TSTP Solution File: SYO634-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYO634-1 : TPTP v8.1.2. Released v7.1.0.
% 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 : n008.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 04:58:44 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO634-1 : TPTP v8.1.2. Released v7.1.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 06:00:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.64 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.64
% 0.20/0.64 % SZS status Unsatisfiable
% 0.20/0.64
% 0.20/0.74 % SZS output start Proof
% 0.20/0.74 Take the following subset of the input axioms:
% 0.20/0.74 fof(clause_0_19, axiom, ![A_0, B_0, A_1, A_4, A_5, A_2, A_6, A_3, K]: (~'E'(f(A_1), s(s(s(s(s(s(s(s('0'))))))))) | (~'E'(f(A_4), s(s(s(s(s('0')))))) | (~'E'(f(B_0), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_5), s(s(s(s('0'))))) | (~'E'(f(A_2), s(s(s(s(s(s(s('0')))))))) | (~'E'(f(A_6), s(s(s('0')))) | (~'E'(f(A_0), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(A_3), s(s(s(s(s(s('0'))))))) | 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))), K)), s(s('0')))))))))))).
% 0.20/0.74 fof(clause_10_22, axiom, ![A_8, A_7, A_0_2, B_0_2, A_1_2, A_4_2, A_2_2, A_3_2, K2, A_5_2, A_6_2]: (~'E'(f(A_1_2), s(s(s(s(s(s(s(s('0'))))))))) | (~'E'(f(A_4_2), s(s(s(s(s('0')))))) | (~'E'(f(A_8), s('0')) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_5_2), s(s(s(s('0'))))) | (~'E'(f(A_7), s(s('0'))) | (~'E'(f(A_2_2), s(s(s(s(s(s(s('0')))))))) | (~'E'(f(A_6_2), s(s(s('0')))) | (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(A_3_2), s(s(s(s(s(s('0'))))))) | 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))), K2)), '0')))))))))))).
% 0.20/0.74 fof(clause_11_03, axiom, ![B]: 'E'(f(B), s(s(s(s(s(s(s(s(s(s('0')))))))))))).
% 0.20/0.75 fof(clause_12_14, axiom, ![A_0_2, B_0_2, A_1_2]: (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_1_2), s(s(s(s(s(s(s(s('0'))))))))) | 'E'(f(B_0_2), s(s(s(s(s(s(s('0')))))))))))).
% 0.20/0.75 fof(clause_15_20, axiom, ![A_0_2, B_0_2, A_1_2, A_2_2, A_3_2]: (~'E'(f(A_1_2), s(s(s(s(s(s(s(s('0'))))))))) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_2_2), s(s(s(s(s(s(s('0')))))))) | (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(A_3_2), s(s(s(s(s(s('0'))))))) | 'E'(f(B_0_2), s(s(s(s(s('0')))))))))))).
% 0.20/0.75 fof(clause_17_09, axiom, ![B_0_2]: 'E'(f(B_0_2), s(s(s(s(s(s(s(s(s('0'))))))))))).
% 0.20/0.75 fof(clause_18_15, axiom, ![A_0_2, B_0_2, A_1_2, A_4_2, A_2_2, A_3_2, K2, A_5_2]: (~'E'(f(A_1_2), s(s(s(s(s(s(s(s('0'))))))))) | (~'E'(f(A_4_2), s(s(s(s(s('0')))))) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_5_2), s(s(s(s('0'))))) | (~'E'(f(A_2_2), s(s(s(s(s(s(s('0')))))))) | (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(A_3_2), s(s(s(s(s(s('0'))))))) | 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))), K2)), s(s(s('0')))))))))))).
% 0.20/0.75 fof(clause_1_06, axiom, ![A_0_2, B_0_2, A_1_2, A_2_2]: (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_1_2), s(s(s(s(s(s(s(s('0'))))))))) | (~'E'(f(A_2_2), s(s(s(s(s(s(s('0')))))))) | 'E'(f(B_0_2), s(s(s(s(s(s('0')))))))))))).
% 0.20/0.75 fof(clause_21_01, axiom, ![A_0_2, B_0_2]: (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | 'E'(f(B_0_2), s(s(s(s(s(s(s(s('0')))))))))))).
% 0.20/0.75 fof(clause_3_17, axiom, ![A_9, A_0_2, B_0_2, A_1_2, A_4_2, A_2_2, A_3_2, A_5_2, A_7_2, A_6_2, A_8_2]: (~'E'(f(A_1_2), s(s(s(s(s(s(s(s('0'))))))))) | (~'E'(f(A_4_2), s(s(s(s(s('0')))))) | (~'E'(f(A_8_2), s('0')) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_5_2), s(s(s(s('0'))))) | (~'E'(f(A_7_2), s(s('0'))) | (~'E'(f(A_2_2), s(s(s(s(s(s(s('0')))))))) | (~'E'(f(A_6_2), s(s(s('0')))) | (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(A_3_2), s(s(s(s(s(s('0'))))))) | ~'E'(f(A_9), '0')))))))))))).
% 0.20/0.75 fof(clause_8_11, axiom, ![A_0_2, B_0_2, A_1_2, A_4_2, A_2_2, A_3_2, K2, A_5_2, A_7_2, A_6_2]: (~'E'(f(A_1_2), s(s(s(s(s(s(s(s('0'))))))))) | (~'E'(f(A_4_2), s(s(s(s(s('0')))))) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_5_2), s(s(s(s('0'))))) | (~'E'(f(A_7_2), s(s('0'))) | (~'E'(f(A_2_2), s(s(s(s(s(s(s('0')))))))) | (~'E'(f(A_6_2), s(s(s('0')))) | (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(A_3_2), s(s(s(s(s(s('0'))))))) | 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))), K2)), s('0')))))))))))).
% 0.20/0.75 fof(clause_9_12, axiom, ![A_0_2, B_0_2, A_1_2, A_4_2, A_2_2, A_3_2, K2]: (~'E'(f(A_1_2), s(s(s(s(s(s(s(s('0'))))))))) | (~'E'(f(A_4_2), s(s(s(s(s('0')))))) | (~'E'(f(B_0_2), s(s(s(s(s(s(s(s(s(s('0'))))))))))) | (~'E'(f(A_2_2), s(s(s(s(s(s(s('0')))))))) | (~'E'(f(A_0_2), s(s(s(s(s(s(s(s(s('0')))))))))) | (~'E'(f(A_3_2), s(s(s(s(s(s('0'))))))) | 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))), K2)), s(s(s(s('0')))))))))))).
% 0.20/0.75
% 0.20/0.75 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.75 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.75 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.75 fresh(y, y, x1...xn) = u
% 0.20/0.75 C => fresh(s, t, x1...xn) = v
% 0.20/0.75 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.75 variables of u and v.
% 0.20/0.75 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.75 input problem has no model of domain size 1).
% 0.20/0.75
% 0.20/0.75 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.75
% 0.20/0.75 Axiom 1 (clause_21_01): fresh108(X, X, Y) = true2.
% 0.20/0.75 Axiom 2 (clause_1_06): fresh90(X, X, Y) = true2.
% 0.20/0.75 Axiom 3 (clause_8_11): fresh66(X, X, Y) = true2.
% 0.20/0.75 Axiom 4 (clause_9_12): fresh57(X, X, Y) = true2.
% 0.20/0.75 Axiom 5 (clause_12_14): fresh51(X, X, Y) = true2.
% 0.20/0.75 Axiom 6 (clause_18_15): fresh49(X, X, Y) = true2.
% 0.20/0.75 Axiom 7 (clause_0_19): fresh38(X, X, Y) = true2.
% 0.20/0.75 Axiom 8 (clause_15_20): fresh30(X, X, Y) = true2.
% 0.20/0.75 Axiom 9 (clause_10_22): fresh20(X, X, Y) = true2.
% 0.20/0.75 Axiom 10 (clause_15_20): fresh27(X, X, Y, Z) = E(f(Z), s(s(s(s(s(0)))))).
% 0.20/0.75 Axiom 11 (clause_10_22): fresh17(X, X, Y, Z, W, V) = fresh18(E(f(W), s(0)), true2, Y, Z, V).
% 0.20/0.75 Axiom 12 (clause_1_06): fresh7(X, X, Y, Z) = E(f(Z), s(s(s(s(s(s(0))))))).
% 0.20/0.75 Axiom 13 (clause_12_14): fresh10(X, X, Y, Z) = E(f(Z), s(s(s(s(s(s(s(0)))))))).
% 0.20/0.75 Axiom 14 (clause_21_01): fresh6(X, X, Y, Z) = E(f(Z), s(s(s(s(s(s(s(s(0))))))))).
% 0.20/0.75 Axiom 15 (clause_8_11): fresh64(X, X, Y, Z, W) = fresh65(E(f(Z), s(s(s(s(s(0)))))), true2, Y, W).
% 0.20/0.75 Axiom 16 (clause_8_11): fresh61(X, X, Y, Z, W, V, U, T) = fresh62(E(f(U), s(s(0))), true2, Y, Z, W, V, T).
% 0.20/0.75 Axiom 17 (clause_9_12): fresh55(X, X, Y, Z, W) = fresh56(E(f(Z), s(s(s(s(s(0)))))), true2, Y, W).
% 0.20/0.75 Axiom 18 (clause_18_15): fresh47(X, X, Y, Z, W) = fresh48(E(f(Z), s(s(s(s(s(0)))))), true2, Y, W).
% 0.20/0.75 Axiom 19 (clause_0_19): fresh36(X, X, Y, Z, W) = fresh37(E(f(Z), s(s(s(s(s(0)))))), true2, Y, W).
% 0.20/0.75 Axiom 20 (clause_10_22): fresh18(X, X, Y, Z, W) = fresh19(E(f(Z), s(s(s(s(s(0)))))), true2, Y, W).
% 0.20/0.75 Axiom 21 (clause_17_09): E(f(X), s(s(s(s(s(s(s(s(s(0)))))))))) = true2.
% 0.20/0.75 Axiom 22 (clause_8_11): fresh62(X, X, Y, Z, W, V, U) = fresh63(E(f(V), s(s(s(s(0))))), true2, Y, Z, W, U).
% 0.20/0.75 Axiom 23 (clause_18_15): fresh45(X, X, Y, Z, W, V, U) = fresh46(E(f(V), s(s(s(s(0))))), true2, Y, Z, W, U).
% 0.20/0.75 Axiom 24 (clause_0_19): fresh34(X, X, Y, Z, W, V, U) = fresh35(E(f(V), s(s(s(s(0))))), true2, Y, Z, W, U).
% 0.20/0.75 Axiom 25 (clause_10_22): fresh14(X, X, Y, Z, W, V, U, T, S) = fresh15(E(f(T), s(s(0))), true2, Y, Z, W, V, U, S).
% 0.20/0.75 Axiom 26 (clause_11_03): E(f(X), s(s(s(s(s(s(s(s(s(s(0))))))))))) = true2.
% 0.20/0.75 Axiom 27 (clause_8_11): fresh65(X, X, Y, Z) = fresh66(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, Z).
% 0.20/0.75 Axiom 28 (clause_9_12): fresh56(X, X, Y, Z) = fresh57(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, Z).
% 0.20/0.75 Axiom 29 (clause_18_15): fresh48(X, X, Y, Z) = fresh49(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, Z).
% 0.20/0.75 Axiom 30 (clause_0_19): fresh37(X, X, Y, Z) = fresh38(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, Z).
% 0.20/0.75 Axiom 31 (clause_0_19): fresh32(X, X, Y, Z, W, V, U, T, S) = fresh33(E(f(T), s(s(s(0)))), true2, Y, Z, W, V, U, S).
% 0.20/0.75 Axiom 32 (clause_15_20): fresh29(X, X, Y, Z) = fresh30(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, Z).
% 0.20/0.75 Axiom 33 (clause_15_20): fresh28(X, X, Y, Z, W) = fresh29(E(f(W), s(s(s(s(s(s(s(0)))))))), true2, Y, Z).
% 0.20/0.75 Axiom 34 (clause_10_22): fresh19(X, X, Y, Z) = fresh20(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, Z).
% 0.20/0.75 Axiom 35 (clause_10_22): fresh15(X, X, Y, Z, W, V, U, T) = fresh16(E(f(U), s(s(s(s(0))))), true2, Y, Z, W, V, T).
% 0.20/0.75 Axiom 36 (clause_1_06): fresh89(X, X, Y, Z) = fresh90(E(f(Y), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Z).
% 0.20/0.75 Axiom 37 (clause_1_06): fresh88(X, X, Y, Z, W) = fresh89(E(f(W), s(s(s(s(s(s(s(s(0))))))))), true2, Y, Z).
% 0.20/0.75 Axiom 38 (clause_8_11): fresh59(X, X, Y, Z, W, V, U, T, S, X2) = fresh60(E(f(S), s(s(s(0)))), true2, Y, Z, W, V, U, T, X2).
% 0.20/0.75 Axiom 39 (clause_12_14): fresh50(X, X, Y, Z) = fresh51(E(f(Y), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Z).
% 0.20/0.75 Axiom 40 (clause_9_12): fresh53(X, X, Y, Z, W, V, U) = fresh54(E(f(V), s(s(s(s(s(s(s(0)))))))), true2, Y, Z, W, U).
% 0.20/0.75 Axiom 41 (clause_10_22): fresh12(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh13(E(f(X2), s(s(s(0)))), true2, Y, Z, W, V, U, T, S, Y2).
% 0.20/0.75 Axiom 42 (clause_10_22): fresh16(X, X, Y, Z, W, V, U) = E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U)), 0).
% 0.20/0.75 Axiom 43 (clause_18_15): fresh44(X, X, Y, Z, W, V, U, T) = fresh45(E(f(U), s(s(s(s(s(s(s(0)))))))), true2, Y, Z, W, V, T).
% 0.20/0.75 Axiom 44 (clause_0_19): fresh33(X, X, Y, Z, W, V, U, T) = fresh34(E(f(U), s(s(s(s(s(s(s(0)))))))), true2, Y, Z, W, V, T).
% 0.20/0.75 Axiom 45 (clause_15_20): fresh26(E(f(X), s(s(s(s(s(s(0))))))), true2, Y, Z, W, V) = fresh28(E(f(V), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, Z, W).
% 0.20/0.75 Axiom 46 (clause_15_20): fresh26(X, X, Y, Z, W, V) = fresh27(E(f(Z), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z).
% 0.20/0.75 Axiom 47 (clause_12_14): fresh50(E(f(X), s(s(s(s(s(s(s(s(0))))))))), true2, Y, Z) = fresh10(E(f(Z), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z).
% 0.20/0.75 Axiom 48 (clause_1_06): fresh88(E(f(X), s(s(s(s(s(s(s(0)))))))), true2, Y, Z, W) = fresh7(E(f(Z), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z).
% 0.20/0.75 Axiom 49 (clause_21_01): fresh6(E(f(X), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, X) = fresh108(E(f(Y), s(s(s(s(s(s(s(s(s(0)))))))))), true2, X).
% 0.20/0.75 Axiom 50 (clause_8_11): fresh63(X, X, Y, Z, W, V) = E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V)), s(0)).
% 0.20/0.75 Axiom 51 (clause_8_11): fresh60(X, X, Y, Z, W, V, U, T, S) = fresh64(E(f(W), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z, S).
% 0.20/0.75 Axiom 52 (clause_8_11): fresh58(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh61(E(f(T), s(s(s(s(s(s(s(0)))))))), true2, Y, Z, W, V, U, Y2).
% 0.20/0.75 Axiom 53 (clause_9_12): fresh54(X, X, Y, Z, W, V) = fresh55(E(f(W), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z, V).
% 0.20/0.75 Axiom 54 (clause_18_15): fresh46(X, X, Y, Z, W, V) = fresh47(E(f(W), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z, V).
% 0.20/0.75 Axiom 55 (clause_0_19): fresh31(X, X, Y, Z, W, V, U, T, S, X2) = fresh36(E(f(W), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z, X2).
% 0.20/0.75 Axiom 56 (clause_0_19): fresh35(X, X, Y, Z, W, V) = E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V)), s(s(0))).
% 0.20/0.75 Axiom 57 (clause_9_12): fresh52(X, X, Y, Z, W, V, U, T) = fresh53(E(f(U), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, Z, W, V, T).
% 0.20/0.75 Axiom 58 (clause_10_22): fresh13(X, X, Y, Z, W, V, U, T, S, X2) = fresh17(E(f(V), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z, W, X2).
% 0.20/0.75 Axiom 59 (clause_10_22): fresh11(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh14(E(f(S), s(s(s(s(s(s(s(0)))))))), true2, Y, Z, W, V, U, T, Z2).
% 0.20/0.75 Axiom 60 (clause_18_15): fresh8(X, X, Y, Z, W, V, U, T, S) = E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S)), s(s(s(0)))).
% 0.20/0.75 Axiom 61 (clause_18_15): fresh8(E(f(X), s(s(s(s(s(s(0))))))), true2, Y, Z, W, V, U, T, S) = fresh44(E(f(T), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, Z, W, V, U, S).
% 0.20/0.75 Axiom 62 (clause_9_12): fresh52(E(f(X), s(s(s(s(s(s(0))))))), true2, Y, Z, W, V, U, T) = E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T)), s(s(s(s(0))))).
% 0.20/0.75 Axiom 63 (clause_0_19): fresh31(E(f(X), s(s(s(s(s(s(0))))))), true2, Y, Z, W, V, U, T, S, X2) = fresh32(E(f(S), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, Z, W, V, U, T, X2).
% 0.20/0.75 Axiom 64 (clause_8_11): fresh58(E(f(X), s(s(s(s(s(s(0))))))), true2, Y, Z, W, V, U, T, S, X2, Y2) = fresh59(E(f(X2), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, Z, W, V, U, T, S, Y2).
% 0.20/0.75 Axiom 65 (clause_10_22): fresh11(E(f(X), s(s(s(s(s(s(0))))))), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh12(E(f(Y2), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, Z, W, V, U, T, S, X2, Z2).
% 0.20/0.75
% 0.20/0.75 Lemma 66: E(f(X), s(s(s(s(s(s(s(s(0))))))))) = true2.
% 0.20/0.75 Proof:
% 0.20/0.75 E(f(X), s(s(s(s(s(s(s(s(0)))))))))
% 0.20/0.75 = { by axiom 14 (clause_21_01) R->L }
% 0.20/0.75 fresh6(true2, true2, Y, X)
% 0.20/0.75 = { by axiom 26 (clause_11_03) R->L }
% 0.20/0.75 fresh6(E(f(X), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, X)
% 0.20/0.75 = { by axiom 49 (clause_21_01) }
% 0.20/0.75 fresh108(E(f(Y), s(s(s(s(s(s(s(s(s(0)))))))))), true2, X)
% 0.20/0.75 = { by axiom 21 (clause_17_09) }
% 0.20/0.75 fresh108(true2, true2, X)
% 0.20/0.75 = { by axiom 1 (clause_21_01) }
% 0.20/0.75 true2
% 0.20/0.75
% 0.20/0.75 Lemma 67: E(f(X), s(s(s(s(s(s(s(0)))))))) = true2.
% 0.20/0.75 Proof:
% 0.20/0.75 E(f(X), s(s(s(s(s(s(s(0))))))))
% 0.20/0.75 = { by axiom 13 (clause_12_14) R->L }
% 0.20/0.75 fresh10(true2, true2, Y, X)
% 0.20/0.75 = { by axiom 26 (clause_11_03) R->L }
% 0.20/0.75 fresh10(E(f(X), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, X)
% 0.20/0.75 = { by axiom 47 (clause_12_14) R->L }
% 0.20/0.75 fresh50(E(f(Z), s(s(s(s(s(s(s(s(0))))))))), true2, Y, X)
% 0.20/0.75 = { by lemma 66 }
% 0.20/0.75 fresh50(true2, true2, Y, X)
% 0.20/0.75 = { by axiom 39 (clause_12_14) }
% 0.20/0.75 fresh51(E(f(Y), s(s(s(s(s(s(s(s(s(0)))))))))), true2, X)
% 0.20/0.75 = { by axiom 21 (clause_17_09) }
% 0.20/0.75 fresh51(true2, true2, X)
% 0.20/0.75 = { by axiom 5 (clause_12_14) }
% 0.20/0.75 true2
% 0.20/0.75
% 0.20/0.75 Lemma 68: E(f(X), s(s(s(s(s(s(0))))))) = true2.
% 0.20/0.75 Proof:
% 0.20/0.75 E(f(X), s(s(s(s(s(s(0)))))))
% 0.20/0.75 = { by axiom 12 (clause_1_06) R->L }
% 0.20/0.75 fresh7(true2, true2, Y, X)
% 0.20/0.75 = { by axiom 26 (clause_11_03) R->L }
% 0.20/0.75 fresh7(E(f(X), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, X)
% 0.20/0.75 = { by axiom 48 (clause_1_06) R->L }
% 0.20/0.75 fresh88(E(f(Z), s(s(s(s(s(s(s(0)))))))), true2, Y, X, W)
% 0.20/0.75 = { by lemma 67 }
% 0.20/0.75 fresh88(true2, true2, Y, X, W)
% 0.20/0.75 = { by axiom 37 (clause_1_06) }
% 0.20/0.75 fresh89(E(f(W), s(s(s(s(s(s(s(s(0))))))))), true2, Y, X)
% 0.20/0.75 = { by lemma 66 }
% 0.20/0.75 fresh89(true2, true2, Y, X)
% 0.20/0.75 = { by axiom 36 (clause_1_06) }
% 0.20/0.75 fresh90(E(f(Y), s(s(s(s(s(s(s(s(s(0)))))))))), true2, X)
% 0.20/0.75 = { by axiom 21 (clause_17_09) }
% 0.20/0.75 fresh90(true2, true2, X)
% 0.20/0.75 = { by axiom 2 (clause_1_06) }
% 0.20/0.75 true2
% 0.20/0.75
% 0.20/0.75 Lemma 69: E(f(X), s(s(s(s(s(0)))))) = true2.
% 0.20/0.75 Proof:
% 0.20/0.75 E(f(X), s(s(s(s(s(0))))))
% 0.20/0.75 = { by axiom 10 (clause_15_20) R->L }
% 0.20/0.75 fresh27(true2, true2, Y, X)
% 0.20/0.75 = { by axiom 26 (clause_11_03) R->L }
% 0.20/0.75 fresh27(E(f(X), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, X)
% 0.20/0.75 = { by axiom 46 (clause_15_20) R->L }
% 0.20/0.75 fresh26(true2, true2, Y, X, Z, W)
% 0.20/0.75 = { by lemma 68 R->L }
% 0.20/0.75 fresh26(E(f(V), s(s(s(s(s(s(0))))))), true2, Y, X, Z, W)
% 0.20/0.75 = { by axiom 45 (clause_15_20) }
% 0.20/0.75 fresh28(E(f(W), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, X, Z)
% 0.20/0.75 = { by axiom 21 (clause_17_09) }
% 0.20/0.75 fresh28(true2, true2, Y, X, Z)
% 0.20/0.75 = { by axiom 33 (clause_15_20) }
% 0.20/0.75 fresh29(E(f(Z), s(s(s(s(s(s(s(0)))))))), true2, Y, X)
% 0.20/0.75 = { by lemma 67 }
% 0.20/0.75 fresh29(true2, true2, Y, X)
% 0.20/0.75 = { by axiom 32 (clause_15_20) }
% 0.20/0.75 fresh30(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, X)
% 0.20/0.75 = { by lemma 66 }
% 0.20/0.75 fresh30(true2, true2, X)
% 0.20/0.75 = { by axiom 8 (clause_15_20) }
% 0.20/0.75 true2
% 0.20/0.75
% 0.20/0.75 Lemma 70: E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), s(s(s(s(0))))) = true2.
% 0.20/0.75 Proof:
% 0.20/0.75 E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), s(s(s(s(0)))))
% 0.20/0.75 = { by axiom 62 (clause_9_12) R->L }
% 0.20/0.75 fresh52(E(f(Y), s(s(s(s(s(s(0))))))), true2, Z, W, V, U, T, X)
% 0.20/0.75 = { by lemma 68 }
% 0.20/0.75 fresh52(true2, true2, Z, W, V, U, T, X)
% 0.20/0.75 = { by axiom 57 (clause_9_12) }
% 0.20/0.75 fresh53(E(f(T), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Z, W, V, U, X)
% 0.20/0.75 = { by axiom 21 (clause_17_09) }
% 0.20/0.75 fresh53(true2, true2, Z, W, V, U, X)
% 0.20/0.75 = { by axiom 40 (clause_9_12) }
% 0.20/0.75 fresh54(E(f(U), s(s(s(s(s(s(s(0)))))))), true2, Z, W, V, X)
% 0.20/0.75 = { by lemma 67 }
% 0.20/0.75 fresh54(true2, true2, Z, W, V, X)
% 0.20/0.75 = { by axiom 53 (clause_9_12) }
% 0.20/0.75 fresh55(E(f(V), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Z, W, X)
% 0.20/0.75 = { by axiom 26 (clause_11_03) }
% 0.20/0.75 fresh55(true2, true2, Z, W, X)
% 0.20/0.75 = { by axiom 17 (clause_9_12) }
% 0.20/0.75 fresh56(E(f(W), s(s(s(s(s(0)))))), true2, Z, X)
% 0.20/0.75 = { by lemma 69 }
% 0.20/0.75 fresh56(true2, true2, Z, X)
% 0.20/0.75 = { by axiom 28 (clause_9_12) }
% 0.20/0.75 fresh57(E(f(Z), s(s(s(s(s(s(s(s(0))))))))), true2, X)
% 0.20/0.75 = { by lemma 66 }
% 0.20/0.75 fresh57(true2, true2, X)
% 0.20/0.75 = { by axiom 4 (clause_9_12) }
% 0.20/0.75 true2
% 0.20/0.75
% 0.20/0.75 Lemma 71: E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), s(s(s(0)))) = true2.
% 0.20/0.75 Proof:
% 0.20/0.75 E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), s(s(s(0))))
% 0.20/0.75 = { by axiom 60 (clause_18_15) R->L }
% 0.20/0.75 fresh8(true2, true2, Y, Z, W, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V), U, T, X)
% 0.20/0.75 = { by lemma 68 R->L }
% 0.20/0.75 fresh8(E(f(S), s(s(s(s(s(s(0))))))), true2, Y, Z, W, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V), U, T, X)
% 0.20/0.75 = { by axiom 61 (clause_18_15) }
% 0.20/0.75 fresh44(E(f(T), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, Z, W, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V), U, X)
% 0.20/0.75 = { by axiom 21 (clause_17_09) }
% 0.20/0.75 fresh44(true2, true2, Y, Z, W, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V), U, X)
% 0.20/0.75 = { by axiom 43 (clause_18_15) }
% 0.20/0.75 fresh45(E(f(U), s(s(s(s(s(s(s(0)))))))), true2, Y, Z, W, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V), X)
% 0.20/0.75 = { by lemma 67 }
% 0.20/0.75 fresh45(true2, true2, Y, Z, W, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V), X)
% 0.20/0.75 = { by axiom 23 (clause_18_15) }
% 0.20/0.75 fresh46(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V)), s(s(s(s(0))))), true2, Y, Z, W, X)
% 0.20/0.75 = { by lemma 70 }
% 0.20/0.75 fresh46(true2, true2, Y, Z, W, X)
% 0.20/0.75 = { by axiom 54 (clause_18_15) }
% 0.20/0.75 fresh47(E(f(W), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z, X)
% 0.20/0.75 = { by axiom 26 (clause_11_03) }
% 0.20/0.75 fresh47(true2, true2, Y, Z, X)
% 0.20/0.75 = { by axiom 18 (clause_18_15) }
% 0.20/0.75 fresh48(E(f(Z), s(s(s(s(s(0)))))), true2, Y, X)
% 0.20/0.75 = { by lemma 69 }
% 0.20/0.75 fresh48(true2, true2, Y, X)
% 0.20/0.75 = { by axiom 29 (clause_18_15) }
% 0.20/0.75 fresh49(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, X)
% 0.20/0.75 = { by lemma 66 }
% 0.20/0.75 fresh49(true2, true2, X)
% 0.20/0.75 = { by axiom 6 (clause_18_15) }
% 0.20/0.75 true2
% 0.20/0.75
% 0.20/0.75 Lemma 72: fresh35(X, X, Y, Z, W, V) = true2.
% 0.20/0.75 Proof:
% 0.20/0.75 fresh35(X, X, Y, Z, W, V)
% 0.20/0.75 = { by axiom 56 (clause_0_19) }
% 0.20/0.75 E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V)), s(s(0)))
% 0.20/0.75 = { by axiom 56 (clause_0_19) R->L }
% 0.20/0.75 fresh35(true2, true2, U, T, S, V)
% 0.20/0.75 = { by lemma 70 R->L }
% 0.20/0.75 fresh35(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2)), s(s(s(s(0))))), true2, U, T, S, V)
% 0.20/0.75 = { by axiom 24 (clause_0_19) R->L }
% 0.20/0.75 fresh34(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), V)
% 0.20/0.75 = { by lemma 67 R->L }
% 0.20/0.75 fresh34(E(f(Y2), s(s(s(s(s(s(s(0)))))))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), V)
% 0.20/0.75 = { by axiom 44 (clause_0_19) R->L }
% 0.20/0.75 fresh33(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), Y2, V)
% 0.20/0.75 = { by lemma 71 R->L }
% 0.20/0.75 fresh33(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2)), s(s(s(0)))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), Y2, V)
% 0.20/0.75 = { by axiom 31 (clause_0_19) R->L }
% 0.20/0.75 fresh32(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), Y2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), V)
% 0.20/0.75 = { by axiom 21 (clause_17_09) R->L }
% 0.20/0.75 fresh32(E(f(W2), s(s(s(s(s(s(s(s(s(0)))))))))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), Y2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), V)
% 0.20/0.75 = { by axiom 63 (clause_0_19) R->L }
% 0.20/0.75 fresh31(E(f(V2), s(s(s(s(s(s(0))))))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), Y2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), W2, V)
% 0.20/0.75 = { by lemma 68 }
% 0.20/0.75 fresh31(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), Y2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), W2, V)
% 0.20/0.75 = { by axiom 55 (clause_0_19) }
% 0.20/0.75 fresh36(E(f(S), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, U, T, V)
% 0.20/0.75 = { by axiom 26 (clause_11_03) }
% 0.20/0.75 fresh36(true2, true2, U, T, V)
% 0.20/0.75 = { by axiom 19 (clause_0_19) }
% 0.20/0.75 fresh37(E(f(T), s(s(s(s(s(0)))))), true2, U, V)
% 0.20/0.75 = { by lemma 69 }
% 0.20/0.75 fresh37(true2, true2, U, V)
% 0.20/0.75 = { by axiom 30 (clause_0_19) }
% 0.20/0.75 fresh38(E(f(U), s(s(s(s(s(s(s(s(0))))))))), true2, V)
% 0.20/0.75 = { by lemma 66 }
% 0.20/0.75 fresh38(true2, true2, V)
% 0.20/0.75 = { by axiom 7 (clause_0_19) }
% 0.20/0.75 true2
% 0.20/0.75
% 0.20/0.75 Lemma 73: fresh63(X, X, Y, Z, W, V) = true2.
% 0.20/0.75 Proof:
% 0.20/0.75 fresh63(X, X, Y, Z, W, V)
% 0.20/0.75 = { by axiom 50 (clause_8_11) }
% 0.20/0.75 E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V)), s(0))
% 0.20/0.75 = { by axiom 50 (clause_8_11) R->L }
% 0.20/0.75 fresh63(true2, true2, U, T, S, V)
% 0.20/0.75 = { by lemma 70 R->L }
% 0.20/0.75 fresh63(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2)), s(s(s(s(0))))), true2, U, T, S, V)
% 0.20/0.75 = { by axiom 22 (clause_8_11) R->L }
% 0.20/0.75 fresh62(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), V)
% 0.20/0.75 = { by lemma 72 R->L }
% 0.20/0.75 fresh62(fresh35(Y2, Y2, Z2, W2, V2, U2), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), V)
% 0.20/0.75 = { by axiom 56 (clause_0_19) }
% 0.20/0.75 fresh62(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2)), s(s(0))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), V)
% 0.20/0.75 = { by axiom 16 (clause_8_11) R->L }
% 0.20/0.75 fresh61(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2), V)
% 0.20/0.75 = { by lemma 67 R->L }
% 0.20/0.75 fresh61(E(f(T2), s(s(s(s(s(s(s(0)))))))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2), V)
% 0.20/0.75 = { by axiom 52 (clause_8_11) R->L }
% 0.20/0.75 fresh58(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2), T2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S2), X3, V)
% 0.20/0.75 = { by lemma 68 R->L }
% 0.20/0.75 fresh58(E(f(Y3), s(s(s(s(s(s(0))))))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2), T2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S2), X3, V)
% 0.20/0.76 = { by axiom 64 (clause_8_11) }
% 0.20/0.76 fresh59(E(f(X3), s(s(s(s(s(s(s(s(s(0)))))))))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2), T2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S2), V)
% 0.20/0.76 = { by axiom 21 (clause_17_09) }
% 0.20/0.76 fresh59(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2), T2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S2), V)
% 0.20/0.76 = { by axiom 38 (clause_8_11) }
% 0.20/0.76 fresh60(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S2)), s(s(s(0)))), true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2), T2, V)
% 0.20/0.76 = { by lemma 71 }
% 0.20/0.76 fresh60(true2, true2, U, T, S, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U2), T2, V)
% 0.20/0.76 = { by axiom 51 (clause_8_11) }
% 0.20/0.76 fresh64(E(f(S), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, U, T, V)
% 0.20/0.76 = { by axiom 26 (clause_11_03) }
% 0.20/0.76 fresh64(true2, true2, U, T, V)
% 0.20/0.76 = { by axiom 15 (clause_8_11) }
% 0.20/0.76 fresh65(E(f(T), s(s(s(s(s(0)))))), true2, U, V)
% 0.20/0.76 = { by lemma 69 }
% 0.20/0.76 fresh65(true2, true2, U, V)
% 0.20/0.76 = { by axiom 27 (clause_8_11) }
% 0.20/0.76 fresh66(E(f(U), s(s(s(s(s(s(s(s(0))))))))), true2, V)
% 0.20/0.76 = { by lemma 66 }
% 0.20/0.76 fresh66(true2, true2, V)
% 0.20/0.76 = { by axiom 3 (clause_8_11) }
% 0.20/0.76 true2
% 0.20/0.76
% 0.20/0.76 Goal 1 (clause_3_17): tuple(E(f(X), s(s(s(s(s(s(s(s(0))))))))), E(f(Y), s(s(s(s(s(0)))))), E(f(Z), s(0)), E(f(W), s(s(s(s(s(s(s(s(s(s(0))))))))))), E(f(V), s(s(s(s(0))))), E(f(U), s(s(0))), E(f(T), s(s(s(s(s(s(s(0)))))))), E(f(S), s(s(s(0)))), E(f(X2), s(s(s(s(s(s(s(s(s(0)))))))))), E(f(Y2), s(s(s(s(s(s(0))))))), E(f(Z2), 0)) = tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2).
% 0.20/0.76 The goal is true when:
% 0.20/0.76 X = V5
% 0.20/0.76 Y = X5
% 0.20/0.76 Z = AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)
% 0.20/0.76 W = W5
% 0.20/0.76 V = AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y5)
% 0.20/0.76 U = AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)
% 0.20/0.76 T = S4
% 0.20/0.76 S = AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)
% 0.20/0.76 X2 = Z5
% 0.20/0.76 Y2 = T4
% 0.20/0.76 Z2 = AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)
% 0.20/0.76
% 0.20/0.76 Proof:
% 0.20/0.76 tuple(E(f(V5), s(s(s(s(s(s(s(s(0))))))))), E(f(X5), s(s(s(s(s(0)))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)), s(0)), E(f(W5), s(s(s(s(s(s(s(s(s(s(0))))))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y5)), s(s(s(s(0))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), E(f(S4), s(s(s(s(s(s(s(0)))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), E(f(Z5), s(s(s(s(s(s(s(s(s(0)))))))))), E(f(T4), s(s(s(s(s(s(0))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by lemma 66 }
% 0.20/0.76 tuple(true2, E(f(X5), s(s(s(s(s(0)))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)), s(0)), E(f(W5), s(s(s(s(s(s(s(s(s(s(0))))))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y5)), s(s(s(s(0))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), E(f(S4), s(s(s(s(s(s(s(0)))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), E(f(Z5), s(s(s(s(s(s(s(s(s(0)))))))))), E(f(T4), s(s(s(s(s(s(0))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by axiom 26 (clause_11_03) }
% 0.20/0.76 tuple(true2, E(f(X5), s(s(s(s(s(0)))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)), s(0)), true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y5)), s(s(s(s(0))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), E(f(S4), s(s(s(s(s(s(s(0)))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), E(f(Z5), s(s(s(s(s(s(s(s(s(0)))))))))), E(f(T4), s(s(s(s(s(s(0))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by axiom 21 (clause_17_09) }
% 0.20/0.76 tuple(true2, E(f(X5), s(s(s(s(s(0)))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)), s(0)), true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y5)), s(s(s(s(0))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), E(f(S4), s(s(s(s(s(s(s(0)))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, E(f(T4), s(s(s(s(s(s(0))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by lemma 70 }
% 0.20/0.76 tuple(true2, E(f(X5), s(s(s(s(s(0)))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)), s(0)), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), E(f(S4), s(s(s(s(s(s(s(0)))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, E(f(T4), s(s(s(s(s(s(0))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by lemma 69 }
% 0.20/0.76 tuple(true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)), s(0)), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), E(f(S4), s(s(s(s(s(s(s(0)))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, E(f(T4), s(s(s(s(s(s(0))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by lemma 67 }
% 0.20/0.76 tuple(true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)), s(0)), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, E(f(T4), s(s(s(s(s(s(0))))))), E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by lemma 68 }
% 0.20/0.76 tuple(true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), U4)), s(0)), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by axiom 50 (clause_8_11) R->L }
% 0.20/0.76 tuple(true2, true2, fresh63(Y4, Y4, Z4, W4, V4, U4), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by lemma 73 }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X4)), s(s(0))), true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by axiom 56 (clause_0_19) R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, fresh35(V3, V3, U3, T3, S3, X4), true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by lemma 72 }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), W3)), s(s(s(0)))), true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by lemma 71 }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X)), 0))
% 0.20/0.76 = { by axiom 42 (clause_10_22) R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh16(true2, true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, X))
% 0.20/0.76 = { by lemma 70 R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh16(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2)), s(s(s(s(0))))), true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, X))
% 0.20/0.76 = { by axiom 35 (clause_10_22) R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh15(true2, true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), X))
% 0.20/0.76 = { by lemma 72 R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh15(fresh35(S2, S2, X3, Y3, Z3, Z2), true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), X))
% 0.20/0.76 = { by axiom 56 (clause_0_19) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh15(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2)), s(s(0))), true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), X))
% 0.20/0.76 = { by axiom 25 (clause_10_22) R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh14(true2, true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), X))
% 0.20/0.76 = { by lemma 67 R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh14(E(f(W2), s(s(s(s(s(s(s(0)))))))), true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), X))
% 0.20/0.76 = { by axiom 59 (clause_10_22) R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh11(true2, true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), W2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V2), U2, X))
% 0.20/0.76 = { by lemma 68 R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh11(E(f(T2), s(s(s(s(s(s(0))))))), true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), W2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V2), U2, X))
% 0.20/0.76 = { by axiom 65 (clause_10_22) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh12(E(f(U2), s(s(s(s(s(s(s(s(s(0)))))))))), true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), W2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V2), X))
% 0.20/0.76 = { by axiom 21 (clause_17_09) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh12(true2, true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), W2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V2), X))
% 0.20/0.76 = { by axiom 41 (clause_10_22) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh13(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), V2)), s(s(s(0)))), true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), W2, X))
% 0.20/0.76 = { by lemma 71 }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh13(true2, true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X2, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Y2), AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), Z2), W2, X))
% 0.20/0.76 = { by axiom 58 (clause_10_22) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh17(E(f(X2), s(s(s(s(s(s(s(s(s(s(0))))))))))), true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X))
% 0.20/0.76 = { by axiom 26 (clause_11_03) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh17(true2, true2, Y, Z, AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S), X))
% 0.20/0.76 = { by axiom 11 (clause_10_22) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh18(E(f(AP(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), S)), s(0)), true2, Y, Z, X))
% 0.20/0.76 = { by axiom 50 (clause_8_11) R->L }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh18(fresh63(W, W, V, U, T, S), true2, Y, Z, X))
% 0.20/0.76 = { by lemma 73 }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh18(true2, true2, Y, Z, X))
% 0.20/0.76 = { by axiom 20 (clause_10_22) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh19(E(f(Z), s(s(s(s(s(0)))))), true2, Y, X))
% 0.20/0.76 = { by lemma 69 }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh19(true2, true2, Y, X))
% 0.20/0.76 = { by axiom 34 (clause_10_22) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh20(E(f(Y), s(s(s(s(s(s(s(s(0))))))))), true2, X))
% 0.20/0.76 = { by lemma 66 }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh20(true2, true2, X))
% 0.20/0.76 = { by axiom 9 (clause_10_22) }
% 0.20/0.76 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 0.20/0.76 % SZS output end Proof
% 0.20/0.76
% 0.20/0.76 RESULT: Unsatisfiable (the axioms are contradictory).
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