TSTP Solution File: NUM023-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : NUM023-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n018.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 : Mon Jul 18 12:32:16 EDT 2022
% Result : Unsatisfiable 3.42s 3.48s
% Output : Proof 3.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM023-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Wed Jul 6 03:29:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.42/3.48 % SZS status Unsatisfiable
% 3.42/3.48 % SZS output start Proof
% 3.42/3.48 The input problem is unsatisfiable because
% 3.42/3.48
% 3.42/3.48 [1] the following set of Horn clauses is unsatisfiable:
% 3.42/3.48
% 3.42/3.48 equalish(add(A, n0), A)
% 3.42/3.48 equalish(add(A, successor(B)), successor(add(A, B)))
% 3.42/3.48 equalish(multiply(A, n0), n0)
% 3.42/3.48 equalish(multiply(A, successor(B)), add(multiply(A, B), A))
% 3.42/3.48 equalish(successor(A), successor(B)) ==> equalish(A, B)
% 3.42/3.48 equalish(A, B) ==> equalish(successor(A), successor(B))
% 3.42/3.48 less(A, B) & less(C, A) ==> less(C, B)
% 3.42/3.48 equalish(add(successor(A), B), C) ==> less(B, C)
% 3.42/3.48 less(A, B) ==> equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)
% 3.42/3.48 equalish(X, X)
% 3.42/3.48 equalish(X, Y) ==> equalish(Y, X)
% 3.42/3.48 equalish(X, Y) & equalish(Y, Z) ==> equalish(X, Z)
% 3.42/3.48 equalish(successor(A), n0) ==> \bottom
% 3.42/3.48 less(A, successor(A))
% 3.42/3.48 less(n0, successor(a)) ==> \bottom
% 3.42/3.48
% 3.42/3.48 This holds because
% 3.42/3.48
% 3.42/3.48 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.42/3.48
% 3.42/3.48 E:
% 3.42/3.48 equalish(X, X) = true__
% 3.42/3.48 equalish(add(A, n0), A) = true__
% 3.42/3.48 equalish(add(A, successor(B)), successor(add(A, B))) = true__
% 3.42/3.48 equalish(multiply(A, n0), n0) = true__
% 3.42/3.48 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) = true__
% 3.42/3.48 f1(equalish(successor(A), successor(B)), A, B) = true__
% 3.42/3.48 f1(true__, A, B) = equalish(A, B)
% 3.42/3.48 f10(equalish(successor(A), n0)) = true__
% 3.42/3.48 f10(true__) = false__
% 3.42/3.48 f11(less(n0, successor(a))) = true__
% 3.42/3.48 f11(true__) = false__
% 3.42/3.48 f2(equalish(A, B), A, B) = true__
% 3.42/3.48 f2(true__, A, B) = equalish(successor(A), successor(B))
% 3.42/3.48 f3(true__, C, B) = less(C, B)
% 3.42/3.48 f4(less(C, A), A, B, C) = true__
% 3.42/3.48 f4(true__, A, B, C) = f3(less(A, B), C, B)
% 3.42/3.48 f5(equalish(add(successor(A), B), C), B, C) = true__
% 3.42/3.48 f5(true__, B, C) = less(B, C)
% 3.42/3.48 f6(less(A, B), B, A) = true__
% 3.42/3.48 f6(true__, B, A) = equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)
% 3.42/3.48 f7(equalish(X, Y), Y, X) = true__
% 3.42/3.48 f7(true__, Y, X) = equalish(Y, X)
% 3.42/3.48 f8(true__, X, Z) = equalish(X, Z)
% 3.42/3.48 f9(equalish(Y, Z), X, Y, Z) = true__
% 3.42/3.48 f9(true__, X, Y, Z) = f8(equalish(X, Y), X, Z)
% 3.42/3.48 less(A, successor(A)) = true__
% 3.42/3.48 G:
% 3.42/3.48 true__ = false__
% 3.42/3.48
% 3.42/3.48 This holds because
% 3.42/3.48
% 3.42/3.48 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.42/3.48
% 3.42/3.48
% 3.42/3.48 equalish(A, B) -> f1(true__, A, B)
% 3.42/3.48 equalish(X, X) -> true__
% 3.42/3.48 equalish(add(A, n0), A) -> true__
% 3.42/3.48 equalish(add(A, successor(B)), successor(add(A, B))) -> true__
% 3.42/3.48 equalish(multiply(A, n0), n0) -> true__
% 3.42/3.48 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) -> true__
% 3.42/3.48 f1(equalish(successor(A), successor(B)), A, B) -> true__
% 3.42/3.48 f1(f1(true__, successor(Y0), successor(Y1)), Y0, Y1) -> true__
% 3.42/3.48 f1(true__, Y1, Y1) -> true__
% 3.42/3.48 f1(true__, Y1, add(Y1, n0)) -> true__
% 3.42/3.48 f1(true__, add(Y0, successor(Y1)), successor(add(Y0, Y1))) -> true__
% 3.42/3.48 f1(true__, add(Y1, n0), Y1) -> true__
% 3.42/3.48 f1(true__, add(add(Y1, n0), n0), Y1) -> true__
% 3.42/3.48 f1(true__, add(add(Y1, successor(Y2)), n0), successor(add(Y1, Y2))) -> true__
% 3.42/3.48 f1(true__, add(multiply(X0, X1), X0), multiply(X0, successor(X1))) -> true__
% 3.42/3.48 f1(true__, add(multiply(Y1, n0), n0), n0) -> true__
% 3.42/3.48 f1(true__, add(multiply(Y1, successor(Y2)), n0), add(multiply(Y1, Y2), Y1)) -> true__
% 3.42/3.48 f1(true__, add(successor(predecessor_of_1st_minus_2nd(add(successor(X1), Y0), Y0)), Y0), add(successor(X1), Y0)) -> true__
% 3.42/3.48 f1(true__, add(successor(predecessor_of_1st_minus_2nd(successor(X0), n0)), n0), successor(X0)) -> true__
% 3.42/3.48 f1(true__, add(successor(predecessor_of_1st_minus_2nd(successor(Y0), Y0)), Y0), successor(Y0)) -> true__
% 3.42/3.48 f1(true__, add(successor(predecessor_of_1st_minus_2nd(successor(add(successor(X1), X0)), successor(X0))), successor(X0)), successor(add(successor(X1), X0))) -> true__
% 3.42/3.48 f1(true__, multiply(X0, n0), n0) -> true__
% 3.42/3.48 f1(true__, multiply(Y0, successor(Y1)), add(multiply(Y0, Y1), Y0)) -> true__
% 3.42/3.48 f1(true__, multiply(n0, successor(X1)), multiply(n0, X1)) -> true__
% 3.42/3.48 f1(true__, multiply(successor(Y2), successor(X1)), successor(add(multiply(successor(Y2), X1), Y2))) -> true__
% 3.42/3.48 f1(true__, n0, multiply(X0, n0)) -> true__
% 3.42/3.48 f1(true__, successor(X0), add(successor(predecessor_of_1st_minus_2nd(successor(X0), X0)), X0)) -> true__
% 3.42/3.48 f1(true__, successor(Y0), successor(add(Y0, n0))) -> true__
% 3.42/3.48 f1(true__, successor(Y1), successor(Y1)) -> true__
% 3.42/3.48 f1(true__, successor(add(X0, X1)), add(X0, successor(X1))) -> true__
% 3.42/3.48 f1(true__, successor(add(X0, successor(X1))), successor(successor(add(X0, X1)))) -> true__
% 3.42/3.48 f1(true__, successor(add(Y1, n0)), successor(Y1)) -> true__
% 3.42/3.48 f1(true__, successor(add(multiply(X0, X1), X0)), successor(multiply(X0, successor(X1)))) -> true__
% 3.42/3.48 f1(true__, successor(add(successor(predecessor_of_1st_minus_2nd(successor(X0), X0)), X0)), successor(successor(X0))) -> true__
% 3.42/3.48 f1(true__, successor(multiply(X0, n0)), successor(n0)) -> true__
% 3.42/3.48 f1(true__, successor(multiply(X0, successor(X1))), successor(add(multiply(X0, X1), X0))) -> true__
% 3.42/3.48 f1(true__, successor(n0), successor(multiply(X0, n0))) -> true__
% 3.42/3.48 f1(true__, successor(successor(add(X0, X1))), successor(add(X0, successor(X1)))) -> true__
% 3.42/3.48 f1(true__, successor(successor(add(X0, n0))), successor(successor(X0))) -> true__
% 3.42/3.48 f1(true__, successor(successor(add(X0, successor(X1)))), successor(successor(successor(add(X0, X1))))) -> true__
% 3.42/3.48 f1(true__, successor(successor(multiply(X0, n0))), successor(successor(n0))) -> true__
% 3.42/3.48 f1(true__, successor(successor(multiply(X0, successor(X1)))), successor(successor(add(multiply(X0, X1), X0)))) -> true__
% 3.42/3.48 f10(equalish(successor(A), n0)) -> true__
% 3.42/3.48 f10(f1(true__, successor(Y0), n0)) -> true__
% 3.42/3.48 f10(true__) -> false__
% 3.42/3.48 f11(f3(true__, n0, successor(a))) -> true__
% 3.42/3.48 f11(less(n0, successor(a))) -> true__
% 3.42/3.48 f11(true__) -> false__
% 3.42/3.48 f2(equalish(A, B), A, B) -> true__
% 3.42/3.48 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__
% 3.42/3.48 f2(true__, A, B) -> equalish(successor(A), successor(B))
% 3.42/3.48 f3(f3(true__, add(successor(X1), Y0), Y2), Y0, Y2) -> true__
% 3.42/3.48 f3(f3(true__, successor(X0), Y2), n0, Y2) -> true__
% 3.42/3.48 f3(f3(true__, successor(Y0), Y2), Y0, Y2) -> true__
% 3.42/3.48 f3(f3(true__, successor(add(successor(X1), X0)), Y2), successor(X0), Y2) -> true__
% 3.42/3.48 f3(true__, Y0, add(successor(X1), successor(Y0))) -> true__
% 3.42/3.48 f3(true__, Y0, successor(Y0)) -> true__
% 3.42/3.48 f3(true__, Y0, successor(add(successor(X1), Y0))) -> true__
% 3.42/3.48 f3(true__, Y0, successor(successor(Y0))) -> true__
% 3.42/3.48 f3(true__, Y1, add(add(successor(Y0), Y1), n0)) -> true__
% 3.42/3.48 f3(true__, Y1, add(successor(Y0), Y1)) -> true__
% 3.42/3.48 f3(true__, n0, successor(Y0)) -> true__
% 3.42/3.48 f3(true__, successor(X1), successor(add(successor(Y0), X1))) -> true__
% 3.42/3.48 f4(f3(true__, Y0, Y1), Y1, Y2, Y0) -> true__
% 3.42/3.48 f4(less(C, A), A, B, C) -> true__
% 3.42/3.48 f4(true__, A, B, C) -> f3(less(A, B), C, B)
% 3.42/3.48 f5(equalish(add(successor(A), B), C), B, C) -> true__
% 3.42/3.48 f5(f1(true__, add(successor(Y0), Y1), Y2), Y1, Y2) -> true__
% 3.42/3.48 f5(true__, B, C) -> less(B, C)
% 3.42/3.48 f6(f3(true__, Y0, Y1), Y1, Y0) -> true__
% 3.42/3.48 f6(less(A, B), B, A) -> true__
% 3.42/3.48 f6(true__, B, A) -> equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)
% 3.42/3.48 f7(equalish(X, Y), Y, X) -> true__
% 3.42/3.48 f7(f1(true__, Y0, Y1), Y1, Y0) -> true__
% 3.42/3.48 f7(true__, Y, X) -> equalish(Y, X)
% 3.42/3.48 f8(f1(true__, Y2, Y0), Y2, add(Y0, n0)) -> true__
% 3.42/3.48 f8(f1(true__, Y2, Y1), Y2, Y1) -> true__
% 3.42/3.48 f8(f1(true__, Y2, add(X0, successor(X1))), Y2, successor(add(X0, X1))) -> true__
% 3.42/3.48 f8(f1(true__, Y2, add(Y1, n0)), Y2, Y1) -> true__
% 3.42/3.48 f8(f1(true__, Y2, add(multiply(X0, X1), X0)), Y2, multiply(X0, successor(X1))) -> true__
% 3.42/3.48 f8(f1(true__, Y2, add(successor(predecessor_of_1st_minus_2nd(successor(X0), X0)), X0)), Y2, successor(X0)) -> true__
% 3.42/3.48 f8(f1(true__, Y2, multiply(X0, n0)), Y2, n0) -> true__
% 3.42/3.48 f8(f1(true__, Y2, multiply(X0, successor(X1))), Y2, add(multiply(X0, X1), X0)) -> true__
% 3.42/3.48 f8(f1(true__, Y2, n0), Y2, multiply(X0, n0)) -> true__
% 3.42/3.48 f8(f1(true__, Y2, successor(add(X0, X1))), Y2, add(X0, successor(X1))) -> true__
% 3.42/3.48 f8(f1(true__, Y2, successor(add(X0, n0))), Y2, successor(X0)) -> true__
% 3.42/3.48 f8(f1(true__, Y2, successor(add(X0, successor(X1)))), Y2, successor(successor(add(X0, X1)))) -> true__
% 3.42/3.48 f8(f1(true__, Y2, successor(multiply(X0, n0))), Y2, successor(n0)) -> true__
% 3.42/3.48 f8(f1(true__, Y2, successor(multiply(X0, successor(X1)))), Y2, successor(add(multiply(X0, X1), X0))) -> true__
% 3.42/3.48 f8(true__, X, Z) -> equalish(X, Z)
% 3.42/3.48 f9(equalish(Y, Z), X, Y, Z) -> true__
% 3.42/3.48 f9(f1(true__, Y0, Y1), Y2, Y0, Y1) -> true__
% 3.42/3.48 f9(true__, X, Y, Z) -> f8(equalish(X, Y), X, Z)
% 3.42/3.48 false__ -> true__
% 3.42/3.48 less(A, successor(A)) -> true__
% 3.42/3.48 less(C, B) -> f3(true__, C, B)
% 3.42/3.48 with the LPO induced by
% 3.42/3.48 a > f11 > f10 > f2 > f9 > f6 > f8 > f7 > equalish > f1 > predecessor_of_1st_minus_2nd > add > f5 > f4 > less > f3 > multiply > n0 > successor > false__ > true__
% 3.42/3.48
% 3.42/3.48 % SZS output end Proof
% 3.42/3.48
%------------------------------------------------------------------------------