TSTP Solution File: PUZ039-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ039-1 : TPTP v8.1.2. Bugfixed v2.6.0.
% 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 : n014.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 2.92s 0.94s
% Output : Proof 4.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ039-1 : TPTP v8.1.2. Bugfixed v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 22:19:02 EDT 2023
% 0.12/0.34 % CPUTime :
% 2.92/0.94 Command-line arguments: --no-flatten-goal
% 2.92/0.94
% 2.92/0.94 % SZS status Unsatisfiable
% 2.92/0.94
% 2.92/0.97 % SZS output start Proof
% 2.92/0.97 Take the following subset of the input axioms:
% 2.92/0.97 fof(goal_state, negated_conjecture, ![B, V1, V2, V3, H, S2, S3, S4, E2, S1, E1]: ~state(B, V1, V2, V3, v4(s(s(o)), s(s(o))), H, S1, S2, S3, S4, E1, E2)).
% 2.92/0.98 fof(h_left, axiom, ![V4, X, Y, B2, V1_2, V2_2, V3_2, S2_2, S3_2, S4_2, S1_2, E2_2]: (~state(B2, V1_2, V2_2, V3_2, V4, h(X, s(Y)), S1_2, S2_2, S3_2, S4_2, e1(X, Y), E2_2) | state(B2, V1_2, V2_2, V3_2, V4, h(X, Y), S1_2, S2_2, S3_2, S4_2, e1(X, s(s(Y))), E2_2))).
% 2.92/0.98 fof(initial_state, hypothesis, 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)))))).
% 2.92/0.98 fof(s2_down, axiom, ![B2, V1_2, V2_2, V3_2, H2, X2, Y2, S3_2, S4_2, S1_2, V4_2, E2_2]: (~state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, s2(X2, Y2), S3_2, S4_2, e1(s(X2), Y2), E2_2) | state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, s2(s(X2), Y2), S3_2, S4_2, e1(X2, Y2), E2_2))).
% 2.92/0.98 fof(s4_right, axiom, ![B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S1_2, V4_2, E2_2]: (~state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, s4(X2, Y2), e1(X2, s(Y2)), E2_2) | state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, s4(X2, s(Y2)), e1(X2, Y2), E2_2))).
% 2.92/0.98 fof(swap_blanks, axiom, ![Q, W, B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S4_2, S1_2, V4_2]: (~state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), e2(Q, W)) | state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(Q, W), e2(X2, Y2)))).
% 2.92/0.98 fof(v3_down, axiom, ![B2, V1_2, V2_2, H2, X2, Y2, S2_2, S3_2, S4_2, S1_2, V4_2, E2_2]: (~state(B2, V1_2, V2_2, v3(X2, Y2), V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(s(s(X2)), Y2), E2_2) | state(B2, V1_2, V2_2, v3(s(X2), Y2), V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), E2_2))).
% 2.92/0.98 fof(v4_left, axiom, ![B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S4_2, S1_2]: (~state(B2, V1_2, V2_2, V3_2, v4(X2, s(Y2)), H2, S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), e2(s(X2), Y2)) | state(B2, V1_2, V2_2, V3_2, v4(X2, Y2), H2, S1_2, S2_2, S3_2, S4_2, e1(X2, s(Y2)), e2(s(X2), s(Y2))))).
% 2.92/0.98
% 2.92/0.98 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.92/0.98 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.92/0.98 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.92/0.98 fresh(y, y, x1...xn) = u
% 2.92/0.98 C => fresh(s, t, x1...xn) = v
% 2.92/0.98 where fresh is a fresh function symbol and x1..xn are the free
% 2.92/0.98 variables of u and v.
% 2.92/0.98 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.92/0.98 input problem has no model of domain size 1).
% 2.92/0.98
% 2.92/0.98 The encoding turns the above axioms into the following unit equations and goals:
% 2.92/0.98
% 2.92/0.98 Axiom 1 (v4_left): fresh3(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = true2.
% 2.92/0.98 Axiom 2 (h_left): fresh36(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 2.92/0.98 Axiom 3 (s2_down): fresh29(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 2.92/0.98 Axiom 4 (s4_right): fresh19(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 2.92/0.98 Axiom 5 (v3_down): fresh8(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 2.92/0.98 Axiom 6 (swap_blanks): fresh17(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = true2.
% 2.92/0.98 Axiom 7 (h_left): fresh36(state(X, Y, Z, W, V, h(U, s(T)), S, X2, Y2, Z2, e1(U, T), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, V, h(U, T), S, X2, Y2, Z2, e1(U, s(s(T))), W2).
% 2.92/0.98 Axiom 8 (s2_down): fresh29(state(X, Y, Z, W, V, U, T, s2(S, X2), Y2, Z2, e1(s(S), X2), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, V, U, T, s2(s(S), X2), Y2, Z2, e1(S, X2), W2).
% 2.92/0.98 Axiom 9 (s4_right): fresh19(state(X, Y, Z, W, V, U, T, S, X2, s4(Y2, Z2), e1(Y2, s(Z2)), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, V, U, T, S, X2, s4(Y2, s(Z2)), e1(Y2, Z2), W2).
% 2.92/0.98 Axiom 10 (swap_blanks): fresh17(state(X, Y, Z, W, V, U, T, S, X2, Y2, e1(Z2, W2), e2(V2, U2)), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2) = state(X, Y, Z, W, V, U, T, S, X2, Y2, e1(V2, U2), e2(Z2, W2)).
% 2.92/0.98 Axiom 11 (v3_down): fresh8(state(X, Y, Z, v3(W, V), U, T, S, X2, Y2, Z2, e1(s(s(W)), V), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, v3(s(W), V), U, T, S, X2, Y2, Z2, e1(W, V), W2).
% 2.92/0.98 Axiom 12 (v4_left): fresh3(state(X, Y, Z, W, v4(V, s(U)), T, S, X2, Y2, Z2, e1(V, U), e2(s(V), U)), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = state(X, Y, Z, W, v4(V, U), T, S, X2, Y2, Z2, e1(V, s(U)), e2(s(V), s(U))).
% 2.92/0.98 Axiom 13 (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))))) = true2.
% 2.92/0.98
% 2.92/0.98 Goal 1 (goal_state): state(X, Y, Z, W, v4(s(s(o)), s(s(o))), V, U, T, S, X2, Y2, Z2) = true2.
% 2.92/0.98 The goal is true when:
% 2.92/0.98 X = bb(o, s(o))
% 2.92/0.98 Y = v1(o, o)
% 2.92/0.98 Z = v2(o, s(s(s(o))))
% 2.92/0.98 W = v3(s(s(s(o))), o)
% 2.92/0.98 V = h(s(s(o)), o)
% 2.92/0.98 U = s1(s(s(s(o))), s(o))
% 2.92/0.98 T = s2(s(s(s(s(o)))), s(s(o)))
% 2.92/0.98 S = s3(s(s(s(s(o)))), s(o))
% 2.92/0.98 X2 = s4(s(s(s(s(o)))), s(s(s(o))))
% 2.92/0.98 Y2 = e1(s(s(o)), s(s(s(o))))
% 2.92/0.98 Z2 = e2(s(s(s(o))), s(s(s(o))))
% 2.92/0.98
% 2.92/0.98 Proof:
% 2.92/0.98 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)))))
% 2.92/0.98 = { by axiom 12 (v4_left) R->L }
% 2.92/0.98 fresh3(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)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 2.92/0.98 = { by axiom 7 (h_left) R->L }
% 2.92/0.98 fresh3(fresh36(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)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 2.92/0.98 = { by axiom 11 (v3_down) R->L }
% 2.92/0.98 fresh3(fresh36(fresh8(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)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 2.92/0.98 = { by axiom 10 (swap_blanks) R->L }
% 2.92/0.99 fresh3(fresh36(fresh8(fresh17(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)), true2, 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)))), s(s(s(o))), s(s(o)), s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 2.92/0.99 = { by axiom 8 (s2_down) R->L }
% 2.92/0.99 fresh3(fresh36(fresh8(fresh17(fresh29(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)), true2, 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)), 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)))), e2(s(s(s(s(o)))), o)), true2, 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)))), s(s(s(o))), s(s(o)), s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 2.92/0.99 = { by axiom 9 (s4_right) R->L }
% 4.85/0.99 fresh3(fresh36(fresh8(fresh17(fresh29(fresh19(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)), true2, 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)), s(s(s(s(o)))), s(s(o)), e2(s(s(s(s(o)))), o)), true2, 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)), 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)))), e2(s(s(s(s(o)))), o)), true2, 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)))), s(s(s(o))), s(s(o)), s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/0.99 = { by axiom 10 (swap_blanks) R->L }
% 4.85/0.99 fresh3(fresh36(fresh8(fresh17(fresh29(fresh19(fresh17(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))))), true2, 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))), s(s(s(s(o)))), o, s(s(s(s(o)))), s(s(s(o)))), true2, 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)), s(s(s(s(o)))), s(s(o)), e2(s(s(s(s(o)))), o)), true2, 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)), 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)))), e2(s(s(s(s(o)))), o)), true2, 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)))), s(s(s(o))), s(s(o)), s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/0.99 = { by axiom 13 (initial_state) }
% 4.85/1.00 fresh3(fresh36(fresh8(fresh17(fresh29(fresh19(fresh17(true2, true2, 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))), s(s(s(s(o)))), o, s(s(s(s(o)))), s(s(s(o)))), true2, 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)), s(s(s(s(o)))), s(s(o)), e2(s(s(s(s(o)))), o)), true2, 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)), 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)))), e2(s(s(s(s(o)))), o)), true2, 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)))), s(s(s(o))), s(s(o)), s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/1.00 = { by axiom 6 (swap_blanks) }
% 4.85/1.00 fresh3(fresh36(fresh8(fresh17(fresh29(fresh19(true2, true2, 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)), s(s(s(s(o)))), s(s(o)), e2(s(s(s(s(o)))), o)), true2, 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)), 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)))), e2(s(s(s(s(o)))), o)), true2, 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)))), s(s(s(o))), s(s(o)), s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/1.00 = { by axiom 4 (s4_right) }
% 4.85/1.00 fresh3(fresh36(fresh8(fresh17(fresh29(true2, true2, 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)), 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)))), e2(s(s(s(s(o)))), o)), true2, 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)))), s(s(s(o))), s(s(o)), s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/1.00 = { by axiom 3 (s2_down) }
% 4.85/1.00 fresh3(fresh36(fresh8(fresh17(true2, true2, 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)))), s(s(s(o))), s(s(o)), s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/1.00 = { by axiom 6 (swap_blanks) }
% 4.85/1.00 fresh3(fresh36(fresh8(true2, true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/1.00 = { by axiom 5 (v3_down) }
% 4.85/1.00 fresh3(fresh36(true2, true2, 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)))), 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)))), e2(s(s(s(o))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/1.00 = { by axiom 2 (h_left) }
% 4.85/1.00 fresh3(true2, true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), 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)))))
% 4.85/1.00 = { by axiom 1 (v4_left) }
% 4.85/1.00 true2
% 4.85/1.00 % SZS output end Proof
% 4.85/1.00
% 4.85/1.00 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------