, B) = a_truth(B)
% 3.46/3.57 f2(a_truth(implies(A, B)), A, B) = true__
% 3.46/3.57 f2(true__, A, B) = f1(a_truth(A), B)
% 3.46/3.57 f3(a_truth(implies(sk1, sk1))) = true__
% 3.46/3.57 f3(true__) = false__
% 3.46/3.57 G:
% 3.46/3.57 true__ = false__
% 3.46/3.57
% 3.46/3.57 This holds because
% 3.46/3.57
% 3.46/3.57 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.46/3.57
% 3.46/3.57
% 3.46/3.57 a_truth(B) -> f1(true__, B)
% 3.46/3.57 f1(f1(true__, Y0), implies(X1, Y0)) -> true__
% 3.46/3.57 f1(f1(true__, Y0), implies(X1, implies(X2, X1))) -> true__
% 3.46/3.57 f1(f1(true__, Y0), implies(X1, implies(X2, Y0))) -> true__
% 3.46/3.57 f1(f1(true__, Y0), implies(X1, implies(X2, implies(X3, X2)))) -> true__
% 3.46/3.57 f1(f1(true__, Y0), implies(implies(X1, X2), implies(X1, X1))) -> true__
% 3.46/3.57 f1(f1(true__, Y0), implies(implies(X1, implies(X2, X3)), implies(implies(X1, X2), implies(X1, X3)))) -> true__
% 3.46/3.57 f1(f1(true__, Y0), implies(implies(not(X1), not(X2)), implies(X2, X1))) -> true__
% 3.46/3.57 f1(f1(true__, Y1), Y1) -> true__
% 3.46/3.57 f1(f1(true__, implies(X0, X1)), implies(X0, X0)) -> true__
% 3.46/3.57 f1(f1(true__, implies(X0, X1)), implies(X0, implies(X2, X1))) -> true__
% 3.46/3.57 f1(f1(true__, implies(X0, implies(X1, X2))), implies(implies(X0, X1), implies(X0, X2))) -> true__
% 3.46/3.57 f1(f1(true__, implies(not(X0), not(X1))), implies(X1, X0)) -> true__
% 3.46/3.57 f1(true__, implies(Y0, Y0)) -> true__
% 3.46/3.57 f1(true__, implies(Y0, implies(Y1, Y0))) -> true__
% 3.46/3.57 f1(true__, implies(Y0, implies(Y2, implies(X1, Y0)))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, X0))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, implies(X1, X0)))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, implies(X1, implies(X2, X0))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, implies(X1, implies(X2, X1))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, implies(X1, implies(X2, implies(X3, X2)))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X3))))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, implies(X1, implies(implies(not(X2), not(X3)), implies(X3, X2)))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, implies(implies(X1, X2), implies(X1, X1))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(X0, implies(implies(not(X1), not(X2)), implies(X2, X1))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(implies(X0, X1), implies(X0, X0)))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(implies(X0, X1), implies(X0, implies(X2, X1))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(implies(X0, implies(X1, X2)), implies(implies(X0, X1), implies(X0, X2))))) -> true__
% 3.46/3.57 f1(true__, implies(Y1, implies(implies(not(X0), not(X1)), implies(X1, X0)))) -> true__
% 3.46/3.57 f1(true__, implies(implies(X0, X1), implies(Y2, implies(X0, X0)))) -> true__
% 3.46/3.57 f1(true__, implies(implies(Y0, Y1), implies(Y0, implies(X2, Y1)))) -> true__
% 3.46/3.57 f1(true__, implies(implies(Y0, implies(Y1, Y2)), implies(implies(Y0, Y1), implies(Y0, Y2)))) -> true__
% 3.46/3.57 f1(true__, implies(implies(Y2, Y1), implies(Y2, Y2))) -> true__
% 3.46/3.57 f1(true__, implies(implies(implies(Y1, Y2), Y1), implies(implies(Y1, Y2), Y2))) -> true__
% 3.46/3.57 f1(true__, implies(implies(not(Y0), not(Y1)), implies(Y1, Y0))) -> true__
% 3.46/3.57 f2(f1(true__, implies(Y0, Y1)), Y0, Y1) -> true__
% 3.46/3.57 f2(true__, A, B) -> f1(f1(true__, A), B)
% 3.46/3.57 f3(f1(true__, implies(sk1, sk1))) -> true__
% 3.46/3.57 f3(true__) -> false__
% 3.46/3.57 false__ -> true__
% 3.46/3.57 with the LPO induced by
% 3.46/3.57 not > f2 > a_truth > f1 > sk1 > implies > f3 > false__ > true__
% 3.46/3.57
% 3.46/3.57 % SZS output end Proof
% 3.46/3.57
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