TSTP Solution File: SYO691-1.000 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SYO691-1.000 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n012.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 21 18:46:34 EDT 2022
% Result : Unsatisfiable 9.82s 9.87s
% Output : Proof 9.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO691-1.000 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n012.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 : Fri Jul 8 18:56:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.82/9.87 % SZS status Unsatisfiable
% 9.82/9.87 % SZS output start Proof
% 9.82/9.87 The input problem is unsatisfiable because
% 9.82/9.87
% 9.82/9.87 [1] the following set of Horn clauses is unsatisfiable:
% 9.82/9.87
% 9.82/9.87 top(f(f(Z, Y), f(X, a)), f(f(X, f(Y, a)), Z))
% 9.82/9.87 seq(succ(succ(succ(zero))), X, X) ==> \bottom
% 9.82/9.87 top(X, Y) ==> step(X, Y)
% 9.82/9.87 step(X, Y) ==> step(f(X, Z), f(Y, Z))
% 9.82/9.87 step(Y, Z) ==> step(f(X, Y), f(X, Z))
% 9.82/9.87 seq(zero, X, X)
% 9.82/9.87 seq(N, X, Y) & step(Y, Z) ==> seq(succ(N), X, Z)
% 9.82/9.87
% 9.82/9.87 This holds because
% 9.82/9.87
% 9.82/9.87 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 9.82/9.87
% 9.82/9.87 E:
% 9.82/9.87 f1(seq(succ(succ(succ(zero))), X, X)) = true__
% 9.82/9.87 f1(true__) = false__
% 9.82/9.87 f2(top(X, Y), X, Y) = true__
% 9.82/9.87 f2(true__, X, Y) = step(X, Y)
% 9.82/9.87 f3(step(X, Y), X, Z, Y) = true__
% 9.82/9.87 f3(true__, X, Z, Y) = step(f(X, Z), f(Y, Z))
% 9.82/9.87 f4(step(Y, Z), X, Y, Z) = true__
% 9.82/9.87 f4(true__, X, Y, Z) = step(f(X, Y), f(X, Z))
% 9.82/9.87 f5(true__, N, X, Z) = seq(succ(N), X, Z)
% 9.82/9.87 f6(step(Y, Z), N, X, Y, Z) = true__
% 9.82/9.87 f6(true__, N, X, Y, Z) = f5(seq(N, X, Y), N, X, Z)
% 9.82/9.87 seq(zero, X, X) = true__
% 9.82/9.87 top(f(f(Z, Y), f(X, a)), f(f(X, f(Y, a)), Z)) = true__
% 9.82/9.87 G:
% 9.82/9.87 true__ = false__
% 9.82/9.87
% 9.82/9.87 This holds because
% 9.82/9.87
% 9.82/9.87 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 9.82/9.87
% 9.82/9.87
% 9.82/9.87 f1(seq(succ(succ(succ(zero))), X, X)) -> true__
% 9.82/9.87 f1(true__) -> false__
% 9.82/9.87 f2(top(X, Y), X, Y) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(X0, f(X1, f(X2, f(f(X3, X4), f(X5, a)))))), f(Y2, f(X0, f(X1, f(X2, f(f(X5, f(X4, a)), X3)))))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(X0, f(X1, f(f(X2, X3), f(X4, a))))), f(Y2, f(X0, f(X1, f(f(X4, f(X3, a)), X2))))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(X0, f(X1, f(f(f(X2, X3), f(X4, a)), X5)))), f(Y2, f(X0, f(X1, f(f(f(X4, f(X3, a)), X2), X5))))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(X0, f(f(X1, X2), f(X3, a)))), f(Y2, f(X0, f(f(X3, f(X2, a)), X1)))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(X0, f(f(X1, f(f(X2, X3), f(X4, a))), X5))), f(Y2, f(X0, f(f(X1, f(f(X4, f(X3, a)), X2)), X5)))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(X0, f(f(f(X1, X2), f(X3, a)), X4))), f(Y2, f(X0, f(f(f(X3, f(X2, a)), X1), X4)))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(X0, f(f(f(f(X1, X2), f(X3, a)), X4), X5))), f(Y2, f(X0, f(f(f(f(X3, f(X2, a)), X1), X4), X5)))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(f(X0, X1), f(X2, a))), f(Y2, f(f(X2, f(X1, a)), X0))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(f(X0, f(X1, f(f(X2, X3), f(X4, a)))), X5)), f(Y2, f(f(X0, f(X1, f(f(X4, f(X3, a)), X2))), X5))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(f(X0, f(f(X1, X2), f(X3, a))), X4)), f(Y2, f(f(X0, f(f(X3, f(X2, a)), X1)), X4))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(f(X0, f(f(f(X1, X2), f(X3, a)), X4)), X5)), f(Y2, f(f(X0, f(f(f(X3, f(X2, a)), X1), X4)), X5))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(f(f(X0, X1), f(X2, a)), X3)), f(Y2, f(f(f(X2, f(X1, a)), X0), X3))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(f(f(X0, f(f(X1, X2), f(X3, a))), X4), X5)), f(Y2, f(f(f(X0, f(f(X3, f(X2, a)), X1)), X4), X5))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(f(f(f(X0, X1), f(X2, a)), X3), X4)), f(Y2, f(f(f(f(X2, f(X1, a)), X0), X3), X4))) -> true__
% 9.82/9.87 f2(true__, f(Y2, f(f(f(f(f(X0, X1), f(X2, a)), X3), X4), X5)), f(Y2, f(f(f(f(f(X2, f(X1, a)), X0), X3), X4), X5))) -> true__
% 9.82/9.87 f2(true__, f(f(X0, X1), f(X2, a)), f(f(X2, f(X1, a)), X0)) -> true__
% 9.82/9.87 f2(true__, f(f(X0, f(X1, f(X2, f(f(X3, X4), f(X5, a))))), Y2), f(f(X0, f(X1, f(X2, f(f(X5, f(X4, a)), X3)))), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(X0, f(X1, f(f(X2, X3), f(X4, a)))), Y2), f(f(X0, f(X1, f(f(X4, f(X3, a)), X2))), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(X0, f(X1, f(f(f(X2, X3), f(X4, a)), X5))), Y2), f(f(X0, f(X1, f(f(f(X4, f(X3, a)), X2), X5))), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(X0, f(f(X1, X2), f(X3, a))), Y2), f(f(X0, f(f(X3, f(X2, a)), X1)), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(X0, f(f(X1, f(f(X2, X3), f(X4, a))), X5)), Y2), f(f(X0, f(f(X1, f(f(X4, f(X3, a)), X2)), X5)), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(X0, f(f(f(X1, X2), f(X3, a)), X4)), Y2), f(f(X0, f(f(f(X3, f(X2, a)), X1), X4)), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(X0, f(f(f(f(X1, X2), f(X3, a)), X4), X5)), Y2), f(f(X0, f(f(f(f(X3, f(X2, a)), X1), X4), X5)), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(f(X0, X1), f(X2, a)), Y2), f(f(f(X2, f(X1, a)), X0), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(f(X0, f(X1, f(f(X2, X3), f(X4, a)))), X5), Y2), f(f(f(X0, f(X1, f(f(X4, f(X3, a)), X2))), X5), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(f(X0, f(f(X1, X2), f(X3, a))), X4), Y2), f(f(f(X0, f(f(X3, f(X2, a)), X1)), X4), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(f(X0, f(f(f(X1, X2), f(X3, a)), X4)), X5), Y2), f(f(f(X0, f(f(f(X3, f(X2, a)), X1), X4)), X5), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(f(f(X0, X1), f(X2, a)), X3), Y2), f(f(f(f(X2, f(X1, a)), X0), X3), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(f(f(X0, f(f(X1, X2), f(X3, a))), X4), X5), Y2), f(f(f(f(X0, f(f(X3, f(X2, a)), X1)), X4), X5), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(f(f(f(X0, X1), f(X2, a)), X3), X4), Y2), f(f(f(f(f(X2, f(X1, a)), X0), X3), X4), Y2)) -> true__
% 9.82/9.87 f2(true__, f(f(f(f(f(f(X0, X1), f(X2, a)), X3), X4), X5), Y2), f(f(f(f(f(f(X2, f(X1, a)), X0), X3), X4), X5), Y2)) -> true__
% 9.82/9.87 f3(f2(true__, Y0, Y1), Y0, Y2, Y1) -> true__
% 9.82/9.87 f3(step(X, Y), X, Z, Y) -> true__
% 9.82/9.87 f3(true__, X, Z, Y) -> step(f(X, Z), f(Y, Z))
% 9.82/9.87 f4(f2(true__, Y0, Y1), Y2, Y0, Y1) -> true__
% 9.82/9.87 f4(step(Y, Z), X, Y, Z) -> true__
% 9.82/9.87 f4(true__, X, Y, Z) -> step(f(X, Y), f(X, Z))
% 9.82/9.87 f5(seq(Y2, Y3, f(X0, f(X1, f(X2, f(f(X3, X4), f(X5, a)))))), Y2, Y3, f(X0, f(X1, f(X2, f(f(X5, f(X4, a)), X3))))) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(X0, f(X1, f(f(X2, X3), f(X4, a))))), Y2, Y3, f(X0, f(X1, f(f(X4, f(X3, a)), X2)))) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(X0, f(X1, f(f(f(X2, X3), f(X4, a)), X5)))), Y2, Y3, f(X0, f(X1, f(f(f(X4, f(X3, a)), X2), X5)))) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(X0, f(f(X1, X2), f(X3, a)))), Y2, Y3, f(X0, f(f(X3, f(X2, a)), X1))) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(X0, f(f(X1, f(f(X2, X3), f(X4, a))), X5))), Y2, Y3, f(X0, f(f(X1, f(f(X4, f(X3, a)), X2)), X5))) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(X0, f(f(f(X1, X2), f(X3, a)), X4))), Y2, Y3, f(X0, f(f(f(X3, f(X2, a)), X1), X4))) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(X0, f(f(f(f(X1, X2), f(X3, a)), X4), X5))), Y2, Y3, f(X0, f(f(f(f(X3, f(X2, a)), X1), X4), X5))) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(f(X0, X1), f(X2, a))), Y2, Y3, f(f(X2, f(X1, a)), X0)) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(f(X0, f(X1, f(f(X2, X3), f(X4, a)))), X5)), Y2, Y3, f(f(X0, f(X1, f(f(X4, f(X3, a)), X2))), X5)) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(f(X0, f(f(X1, X2), f(X3, a))), X4)), Y2, Y3, f(f(X0, f(f(X3, f(X2, a)), X1)), X4)) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(f(X0, f(f(f(X1, X2), f(X3, a)), X4)), X5)), Y2, Y3, f(f(X0, f(f(f(X3, f(X2, a)), X1), X4)), X5)) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(f(f(X0, X1), f(X2, a)), X3)), Y2, Y3, f(f(f(X2, f(X1, a)), X0), X3)) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(f(f(X0, f(f(X1, X2), f(X3, a))), X4), X5)), Y2, Y3, f(f(f(X0, f(f(X3, f(X2, a)), X1)), X4), X5)) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(f(f(f(X0, X1), f(X2, a)), X3), X4)), Y2, Y3, f(f(f(f(X2, f(X1, a)), X0), X3), X4)) -> true__
% 9.82/9.87 f5(seq(Y2, Y3, f(f(f(f(f(X0, X1), f(X2, a)), X3), X4), X5)), Y2, Y3, f(f(f(f(f(X2, f(X1, a)), X0), X3), X4), X5)) -> true__
% 9.82/9.87 f5(true__, N, X, Z) -> seq(succ(N), X, Z)
% 9.82/9.87 f6(f2(true__, Y0, Y1), Y2, Y3, Y0, Y1) -> true__
% 9.82/9.87 f6(step(Y, Z), N, X, Y, Z) -> true__
% 9.82/9.87 f6(true__, N, X, Y, Z) -> f5(seq(N, X, Y), N, X, Z)
% 9.82/9.87 false__ -> true__
% 9.82/9.87 seq(succ(succ(succ(succ(zero)))), f(f(f(Y4, a), X1), f(f(a, X2), f(Y3, a))), f(f(Y4, f(Y3, a)), f(X1, f(f(X2, a), a)))) -> true__
% 9.82/9.87 seq(succ(succ(succ(succ(zero)))), f(f(f(Y4, a), Y3), f(f(f(X2, a), X3), a)), f(f(Y4, f(Y3, a)), f(X2, f(f(X3, a), a)))) -> true__
% 9.82/9.87 seq(succ(succ(succ(succ(zero)))), f(f(f(Y5, a), X1), f(f(f(Y2, Y3), a), a)), f(f(f(f(f(X1, a), a), f(Y3, a)), Y2), Y5)) -> true__
% 9.82/9.87 seq(succ(succ(succ(succ(zero)))), f(f(f(f(Y3, X1), a), X2), f(f(Y4, a), a)), f(f(Y4, f(Y3, a)), f(f(X2, a), f(X1, a)))) -> true__
% 9.82/9.87 seq(succ(succ(succ(succ(zero)))), f(f(f(f(Y4, a), a), X1), f(f(Y2, a), a)), f(f(Y4, f(f(f(f(X1, a), a), a), a)), Y2)) -> true__
% 9.82/9.87 seq(succ(succ(succ(zero))), f(Y2, f(f(f(Y3, a), X2), f(f(Y5, a), a))), f(Y2, f(f(Y5, f(f(f(X2, a), a), a)), Y3))) -> true__
% 9.82/9.87 seq(succ(succ(succ(zero))), f(f(Y2, Y3), f(f(f(X1, a), X2), f(a, a))), f(f(f(X1, f(f(X2, a), a)), f(Y3, a)), Y2)) -> true__
% 9.82/9.87 seq(succ(succ(succ(zero))), f(f(Y5, Y2), f(f(f(Y4, a), X3), a)), f(f(f(Y4, f(f(X3, a), a)), Y2), Y5)) -> true__
% 9.82/9.87 seq(succ(succ(succ(zero))), f(f(Y5, Y4), f(f(a, X2), f(Y2, a))), f(f(f(Y4, f(f(X2, a), a)), Y2), Y5)) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(X0, Y5), f(f(Y3, Y4), a)), f(X3, a)), f(f(X3, f(X0, a)), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(X0, a), X1), f(f(f(Y3, Y4), f(Y5, a)), a)), f(f(X0, f(f(X1, a), a)), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(Y2, Y3), f(Y4, a)), f(f(f(X1, a), X2), f(X3, a))), f(f(f(Y4, f(Y3, a)), Y2), f(f(X1, f(f(X2, a), a)), X3))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(Y2, a), X1), f(f(Y4, a), a)), f(f(Y4, f(f(f(X1, a), a), a)), Y2)) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(Y4, X1), f(X2, a)), f(f(Y2, Y3), a)), f(f(f(Y4, f(Y3, a)), Y2), f(X2, f(X1, a)))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(Y4, a), X1), f(f(Y3, X3), a)), f(f(Y4, f(Y3, a)), f(X1, f(X3, a)))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(Y4, a), X1), f(f(a, X2), f(X3, a))), f(f(Y4, f(f(X1, a), a)), f(X3, f(X2, a)))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(f(X0, a), X1), f(X2, a)), f(f(Y3, Y4), f(Y5, a))), f(f(f(X0, f(f(X1, a), a)), X2), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(f(X0, a), X1), f(Y3, a)), f(Y4, a)), f(f(Y4, f(Y3, a)), f(X0, f(f(X1, a), a)))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(f(Y2, Y3), a), X1), f(Y5, a)), f(f(f(f(X1, a), f(Y3, a)), Y2), Y5)) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(f(Y2, a), X1), f(f(Y4, a), a)), Y5), f(f(f(Y4, f(f(f(X1, a), a), a)), Y2), Y5)) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(f(Y3, Y4), f(Y5, a)), X1), f(f(X2, X3), a)), f(f(f(X1, f(X3, a)), X2), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(succ(zero))), f(f(f(f(Y3, Y4), f(Y5, a)), X1), f(f(a, X2), f(X3, a))), f(f(f(X3, f(X2, a)), f(X1, a)), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(Y2, f(f(Y3, Y4), f(f(a, X3), f(X4, a)))), f(Y2, f(f(f(X4, f(X3, a)), f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(Y2, f(f(f(Y4, X2), f(X3, a)), f(Y5, a))), f(Y2, f(f(Y5, f(Y4, a)), f(X3, f(X2, a))))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(Y2, f(f(f(Y5, a), X2), f(Y3, a))), f(Y2, f(f(Y5, f(f(X2, a), a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(X0, f(f(X1, X2), f(X3, a))), f(f(Y3, Y4), f(Y5, a))), f(f(X0, f(f(X3, f(X2, a)), X1)), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(Y2, Y3), f(f(a, X2), f(X3, a))), f(f(f(X3, f(X2, a)), f(Y3, a)), Y2)) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(Y2, Y3), f(f(f(X1, X2), f(X3, a)), a)), f(f(f(f(X3, f(X2, a)), X1), f(Y3, a)), Y2)) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(Y2, f(f(X1, X2), f(X3, a))), f(Y4, a)), f(f(Y4, f(f(f(X3, f(X2, a)), X1), a)), Y2)) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(Y5, Y4), f(f(Y2, Y3), a)), f(f(f(Y4, f(Y3, a)), Y2), Y5)) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(X0, X1), f(X2, a)), f(f(Y3, Y4), f(Y5, a))), f(f(f(X2, f(X1, a)), X0), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(Y2, Y3), f(Y4, a)), f(X1, f(f(X2, X3), f(X4, a)))), f(f(f(Y4, f(Y3, a)), Y2), f(X1, f(f(X4, f(X3, a)), X2)))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(Y2, Y3), f(Y4, a)), f(f(f(X1, X2), f(X3, a)), X4)), f(f(f(Y4, f(Y3, a)), Y2), f(f(f(X3, f(X2, a)), X1), X4))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(Y2, Y3), f(f(a, X2), f(X3, a))), Y5), f(f(f(f(X3, f(X2, a)), f(Y3, a)), Y2), Y5)) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(Y3, X1), f(X2, a)), f(Y4, a)), f(f(Y4, f(Y3, a)), f(X2, f(X1, a)))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(Y4, a), X1), f(Y2, a)), f(f(Y4, f(f(X1, a), a)), Y2)) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(f(X0, X1), f(X2, a)), X3), f(f(Y3, Y4), f(Y5, a))), f(f(f(f(X2, f(X1, a)), X0), X3), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(f(Y3, X1), f(X2, a)), f(Y4, a)), Y5), f(f(f(Y4, f(Y3, a)), f(X2, f(X1, a))), Y5)) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(f(Y3, Y4), f(Y5, a)), X1), f(X2, a)), f(f(X2, f(X1, a)), f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(f(Y4, a), X1), f(Y2, a)), Y5), f(f(f(Y4, f(f(X1, a), a)), Y2), Y5)) -> true__
% 9.82/9.88 seq(succ(succ(zero)), f(f(f(f(f(Y3, Y4), f(Y5, a)), Y6), X1), f(X2, a)), f(f(X2, f(X1, a)), f(f(f(Y5, f(Y4, a)), Y3), Y6))) -> true__
% 9.82/9.88 seq(succ(zero), f(Y2, f(Y3, f(f(Y4, Y5), f(Y6, a)))), f(Y2, f(Y3, f(f(Y6, f(Y5, a)), Y4)))) -> true__
% 9.82/9.88 seq(succ(zero), f(Y2, f(f(Y3, Y4), f(Y5, a))), f(Y2, f(f(Y5, f(Y4, a)), Y3))) -> true__
% 9.82/9.88 seq(succ(zero), f(Y2, f(f(f(Y3, Y4), f(Y5, a)), Y6)), f(Y2, f(f(f(Y5, f(Y4, a)), Y3), Y6))) -> true__
% 9.82/9.88 seq(succ(zero), f(f(Y2, Y3), f(Y4, a)), f(f(Y4, f(Y3, a)), Y2)) -> true__
% 9.82/9.88 seq(succ(zero), f(f(Y2, f(f(Y3, Y4), f(Y5, a))), Y6), f(f(Y2, f(f(Y5, f(Y4, a)), Y3)), Y6)) -> true__
% 9.82/9.88 seq(succ(zero), f(f(f(Y2, Y3), f(Y4, a)), Y5), f(f(f(Y4, f(Y3, a)), Y2), Y5)) -> true__
% 9.82/9.88 seq(succ(zero), f(f(f(f(Y2, Y3), f(Y4, a)), Y5), Y6), f(f(f(f(Y4, f(Y3, a)), Y2), Y5), Y6)) -> true__
% 9.82/9.88 seq(zero, X, X) -> true__
% 9.82/9.88 step(X, Y) -> f2(true__, X, Y)
% 9.82/9.88 top(f(f(Z, Y), f(X, a)), f(f(X, f(Y, a)), Z)) -> true__
% 9.82/9.88 with the LPO induced by
% 9.82/9.88 f6 > f5 > succ > f4 > f3 > f > step > f2 > zero > seq > f1 > a > top > false__ > true__
% 9.82/9.88
% 9.82/9.88 % SZS output end Proof
% 9.82/9.88
%------------------------------------------------------------------------------