TSTP Solution File: SYN156-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN156-1 : 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 : n009.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 03:33:24 EDT 2023
% Result : Unsatisfiable 45.16s 6.03s
% Output : Proof 46.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN156-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n009.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 18:49:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 45.16/6.03 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 45.16/6.03
% 45.16/6.03 % SZS status Unsatisfiable
% 45.16/6.03
% 46.92/6.26 % SZS output start Proof
% 46.92/6.26 Take the following subset of the input axioms:
% 46.92/6.27 fof(axiom_1, axiom, s0(d)).
% 46.92/6.27 fof(axiom_11, axiom, n0(e, b)).
% 46.92/6.27 fof(axiom_12, axiom, ![X]: m0(a, X, a)).
% 46.92/6.27 fof(axiom_13, axiom, r0(e)).
% 46.92/6.27 fof(axiom_14, axiom, ![X2]: p0(b, X2)).
% 46.92/6.27 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 46.92/6.27 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 46.92/6.27 fof(axiom_20, axiom, l0(a)).
% 46.92/6.27 fof(axiom_28, axiom, k0(e)).
% 46.92/6.27 fof(axiom_31, axiom, m0(b, b, e)).
% 46.92/6.27 fof(axiom_34, axiom, n0(c, d)).
% 46.92/6.27 fof(axiom_37, axiom, n0(b, a)).
% 46.92/6.27 fof(prove_this, negated_conjecture, ~n4(a, e)).
% 46.92/6.27 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 46.92/6.27 fof(rule_021, axiom, ![I2, J2]: (m1(I2, J2, I2) | (~l0(I2) | ~k0(J2)))).
% 46.92/6.27 fof(rule_036, axiom, ![B, A2]: (n1(A2, A2, B) | ~m0(b, B, A2))).
% 46.92/6.27 fof(rule_040, axiom, ![C, D]: (n1(C, e, e) | (~m0(C, D, e) | ~k1(C)))).
% 46.92/6.27 fof(rule_082, axiom, ![H, I2, J2, A2_2]: (p1(H, I2, J2) | (~m0(J2, H, A2_2) | ~p1(J2, H, A2_2)))).
% 46.92/6.27 fof(rule_085, axiom, ![C2, B2]: (p1(B2, B2, B2) | ~p0(C2, B2))).
% 46.92/6.27 fof(rule_090, axiom, p1(e, e, e) | (~r0(e) | ~k0(e))).
% 46.92/6.27 fof(rule_107, axiom, ![A2_2]: (q1(e, A2_2, A2_2) | (~m0(A2_2, d, A2_2) | ~m0(e, d, A2_2)))).
% 46.92/6.27 fof(rule_117, axiom, q1(d, d, d) | (~k0(e) | ~s0(d))).
% 46.92/6.27 fof(rule_122, axiom, ![G, H2]: (q1(G, G, G) | ~m0(G, H2, G))).
% 46.92/6.27 fof(rule_124, axiom, ![E, D2]: (r1(D2) | (~q0(D2, E) | (~s0(d) | ~q1(d, E, d))))).
% 46.92/6.27 fof(rule_125, axiom, ![I2]: (s1(I2) | ~p0(I2, I2))).
% 46.92/6.27 fof(rule_136, axiom, m2(b) | ~k1(b)).
% 46.92/6.27 fof(rule_154, axiom, ![A2_2]: (p2(A2_2, A2_2, A2_2) | ~q1(A2_2, A2_2, A2_2))).
% 46.92/6.27 fof(rule_155, axiom, ![I2, H2, J2]: (p2(H2, I2, I2) | (~k1(J2) | ~p2(e, H2, I2)))).
% 46.92/6.27 fof(rule_176, axiom, ![D2, E2]: (p2(D2, E2, D2) | ~m1(E2, D2, E2))).
% 46.92/6.27 fof(rule_177, axiom, ![F, E2]: (q2(E2, F, F) | (~k0(F) | ~p1(E2, E2, E2)))).
% 46.92/6.27 fof(rule_181, axiom, ![I2]: (q2(I2, I2, I2) | ~p1(I2, I2, I2))).
% 46.92/6.27 fof(rule_182, axiom, ![H2, G2, F2]: (q2(F2, G2, F2) | (~p1(F2, F2, H2) | (~n1(G2, F2, H2) | ~q2(G2, H2, F2))))).
% 46.92/6.27 fof(rule_187, axiom, ![C2, D2, E2, F2]: (q2(C2, D2, C2) | (~r1(D2) | (~m0(E2, F2, C2) | (~k0(D2) | ~q2(D2, D2, D2)))))).
% 46.92/6.27 fof(rule_188, axiom, ![G2]: (r2(G2) | (~r1(G2) | ~l0(G2)))).
% 46.92/6.27 fof(rule_189, axiom, ![H2]: (s2(H2) | (~q2(b, H2, b) | ~s1(b)))).
% 46.92/6.27 fof(rule_201, axiom, ![C2, D2, B2, E2]: (k3(B2, B2, C2) | (~p1(C2, D2, B2) | (~m2(E2) | ~m2(D2))))).
% 46.92/6.27 fof(rule_238, axiom, ![I2]: (m3(I2, I2, I2) | ~p2(I2, I2, I2))).
% 46.92/6.27 fof(rule_240, axiom, ![D2, E2, F2]: (n3(D2) | ~p2(E2, F2, D2))).
% 46.92/6.27 fof(rule_242, axiom, ![J2, A2_2, B2]: (p3(J2, A2_2, B2) | (~r2(A2_2) | ~k3(A2_2, B2, J2)))).
% 46.92/6.27 fof(rule_251, axiom, ![A2_2, C2, D2, B2]: (p3(A2_2, B2, B2) | (~m3(B2, C2, D2) | ~p2(A2_2, B2, D2)))).
% 46.92/6.27 fof(rule_255, axiom, ![I2, H2, G2]: (q3(G2, H2) | (~q2(I2, G2, H2) | ~n0(I2, G2)))).
% 46.92/6.27 fof(rule_257, axiom, ![C2, D2, B2]: (q3(B2, C2) | (~n1(D2, B2, C2) | (~s2(B2) | ~q3(C2, B2))))).
% 46.92/6.27 fof(rule_274, axiom, k4(c) | (~n0(c, d) | (~q3(e, b) | ~n3(e)))).
% 46.92/6.27 fof(rule_281, axiom, ![J2, A2_2]: (n4(J2, A2_2) | (~p3(J2, A2_2, A2_2) | ~n4(J2, J2)))).
% 46.92/6.27 fof(rule_284, axiom, ![I2, H2]: (n4(H2, H2) | (~k4(I2) | ~m3(H2, H2, H2)))).
% 46.92/6.27
% 46.92/6.27 Now clausify the problem and encode Horn clauses using encoding 3 of
% 46.92/6.27 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 46.92/6.27 We repeatedly replace C & s=t => u=v by the two clauses:
% 46.92/6.27 fresh(y, y, x1...xn) = u
% 46.92/6.27 C => fresh(s, t, x1...xn) = v
% 46.92/6.27 where fresh is a fresh function symbol and x1..xn are the free
% 46.92/6.27 variables of u and v.
% 46.92/6.27 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 46.92/6.27 input problem has no model of domain size 1).
% 46.92/6.27
% 46.92/6.27 The encoding turns the above axioms into the following unit equations and goals:
% 46.92/6.27
% 46.92/6.27 Axiom 1 (axiom_14): p0(b, X) = true.
% 46.92/6.27 Axiom 2 (axiom_17): q0(X, d) = true.
% 46.92/6.27 Axiom 3 (axiom_13): r0(e) = true.
% 46.92/6.27 Axiom 4 (axiom_1): s0(d) = true.
% 46.92/6.27 Axiom 5 (axiom_20): l0(a) = true.
% 46.92/6.27 Axiom 6 (axiom_37): n0(b, a) = true.
% 46.92/6.27 Axiom 7 (axiom_11): n0(e, b) = true.
% 46.92/6.27 Axiom 8 (axiom_34): n0(c, d) = true.
% 46.92/6.27 Axiom 9 (axiom_28): k0(e) = true.
% 46.92/6.27 Axiom 10 (rule_274): fresh473(X, X) = k4(c).
% 46.92/6.27 Axiom 11 (rule_090): fresh320(X, X) = true.
% 46.92/6.27 Axiom 12 (rule_117): fresh285(X, X) = true.
% 46.92/6.27 Axiom 13 (rule_136): fresh263(X, X) = true.
% 46.92/6.27 Axiom 14 (rule_274): fresh81(X, X) = true.
% 46.92/6.27 Axiom 15 (axiom_19): m0(X, d, Y) = true.
% 46.92/6.27 Axiom 16 (axiom_31): m0(b, b, e) = true.
% 46.92/6.27 Axiom 17 (axiom_12): m0(a, X, a) = true.
% 46.92/6.27 Axiom 18 (rule_117): fresh286(X, X) = q1(d, d, d).
% 46.92/6.27 Axiom 19 (rule_090): fresh321(X, X) = p1(e, e, e).
% 46.92/6.27 Axiom 20 (rule_124): fresh593(X, X, Y) = true.
% 46.92/6.27 Axiom 21 (rule_274): fresh472(X, X) = fresh473(n3(e), true).
% 46.92/6.27 Axiom 22 (rule_001): fresh440(X, X, Y) = true.
% 46.92/6.27 Axiom 23 (rule_040): fresh388(X, X, Y) = true.
% 46.92/6.27 Axiom 24 (rule_085): fresh328(X, X, Y) = true.
% 46.92/6.27 Axiom 25 (rule_090): fresh321(k0(e), true) = fresh320(r0(e), true).
% 46.92/6.27 Axiom 26 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 46.92/6.27 Axiom 27 (rule_107): fresh300(X, X, Y) = true.
% 46.92/6.27 Axiom 28 (rule_117): fresh286(k0(e), true) = fresh285(s0(d), true).
% 46.92/6.27 Axiom 29 (rule_122): fresh279(X, X, Y) = true.
% 46.92/6.27 Axiom 30 (rule_124): fresh276(X, X, Y) = r1(Y).
% 46.92/6.27 Axiom 31 (rule_125): fresh275(X, X, Y) = true.
% 46.92/6.27 Axiom 32 (rule_136): fresh263(k1(b), true) = m2(b).
% 46.92/6.27 Axiom 33 (rule_154): fresh241(X, X, Y) = true.
% 46.92/6.27 Axiom 34 (rule_181): fresh200(X, X, Y) = true.
% 46.92/6.27 Axiom 35 (rule_188): fresh194(X, X, Y) = r2(Y).
% 46.92/6.27 Axiom 36 (rule_188): fresh193(X, X, Y) = true.
% 46.92/6.27 Axiom 37 (rule_189): fresh192(X, X, Y) = s2(Y).
% 46.92/6.27 Axiom 38 (rule_189): fresh191(X, X, Y) = true.
% 46.92/6.27 Axiom 39 (rule_238): fresh129(X, X, Y) = true.
% 46.92/6.27 Axiom 40 (rule_240): fresh127(X, X, Y) = true.
% 46.92/6.27 Axiom 41 (rule_274): fresh472(q3(e, b), true) = fresh81(n0(c, d), true).
% 46.92/6.27 Axiom 42 (rule_284): fresh68(X, X, Y) = n4(Y, Y).
% 46.92/6.27 Axiom 43 (rule_284): fresh67(X, X, Y) = true.
% 46.92/6.27 Axiom 44 (rule_124): fresh592(X, X, Y, Z) = fresh593(s0(d), true, Y).
% 46.92/6.27 Axiom 45 (rule_182): fresh551(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 46 (rule_187): fresh545(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 47 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 46.92/6.27 Axiom 48 (rule_021): fresh415(X, X, Y, Z) = m1(Y, Z, Y).
% 46.92/6.27 Axiom 49 (rule_021): fresh414(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 50 (rule_036): fresh394(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 51 (rule_040): fresh389(X, X, Y, Z) = n1(Y, e, e).
% 46.92/6.27 Axiom 52 (rule_085): fresh328(p0(X, Y), true, Y) = p1(Y, Y, Y).
% 46.92/6.27 Axiom 53 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 46.92/6.27 Axiom 54 (rule_155): fresh239(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 55 (rule_176): fresh208(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 56 (rule_177): fresh207(X, X, Y, Z) = q2(Y, Z, Z).
% 46.92/6.27 Axiom 57 (rule_177): fresh206(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 58 (rule_188): fresh194(r1(X), true, X) = fresh193(l0(X), true, X).
% 46.92/6.27 Axiom 59 (rule_201): fresh174(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 60 (rule_251): fresh110(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 61 (rule_255): fresh103(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 62 (rule_257): fresh100(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 63 (rule_281): fresh74(X, X, Y, Z) = n4(Y, Z).
% 46.92/6.27 Axiom 64 (rule_281): fresh73(X, X, Y, Z) = true.
% 46.92/6.27 Axiom 65 (rule_201): fresh535(X, X, Y, Z, W) = k3(Y, Y, W).
% 46.92/6.27 Axiom 66 (rule_257): fresh496(X, X, Y, Z, W) = q3(Y, Z).
% 46.92/6.27 Axiom 67 (rule_021): fresh415(k0(X), true, Y, X) = fresh414(l0(Y), true, Y, X).
% 46.92/6.27 Axiom 68 (rule_040): fresh389(k1(X), true, X, Y) = fresh388(m0(X, Y, e), true, X).
% 46.92/6.27 Axiom 69 (rule_082): fresh333(X, X, Y, Z, W) = true.
% 46.92/6.27 Axiom 70 (rule_107): fresh301(m0(e, d, X), true, X) = fresh300(m0(X, d, X), true, X).
% 46.92/6.27 Axiom 71 (rule_122): fresh279(m0(X, Y, X), true, X) = q1(X, X, X).
% 46.92/6.27 Axiom 72 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 46.92/6.27 Axiom 73 (rule_155): fresh240(X, X, Y, Z, W) = p2(Y, Z, Z).
% 46.92/6.27 Axiom 74 (rule_181): fresh200(p1(X, X, X), true, X) = q2(X, X, X).
% 46.92/6.27 Axiom 75 (rule_182): fresh199(X, X, Y, Z, W) = q2(Y, Z, Y).
% 46.92/6.27 Axiom 76 (rule_189): fresh192(q2(b, X, b), true, X) = fresh191(s1(b), true, X).
% 46.92/6.27 Axiom 77 (rule_238): fresh129(p2(X, X, X), true, X) = m3(X, X, X).
% 46.92/6.27 Axiom 78 (rule_240): fresh127(p2(X, Y, Z), true, Z) = n3(Z).
% 46.92/6.27 Axiom 79 (rule_242): fresh124(X, X, Y, Z, W) = p3(Y, Z, W).
% 46.92/6.27 Axiom 80 (rule_242): fresh123(X, X, Y, Z, W) = true.
% 46.92/6.27 Axiom 81 (rule_251): fresh111(X, X, Y, Z, W) = p3(Y, Z, Z).
% 46.92/6.27 Axiom 82 (rule_255): fresh104(X, X, Y, Z, W) = q3(Y, Z).
% 46.92/6.27 Axiom 83 (rule_284): fresh68(k4(X), true, Y) = fresh67(m3(Y, Y, Y), true, Y).
% 46.92/6.27 Axiom 84 (rule_124): fresh592(q1(d, X, d), true, Y, X) = fresh276(q0(Y, X), true, Y).
% 46.92/6.27 Axiom 85 (rule_182): fresh550(X, X, Y, Z, W) = fresh551(n1(Z, Y, W), true, Y, Z).
% 46.92/6.27 Axiom 86 (rule_187): fresh544(X, X, Y, Z, W, V) = fresh545(m0(W, V, Y), true, Y, Z).
% 46.92/6.27 Axiom 87 (rule_187): fresh543(X, X, Y, Z, W, V) = q2(Y, Z, Y).
% 46.92/6.27 Axiom 88 (rule_201): fresh534(X, X, Y, Z, W) = fresh535(m2(Z), true, Y, Z, W).
% 46.92/6.27 Axiom 89 (rule_257): fresh495(X, X, Y, Z, W) = fresh496(s2(Y), true, Y, Z, W).
% 46.92/6.27 Axiom 90 (rule_036): fresh394(m0(b, X, Y), true, Y, X) = n1(Y, Y, X).
% 46.92/6.27 Axiom 91 (rule_082): fresh334(X, X, Y, Z, W, V) = p1(Y, Z, W).
% 46.92/6.27 Axiom 92 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 46.92/6.27 Axiom 93 (rule_177): fresh207(p1(X, X, X), true, X, Y) = fresh206(k0(Y), true, X, Y).
% 46.92/6.27 Axiom 94 (rule_201): fresh534(m2(X), true, Y, Z, W) = fresh174(p1(W, Z, Y), true, Y, W).
% 46.92/6.27 Axiom 95 (rule_257): fresh495(q3(X, Y), true, Y, X, Z) = fresh100(n1(Z, Y, X), true, Y, X).
% 46.92/6.27 Axiom 96 (rule_281): fresh74(n4(X, X), true, X, Y) = fresh73(p3(X, Y, Y), true, X, Y).
% 46.92/6.27 Axiom 97 (rule_187): fresh542(X, X, Y, Z, W, V) = fresh543(k0(Z), true, Y, Z, W, V).
% 46.92/6.27 Axiom 98 (rule_155): fresh240(p2(e, X, Y), true, X, Y, Z) = fresh239(k1(Z), true, X, Y).
% 46.92/6.27 Axiom 99 (rule_182): fresh550(q2(X, Y, Z), true, Z, X, Y) = fresh199(p1(Z, Z, Y), true, Z, X, Y).
% 46.92/6.27 Axiom 100 (rule_242): fresh124(k3(X, Y, Z), true, Z, X, Y) = fresh123(r2(X), true, Z, X, Y).
% 46.92/6.27 Axiom 101 (rule_251): fresh111(m3(X, Y, Z), true, W, X, Z) = fresh110(p2(W, X, Z), true, W, X).
% 46.92/6.27 Axiom 102 (rule_255): fresh104(q2(X, Y, Z), true, Y, Z, X) = fresh103(n0(X, Y), true, Y, Z).
% 46.92/6.27 Axiom 103 (rule_187): fresh542(q2(X, X, X), true, Y, X, Z, W) = fresh544(r1(X), true, Y, X, Z, W).
% 46.92/6.27 Axiom 104 (rule_082): fresh334(p1(X, Y, Z), true, Y, W, X, Z) = fresh333(m0(X, Y, Z), true, Y, W, X).
% 46.92/6.27
% 46.92/6.27 Lemma 105: r1(X) = true.
% 46.92/6.27 Proof:
% 46.92/6.27 r1(X)
% 46.92/6.27 = { by axiom 30 (rule_124) R->L }
% 46.92/6.27 fresh276(true, true, X)
% 46.92/6.27 = { by axiom 2 (axiom_17) R->L }
% 46.92/6.27 fresh276(q0(X, d), true, X)
% 46.92/6.27 = { by axiom 84 (rule_124) R->L }
% 46.92/6.27 fresh592(q1(d, d, d), true, X, d)
% 46.92/6.27 = { by axiom 18 (rule_117) R->L }
% 46.92/6.27 fresh592(fresh286(true, true), true, X, d)
% 46.92/6.27 = { by axiom 9 (axiom_28) R->L }
% 46.92/6.27 fresh592(fresh286(k0(e), true), true, X, d)
% 46.92/6.27 = { by axiom 28 (rule_117) }
% 46.92/6.27 fresh592(fresh285(s0(d), true), true, X, d)
% 46.92/6.27 = { by axiom 4 (axiom_1) }
% 46.92/6.27 fresh592(fresh285(true, true), true, X, d)
% 46.92/6.27 = { by axiom 12 (rule_117) }
% 46.92/6.27 fresh592(true, true, X, d)
% 46.92/6.27 = { by axiom 44 (rule_124) }
% 46.92/6.27 fresh593(s0(d), true, X)
% 46.92/6.27 = { by axiom 4 (axiom_1) }
% 46.92/6.27 fresh593(true, true, X)
% 46.92/6.27 = { by axiom 20 (rule_124) }
% 46.92/6.27 true
% 46.92/6.27
% 46.92/6.27 Lemma 106: k1(b) = true.
% 46.92/6.27 Proof:
% 46.92/6.27 k1(b)
% 46.92/6.27 = { by axiom 47 (rule_001) R->L }
% 46.92/6.27 fresh440(n0(e, b), true, b)
% 46.92/6.27 = { by axiom 7 (axiom_11) }
% 46.92/6.27 fresh440(true, true, b)
% 46.92/6.27 = { by axiom 22 (rule_001) }
% 46.92/6.27 true
% 46.92/6.27
% 46.92/6.27 Lemma 107: m2(b) = true.
% 46.92/6.27 Proof:
% 46.92/6.27 m2(b)
% 46.92/6.27 = { by axiom 32 (rule_136) R->L }
% 46.92/6.27 fresh263(k1(b), true)
% 46.92/6.27 = { by lemma 106 }
% 46.92/6.27 fresh263(true, true)
% 46.92/6.27 = { by axiom 13 (rule_136) }
% 46.92/6.27 true
% 46.92/6.27
% 46.92/6.27 Lemma 108: p1(X, X, X) = true.
% 46.92/6.27 Proof:
% 46.92/6.27 p1(X, X, X)
% 46.92/6.27 = { by axiom 52 (rule_085) R->L }
% 46.92/6.27 fresh328(p0(b, X), true, X)
% 46.92/6.27 = { by axiom 1 (axiom_14) }
% 46.92/6.27 fresh328(true, true, X)
% 46.92/6.27 = { by axiom 24 (rule_085) }
% 46.92/6.27 true
% 46.92/6.27
% 46.92/6.27 Lemma 109: m3(X, X, X) = true.
% 46.92/6.27 Proof:
% 46.92/6.27 m3(X, X, X)
% 46.92/6.27 = { by axiom 77 (rule_238) R->L }
% 46.92/6.27 fresh129(p2(X, X, X), true, X)
% 46.92/6.27 = { by axiom 72 (rule_154) R->L }
% 46.92/6.27 fresh129(fresh241(q1(X, X, X), true, X), true, X)
% 46.92/6.27 = { by axiom 71 (rule_122) R->L }
% 46.92/6.27 fresh129(fresh241(fresh279(m0(X, d, X), true, X), true, X), true, X)
% 46.92/6.27 = { by axiom 15 (axiom_19) }
% 46.92/6.27 fresh129(fresh241(fresh279(true, true, X), true, X), true, X)
% 46.92/6.27 = { by axiom 29 (rule_122) }
% 46.92/6.27 fresh129(fresh241(true, true, X), true, X)
% 46.92/6.27 = { by axiom 33 (rule_154) }
% 46.92/6.27 fresh129(true, true, X)
% 46.92/6.27 = { by axiom 39 (rule_238) }
% 46.92/6.27 true
% 46.92/6.27
% 46.92/6.27 Goal 1 (prove_this): n4(a, e) = true.
% 46.92/6.27 Proof:
% 46.92/6.27 n4(a, e)
% 46.92/6.27 = { by axiom 63 (rule_281) R->L }
% 46.92/6.27 fresh74(true, true, a, e)
% 46.92/6.27 = { by axiom 64 (rule_281) R->L }
% 46.92/6.27 fresh74(fresh73(true, true, a, a), true, a, e)
% 46.92/6.27 = { by axiom 80 (rule_242) R->L }
% 46.92/6.27 fresh74(fresh73(fresh123(true, true, a, a, a), true, a, a), true, a, e)
% 46.92/6.27 = { by axiom 36 (rule_188) R->L }
% 46.92/6.27 fresh74(fresh73(fresh123(fresh193(true, true, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.27 = { by axiom 5 (axiom_20) R->L }
% 46.92/6.27 fresh74(fresh73(fresh123(fresh193(l0(a), true, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.27 = { by axiom 58 (rule_188) R->L }
% 46.92/6.27 fresh74(fresh73(fresh123(fresh194(r1(a), true, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.27 = { by lemma 105 }
% 46.92/6.27 fresh74(fresh73(fresh123(fresh194(true, true, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.27 = { by axiom 35 (rule_188) }
% 46.92/6.27 fresh74(fresh73(fresh123(r2(a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 100 (rule_242) R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(k3(a, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 65 (rule_201) R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh535(true, true, a, b, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by lemma 107 R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh535(m2(b), true, a, b, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 88 (rule_201) R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh534(true, true, a, b, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by lemma 107 R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh534(m2(b), true, a, b, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 94 (rule_201) }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(p1(a, b, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 91 (rule_082) R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(fresh334(true, true, a, b, a, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 69 (rule_082) R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(fresh334(fresh333(true, true, a, a, a), true, a, b, a, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 17 (axiom_12) R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(fresh334(fresh333(m0(a, a, a), true, a, a, a), true, a, b, a, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 104 (rule_082) R->L }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(fresh334(fresh334(p1(a, a, a), true, a, a, a, a), true, a, b, a, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by lemma 108 }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(fresh334(fresh334(true, true, a, a, a, a), true, a, b, a, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 91 (rule_082) }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(fresh334(p1(a, a, a), true, a, b, a, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 104 (rule_082) }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(fresh333(m0(a, a, a), true, a, b, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 17 (axiom_12) }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(fresh333(true, true, a, b, a), true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 69 (rule_082) }
% 46.92/6.28 fresh74(fresh73(fresh124(fresh174(true, true, a, a), true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 59 (rule_201) }
% 46.92/6.28 fresh74(fresh73(fresh124(true, true, a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 79 (rule_242) }
% 46.92/6.28 fresh74(fresh73(p3(a, a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 96 (rule_281) R->L }
% 46.92/6.28 fresh74(fresh74(n4(a, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 42 (rule_284) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(true, true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 14 (rule_274) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh81(true, true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 8 (axiom_34) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh81(n0(c, d), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 41 (rule_274) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(q3(e, b), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 66 (rule_257) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(true, true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 38 (rule_189) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh191(true, true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 31 (rule_125) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh191(fresh275(true, true, b), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 1 (axiom_14) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh191(fresh275(p0(b, b), true, b), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 53 (rule_125) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh191(s1(b), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 76 (rule_189) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(q2(b, e, b), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 87 (rule_187) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh543(true, true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 9 (axiom_28) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh543(k0(e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 97 (rule_187) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh542(true, true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 34 (rule_181) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh542(fresh200(true, true, e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 11 (rule_090) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh542(fresh200(fresh320(true, true), true, e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 3 (axiom_13) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh542(fresh200(fresh320(r0(e), true), true, e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 25 (rule_090) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh542(fresh200(fresh321(k0(e), true), true, e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 9 (axiom_28) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh542(fresh200(fresh321(true, true), true, e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 19 (rule_090) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh542(fresh200(p1(e, e, e), true, e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 74 (rule_181) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh542(q2(e, e, e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 103 (rule_187) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh544(r1(e), true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by lemma 105 }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh544(true, true, b, e, X, d), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 86 (rule_187) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh545(m0(X, d, b), true, b, e), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 15 (axiom_19) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(fresh545(true, true, b, e), true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 46 (rule_187) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(fresh192(true, true, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 37 (rule_189) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh496(s2(e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 89 (rule_257) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(true, true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 61 (rule_255) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh103(true, true, b, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 7 (axiom_11) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh103(n0(e, b), true, b, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 102 (rule_255) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(q2(e, b, e), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 75 (rule_182) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh199(true, true, e, b, e), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by lemma 108 R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh199(p1(e, e, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 99 (rule_182) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh550(q2(b, e, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 56 (rule_177) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh550(fresh207(true, true, b, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by lemma 108 R->L }
% 46.92/6.28 fresh74(fresh74(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, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 93 (rule_177) }
% 46.92/6.28 fresh74(fresh74(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, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 9 (axiom_28) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh550(fresh206(true, true, b, e), true, e, b, e), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 57 (rule_177) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh550(true, true, e, b, e), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 85 (rule_182) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh551(n1(b, e, e), true, e, b), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 51 (rule_040) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh551(fresh389(true, true, b, d), true, e, b), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by lemma 106 R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh551(fresh389(k1(b), true, b, d), true, e, b), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 68 (rule_040) }
% 46.92/6.28 fresh74(fresh74(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, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 15 (axiom_19) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh551(fresh388(true, true, b), true, e, b), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 23 (rule_040) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(fresh551(true, true, e, b), true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 45 (rule_182) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(fresh104(true, true, b, e, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 82 (rule_255) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh495(q3(b, e), true, e, b, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 95 (rule_257) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh100(n1(e, e, b), true, e, b), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 90 (rule_036) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh100(fresh394(m0(b, b, e), true, e, b), true, e, b), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 16 (axiom_31) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh100(fresh394(true, true, e, b), true, e, b), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 50 (rule_036) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(fresh100(true, true, e, b), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 62 (rule_257) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh472(true, true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 21 (rule_274) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh473(n3(e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 78 (rule_240) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh473(fresh127(p2(e, e, e), true, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 72 (rule_154) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh473(fresh127(fresh241(q1(e, e, e), true, e), true, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 26 (rule_107) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh473(fresh127(fresh241(fresh301(true, true, e), true, e), true, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 15 (axiom_19) R->L }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh473(fresh127(fresh241(fresh301(m0(e, d, e), true, e), true, e), true, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 70 (rule_107) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh473(fresh127(fresh241(fresh300(m0(e, d, e), true, e), true, e), true, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.28 = { by axiom 15 (axiom_19) }
% 46.92/6.28 fresh74(fresh74(fresh68(fresh473(fresh127(fresh241(fresh300(true, true, e), true, e), true, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.29 = { by axiom 27 (rule_107) }
% 46.92/6.29 fresh74(fresh74(fresh68(fresh473(fresh127(fresh241(true, true, e), true, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.29 = { by axiom 33 (rule_154) }
% 46.92/6.29 fresh74(fresh74(fresh68(fresh473(fresh127(true, true, e), true), true, a), true, a, a), true, a, e)
% 46.92/6.29 = { by axiom 40 (rule_240) }
% 46.92/6.29 fresh74(fresh74(fresh68(fresh473(true, true), true, a), true, a, a), true, a, e)
% 46.92/6.29 = { by axiom 10 (rule_274) }
% 46.92/6.29 fresh74(fresh74(fresh68(k4(c), true, a), true, a, a), true, a, e)
% 46.92/6.29 = { by axiom 83 (rule_284) }
% 46.92/6.29 fresh74(fresh74(fresh67(m3(a, a, a), true, a), true, a, a), true, a, e)
% 46.92/6.29 = { by lemma 109 }
% 46.92/6.29 fresh74(fresh74(fresh67(true, true, a), true, a, a), true, a, e)
% 46.92/6.29 = { by axiom 43 (rule_284) }
% 46.92/6.29 fresh74(fresh74(true, true, a, a), true, a, e)
% 46.92/6.29 = { by axiom 63 (rule_281) }
% 46.92/6.29 fresh74(n4(a, a), true, a, e)
% 46.92/6.29 = { by axiom 96 (rule_281) }
% 46.92/6.29 fresh73(p3(a, e, e), true, a, e)
% 46.92/6.29 = { by axiom 81 (rule_251) R->L }
% 46.92/6.29 fresh73(fresh111(true, true, a, e, e), true, a, e)
% 46.92/6.29 = { by lemma 109 R->L }
% 46.92/6.29 fresh73(fresh111(m3(e, e, e), true, a, e, e), true, a, e)
% 46.92/6.29 = { by axiom 101 (rule_251) }
% 46.92/6.29 fresh73(fresh110(p2(a, e, e), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 73 (rule_155) R->L }
% 46.92/6.29 fresh73(fresh110(fresh240(true, true, a, e, a), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 55 (rule_176) R->L }
% 46.92/6.29 fresh73(fresh110(fresh240(fresh208(true, true, e, a), true, a, e, a), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 49 (rule_021) R->L }
% 46.92/6.29 fresh73(fresh110(fresh240(fresh208(fresh414(true, true, a, e), true, e, a), true, a, e, a), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 5 (axiom_20) R->L }
% 46.92/6.29 fresh73(fresh110(fresh240(fresh208(fresh414(l0(a), true, a, e), true, e, a), true, a, e, a), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 67 (rule_021) R->L }
% 46.92/6.29 fresh73(fresh110(fresh240(fresh208(fresh415(k0(e), true, a, e), true, e, a), true, a, e, a), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 9 (axiom_28) }
% 46.92/6.29 fresh73(fresh110(fresh240(fresh208(fresh415(true, true, a, e), true, e, a), true, a, e, a), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 48 (rule_021) }
% 46.92/6.29 fresh73(fresh110(fresh240(fresh208(m1(a, e, a), true, e, a), true, a, e, a), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 92 (rule_176) }
% 46.92/6.29 fresh73(fresh110(fresh240(p2(e, a, e), true, a, e, a), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 98 (rule_155) }
% 46.92/6.29 fresh73(fresh110(fresh239(k1(a), true, a, e), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 47 (rule_001) R->L }
% 46.92/6.29 fresh73(fresh110(fresh239(fresh440(n0(b, a), true, a), true, a, e), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 6 (axiom_37) }
% 46.92/6.29 fresh73(fresh110(fresh239(fresh440(true, true, a), true, a, e), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 22 (rule_001) }
% 46.92/6.29 fresh73(fresh110(fresh239(true, true, a, e), true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 54 (rule_155) }
% 46.92/6.29 fresh73(fresh110(true, true, a, e), true, a, e)
% 46.92/6.29 = { by axiom 60 (rule_251) }
% 46.92/6.29 fresh73(true, true, a, e)
% 46.92/6.29 = { by axiom 64 (rule_281) }
% 46.92/6.29 true
% 46.92/6.29 % SZS output end Proof
% 46.92/6.29
% 46.92/6.29 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------