TSTP Solution File: ALG235-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : ALG235-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n029.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 : Thu Jul 14 17:41:54 EDT 2022
% Result : Unsatisfiable 0.90s 1.12s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG235-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n029.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 16:08:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.90/1.12 % SZS status Unsatisfiable
% 0.90/1.12 % SZS output start Proof
% 0.90/1.12 The input problem is unsatisfiable because
% 0.90/1.12
% 0.90/1.12 [1] the following set of Horn clauses is unsatisfiable:
% 0.90/1.12
% 0.90/1.12 mult(A, mult(B, mult(A, B))) = mult(A, B)
% 0.90/1.12 mult(A, mult(B, mult(C, D))) = mult(C, mult(B, mult(A, D)))
% 0.90/1.12 mult(mult(A, mult(B, mult(C, B))), D) = mult(A, mult(D, mult(mult(C, B), D)))
% 0.90/1.12 mult(a, mult(b, mult(a, mult(c, mult(d, c))))) = mult(a, mult(b, mult(d, c))) ==> \bottom
% 0.90/1.12
% 0.90/1.12 This holds because
% 0.90/1.12
% 0.90/1.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.90/1.12
% 0.90/1.12 E:
% 0.90/1.12 f1(mult(a, mult(b, mult(a, mult(c, mult(d, c)))))) = true__
% 0.90/1.12 f1(mult(a, mult(b, mult(d, c)))) = false__
% 0.90/1.12 mult(A, mult(B, mult(A, B))) = mult(A, B)
% 0.90/1.12 mult(A, mult(B, mult(C, D))) = mult(C, mult(B, mult(A, D)))
% 0.90/1.12 mult(mult(A, mult(B, mult(C, B))), D) = mult(A, mult(D, mult(mult(C, B), D)))
% 0.90/1.12 G:
% 0.90/1.12 true__ = false__
% 0.90/1.12
% 0.90/1.12 This holds because
% 0.90/1.12
% 0.90/1.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.90/1.12
% 0.90/1.12 mult(A, mult(B, mult(C, D))) = mult(C, mult(B, mult(A, D)))
% 0.90/1.12 mult(Y0, mult(X2, mult(Y2, mult(Y1, X3)))) = mult(Y2, mult(Y1, mult(Y0, mult(X2, X3))))
% 0.90/1.12 mult(Y0, mult(Y1, mult(X2, mult(X1, mult(Y2, X3))))) = mult(Y2, mult(Y1, mult(Y0, mult(X1, mult(X2, X3)))))
% 0.90/1.12 mult(Y0, mult(Y1, mult(Y2, X1))) = mult(Y2, mult(Y1, mult(Y0, mult(X1, mult(Y2, X1)))))
% 0.90/1.12 mult(mult(A, mult(B, mult(C, B))), D) = mult(A, mult(D, mult(mult(C, B), D)))
% 0.90/1.12 mult(mult(Y0, mult(mult(X1, mult(Y2, X1)), mult(Y2, X1))), Y3) = mult(Y0, mult(Y3, mult(mult(Y2, X1), Y3)))
% 0.90/1.12 f1(mult(a, mult(b, mult(a, mult(c, mult(d, c)))))) -> true__
% 0.90/1.12 f1(mult(a, mult(b, mult(d, c)))) -> false__
% 0.90/1.12 mult(A, mult(B, mult(A, B))) -> mult(A, B)
% 0.90/1.12 mult(Y0, mult(X1, mult(X2, mult(mult(X1, mult(X2, X3)), mult(Y0, X3))))) -> mult(Y0, mult(X1, mult(X2, X3)))
% 0.90/1.12 mult(Y0, mult(X1, mult(X2, mult(mult(X1, mult(X2, mult(X1, Y0))), Y0)))) -> mult(X2, mult(X1, Y0))
% 0.90/1.12 mult(Y0, mult(X2, mult(Y0, mult(mult(X2, X3), X3)))) -> mult(Y0, mult(X2, X3))
% 0.90/1.12 mult(Y0, mult(mult(X1, mult(Y0, X1)), mult(Y0, X1))) -> mult(Y0, X1)
% 0.90/1.12 mult(Y0, mult(mult(mult(X1, mult(Y0, X1)), mult(Y0, X1)), mult(Y0, X1))) -> mult(Y0, X1)
% 0.90/1.12 mult(Y2, mult(Y1, mult(Y0, mult(Y1, Y2)))) -> mult(Y0, mult(Y1, Y2))
% 0.90/1.12 mult(Y2, mult(Y3, mult(mult(Y2, Y1), Y3))) -> mult(mult(Y2, Y1), Y3)
% 0.90/1.12 mult(mult(X1, mult(Y1, X1)), mult(Y1, mult(Y2, mult(Y1, X1)))) -> mult(Y2, mult(Y1, X1))
% 0.90/1.12 mult(mult(Y2, Y1), Y1) -> mult(Y2, Y1)
% 0.90/1.12 true__ -> false__
% 0.90/1.12 with the LPO induced by
% 0.90/1.12 c > d > b > a > f1 > mult > true__ > false__
% 0.90/1.12
% 0.90/1.12 % SZS output end Proof
% 0.90/1.12
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