TSTP Solution File: GRP017-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP017-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n028.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 10:51:51 EDT 2022
% Result : Unsatisfiable 8.64s 8.61s
% Output : Proof 8.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP017-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 12:46:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 8.64/8.61 % SZS status Unsatisfiable
% 8.64/8.61 % SZS output start Proof
% 8.64/8.61 The input problem is unsatisfiable because
% 8.64/8.61
% 8.64/8.61 [1] the following set of Horn clauses is unsatisfiable:
% 8.64/8.61
% 8.64/8.61 product(identity, X, X)
% 8.64/8.61 product(X, identity, X)
% 8.64/8.61 product(inverse(X), X, identity)
% 8.64/8.61 product(X, inverse(X), identity)
% 8.64/8.61 product(X, Y, multiply(X, Y))
% 8.64/8.61 product(X, Y, Z) & product(X, Y, W) ==> Z = W
% 8.64/8.61 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W)
% 8.64/8.61 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W)
% 8.64/8.61 product(a, b, identity)
% 8.64/8.61 product(b, a, identity)
% 8.64/8.61 product(a, c, identity)
% 8.64/8.61 product(c, a, identity)
% 8.64/8.61 b = c ==> \bottom
% 8.64/8.61
% 8.64/8.61 This holds because
% 8.64/8.61
% 8.64/8.61 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.64/8.61
% 8.64/8.61 E:
% 8.64/8.61 f1(true__, Z, W) = Z
% 8.64/8.61 f2(product(X, Y, W), X, Y, Z, W) = W
% 8.64/8.61 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W)
% 8.64/8.61 f3(true__, X, V, W) = product(X, V, W)
% 8.64/8.61 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W)
% 8.64/8.61 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__
% 8.64/8.61 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W)
% 8.64/8.61 f6(true__, U, Z, W) = product(U, Z, W)
% 8.64/8.61 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W)
% 8.64/8.61 f8(product(X, V, W), Y, Z, V, X, U, W) = true__
% 8.64/8.61 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W)
% 8.64/8.61 f9(b) = true__
% 8.64/8.61 f9(c) = false__
% 8.64/8.61 product(X, Y, multiply(X, Y)) = true__
% 8.64/8.61 product(X, identity, X) = true__
% 8.64/8.61 product(X, inverse(X), identity) = true__
% 8.64/8.61 product(a, b, identity) = true__
% 8.64/8.61 product(a, c, identity) = true__
% 8.64/8.61 product(b, a, identity) = true__
% 8.64/8.61 product(c, a, identity) = true__
% 8.64/8.61 product(identity, X, X) = true__
% 8.64/8.61 product(inverse(X), X, identity) = true__
% 8.64/8.61 G:
% 8.64/8.61 true__ = false__
% 8.64/8.61
% 8.64/8.61 This holds because
% 8.64/8.61
% 8.64/8.61 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.64/8.61
% 8.64/8.61
% 8.64/8.61 b -> inverse(a)
% 8.64/8.61 c -> b
% 8.64/8.61 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1)
% 8.64/8.61 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity
% 8.64/8.61 f1(f3(true__, Y2, identity, Y3), Y3, Y2) -> Y2
% 8.64/8.61 f1(f3(true__, a, b, Y3), Y3, identity) -> identity
% 8.64/8.61 f1(f3(true__, a, c, Y3), Y3, identity) -> identity
% 8.64/8.61 f1(f3(true__, b, a, Y3), Y3, identity) -> identity
% 8.64/8.61 f1(f3(true__, c, a, Y3), Y3, identity) -> identity
% 8.64/8.61 f1(f3(true__, c, identity, Y3), Y3, b) -> b
% 8.64/8.61 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2
% 8.64/8.61 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity
% 8.64/8.61 f1(true__, Z, W) -> Z
% 8.64/8.61 f2(f3(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> Y2
% 8.64/8.61 f2(product(X, Y, W), X, Y, Z, W) -> W
% 8.64/8.61 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W)
% 8.64/8.61 f3(f3(true__, Y0, a, identity), Y0, identity, inverse(a)) -> true__
% 8.64/8.61 f3(f3(true__, Y0, identity, a), Y0, inverse(a), identity) -> true__
% 8.64/8.61 f3(f3(true__, Y0, inverse(a), identity), Y0, identity, a) -> true__
% 8.64/8.61 f3(f3(true__, Y2, Y1, Y3), Y2, Y1, Y3) -> true__
% 8.64/8.61 f3(f3(true__, Y2, identity, Y3), Y2, identity, Y3) -> true__
% 8.64/8.61 f3(f3(true__, Y2, identity, a), Y2, b, identity) -> true__
% 8.64/8.61 f3(f3(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__
% 8.64/8.61 f3(f3(true__, Y3, a, identity), Y3, identity, b) -> true__
% 8.64/8.61 f3(f3(true__, Y3, b, identity), Y3, identity, a) -> true__
% 8.64/8.61 f3(f3(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__
% 8.64/8.61 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__
% 8.64/8.61 f3(true__, Y0, inverse(Y0), identity) -> true__
% 8.64/8.61 f3(true__, Y2, identity, Y2) -> true__
% 8.64/8.61 f3(true__, a, b, identity) -> true__
% 8.64/8.61 f3(true__, a, c, identity) -> true__
% 8.64/8.61 f3(true__, b, a, identity) -> true__
% 8.64/8.61 f3(true__, b, identity, c) -> true__
% 8.64/8.61 f3(true__, b, identity, inverse(a)) -> true__
% 8.64/8.61 f3(true__, c, a, identity) -> true__
% 8.64/8.61 f3(true__, c, identity, b) -> true__
% 8.64/8.61 f3(true__, identity, Y2, Y2) -> true__
% 8.64/8.61 f3(true__, inverse(Y1), Y1, identity) -> true__
% 8.64/8.61 f3(true__, inverse(a), identity, b) -> true__
% 8.64/8.61 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__
% 8.64/8.61 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__
% 8.64/8.61 f4(f3(true__, Y3, a, Y4), Y5, Y3, b, Y4, identity) -> true__
% 8.64/8.61 f4(f3(true__, Y3, a, Y4), Y5, Y3, c, Y4, identity) -> true__
% 8.64/8.61 f4(f3(true__, Y3, b, Y4), Y5, Y3, a, Y4, identity) -> true__
% 8.64/8.61 f4(f3(true__, Y3, c, Y4), Y5, Y3, a, Y4, identity) -> true__
% 8.64/8.61 f4(f3(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__
% 8.64/8.61 f4(f3(true__, Y3, inverse(Y0), Y4), Y5, Y3, Y0, Y4, identity) -> true__
% 8.64/8.61 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W)
% 8.64/8.61 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__
% 8.64/8.61 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W)
% 8.64/8.61 f6(f3(true__, Y2, identity, Y3), Y3, identity, Y2) -> true__
% 8.64/8.61 f6(f3(true__, identity, Y2, Y3), Y3, identity, Y2) -> true__
% 8.64/8.61 f6(f3(true__, identity, a, Y0), Y0, inverse(a), identity) -> true__
% 8.64/8.61 f6(f3(true__, identity, a, Y3), Y3, b, identity) -> true__
% 8.64/8.61 f6(f3(true__, identity, b, Y3), Y3, a, identity) -> true__
% 8.64/8.61 f6(f3(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__
% 8.64/8.61 f6(f3(true__, identity, inverse(a), Y0), Y0, a, identity) -> true__
% 8.64/8.61 f6(true__, U, Z, W) -> product(U, Z, W)
% 8.64/8.61 f7(f3(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__
% 8.64/8.61 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__
% 8.64/8.61 f7(f3(true__, Y3, Y4, a), b, Y3, Y5, Y4, identity) -> true__
% 8.64/8.61 f7(f3(true__, Y3, Y4, a), c, Y3, Y5, Y4, identity) -> true__
% 8.64/8.61 f7(f3(true__, Y3, Y4, b), a, Y3, Y5, Y4, identity) -> true__
% 8.64/8.61 f7(f3(true__, Y3, Y4, c), a, Y3, Y5, Y4, identity) -> true__
% 8.64/8.61 f7(f3(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__
% 8.64/8.61 f7(f3(true__, Y3, Y4, inverse(Y0)), Y0, Y3, Y5, Y4, identity) -> true__
% 8.64/8.61 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W)
% 8.64/8.61 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__
% 8.64/8.61 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W)
% 8.64/8.61 f9(b) -> true__
% 8.64/8.61 f9(c) -> false__
% 8.64/8.61 f9(inverse(a)) -> true__
% 8.64/8.61 false__ -> true__
% 8.64/8.61 inverse(identity) -> identity
% 8.64/8.61 multiply(Y0, identity) -> Y0
% 8.64/8.61 multiply(Y0, inverse(Y0)) -> identity
% 8.64/8.61 multiply(a, b) -> identity
% 8.64/8.61 multiply(a, c) -> identity
% 8.64/8.61 multiply(b, a) -> identity
% 8.64/8.61 multiply(c, a) -> identity
% 8.64/8.61 multiply(identity, Y0) -> Y0
% 8.64/8.61 multiply(inverse(Y0), Y0) -> identity
% 8.64/8.61 product(X, V, W) -> f3(true__, X, V, W)
% 8.64/8.61 product(X, Y, multiply(X, Y)) -> true__
% 8.64/8.61 product(X, identity, X) -> true__
% 8.64/8.61 product(X, inverse(X), identity) -> true__
% 8.64/8.61 product(a, b, identity) -> true__
% 8.64/8.61 product(a, c, identity) -> true__
% 8.64/8.61 product(b, a, identity) -> true__
% 8.64/8.61 product(c, a, identity) -> true__
% 8.64/8.61 product(identity, X, X) -> true__
% 8.64/8.61 product(inverse(X), X, identity) -> true__
% 8.64/8.61 with the LPO induced by
% 8.64/8.61 f9 > c > b > a > f5 > f4 > f2 > f1 > f8 > f7 > f6 > product > f3 > multiply > inverse > identity > false__ > true__
% 8.64/8.61
% 8.64/8.61 % SZS output end Proof
% 8.64/8.61
%------------------------------------------------------------------------------