TSTP Solution File: GRP467-1 by Moca---0.1
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% File : Moca---0.1
% Problem : GRP467-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n006.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 : Sat Jul 16 10:55:39 EDT 2022
% Result : Unsatisfiable 2.01s 2.15s
% Output : Proof 2.01s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP467-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 02:05:26 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.01/2.15 % SZS status Unsatisfiable
% 2.01/2.15 % SZS output start Proof
% 2.01/2.15 The input problem is unsatisfiable because
% 2.01/2.15
% 2.01/2.15 [1] the following set of Horn clauses is unsatisfiable:
% 2.01/2.15
% 2.01/2.15 divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D)))) = C
% 2.01/2.15 multiply(A, B) = divide(A, inverse(B))
% 2.01/2.15 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 2.01/2.15
% 2.01/2.15 This holds because
% 2.01/2.15
% 2.01/2.15 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.01/2.15
% 2.01/2.15 E:
% 2.01/2.15 divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D)))) = C
% 2.01/2.15 f1(a2) = false__
% 2.01/2.15 f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 2.01/2.15 multiply(A, B) = divide(A, inverse(B))
% 2.01/2.15 G:
% 2.01/2.15 true__ = false__
% 2.01/2.15
% 2.01/2.15 This holds because
% 2.01/2.15
% 2.01/2.15 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.01/2.15
% 2.01/2.15 divide(g1, divide(Y1, Y3)) = divide(Y3, Y1)
% 2.01/2.15 divide(g1, divide(inverse(Y1), Y3)) = divide(Y3, inverse(Y1))
% 2.01/2.15 divide(X0, X0) -> g1
% 2.01/2.15 divide(divide(Y0, Y0), divide(divide(X1, divide(divide(X2, divide(X3, X1)), inverse(X3))), divide(divide(Y2, X2), inverse(divide(X0, X0))))) -> Y2
% 2.01/2.15 divide(g1, divide(Y0, divide(divide(Y0, Y1), inverse(Y1)))) -> g1
% 2.01/2.15 divide(g1, divide(Y1, divide(divide(Y2, divide(Y3, Y1)), inverse(Y3)))) -> Y2
% 2.01/2.15 divide(g1, divide(Y1, divide(divide(Y2, g1), inverse(Y1)))) -> Y2
% 2.01/2.15 divide(g1, divide(divide(X0, divide(g1, inverse(X1))), divide(divide(Y1, divide(X1, X0)), inverse(g1)))) -> Y1
% 2.01/2.15 divide(g1, divide(divide(divide(Y0, g1), inverse(Y2)), divide(Y0, inverse(Y2)))) -> g1
% 2.01/2.15 divide(g1, divide(divide(divide(Y1, divide(Y2, Y3)), inverse(Y2)), divide(Y1, inverse(Y3)))) -> g1
% 2.01/2.15 divide(g1, divide(divide(divide(Y1, divide(Y2, inverse(X1))), inverse(Y2)), divide(Y1, inverse(inverse(X1))))) -> g1
% 2.01/2.15 divide(g1, divide(divide(divide(inverse(Y2), divide(Y1, Y2)), inverse(Y1)), g1)) -> g1
% 2.01/2.15 divide(g1, divide(divide(divide(inverse(false__), g1), inverse(false__)), g1)) -> g1
% 2.01/2.15 divide(g1, divide(divide(g1, Y1), inverse(Y1))) -> g1
% 2.01/2.15 divide(g1, divide(divide(g1, inverse(Y1)), divide(divide(Y1, Y2), inverse(Y2)))) -> g1
% 2.01/2.15 divide(g1, divide(g1, divide(Y1, Y0))) -> divide(Y1, Y0)
% 2.01/2.15 divide(g1, divide(g1, divide(Y1, inverse(Y0)))) -> divide(Y1, inverse(Y0))
% 2.01/2.15 divide(g1, divide(g1, divide(inverse(X1), Y0))) -> divide(inverse(X1), Y0)
% 2.01/2.15 divide(g1, divide(inverse(X0), divide(divide(Y1, X0), inverse(g1)))) -> Y1
% 2.01/2.15 divide(g1, inverse(Y1)) -> Y1
% 2.01/2.15 f1(a2) -> false__
% 2.01/2.15 f1(divide(g1, inverse(a2))) -> true__
% 2.01/2.15 multiply(A, B) -> divide(A, inverse(B))
% 2.01/2.15 true__ -> false__
% 2.01/2.15 with the LPO induced by
% 2.01/2.15 b2 > multiply > inverse > divide > g1 > a2 > f1 > true__ > false__
% 2.01/2.15
% 2.01/2.15 % SZS output end Proof
% 2.01/2.15
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