TSTP Solution File: SYN163-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN163-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n031.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 : Fri Sep 1 03:33:25 EDT 2023
% Result : Unsatisfiable 33.39s 4.62s
% Output : Proof 33.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN163-1 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.14 % 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 : n031.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 21:08:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 33.39/4.62 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 33.39/4.62
% 33.39/4.62 % SZS status Unsatisfiable
% 33.39/4.62
% 33.73/4.68 % SZS output start Proof
% 33.73/4.68 Take the following subset of the input axioms:
% 33.73/4.69 fof(axiom_1, axiom, s0(d)).
% 33.73/4.69 fof(axiom_11, axiom, n0(e, b)).
% 33.73/4.69 fof(axiom_13, axiom, r0(e)).
% 33.73/4.69 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 33.73/4.69 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 33.73/4.69 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 33.73/4.69 fof(axiom_28, axiom, k0(e)).
% 33.73/4.69 fof(axiom_31, axiom, m0(b, b, e)).
% 33.73/4.69 fof(axiom_34, axiom, n0(c, d)).
% 33.73/4.69 fof(prove_this, negated_conjecture, ~n5(e, a)).
% 33.73/4.69 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 33.73/4.69 fof(rule_005, axiom, ![C, B]: (m1(B, C, B) | ~m0(C, C, B))).
% 33.73/4.69 fof(rule_036, axiom, ![A2, B2]: (n1(A2, A2, B2) | ~m0(b, B2, A2))).
% 33.73/4.69 fof(rule_040, axiom, ![D, C2]: (n1(C2, e, e) | (~m0(C2, D, e) | ~k1(C2)))).
% 33.73/4.69 fof(rule_085, axiom, ![C2, B2]: (p1(B2, B2, B2) | ~p0(C2, B2))).
% 33.73/4.69 fof(rule_090, axiom, p1(e, e, e) | (~r0(e) | ~k0(e))).
% 33.73/4.69 fof(rule_107, axiom, ![A2_2]: (q1(e, A2_2, A2_2) | (~m0(A2_2, d, A2_2) | ~m0(e, d, A2_2)))).
% 33.73/4.69 fof(rule_117, axiom, q1(d, d, d) | (~k0(e) | ~s0(d))).
% 33.73/4.69 fof(rule_122, axiom, ![G, H]: (q1(G, G, G) | ~m0(G, H, G))).
% 33.73/4.69 fof(rule_124, axiom, ![E, D2]: (r1(D2) | (~q0(D2, E) | (~s0(d) | ~q1(d, E, d))))).
% 33.73/4.69 fof(rule_125, axiom, ![I2]: (s1(I2) | ~p0(I2, I2))).
% 33.73/4.69 fof(rule_127, axiom, ![F, C2, D2, E2]: (k2(C2, D2) | (~m1(E2, D2, C2) | (~k1(F) | ~k2(F, D2))))).
% 33.73/4.69 fof(rule_129, axiom, ![A, J2]: (k2(J2, J2) | ~q1(A, J2, J2))).
% 33.73/4.69 fof(rule_154, axiom, ![A2_2]: (p2(A2_2, A2_2, A2_2) | ~q1(A2_2, A2_2, A2_2))).
% 33.73/4.69 fof(rule_177, axiom, ![E2, F2]: (q2(E2, F2, F2) | (~k0(F2) | ~p1(E2, E2, E2)))).
% 33.73/4.69 fof(rule_181, axiom, ![I2]: (q2(I2, I2, I2) | ~p1(I2, I2, I2))).
% 33.73/4.69 fof(rule_182, axiom, ![H2, F2, G2]: (q2(F2, G2, F2) | (~p1(F2, F2, H2) | (~n1(G2, F2, H2) | ~q2(G2, H2, F2))))).
% 33.73/4.69 fof(rule_187, axiom, ![C2, D2, E2, F2]: (q2(C2, D2, C2) | (~r1(D2) | (~m0(E2, F2, C2) | (~k0(D2) | ~q2(D2, D2, D2)))))).
% 33.73/4.69 fof(rule_189, axiom, ![H2]: (s2(H2) | (~q2(b, H2, b) | ~s1(b)))).
% 33.73/4.69 fof(rule_194, axiom, ![F2, G2]: (k3(F2, F2, G2) | ~k2(G2, F2))).
% 33.73/4.69 fof(rule_202, axiom, ![I2, H2, G2, J2, A3]: (k3(G2, G2, H2) | (~q0(I2, H2) | (~k2(G2, J2) | ~k3(H2, A3, J2))))).
% 33.73/4.69 fof(rule_205, axiom, ![E2, F2]: (k3(E2, E2, E2) | ~p2(F2, E2, E2))).
% 33.73/4.69 fof(rule_238, axiom, ![I2]: (m3(I2, I2, I2) | ~p2(I2, I2, I2))).
% 33.73/4.69 fof(rule_240, axiom, ![D2, E2, F2]: (n3(D2) | ~p2(E2, F2, D2))).
% 33.73/4.69 fof(rule_255, axiom, ![I2, H2, G2]: (q3(G2, H2) | (~q2(I2, G2, H2) | ~n0(I2, G2)))).
% 33.73/4.69 fof(rule_257, axiom, ![C2, D2, B2]: (q3(B2, C2) | (~n1(D2, B2, C2) | (~s2(B2) | ~q3(C2, B2))))).
% 33.73/4.69 fof(rule_274, axiom, k4(c) | (~n0(c, d) | (~q3(e, b) | ~n3(e)))).
% 33.73/4.69 fof(rule_284, axiom, ![I2, H2]: (n4(H2, H2) | (~k4(I2) | ~m3(H2, H2, H2)))).
% 33.73/4.69 fof(rule_287, axiom, ![C2, B2]: (p4(B2, C2, B2) | ~k3(B2, B2, C2))).
% 33.73/4.69 fof(rule_295, axiom, ![C2, D2, E2, F2, B2]: (q4(B2, C2) | (~k3(D2, D2, B2) | (~q2(E2, C2, B2) | ~m3(E2, F2, E2))))).
% 33.73/4.69 fof(rule_307, axiom, ![C2, D2, E2, F2, B2]: (n5(B2, C2) | (~q4(D2, E2) | (~n4(B2, E2) | (~p4(F2, F2, C2) | ~n5(F2, C2)))))).
% 33.73/4.69 fof(rule_309, axiom, ![I2, H2]: (n5(H2, H2) | ~n4(I2, H2))).
% 33.73/4.69
% 33.73/4.69 Now clausify the problem and encode Horn clauses using encoding 3 of
% 33.73/4.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 33.73/4.69 We repeatedly replace C & s=t => u=v by the two clauses:
% 33.73/4.69 fresh(y, y, x1...xn) = u
% 33.73/4.69 C => fresh(s, t, x1...xn) = v
% 33.73/4.69 where fresh is a fresh function symbol and x1..xn are the free
% 33.73/4.69 variables of u and v.
% 33.73/4.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 33.73/4.69 input problem has no model of domain size 1).
% 33.73/4.69
% 33.73/4.69 The encoding turns the above axioms into the following unit equations and goals:
% 33.73/4.69
% 33.73/4.69 Axiom 1 (axiom_14): p0(b, X) = true.
% 33.73/4.69 Axiom 2 (axiom_17): q0(X, d) = true.
% 33.73/4.69 Axiom 3 (axiom_13): r0(e) = true.
% 33.73/4.69 Axiom 4 (axiom_1): s0(d) = true.
% 33.73/4.69 Axiom 5 (axiom_11): n0(e, b) = true.
% 33.73/4.69 Axiom 6 (axiom_34): n0(c, d) = true.
% 33.73/4.69 Axiom 7 (axiom_28): k0(e) = true.
% 33.73/4.69 Axiom 8 (rule_274): fresh473(X, X) = k4(c).
% 33.73/4.69 Axiom 9 (rule_090): fresh320(X, X) = true.
% 33.73/4.69 Axiom 10 (rule_117): fresh285(X, X) = true.
% 33.73/4.69 Axiom 11 (rule_274): fresh81(X, X) = true.
% 33.73/4.69 Axiom 12 (axiom_19): m0(X, d, Y) = true.
% 33.73/4.69 Axiom 13 (axiom_31): m0(b, b, e) = true.
% 33.73/4.69 Axiom 14 (rule_117): fresh286(X, X) = q1(d, d, d).
% 33.73/4.69 Axiom 15 (rule_090): fresh321(X, X) = p1(e, e, e).
% 33.73/4.69 Axiom 16 (rule_124): fresh593(X, X, Y) = true.
% 33.73/4.69 Axiom 17 (rule_274): fresh472(X, X) = fresh473(n3(e), true).
% 33.73/4.69 Axiom 18 (rule_001): fresh440(X, X, Y) = true.
% 33.73/4.69 Axiom 19 (rule_040): fresh388(X, X, Y) = true.
% 33.73/4.69 Axiom 20 (rule_085): fresh328(X, X, Y) = true.
% 33.73/4.69 Axiom 21 (rule_090): fresh321(k0(e), true) = fresh320(r0(e), true).
% 33.73/4.69 Axiom 22 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 33.73/4.69 Axiom 23 (rule_107): fresh300(X, X, Y) = true.
% 33.73/4.69 Axiom 24 (rule_117): fresh286(k0(e), true) = fresh285(s0(d), true).
% 33.73/4.69 Axiom 25 (rule_122): fresh279(X, X, Y) = true.
% 33.73/4.69 Axiom 26 (rule_124): fresh276(X, X, Y) = r1(Y).
% 33.73/4.69 Axiom 27 (rule_125): fresh275(X, X, Y) = true.
% 33.73/4.69 Axiom 28 (rule_129): fresh270(X, X, Y) = true.
% 33.73/4.69 Axiom 29 (rule_154): fresh241(X, X, Y) = true.
% 33.73/4.69 Axiom 30 (rule_181): fresh200(X, X, Y) = true.
% 33.73/4.69 Axiom 31 (rule_189): fresh192(X, X, Y) = s2(Y).
% 33.73/4.69 Axiom 32 (rule_189): fresh191(X, X, Y) = true.
% 33.73/4.69 Axiom 33 (rule_205): fresh170(X, X, Y) = true.
% 33.73/4.69 Axiom 34 (rule_238): fresh129(X, X, Y) = true.
% 33.73/4.69 Axiom 35 (rule_240): fresh127(X, X, Y) = true.
% 33.73/4.69 Axiom 36 (rule_274): fresh472(q3(e, b), true) = fresh81(n0(c, d), true).
% 33.73/4.69 Axiom 37 (rule_284): fresh68(X, X, Y) = n4(Y, Y).
% 33.73/4.69 Axiom 38 (rule_284): fresh67(X, X, Y) = true.
% 33.73/4.69 Axiom 39 (rule_309): fresh29(X, X, Y) = true.
% 33.73/4.69 Axiom 40 (rule_124): fresh592(X, X, Y, Z) = fresh593(s0(d), true, Y).
% 33.73/4.69 Axiom 41 (rule_127): fresh591(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 42 (rule_182): fresh551(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 43 (rule_187): fresh545(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 44 (rule_202): fresh533(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 45 (rule_295): fresh463(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 46 (rule_307): fresh457(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 47 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 33.73/4.69 Axiom 48 (rule_005): fresh437(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 49 (rule_036): fresh394(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 50 (rule_040): fresh389(X, X, Y, Z) = n1(Y, e, e).
% 33.73/4.69 Axiom 51 (rule_085): fresh328(p0(X, Y), true, Y) = p1(Y, Y, Y).
% 33.73/4.69 Axiom 52 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 33.73/4.69 Axiom 53 (rule_177): fresh207(X, X, Y, Z) = q2(Y, Z, Z).
% 33.73/4.69 Axiom 54 (rule_177): fresh206(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 55 (rule_194): fresh184(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 56 (rule_255): fresh103(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 57 (rule_257): fresh100(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 58 (rule_287): fresh62(X, X, Y, Z) = true.
% 33.73/4.69 Axiom 59 (rule_309): fresh29(n4(X, Y), true, Y) = n5(Y, Y).
% 33.73/4.69 Axiom 60 (rule_257): fresh496(X, X, Y, Z, W) = q3(Y, Z).
% 33.73/4.69 Axiom 61 (rule_307): fresh455(X, X, Y, Z, W) = n5(Y, Z).
% 33.73/4.69 Axiom 62 (rule_040): fresh389(k1(X), true, X, Y) = fresh388(m0(X, Y, e), true, X).
% 33.73/4.69 Axiom 63 (rule_107): fresh301(m0(e, d, X), true, X) = fresh300(m0(X, d, X), true, X).
% 33.73/4.69 Axiom 64 (rule_122): fresh279(m0(X, Y, X), true, X) = q1(X, X, X).
% 33.73/4.69 Axiom 65 (rule_127): fresh272(X, X, Y, Z, W) = k2(Y, Z).
% 33.73/4.69 Axiom 66 (rule_129): fresh270(q1(X, Y, Y), true, Y) = k2(Y, Y).
% 33.73/4.69 Axiom 67 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 33.73/4.69 Axiom 68 (rule_181): fresh200(p1(X, X, X), true, X) = q2(X, X, X).
% 33.73/4.69 Axiom 69 (rule_182): fresh199(X, X, Y, Z, W) = q2(Y, Z, Y).
% 33.73/4.69 Axiom 70 (rule_189): fresh192(q2(b, X, b), true, X) = fresh191(s1(b), true, X).
% 33.73/4.69 Axiom 71 (rule_194): fresh184(k2(X, Y), true, Y, X) = k3(Y, Y, X).
% 33.73/4.69 Axiom 72 (rule_202): fresh173(X, X, Y, Z, W) = k3(Y, Y, Z).
% 33.73/4.69 Axiom 73 (rule_205): fresh170(p2(X, Y, Y), true, Y) = k3(Y, Y, Y).
% 33.73/4.69 Axiom 74 (rule_238): fresh129(p2(X, X, X), true, X) = m3(X, X, X).
% 33.73/4.69 Axiom 75 (rule_240): fresh127(p2(X, Y, Z), true, Z) = n3(Z).
% 33.73/4.69 Axiom 76 (rule_255): fresh104(X, X, Y, Z, W) = q3(Y, Z).
% 33.73/4.69 Axiom 77 (rule_284): fresh68(k4(X), true, Y) = fresh67(m3(Y, Y, Y), true, Y).
% 33.73/4.69 Axiom 78 (rule_295): fresh51(X, X, Y, Z, W) = q4(Y, Z).
% 33.73/4.69 Axiom 79 (rule_124): fresh592(q1(d, X, d), true, Y, X) = fresh276(q0(Y, X), true, Y).
% 33.73/4.69 Axiom 80 (rule_127): fresh590(X, X, Y, Z, W, V) = fresh591(k1(W), true, Y, Z).
% 33.73/4.69 Axiom 81 (rule_182): fresh550(X, X, Y, Z, W) = fresh551(n1(Z, Y, W), true, Y, Z).
% 33.73/4.69 Axiom 82 (rule_187): fresh544(X, X, Y, Z, W, V) = fresh545(m0(W, V, Y), true, Y, Z).
% 33.73/4.69 Axiom 83 (rule_187): fresh543(X, X, Y, Z, W, V) = q2(Y, Z, Y).
% 33.73/4.69 Axiom 84 (rule_202): fresh532(X, X, Y, Z, W, V) = fresh533(q0(W, Z), true, Y, Z).
% 33.73/4.69 Axiom 85 (rule_257): fresh495(X, X, Y, Z, W) = fresh496(s2(Y), true, Y, Z, W).
% 33.73/4.69 Axiom 86 (rule_295): fresh462(X, X, Y, Z, W, V) = fresh463(q2(W, Z, Y), true, Y, Z).
% 33.73/4.69 Axiom 87 (rule_307): fresh456(X, X, Y, Z, W, V) = fresh457(n4(Y, W), true, Y, Z).
% 33.73/4.69 Axiom 88 (rule_005): fresh437(m0(X, X, Y), true, Y, X) = m1(Y, X, Y).
% 33.73/4.69 Axiom 89 (rule_036): fresh394(m0(b, X, Y), true, Y, X) = n1(Y, Y, X).
% 33.73/4.69 Axiom 90 (rule_177): fresh207(p1(X, X, X), true, X, Y) = fresh206(k0(Y), true, X, Y).
% 33.73/4.69 Axiom 91 (rule_257): fresh495(q3(X, Y), true, Y, X, Z) = fresh100(n1(Z, Y, X), true, Y, X).
% 33.73/4.69 Axiom 92 (rule_287): fresh62(k3(X, X, Y), true, X, Y) = p4(X, Y, X).
% 33.73/4.69 Axiom 93 (rule_187): fresh542(X, X, Y, Z, W, V) = fresh543(k0(Z), true, Y, Z, W, V).
% 33.73/4.69 Axiom 94 (rule_307): fresh454(X, X, Y, Z, W, V, U) = fresh455(p4(U, U, Z), true, Y, Z, V).
% 33.73/4.69 Axiom 95 (rule_127): fresh590(k2(X, Y), true, Z, Y, X, W) = fresh272(m1(W, Y, Z), true, Z, Y, X).
% 33.73/4.69 Axiom 96 (rule_182): fresh550(q2(X, Y, Z), true, Z, X, Y) = fresh199(p1(Z, Z, Y), true, Z, X, Y).
% 33.73/4.69 Axiom 97 (rule_255): fresh104(q2(X, Y, Z), true, Y, Z, X) = fresh103(n0(X, Y), true, Y, Z).
% 33.73/4.69 Axiom 98 (rule_187): fresh542(q2(X, X, X), true, Y, X, Z, W) = fresh544(r1(X), true, Y, X, Z, W).
% 33.73/4.69 Axiom 99 (rule_202): fresh532(k3(X, Y, Z), true, W, X, V, Z) = fresh173(k2(W, Z), true, W, X, V).
% 33.73/4.69 Axiom 100 (rule_295): fresh462(m3(X, Y, X), true, Z, W, X, V) = fresh51(k3(V, V, Z), true, Z, W, X).
% 33.73/4.69 Axiom 101 (rule_307): fresh454(n5(X, Y), true, Z, Y, W, V, X) = fresh456(q4(W, V), true, Z, Y, V, X).
% 33.73/4.69
% 33.73/4.69 Lemma 102: k2(X, X) = true.
% 33.73/4.69 Proof:
% 33.73/4.69 k2(X, X)
% 33.73/4.69 = { by axiom 66 (rule_129) R->L }
% 33.73/4.69 fresh270(q1(e, X, X), true, X)
% 33.73/4.69 = { by axiom 22 (rule_107) R->L }
% 33.73/4.69 fresh270(fresh301(true, true, X), true, X)
% 33.73/4.69 = { by axiom 12 (axiom_19) R->L }
% 33.73/4.69 fresh270(fresh301(m0(e, d, X), true, X), true, X)
% 33.73/4.69 = { by axiom 63 (rule_107) }
% 33.73/4.69 fresh270(fresh300(m0(X, d, X), true, X), true, X)
% 33.73/4.69 = { by axiom 12 (axiom_19) }
% 33.73/4.69 fresh270(fresh300(true, true, X), true, X)
% 33.73/4.69 = { by axiom 23 (rule_107) }
% 33.73/4.69 fresh270(true, true, X)
% 33.73/4.69 = { by axiom 28 (rule_129) }
% 33.73/4.69 true
% 33.73/4.69
% 33.73/4.69 Lemma 103: p2(X, X, X) = true.
% 33.73/4.69 Proof:
% 33.73/4.69 p2(X, X, X)
% 33.73/4.69 = { by axiom 67 (rule_154) R->L }
% 33.73/4.69 fresh241(q1(X, X, X), true, X)
% 33.73/4.69 = { by axiom 64 (rule_122) R->L }
% 33.73/4.69 fresh241(fresh279(m0(X, d, X), true, X), true, X)
% 33.73/4.69 = { by axiom 12 (axiom_19) }
% 33.73/4.69 fresh241(fresh279(true, true, X), true, X)
% 33.73/4.69 = { by axiom 25 (rule_122) }
% 33.73/4.69 fresh241(true, true, X)
% 33.73/4.69 = { by axiom 29 (rule_154) }
% 33.73/4.69 true
% 33.73/4.69
% 33.73/4.69 Lemma 104: p1(e, e, e) = true.
% 33.73/4.69 Proof:
% 33.73/4.69 p1(e, e, e)
% 33.73/4.69 = { by axiom 15 (rule_090) R->L }
% 33.73/4.69 fresh321(true, true)
% 33.73/4.69 = { by axiom 7 (axiom_28) R->L }
% 33.73/4.69 fresh321(k0(e), true)
% 33.73/4.69 = { by axiom 21 (rule_090) }
% 33.73/4.69 fresh320(r0(e), true)
% 33.73/4.69 = { by axiom 3 (axiom_13) }
% 33.73/4.69 fresh320(true, true)
% 33.73/4.69 = { by axiom 9 (rule_090) }
% 33.73/4.69 true
% 33.73/4.69
% 33.73/4.69 Lemma 105: q2(X, e, X) = true.
% 33.73/4.69 Proof:
% 33.73/4.69 q2(X, e, X)
% 33.73/4.69 = { by axiom 83 (rule_187) R->L }
% 33.73/4.69 fresh543(true, true, X, e, Y, d)
% 33.73/4.69 = { by axiom 7 (axiom_28) R->L }
% 33.73/4.69 fresh543(k0(e), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 93 (rule_187) R->L }
% 33.73/4.69 fresh542(true, true, X, e, Y, d)
% 33.73/4.69 = { by axiom 30 (rule_181) R->L }
% 33.73/4.69 fresh542(fresh200(true, true, e), true, X, e, Y, d)
% 33.73/4.69 = { by lemma 104 R->L }
% 33.73/4.69 fresh542(fresh200(p1(e, e, e), true, e), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 68 (rule_181) }
% 33.73/4.69 fresh542(q2(e, e, e), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 98 (rule_187) }
% 33.73/4.69 fresh544(r1(e), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 26 (rule_124) R->L }
% 33.73/4.69 fresh544(fresh276(true, true, e), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 2 (axiom_17) R->L }
% 33.73/4.69 fresh544(fresh276(q0(e, d), true, e), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 79 (rule_124) R->L }
% 33.73/4.69 fresh544(fresh592(q1(d, d, d), true, e, d), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 14 (rule_117) R->L }
% 33.73/4.69 fresh544(fresh592(fresh286(true, true), true, e, d), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 7 (axiom_28) R->L }
% 33.73/4.69 fresh544(fresh592(fresh286(k0(e), true), true, e, d), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 24 (rule_117) }
% 33.73/4.69 fresh544(fresh592(fresh285(s0(d), true), true, e, d), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 4 (axiom_1) }
% 33.73/4.69 fresh544(fresh592(fresh285(true, true), true, e, d), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 10 (rule_117) }
% 33.73/4.69 fresh544(fresh592(true, true, e, d), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 40 (rule_124) }
% 33.73/4.69 fresh544(fresh593(s0(d), true, e), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 4 (axiom_1) }
% 33.73/4.69 fresh544(fresh593(true, true, e), true, X, e, Y, d)
% 33.73/4.69 = { by axiom 16 (rule_124) }
% 33.73/4.69 fresh544(true, true, X, e, Y, d)
% 33.73/4.69 = { by axiom 82 (rule_187) }
% 33.73/4.69 fresh545(m0(Y, d, X), true, X, e)
% 33.73/4.69 = { by axiom 12 (axiom_19) }
% 33.73/4.69 fresh545(true, true, X, e)
% 33.73/4.69 = { by axiom 43 (rule_187) }
% 33.73/4.69 true
% 33.73/4.69
% 33.73/4.69 Lemma 106: m3(X, X, X) = true.
% 33.73/4.70 Proof:
% 33.73/4.70 m3(X, X, X)
% 33.73/4.70 = { by axiom 74 (rule_238) R->L }
% 33.73/4.70 fresh129(p2(X, X, X), true, X)
% 33.73/4.70 = { by lemma 103 }
% 33.73/4.70 fresh129(true, true, X)
% 33.73/4.70 = { by axiom 34 (rule_238) }
% 33.73/4.70 true
% 33.73/4.70
% 33.73/4.70 Lemma 107: fresh68(X, X, Y) = true.
% 33.73/4.70 Proof:
% 33.73/4.70 fresh68(X, X, Y)
% 33.73/4.70 = { by axiom 37 (rule_284) }
% 33.73/4.70 n4(Y, Y)
% 33.73/4.70 = { by axiom 37 (rule_284) R->L }
% 33.73/4.70 fresh68(true, true, Y)
% 33.73/4.70 = { by axiom 11 (rule_274) R->L }
% 33.73/4.70 fresh68(fresh81(true, true), true, Y)
% 33.73/4.70 = { by axiom 6 (axiom_34) R->L }
% 33.73/4.70 fresh68(fresh81(n0(c, d), true), true, Y)
% 33.73/4.70 = { by axiom 36 (rule_274) R->L }
% 33.73/4.70 fresh68(fresh472(q3(e, b), true), true, Y)
% 33.73/4.70 = { by axiom 60 (rule_257) R->L }
% 33.73/4.70 fresh68(fresh472(fresh496(true, true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 32 (rule_189) R->L }
% 33.73/4.70 fresh68(fresh472(fresh496(fresh191(true, true, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 27 (rule_125) R->L }
% 33.73/4.70 fresh68(fresh472(fresh496(fresh191(fresh275(true, true, b), true, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 1 (axiom_14) R->L }
% 33.73/4.70 fresh68(fresh472(fresh496(fresh191(fresh275(p0(b, b), true, b), true, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 52 (rule_125) }
% 33.73/4.70 fresh68(fresh472(fresh496(fresh191(s1(b), true, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 70 (rule_189) R->L }
% 33.73/4.70 fresh68(fresh472(fresh496(fresh192(q2(b, e, b), true, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by lemma 105 }
% 33.73/4.70 fresh68(fresh472(fresh496(fresh192(true, true, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 31 (rule_189) }
% 33.73/4.70 fresh68(fresh472(fresh496(s2(e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 85 (rule_257) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(true, true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 56 (rule_255) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh103(true, true, b, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 5 (axiom_11) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh103(n0(e, b), true, b, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 97 (rule_255) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(q2(e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 69 (rule_182) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh199(true, true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by lemma 104 R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh199(p1(e, e, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 96 (rule_182) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh550(q2(b, e, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 53 (rule_177) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh550(fresh207(true, true, b, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 20 (rule_085) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh550(fresh207(fresh328(true, true, b), true, b, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 1 (axiom_14) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh550(fresh207(fresh328(p0(b, b), true, b), true, b, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 51 (rule_085) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh550(fresh207(p1(b, b, b), true, b, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 90 (rule_177) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh550(fresh206(k0(e), true, b, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 7 (axiom_28) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh550(fresh206(true, true, b, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 54 (rule_177) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh550(true, true, e, b, e), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 81 (rule_182) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh551(n1(b, e, e), true, e, b), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 50 (rule_040) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh551(fresh389(true, true, b, d), true, e, b), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 18 (rule_001) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh551(fresh389(fresh440(true, true, b), true, b, d), true, e, b), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 5 (axiom_11) R->L }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh551(fresh389(fresh440(n0(e, b), true, b), true, b, d), true, e, b), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 47 (rule_001) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh551(fresh389(k1(b), true, b, d), true, e, b), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 62 (rule_040) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh551(fresh388(m0(b, d, e), true, b), true, e, b), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 12 (axiom_19) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh551(fresh388(true, true, b), true, e, b), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 19 (rule_040) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(fresh551(true, true, e, b), true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 42 (rule_182) }
% 33.73/4.70 fresh68(fresh472(fresh495(fresh104(true, true, b, e, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 76 (rule_255) }
% 33.73/4.70 fresh68(fresh472(fresh495(q3(b, e), true, e, b, e), true), true, Y)
% 33.73/4.70 = { by axiom 91 (rule_257) }
% 33.73/4.70 fresh68(fresh472(fresh100(n1(e, e, b), true, e, b), true), true, Y)
% 33.73/4.70 = { by axiom 89 (rule_036) R->L }
% 33.73/4.70 fresh68(fresh472(fresh100(fresh394(m0(b, b, e), true, e, b), true, e, b), true), true, Y)
% 33.73/4.70 = { by axiom 13 (axiom_31) }
% 33.73/4.70 fresh68(fresh472(fresh100(fresh394(true, true, e, b), true, e, b), true), true, Y)
% 33.73/4.70 = { by axiom 49 (rule_036) }
% 33.73/4.70 fresh68(fresh472(fresh100(true, true, e, b), true), true, Y)
% 33.73/4.70 = { by axiom 57 (rule_257) }
% 33.73/4.70 fresh68(fresh472(true, true), true, Y)
% 33.73/4.70 = { by axiom 17 (rule_274) }
% 33.73/4.70 fresh68(fresh473(n3(e), true), true, Y)
% 33.73/4.70 = { by axiom 75 (rule_240) R->L }
% 33.73/4.70 fresh68(fresh473(fresh127(p2(e, e, e), true, e), true), true, Y)
% 33.73/4.70 = { by lemma 103 }
% 33.73/4.70 fresh68(fresh473(fresh127(true, true, e), true), true, Y)
% 33.73/4.70 = { by axiom 35 (rule_240) }
% 33.73/4.70 fresh68(fresh473(true, true), true, Y)
% 33.73/4.70 = { by axiom 8 (rule_274) }
% 33.73/4.70 fresh68(k4(c), true, Y)
% 33.73/4.70 = { by axiom 77 (rule_284) }
% 33.73/4.70 fresh67(m3(Y, Y, Y), true, Y)
% 33.73/4.70 = { by lemma 106 }
% 33.73/4.70 fresh67(true, true, Y)
% 33.73/4.70 = { by axiom 38 (rule_284) }
% 33.73/4.70 true
% 33.73/4.70
% 33.73/4.70 Goal 1 (prove_this): n5(e, a) = true.
% 33.73/4.70 Proof:
% 33.73/4.70 n5(e, a)
% 33.73/4.70 = { by axiom 61 (rule_307) R->L }
% 33.73/4.70 fresh455(true, true, e, a, e)
% 33.73/4.70 = { by axiom 58 (rule_287) R->L }
% 33.73/4.70 fresh455(fresh62(true, true, a, a), true, e, a, e)
% 33.73/4.70 = { by axiom 33 (rule_205) R->L }
% 33.73/4.70 fresh455(fresh62(fresh170(true, true, a), true, a, a), true, e, a, e)
% 33.73/4.70 = { by lemma 103 R->L }
% 33.73/4.70 fresh455(fresh62(fresh170(p2(a, a, a), true, a), true, a, a), true, e, a, e)
% 33.73/4.70 = { by axiom 73 (rule_205) }
% 33.73/4.70 fresh455(fresh62(k3(a, a, a), true, a, a), true, e, a, e)
% 33.73/4.70 = { by axiom 92 (rule_287) }
% 33.73/4.70 fresh455(p4(a, a, a), true, e, a, e)
% 33.73/4.70 = { by axiom 94 (rule_307) R->L }
% 33.73/4.70 fresh454(true, true, e, a, d, e, a)
% 33.73/4.70 = { by axiom 39 (rule_309) R->L }
% 33.73/4.70 fresh454(fresh29(true, true, a), true, e, a, d, e, a)
% 33.73/4.70 = { by lemma 107 R->L }
% 33.73/4.70 fresh454(fresh29(fresh68(X, X, a), true, a), true, e, a, d, e, a)
% 33.73/4.70 = { by axiom 37 (rule_284) }
% 33.73/4.70 fresh454(fresh29(n4(a, a), true, a), true, e, a, d, e, a)
% 33.73/4.70 = { by axiom 59 (rule_309) }
% 33.73/4.70 fresh454(n5(a, a), true, e, a, d, e, a)
% 33.73/4.70 = { by axiom 101 (rule_307) }
% 33.73/4.70 fresh456(q4(d, e), true, e, a, e, a)
% 33.73/4.70 = { by axiom 78 (rule_295) R->L }
% 33.73/4.70 fresh456(fresh51(true, true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 44 (rule_202) R->L }
% 33.73/4.70 fresh456(fresh51(fresh533(true, true, Y, d), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 2 (axiom_17) R->L }
% 33.73/4.70 fresh456(fresh51(fresh533(q0(Z, d), true, Y, d), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 84 (rule_202) R->L }
% 33.73/4.70 fresh456(fresh51(fresh532(true, true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 55 (rule_194) R->L }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(true, true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 41 (rule_127) R->L }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh591(true, true, Y, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 18 (rule_001) R->L }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh591(fresh440(true, true, d), true, Y, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 6 (axiom_34) R->L }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh591(fresh440(n0(c, d), true, d), true, Y, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 47 (rule_001) }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh591(k1(d), true, Y, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 80 (rule_127) R->L }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh590(true, true, Y, d, d, Y), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by lemma 102 R->L }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh590(k2(d, d), true, Y, d, d, Y), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 95 (rule_127) }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh272(m1(Y, d, Y), true, Y, d, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 88 (rule_005) R->L }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh272(fresh437(m0(d, d, Y), true, Y, d), true, Y, d, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 12 (axiom_19) }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh272(fresh437(true, true, Y, d), true, Y, d, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 48 (rule_005) }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(fresh272(true, true, Y, d, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 65 (rule_127) }
% 33.73/4.70 fresh456(fresh51(fresh532(fresh184(k2(Y, d), true, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 71 (rule_194) }
% 33.73/4.70 fresh456(fresh51(fresh532(k3(d, d, Y), true, Y, d, Z, Y), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 99 (rule_202) }
% 33.73/4.70 fresh456(fresh51(fresh173(k2(Y, Y), true, Y, d, Z), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by lemma 102 }
% 33.73/4.70 fresh456(fresh51(fresh173(true, true, Y, d, Z), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 72 (rule_202) }
% 33.73/4.70 fresh456(fresh51(k3(Y, Y, d), true, d, e, d), true, e, a, e, a)
% 33.73/4.70 = { by axiom 100 (rule_295) R->L }
% 33.73/4.70 fresh456(fresh462(m3(d, d, d), true, d, e, d, Y), true, e, a, e, a)
% 33.73/4.70 = { by lemma 106 }
% 33.73/4.70 fresh456(fresh462(true, true, d, e, d, Y), true, e, a, e, a)
% 33.73/4.70 = { by axiom 86 (rule_295) }
% 33.73/4.70 fresh456(fresh463(q2(d, e, d), true, d, e), true, e, a, e, a)
% 33.73/4.70 = { by lemma 105 }
% 33.73/4.70 fresh456(fresh463(true, true, d, e), true, e, a, e, a)
% 33.73/4.70 = { by axiom 45 (rule_295) }
% 33.73/4.70 fresh456(true, true, e, a, e, a)
% 33.73/4.70 = { by axiom 87 (rule_307) }
% 33.73/4.70 fresh457(n4(e, e), true, e, a)
% 33.73/4.70 = { by axiom 37 (rule_284) R->L }
% 33.73/4.70 fresh457(fresh68(W, W, e), true, e, a)
% 33.73/4.70 = { by lemma 107 }
% 33.73/4.70 fresh457(true, true, e, a)
% 33.73/4.71 = { by axiom 46 (rule_307) }
% 33.73/4.71 true
% 33.73/4.71 % SZS output end Proof
% 33.73/4.71
% 33.73/4.71 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------