TSTP Solution File: NUM025-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : NUM025-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 : Mon Jul 18 12:32:16 EDT 2022
% Result : Unsatisfiable 2.23s 2.41s
% Output : Proof 2.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM025-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 : Tue Jul 5 14:10:02 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.23/2.41 % SZS status Unsatisfiable
% 2.23/2.41 % SZS output start Proof
% 2.23/2.41 The input problem is unsatisfiable because
% 2.23/2.41
% 2.23/2.41 [1] the following set of Horn clauses is unsatisfiable:
% 2.23/2.41
% 2.23/2.41 equalish(add(A, n0), A)
% 2.23/2.41 equalish(add(A, successor(B)), successor(add(A, B)))
% 2.23/2.41 equalish(multiply(A, n0), n0)
% 2.23/2.41 equalish(multiply(A, successor(B)), add(multiply(A, B), A))
% 2.23/2.41 equalish(successor(A), successor(B)) ==> equalish(A, B)
% 2.23/2.41 equalish(A, B) ==> equalish(successor(A), successor(B))
% 2.23/2.41 less(A, B) & less(C, A) ==> less(C, B)
% 2.23/2.41 equalish(add(successor(A), B), C) ==> less(B, C)
% 2.23/2.41 less(A, B) ==> equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)
% 2.23/2.41 equalish(X, X)
% 2.23/2.41 equalish(X, Y) ==> equalish(Y, X)
% 2.23/2.41 equalish(X, Y) & equalish(Y, Z) ==> equalish(X, Z)
% 2.23/2.41 equalish(successor(A), n0) ==> \bottom
% 2.23/2.41 less(A, A) ==> \bottom
% 2.23/2.41 less(a, b)
% 2.23/2.41 less(b, a)
% 2.23/2.41
% 2.23/2.41 This holds because
% 2.23/2.41
% 2.23/2.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.23/2.41
% 2.23/2.41 E:
% 2.23/2.41 equalish(X, X) = true__
% 2.23/2.41 equalish(add(A, n0), A) = true__
% 2.23/2.41 equalish(add(A, successor(B)), successor(add(A, B))) = true__
% 2.23/2.41 equalish(multiply(A, n0), n0) = true__
% 2.23/2.41 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) = true__
% 2.23/2.41 f1(equalish(successor(A), successor(B)), A, B) = true__
% 2.23/2.41 f1(true__, A, B) = equalish(A, B)
% 2.23/2.41 f10(equalish(successor(A), n0)) = true__
% 2.23/2.41 f10(true__) = false__
% 2.23/2.41 f11(less(A, A)) = true__
% 2.23/2.41 f11(true__) = false__
% 2.23/2.41 f2(equalish(A, B), A, B) = true__
% 2.23/2.41 f2(true__, A, B) = equalish(successor(A), successor(B))
% 2.23/2.41 f3(true__, C, B) = less(C, B)
% 2.23/2.41 f4(less(C, A), A, B, C) = true__
% 2.23/2.41 f4(true__, A, B, C) = f3(less(A, B), C, B)
% 2.23/2.41 f5(equalish(add(successor(A), B), C), B, C) = true__
% 2.23/2.41 f5(true__, B, C) = less(B, C)
% 2.23/2.41 f6(less(A, B), B, A) = true__
% 2.23/2.41 f6(true__, B, A) = equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)
% 2.23/2.41 f7(equalish(X, Y), Y, X) = true__
% 2.23/2.41 f7(true__, Y, X) = equalish(Y, X)
% 2.23/2.41 f8(true__, X, Z) = equalish(X, Z)
% 2.23/2.41 f9(equalish(Y, Z), X, Y, Z) = true__
% 2.23/2.41 f9(true__, X, Y, Z) = f8(equalish(X, Y), X, Z)
% 2.23/2.41 less(a, b) = true__
% 2.23/2.41 less(b, a) = true__
% 2.23/2.41 G:
% 2.23/2.41 true__ = false__
% 2.23/2.41
% 2.23/2.41 This holds because
% 2.23/2.41
% 2.23/2.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.23/2.41
% 2.23/2.41
% 2.23/2.41 equalish(A, B) -> f1(true__, A, B)
% 2.23/2.41 equalish(add(A, successor(B)), successor(add(A, B))) -> true__
% 2.23/2.41 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) -> true__
% 2.23/2.41 f1(equalish(successor(A), successor(B)), A, B) -> true__
% 2.23/2.41 f1(true__, Y1, Y1) -> true__
% 2.23/2.41 f1(true__, Y1, add(Y1, n0)) -> true__
% 2.23/2.41 f1(true__, add(Y1, n0), Y1) -> true__
% 2.23/2.41 f1(true__, add(successor(predecessor_of_1st_minus_2nd(a, b)), b), a) -> true__
% 2.23/2.41 f1(true__, add(successor(predecessor_of_1st_minus_2nd(b, a)), a), b) -> true__
% 2.23/2.41 f1(true__, add(successor(predecessor_of_1st_minus_2nd(b, b)), b), b) -> true__
% 2.23/2.41 f1(true__, multiply(X0, n0), n0) -> true__
% 2.23/2.41 f1(true__, n0, multiply(X0, n0)) -> true__
% 2.23/2.41 f1(true__, successor(Y0), successor(add(Y0, n0))) -> true__
% 2.23/2.41 f1(true__, successor(add(Y1, n0)), successor(Y1)) -> true__
% 2.23/2.41 f1(true__, successor(multiply(X0, n0)), successor(n0)) -> true__
% 2.23/2.41 f1(true__, successor(n0), successor(multiply(X0, n0))) -> true__
% 2.23/2.41 f10(f1(true__, successor(Y0), n0)) -> true__
% 2.23/2.41 f10(true__) -> false__
% 2.23/2.41 f11(f3(true__, Y0, Y0)) -> true__
% 2.23/2.41 f11(true__) -> false__
% 2.23/2.41 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__
% 2.23/2.41 f2(true__, A, B) -> f1(true__, successor(A), successor(B))
% 2.23/2.41 f3(f3(true__, a, Y2), b, Y2) -> true__
% 2.23/2.41 f3(f3(true__, b, Y2), a, Y2) -> true__
% 2.23/2.41 f3(f3(true__, b, Y2), b, Y2) -> true__
% 2.23/2.41 f3(true__, a, b) -> true__
% 2.23/2.41 f3(true__, b, a) -> true__
% 2.23/2.41 f3(true__, b, b) -> true__
% 2.23/2.41 f4(f3(true__, Y0, Y1), Y1, Y2, Y0) -> true__
% 2.23/2.41 f4(true__, A, B, C) -> f3(f3(true__, A, B), C, B)
% 2.23/2.41 f5(equalish(add(successor(A), B), C), B, C) -> true__
% 2.23/2.41 f5(true__, B, C) -> f3(true__, B, C)
% 2.23/2.41 f6(f3(true__, Y0, Y1), Y1, Y0) -> true__
% 2.23/2.41 f6(true__, B, A) -> f1(true__, add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)
% 2.23/2.41 f7(f1(true__, Y0, Y1), Y1, Y0) -> true__
% 2.23/2.41 f7(true__, Y, X) -> f1(true__, Y, X)
% 2.23/2.41 f8(f1(true__, Y2, Y1), Y2, Y1) -> true__
% 2.23/2.41 f8(true__, X, Z) -> f1(true__, X, Z)
% 2.23/2.41 f9(f1(true__, Y0, Y1), Y2, Y0, Y1) -> true__
% 2.23/2.41 f9(true__, X, Y, Z) -> f8(f1(true__, X, Y), X, Z)
% 2.23/2.41 less(C, B) -> f3(true__, C, B)
% 2.23/2.41 true__ -> false__
% 2.23/2.41 with the LPO induced by
% 2.23/2.41 f10 > f6 > predecessor_of_1st_minus_2nd > a > f9 > f8 > f7 > f2 > successor > equalish > f1 > multiply > n0 > f4 > add > f5 > less > f3 > b > f11 > true__ > false__
% 2.23/2.41
% 2.23/2.41 % SZS output end Proof
% 2.23/2.41
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