TSTP Solution File: PUZ039-10 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ039-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n024.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 : 300s
% DateTime : Thu Aug 31 13:24:03 EDT 2023
% Result : Unsatisfiable 1.52s 0.70s
% Output : Proof 2.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ039-10 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 22:30:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.52/0.70 Command-line arguments: --no-flatten-goal
% 1.52/0.70
% 1.52/0.70 % SZS status Unsatisfiable
% 1.52/0.70
% 2.67/0.71 % SZS output start Proof
% 2.67/0.71 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.67/0.71 Axiom 2 (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.
% 2.67/0.71 Axiom 3 (s4_right): ifeq(state(X, Y, Z, W, V, U, T, S, X2, s4(Y2, Z2), e1(Y2, s(Z2)), W2), true, state(X, Y, Z, W, V, U, T, S, X2, s4(Y2, s(Z2)), e1(Y2, Z2), W2), true) = true.
% 2.67/0.71 Axiom 4 (s2_down): ifeq(state(X, Y, Z, W, V, U, T, s2(S, X2), Y2, Z2, e1(s(S), X2), W2), true, state(X, Y, Z, W, V, U, T, s2(s(S), X2), Y2, Z2, e1(S, X2), W2), true) = true.
% 2.67/0.71 Axiom 5 (h_left): ifeq(state(X, Y, Z, W, V, h(U, s(T)), S, X2, Y2, Z2, e1(U, T), W2), true, state(X, Y, Z, W, V, h(U, T), S, X2, Y2, Z2, e1(U, s(s(T))), W2), true) = true.
% 2.67/0.71 Axiom 6 (v3_down): ifeq(state(X, Y, Z, v3(W, V), U, T, S, X2, Y2, Z2, e1(s(s(W)), V), W2), true, state(X, Y, Z, v3(s(W), V), U, T, S, X2, Y2, Z2, e1(W, V), W2), true) = true.
% 2.67/0.71 Axiom 7 (v4_left): ifeq(state(X, Y, Z, W, v4(V, s(U)), T, S, X2, Y2, Z2, e1(V, U), e2(s(V), U)), true, state(X, Y, Z, W, v4(V, U), T, S, X2, Y2, Z2, e1(V, s(U)), e2(s(V), s(U))), true) = true.
% 2.67/0.71 Axiom 8 (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.
% 2.67/0.71
% 2.67/0.71 Goal 1 (goal_state): state(X, Y, Z, W, v4(s(s(o)), s(s(o))), V, U, T, S, X2, Y2, Z2) = true.
% 2.67/0.71 The goal is true when:
% 2.67/0.71 X = bb(o, s(o))
% 2.67/0.71 Y = v1(o, o)
% 2.67/0.71 Z = v2(o, s(s(s(o))))
% 2.67/0.71 W = v3(s(s(s(o))), o)
% 2.67/0.71 V = h(s(s(o)), o)
% 2.67/0.71 U = s1(s(s(s(o))), s(o))
% 2.67/0.71 T = s2(s(s(s(s(o)))), s(s(o)))
% 2.67/0.71 S = s3(s(s(s(s(o)))), s(o))
% 2.67/0.71 X2 = s4(s(s(s(s(o)))), s(s(s(o))))
% 2.67/0.71 Y2 = e1(s(s(o)), s(s(s(o))))
% 2.67/0.71 Z2 = e2(s(s(s(o))), s(s(s(o))))
% 2.67/0.71
% 2.67/0.71 Proof:
% 2.67/0.71 state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o)))))
% 2.67/0.71 = { by axiom 1 (ifeq_axiom) R->L }
% 2.67/0.72 ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.72 = { by axiom 5 (h_left) R->L }
% 2.67/0.72 ifeq(ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.72 = { by axiom 1 (ifeq_axiom) R->L }
% 2.67/0.72 ifeq(ifeq(ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.72 = { by axiom 2 (swap_blanks) R->L }
% 2.67/0.72 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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(o))), s(s(o))), e2(s(s(s(s(o)))), 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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.72 = { by axiom 1 (ifeq_axiom) R->L }
% 2.67/0.72 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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(o))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.72 = { by axiom 3 (s4_right) R->L }
% 2.67/0.72 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)))), s(s(s(o)))), e2(s(s(s(s(o)))), 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)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(o))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.72 = { by axiom 1 (ifeq_axiom) R->L }
% 2.67/0.72 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)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(s(o)))), 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(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(s(o)))), e1(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(o))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.72 = { by axiom 8 (initial_state) R->L }
% 2.67/0.73 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)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(s(s(o)))), 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(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(s(o)))), e1(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(o))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.73 = { by axiom 2 (swap_blanks) }
% 2.67/0.73 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)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(o))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.73 = { by axiom 1 (ifeq_axiom) }
% 2.67/0.73 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(s(o)))), e1(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), 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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(o))), s(s(o))), e2(s(s(s(s(o)))), 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(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.73 = { by axiom 4 (s2_down) }
% 2.67/0.74 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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.74 = { by axiom 1 (ifeq_axiom) }
% 2.67/0.74 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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(s(s(o)))), o), e2(s(s(s(o))), s(s(o)))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(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(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), o), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.74 = { by axiom 6 (v3_down) }
% 2.67/0.74 ifeq(ifeq(true, true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.74 = { by axiom 1 (ifeq_axiom) }
% 2.67/0.74 ifeq(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(o))), e2(s(s(s(o))), s(s(o)))), true, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(o))), h(s(s(o)), o), s1(s(s(s(o))), s(o)), s2(s(s(s(s(o)))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(s(o)))), e1(s(s(o)), s(s(s(o)))), e2(s(s(s(o))), s(s(s(o))))), true)
% 2.67/0.74 = { by axiom 7 (v4_left) }
% 2.67/0.74 true
% 2.67/0.74 % SZS output end Proof
% 2.67/0.74
% 2.67/0.74 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------