%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : PUZ040-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:30:49 PM UTC 2026
% Result : Unsatisfiable 14.16s 2.22s
% Output : Proof 14.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ040-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 22:36:24 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.16/2.22 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 14.16/2.22
% 14.16/2.22 % SZS status Unsatisfiable
% 14.16/2.22
% 14.16/2.30 % SZS output start Proof
% 14.16/2.30 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 14.16/2.30 Axiom 2 (initial_state): state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), o), e2(s(s(s(s(o)))), s(s(s(o))))) = true.
% 14.16/2.30 Axiom 3 (swap_blanks): ifeq(state(X, Y, Z, W, V, U, T, S, X2, Y2, e1(Z2, W2), e2(V2, U2)), true, state(X, Y, Z, W, V, U, T, S, X2, Y2, e1(V2, U2), e2(Z2, W2)), true) = true.
% 14.16/2.30 Axiom 4 (s3_left): ifeq(state(X, Y, Z, W, V, U, T, S, s3(X2, s(Y2)), Z2, e1(X2, Y2), W2), true, state(X, Y, Z, W, V, U, T, S, s3(X2, Y2), Z2, e1(X2, s(Y2)), W2), true) = true.
% 14.16/2.30 Axiom 5 (s1_down): ifeq(state(X, Y, Z, W, V, U, s1(T, S), X2, Y2, Z2, e1(s(T), S), W2), true, state(X, Y, Z, W, V, U, s1(s(T), S), X2, Y2, Z2, e1(T, S), W2), true) = true.
% 14.16/2.30 Axiom 6 (h_right): ifeq(state(X, Y, Z, W, V, h(U, T), S, X2, Y2, Z2, e1(U, s(s(T))), W2), true, state(X, Y, Z, W, V, h(U, s(T)), S, X2, Y2, Z2, e1(U, T), W2), true) = true.
% 14.16/2.30 Axiom 7 (v4_down): ifeq(state(X, Y, Z, W, v4(V, U), T, S, X2, Y2, Z2, e1(s(s(V)), U), W2), true, state(X, Y, Z, W, v4(s(V), U), T, S, X2, Y2, Z2, e1(V, U), W2), true) = true.
% 14.16/2.30 Axiom 8 (v1_down): ifeq(state(X, v1(Y, Z), W, V, U, T, S, X2, Y2, Z2, e1(s(s(Y)), Z), W2), true, state(X, v1(s(Y), Z), W, V, U, T, S, X2, Y2, Z2, e1(Y, Z), W2), true) = true.
% 14.16/2.30 Axiom 9 (v3_right): ifeq(state(X, Y, Z, v3(W, V), U, T, S, X2, Y2, Z2, e1(W, s(V)), e2(s(W), s(V))), true, state(X, Y, Z, v3(W, s(V)), U, T, S, X2, Y2, Z2, e1(W, V), e2(s(W), V)), true) = true.
% 14.16/2.30 Axiom 10 (b_left): ifeq(state(bb(X, s(Y)), Z, W, V, U, T, S, X2, Y2, Z2, e1(X, Y), e2(s(X), Y)), true, state(bb(X, Y), Z, W, V, U, T, S, X2, Y2, Z2, e1(X, s(s(Y))), e2(s(X), s(s(Y)))), true) = true.
% 14.16/2.30
% 14.16/2.30 Goal 1 (goal_state): state(bb(o, o), X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = true.
% 14.16/2.30 The goal is true when:
% 14.16/2.30 X = v1(s(s(o)), o)
% 14.16/2.30 Y = v2(o, s(s(s(o))))
% 14.16/2.30 Z = v3(s(s(o)), s(o))
% 14.16/2.30 W = v4(s(s(s(o))), s(s(s(o))))
% 14.16/2.30 V = h(s(s(o)), s(s(o)))
% 14.16/2.30 U = s1(s(s(s(s(o)))), s(o))
% 14.16/2.30 T = s2(s(s(s(o))), s(s(o)))
% 14.16/2.30 S = s3(s(s(s(s(o)))), o)
% 14.16/2.30 X2 = s4(s(s(s(s(o)))), s(s(o)))
% 14.16/2.30 Y2 = e1(o, s(s(o)))
% 14.16/2.30 Z2 = e2(s(o), s(s(o)))
% 14.16/2.30
% 14.16/2.30 Proof:
% 14.16/2.30 state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o))))
% 14.16/2.30 = { by axiom 1 (ifeq_axiom) R->L }
% 14.16/2.30 ifeq(true, true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.16/2.30 = { by axiom 3 (swap_blanks) R->L }
% 14.16/2.30 ifeq(ifeq(state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.16/2.30 = { by axiom 1 (ifeq_axiom) R->L }
% 14.16/2.30 ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.30 = { by axiom 3 (swap_blanks) R->L }
% 14.95/2.30 ifeq(ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.30 = { by axiom 1 (ifeq_axiom) R->L }
% 14.95/2.30 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.30 = { by axiom 9 (v3_right) R->L }
% 14.95/2.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.30 = { by axiom 1 (ifeq_axiom) R->L }
% 14.95/2.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.31 = { by axiom 7 (v4_down) R->L }
% 14.95/2.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(o))), s(o))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.31 = { by axiom 1 (ifeq_axiom) R->L }
% 14.95/2.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.32 = { by axiom 5 (s1_down) R->L }
% 14.95/2.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(o)), e2(s(s(s(s(o)))), s(s(s(o))))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), s(o)), e2(s(s(s(s(o)))), s(s(s(o))))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.32 = { by axiom 1 (ifeq_axiom) R->L }
% 14.95/2.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(o)), e2(s(s(s(s(o)))), s(s(s(o))))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), s(o)), e2(s(s(s(s(o)))), s(s(s(o))))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.33 = { by axiom 2 (initial_state) R->L }
% 14.95/2.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), o), e2(s(s(s(s(o)))), s(s(s(o))))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(o)), e2(s(s(s(s(o)))), s(s(s(o))))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), s(o)), e2(s(s(s(s(o)))), s(s(s(o))))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.33 = { by axiom 4 (s3_left) }
% 14.95/2.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), s(o)), e2(s(s(s(s(o)))), s(s(s(o))))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.33 = { by axiom 1 (ifeq_axiom) }
% 14.95/2.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), s(o)), e2(s(s(s(s(o)))), s(s(s(o))))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.34 = { by axiom 3 (swap_blanks) }
% 14.95/2.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.34 = { by axiom 1 (ifeq_axiom) }
% 14.95/2.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(o))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(o))), s(o))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.35 = { by axiom 6 (h_right) }
% 14.95/2.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.35 = { by axiom 1 (ifeq_axiom) }
% 14.95/2.35 ifeq(ifeq(ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(o))), o)), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(o))), o)), true), true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.35 = { by axiom 8 (v1_down) }
% 14.95/2.35 ifeq(ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.35 = { by axiom 1 (ifeq_axiom) }
% 14.95/2.35 ifeq(ifeq(ifeq(state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true), true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.35 = { by axiom 8 (v1_down) }
% 14.95/2.35 ifeq(ifeq(true, true, state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.35 = { by axiom 1 (ifeq_axiom) }
% 14.95/2.35 ifeq(state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true, state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(o)), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), o), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o)))), true)
% 14.95/2.35 = { by axiom 10 (b_left) }
% 14.95/2.35 true
% 14.95/2.35 % SZS output end Proof
% 14.95/2.35
% 14.95/2.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------