TSTP Solution File: SYN102-1.007.007 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN102-1.007.007 : TPTP v8.1.2. Bugfixed v1.2.0.
% 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 : n018.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 03:33:10 EDT 2023
% Result : Unsatisfiable 80.95s 10.73s
% Output : Proof 80.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYN102-1.007.007 : TPTP v8.1.2. Bugfixed v1.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 20:14:30 EDT 2023
% 0.14/0.36 % CPUTime :
% 80.95/10.73 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 80.95/10.73
% 80.95/10.73 % SZS status Unsatisfiable
% 80.95/10.73
% 80.95/10.78 % SZS output start Proof
% 80.95/10.78 Take the following subset of the input axioms:
% 80.95/10.79 fof(n_1, axiom, nq_1(a)).
% 80.95/10.79 fof(n_11, axiom, nq_6(a)).
% 80.95/10.79 fof(n_13, axiom, nq_7(a)).
% 80.95/10.79 fof(n_3, axiom, nq_2(a)).
% 80.95/10.79 fof(n_5, axiom, nq_3(a)).
% 80.95/10.79 fof(n_7, axiom, nq_4(a)).
% 80.95/10.79 fof(n_9, axiom, nq_5(a)).
% 80.95/10.79 fof(n_s3_goal_1, negated_conjecture, ~p_0(a, a, a, a, a, a, a) | ~q_0(a, a, a, a, a, a, a)).
% 80.95/10.79 fof(n_s3_type11_11, axiom, ![X_1, X_2, X_3, X_4, X_5, X_6, X_7]: (p_5(X_1, X_2, X_3, X_4, X_5, X_6, X_7) | (~p_6(X_1, X_2, X_3, X_4, X_5, X_6, X_7) | ~p_7(X_1, X_2, X_3, X_4, X_5, X_6, X_7)))).
% 80.95/10.79 fof(n_s3_type11_13, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_6(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_7(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_8(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_15, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_7(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_8(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_9(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_18, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_8(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~q_9(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_10(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_2, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_0(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~q_1(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_2(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_20, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_9(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~q_10(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_11(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_22, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_10(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~q_11(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_12(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_3, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_1(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_2(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_3(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_5, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_2(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_3(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_4(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_7, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_3(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_4(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_5(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type11_9, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_4(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_5(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_6(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_1, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_0(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_1(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_2(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_11, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_5(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_6(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_7(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_13, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_6(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_7(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_8(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_15, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_7(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_8(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_9(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_18, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_8(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~q_9(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_10(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_19, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_9(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_10(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_11(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_22, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_10(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~q_11(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_12(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_24, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_11(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~q_12(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~p_13(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_3, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_1(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_2(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_3(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_5, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_2(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_3(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_4(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_7, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_3(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_4(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_5(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_s3_type12_9, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_4(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~p_5(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | ~q_6(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2)))).
% 80.95/10.79 fof(n_t3_1, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_12(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~nq_1(X_1_2) | (~nq_2(X_2_2) | (~nq_3(X_3_2) | (~nq_4(X_4_2) | (~nq_5(X_5_2) | (~nq_6(X_6_2) | ~nq_7(X_7_2))))))))).
% 80.95/10.79 fof(n_t3_2, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (p_13(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~nq_1(X_1_2) | (~nq_2(X_2_2) | (~nq_3(X_3_2) | (~nq_4(X_4_2) | (~nq_5(X_5_2) | (~nq_6(X_6_2) | ~nq_7(X_7_2))))))))).
% 80.95/10.79 fof(n_t3_3, axiom, ![X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2]: (q_12(X_1_2, X_2_2, X_3_2, X_4_2, X_5_2, X_6_2, X_7_2) | (~nq_1(X_1_2) | (~nq_2(X_2_2) | (~nq_3(X_3_2) | (~nq_4(X_4_2) | (~nq_5(X_5_2) | (~nq_6(X_6_2) | ~nq_7(X_7_2))))))))).
% 80.95/10.79
% 80.95/10.79 Now clausify the problem and encode Horn clauses using encoding 3 of
% 80.95/10.79 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 80.95/10.79 We repeatedly replace C & s=t => u=v by the two clauses:
% 80.95/10.79 fresh(y, y, x1...xn) = u
% 80.95/10.79 C => fresh(s, t, x1...xn) = v
% 80.95/10.79 where fresh is a fresh function symbol and x1..xn are the free
% 80.95/10.79 variables of u and v.
% 80.95/10.79 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 80.95/10.79 input problem has no model of domain size 1).
% 80.95/10.79
% 80.95/10.79 The encoding turns the above axioms into the following unit equations and goals:
% 80.95/10.79
% 80.95/10.79 Axiom 1 (n_1): nq_1(a) = true.
% 80.95/10.79 Axiom 2 (n_3): nq_2(a) = true.
% 80.95/10.79 Axiom 3 (n_5): nq_3(a) = true.
% 80.95/10.79 Axiom 4 (n_7): nq_4(a) = true.
% 80.95/10.79 Axiom 5 (n_9): nq_5(a) = true.
% 80.95/10.79 Axiom 6 (n_11): nq_6(a) = true.
% 80.95/10.79 Axiom 7 (n_13): nq_7(a) = true.
% 80.95/10.79 Axiom 8 (n_t3_1): fresh128(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 9 (n_t3_1): fresh126(X, X, Y, Z, W, V, U, T, S) = p_12(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 10 (n_t3_2): fresh121(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 11 (n_t3_2): fresh119(X, X, Y, Z, W, V, U, T, S) = p_13(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 12 (n_t3_3): fresh114(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 13 (n_t3_3): fresh112(X, X, Y, Z, W, V, U, T, S) = q_12(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 14 (n_s3_type11_11): fresh96(X, X, Y, Z, W, V, U, T, S) = p_5(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 15 (n_s3_type11_11): fresh95(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 16 (n_s3_type11_13): fresh92(X, X, Y, Z, W, V, U, T, S) = p_6(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 17 (n_s3_type11_13): fresh91(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 18 (n_s3_type11_15): fresh88(X, X, Y, Z, W, V, U, T, S) = p_7(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 19 (n_s3_type11_15): fresh87(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 20 (n_s3_type11_18): fresh82(X, X, Y, Z, W, V, U, T, S) = p_8(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 21 (n_s3_type11_18): fresh81(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 22 (n_s3_type11_2): fresh78(X, X, Y, Z, W, V, U, T, S) = p_0(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 23 (n_s3_type11_2): fresh77(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 24 (n_s3_type11_20): fresh76(X, X, Y, Z, W, V, U, T, S) = p_9(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 25 (n_s3_type11_20): fresh75(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 26 (n_s3_type11_22): fresh72(X, X, Y, Z, W, V, U, T, S) = p_10(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 27 (n_s3_type11_22): fresh71(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 28 (n_s3_type11_3): fresh66(X, X, Y, Z, W, V, U, T, S) = p_1(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 29 (n_s3_type11_3): fresh65(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 30 (n_s3_type11_5): fresh62(X, X, Y, Z, W, V, U, T, S) = p_2(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 31 (n_s3_type11_5): fresh61(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 32 (n_s3_type11_7): fresh58(X, X, Y, Z, W, V, U, T, S) = p_3(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 33 (n_s3_type11_7): fresh57(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 34 (n_s3_type11_9): fresh54(X, X, Y, Z, W, V, U, T, S) = p_4(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 35 (n_s3_type11_9): fresh53(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 36 (n_s3_type12_1): fresh52(X, X, Y, Z, W, V, U, T, S) = q_0(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 37 (n_s3_type12_1): fresh51(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 38 (n_s3_type12_11): fresh48(X, X, Y, Z, W, V, U, T, S) = q_5(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 39 (n_s3_type12_11): fresh47(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 40 (n_s3_type12_13): fresh44(X, X, Y, Z, W, V, U, T, S) = q_6(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 41 (n_s3_type12_13): fresh43(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 42 (n_s3_type12_15): fresh40(X, X, Y, Z, W, V, U, T, S) = q_7(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 43 (n_s3_type12_15): fresh39(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 44 (n_s3_type12_18): fresh34(X, X, Y, Z, W, V, U, T, S) = q_8(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 45 (n_s3_type12_18): fresh33(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 46 (n_s3_type12_19): fresh32(X, X, Y, Z, W, V, U, T, S) = q_9(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 47 (n_s3_type12_19): fresh31(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 48 (n_s3_type12_22): fresh24(X, X, Y, Z, W, V, U, T, S) = q_10(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 49 (n_s3_type12_22): fresh23(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 50 (n_s3_type12_24): fresh20(X, X, Y, Z, W, V, U, T, S) = q_11(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 51 (n_s3_type12_24): fresh19(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 52 (n_s3_type12_3): fresh18(X, X, Y, Z, W, V, U, T, S) = q_1(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 53 (n_s3_type12_3): fresh17(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 54 (n_s3_type12_5): fresh14(X, X, Y, Z, W, V, U, T, S) = q_2(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 55 (n_s3_type12_5): fresh13(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 56 (n_s3_type12_7): fresh10(X, X, Y, Z, W, V, U, T, S) = q_3(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 57 (n_s3_type12_7): fresh9(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 58 (n_s3_type12_9): fresh6(X, X, Y, Z, W, V, U, T, S) = q_4(Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 59 (n_s3_type12_9): fresh5(X, X, Y, Z, W, V, U, T, S) = true.
% 80.95/10.79 Axiom 60 (n_t3_1): fresh127(X, X, Y, Z, W, V, U, T, S) = fresh128(nq_1(Y), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 61 (n_t3_1): fresh124(X, X, Y, Z, W, V, U, T, S) = fresh127(nq_3(W), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 62 (n_t3_1): fresh125(X, X, Y, Z, W, V, U, T, S) = fresh126(nq_2(Z), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 63 (n_t3_1): fresh123(X, X, Y, Z, W, V, U, T, S) = fresh125(nq_4(V), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 64 (n_t3_1): fresh122(X, X, Y, Z, W, V, U, T, S) = fresh124(nq_5(U), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 65 (n_t3_1): fresh122(nq_7(X), true, Y, Z, W, V, U, T, X) = fresh123(nq_6(T), true, Y, Z, W, V, U, T, X).
% 80.95/10.79 Axiom 66 (n_t3_2): fresh120(X, X, Y, Z, W, V, U, T, S) = fresh121(nq_1(Y), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 67 (n_t3_2): fresh117(X, X, Y, Z, W, V, U, T, S) = fresh120(nq_3(W), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 68 (n_t3_2): fresh118(X, X, Y, Z, W, V, U, T, S) = fresh119(nq_2(Z), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 69 (n_t3_2): fresh116(X, X, Y, Z, W, V, U, T, S) = fresh118(nq_4(V), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 70 (n_t3_2): fresh115(X, X, Y, Z, W, V, U, T, S) = fresh117(nq_5(U), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 71 (n_t3_2): fresh115(nq_7(X), true, Y, Z, W, V, U, T, X) = fresh116(nq_6(T), true, Y, Z, W, V, U, T, X).
% 80.95/10.79 Axiom 72 (n_t3_3): fresh113(X, X, Y, Z, W, V, U, T, S) = fresh114(nq_1(Y), true, Y, Z, W, V, U, T, S).
% 80.95/10.79 Axiom 73 (n_t3_3): fresh110(X, X, Y, Z, W, V, U, T, S) = fresh113(nq_3(W), true, Y, Z, W, V, U, T, S).
% 80.95/10.80 Axiom 74 (n_t3_3): fresh111(X, X, Y, Z, W, V, U, T, S) = fresh112(nq_2(Z), true, Y, Z, W, V, U, T, S).
% 80.95/10.80 Axiom 75 (n_t3_3): fresh109(X, X, Y, Z, W, V, U, T, S) = fresh111(nq_4(V), true, Y, Z, W, V, U, T, S).
% 80.95/10.80 Axiom 76 (n_t3_3): fresh108(X, X, Y, Z, W, V, U, T, S) = fresh110(nq_5(U), true, Y, Z, W, V, U, T, S).
% 80.95/10.80 Axiom 77 (n_t3_3): fresh108(nq_7(X), true, Y, Z, W, V, U, T, X) = fresh109(nq_6(T), true, Y, Z, W, V, U, T, X).
% 80.95/10.80 Axiom 78 (n_s3_type11_11): fresh96(p_7(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh95(p_6(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 79 (n_s3_type11_13): fresh92(p_8(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh91(p_7(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 80 (n_s3_type11_15): fresh88(p_9(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh87(p_8(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 81 (n_s3_type11_18): fresh82(q_10(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh81(q_9(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 82 (n_s3_type11_2): fresh78(q_2(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh77(q_1(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 83 (n_s3_type11_20): fresh76(q_11(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh75(q_10(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 84 (n_s3_type11_22): fresh72(q_12(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh71(q_11(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 85 (n_s3_type11_3): fresh66(p_3(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh65(p_2(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 86 (n_s3_type11_5): fresh62(p_4(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh61(p_3(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 87 (n_s3_type11_7): fresh58(p_5(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh57(p_4(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 88 (n_s3_type11_9): fresh54(p_6(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh53(p_5(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 89 (n_s3_type12_1): fresh52(q_2(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh51(p_1(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 90 (n_s3_type12_11): fresh48(q_7(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh47(p_6(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 91 (n_s3_type12_13): fresh44(q_8(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh43(p_7(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 92 (n_s3_type12_15): fresh40(q_9(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh39(p_8(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 93 (n_s3_type12_18): fresh34(p_10(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh33(q_9(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 94 (n_s3_type12_19): fresh32(q_11(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh31(p_10(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 95 (n_s3_type12_22): fresh24(p_12(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh23(q_11(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 96 (n_s3_type12_24): fresh20(p_13(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh19(q_12(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 97 (n_s3_type12_3): fresh18(q_3(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh17(p_2(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 98 (n_s3_type12_5): fresh14(q_4(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh13(p_3(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 99 (n_s3_type12_7): fresh10(q_5(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh9(p_4(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80 Axiom 100 (n_s3_type12_9): fresh6(q_6(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T) = fresh5(p_5(X, Y, Z, W, V, U, T), true, X, Y, Z, W, V, U, T).
% 80.95/10.80
% 80.95/10.80 Lemma 101: q_12(a, a, a, a, a, a, a) = true.
% 80.95/10.80 Proof:
% 80.95/10.80 q_12(a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 13 (n_t3_3) R->L }
% 80.95/10.80 fresh112(true, true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 2 (n_3) R->L }
% 80.95/10.80 fresh112(nq_2(a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 74 (n_t3_3) R->L }
% 80.95/10.80 fresh111(true, true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 4 (n_7) R->L }
% 80.95/10.80 fresh111(nq_4(a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 75 (n_t3_3) R->L }
% 80.95/10.80 fresh109(true, true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 6 (n_11) R->L }
% 80.95/10.80 fresh109(nq_6(a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 77 (n_t3_3) R->L }
% 80.95/10.80 fresh108(nq_7(a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 7 (n_13) }
% 80.95/10.80 fresh108(true, true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 76 (n_t3_3) }
% 80.95/10.80 fresh110(nq_5(a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 5 (n_9) }
% 80.95/10.80 fresh110(true, true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 73 (n_t3_3) }
% 80.95/10.80 fresh113(nq_3(a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 3 (n_5) }
% 80.95/10.80 fresh113(true, true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 72 (n_t3_3) }
% 80.95/10.80 fresh114(nq_1(a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 1 (n_1) }
% 80.95/10.80 fresh114(true, true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 12 (n_t3_3) }
% 80.95/10.80 true
% 80.95/10.80
% 80.95/10.80 Lemma 102: q_11(a, a, a, a, a, a, a) = true.
% 80.95/10.80 Proof:
% 80.95/10.80 q_11(a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 50 (n_s3_type12_24) R->L }
% 80.95/10.80 fresh20(true, true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 10 (n_t3_2) R->L }
% 80.95/10.80 fresh20(fresh121(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 1 (n_1) R->L }
% 80.95/10.80 fresh20(fresh121(nq_1(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 66 (n_t3_2) R->L }
% 80.95/10.80 fresh20(fresh120(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 3 (n_5) R->L }
% 80.95/10.80 fresh20(fresh120(nq_3(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 67 (n_t3_2) R->L }
% 80.95/10.80 fresh20(fresh117(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 5 (n_9) R->L }
% 80.95/10.80 fresh20(fresh117(nq_5(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 70 (n_t3_2) R->L }
% 80.95/10.80 fresh20(fresh115(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 7 (n_13) R->L }
% 80.95/10.80 fresh20(fresh115(nq_7(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 71 (n_t3_2) }
% 80.95/10.80 fresh20(fresh116(nq_6(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 6 (n_11) }
% 80.95/10.80 fresh20(fresh116(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 69 (n_t3_2) }
% 80.95/10.80 fresh20(fresh118(nq_4(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 4 (n_7) }
% 80.95/10.80 fresh20(fresh118(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 68 (n_t3_2) }
% 80.95/10.80 fresh20(fresh119(nq_2(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.80 = { by axiom 2 (n_3) }
% 80.95/10.80 fresh20(fresh119(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 11 (n_t3_2) }
% 80.95/10.81 fresh20(p_13(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 96 (n_s3_type12_24) }
% 80.95/10.81 fresh19(q_12(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by lemma 101 }
% 80.95/10.81 fresh19(true, true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 51 (n_s3_type12_24) }
% 80.95/10.81 true
% 80.95/10.81
% 80.95/10.81 Lemma 103: q_10(a, a, a, a, a, a, a) = true.
% 80.95/10.81 Proof:
% 80.95/10.81 q_10(a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 48 (n_s3_type12_22) R->L }
% 80.95/10.81 fresh24(true, true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 8 (n_t3_1) R->L }
% 80.95/10.81 fresh24(fresh128(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 1 (n_1) R->L }
% 80.95/10.81 fresh24(fresh128(nq_1(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 60 (n_t3_1) R->L }
% 80.95/10.81 fresh24(fresh127(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 3 (n_5) R->L }
% 80.95/10.81 fresh24(fresh127(nq_3(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 61 (n_t3_1) R->L }
% 80.95/10.81 fresh24(fresh124(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 5 (n_9) R->L }
% 80.95/10.81 fresh24(fresh124(nq_5(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 64 (n_t3_1) R->L }
% 80.95/10.81 fresh24(fresh122(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 7 (n_13) R->L }
% 80.95/10.81 fresh24(fresh122(nq_7(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 65 (n_t3_1) }
% 80.95/10.81 fresh24(fresh123(nq_6(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 6 (n_11) }
% 80.95/10.81 fresh24(fresh123(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 63 (n_t3_1) }
% 80.95/10.81 fresh24(fresh125(nq_4(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 4 (n_7) }
% 80.95/10.81 fresh24(fresh125(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 62 (n_t3_1) }
% 80.95/10.81 fresh24(fresh126(nq_2(a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 2 (n_3) }
% 80.95/10.81 fresh24(fresh126(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 9 (n_t3_1) }
% 80.95/10.81 fresh24(p_12(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 95 (n_s3_type12_22) }
% 80.95/10.81 fresh23(q_11(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by lemma 102 }
% 80.95/10.81 fresh23(true, true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 49 (n_s3_type12_22) }
% 80.95/10.81 true
% 80.95/10.81
% 80.95/10.81 Lemma 104: p_10(a, a, a, a, a, a, a) = true.
% 80.95/10.81 Proof:
% 80.95/10.81 p_10(a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 26 (n_s3_type11_22) R->L }
% 80.95/10.81 fresh72(true, true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by lemma 101 R->L }
% 80.95/10.81 fresh72(q_12(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.81 = { by axiom 84 (n_s3_type11_22) }
% 80.95/10.81 fresh71(q_11(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by lemma 102 }
% 80.95/10.82 fresh71(true, true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 27 (n_s3_type11_22) }
% 80.95/10.82 true
% 80.95/10.82
% 80.95/10.82 Lemma 105: q_9(a, a, a, a, a, a, a) = true.
% 80.95/10.82 Proof:
% 80.95/10.82 q_9(a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 46 (n_s3_type12_19) R->L }
% 80.95/10.82 fresh32(true, true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by lemma 102 R->L }
% 80.95/10.82 fresh32(q_11(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 94 (n_s3_type12_19) }
% 80.95/10.82 fresh31(p_10(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by lemma 104 }
% 80.95/10.82 fresh31(true, true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 47 (n_s3_type12_19) }
% 80.95/10.82 true
% 80.95/10.82
% 80.95/10.82 Lemma 106: p_8(a, a, a, a, a, a, a) = true.
% 80.95/10.82 Proof:
% 80.95/10.82 p_8(a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 20 (n_s3_type11_18) R->L }
% 80.95/10.82 fresh82(true, true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by lemma 103 R->L }
% 80.95/10.82 fresh82(q_10(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 81 (n_s3_type11_18) }
% 80.95/10.82 fresh81(q_9(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by lemma 105 }
% 80.95/10.82 fresh81(true, true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 21 (n_s3_type11_18) }
% 80.95/10.82 true
% 80.95/10.82
% 80.95/10.82 Lemma 107: p_7(a, a, a, a, a, a, a) = true.
% 80.95/10.82 Proof:
% 80.95/10.82 p_7(a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 18 (n_s3_type11_15) R->L }
% 80.95/10.82 fresh88(true, true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 25 (n_s3_type11_20) R->L }
% 80.95/10.82 fresh88(fresh75(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by lemma 103 R->L }
% 80.95/10.82 fresh88(fresh75(q_10(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 83 (n_s3_type11_20) R->L }
% 80.95/10.82 fresh88(fresh76(q_11(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by lemma 102 }
% 80.95/10.82 fresh88(fresh76(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 24 (n_s3_type11_20) }
% 80.95/10.82 fresh88(p_9(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by axiom 80 (n_s3_type11_15) }
% 80.95/10.82 fresh87(p_8(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.82 = { by lemma 106 }
% 80.95/10.82 fresh87(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 19 (n_s3_type11_15) }
% 80.95/10.83 true
% 80.95/10.83
% 80.95/10.83 Lemma 108: p_6(a, a, a, a, a, a, a) = true.
% 80.95/10.83 Proof:
% 80.95/10.83 p_6(a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 16 (n_s3_type11_13) R->L }
% 80.95/10.83 fresh92(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 106 R->L }
% 80.95/10.83 fresh92(p_8(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 79 (n_s3_type11_13) }
% 80.95/10.83 fresh91(p_7(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 107 }
% 80.95/10.83 fresh91(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 17 (n_s3_type11_13) }
% 80.95/10.83 true
% 80.95/10.83
% 80.95/10.83 Lemma 109: p_5(a, a, a, a, a, a, a) = true.
% 80.95/10.83 Proof:
% 80.95/10.83 p_5(a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 14 (n_s3_type11_11) R->L }
% 80.95/10.83 fresh96(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 107 R->L }
% 80.95/10.83 fresh96(p_7(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 78 (n_s3_type11_11) }
% 80.95/10.83 fresh95(p_6(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 108 }
% 80.95/10.83 fresh95(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 15 (n_s3_type11_11) }
% 80.95/10.83 true
% 80.95/10.83
% 80.95/10.83 Lemma 110: p_4(a, a, a, a, a, a, a) = true.
% 80.95/10.83 Proof:
% 80.95/10.83 p_4(a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 34 (n_s3_type11_9) R->L }
% 80.95/10.83 fresh54(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 108 R->L }
% 80.95/10.83 fresh54(p_6(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 88 (n_s3_type11_9) }
% 80.95/10.83 fresh53(p_5(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 109 }
% 80.95/10.83 fresh53(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 35 (n_s3_type11_9) }
% 80.95/10.83 true
% 80.95/10.83
% 80.95/10.83 Lemma 111: p_3(a, a, a, a, a, a, a) = true.
% 80.95/10.83 Proof:
% 80.95/10.83 p_3(a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 32 (n_s3_type11_7) R->L }
% 80.95/10.83 fresh58(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 109 R->L }
% 80.95/10.83 fresh58(p_5(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 87 (n_s3_type11_7) }
% 80.95/10.83 fresh57(p_4(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 110 }
% 80.95/10.83 fresh57(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 33 (n_s3_type11_7) }
% 80.95/10.83 true
% 80.95/10.83
% 80.95/10.83 Lemma 112: p_2(a, a, a, a, a, a, a) = true.
% 80.95/10.83 Proof:
% 80.95/10.83 p_2(a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 30 (n_s3_type11_5) R->L }
% 80.95/10.83 fresh62(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 110 R->L }
% 80.95/10.83 fresh62(p_4(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 86 (n_s3_type11_5) }
% 80.95/10.83 fresh61(p_3(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 111 }
% 80.95/10.83 fresh61(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 31 (n_s3_type11_5) }
% 80.95/10.83 true
% 80.95/10.83
% 80.95/10.83 Lemma 113: q_2(a, a, a, a, a, a, a) = true.
% 80.95/10.83 Proof:
% 80.95/10.83 q_2(a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 54 (n_s3_type12_5) R->L }
% 80.95/10.83 fresh14(true, true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 59 (n_s3_type12_9) R->L }
% 80.95/10.83 fresh14(fresh5(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 109 R->L }
% 80.95/10.83 fresh14(fresh5(p_5(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 100 (n_s3_type12_9) R->L }
% 80.95/10.83 fresh14(fresh6(q_6(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 40 (n_s3_type12_13) R->L }
% 80.95/10.83 fresh14(fresh6(fresh44(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 45 (n_s3_type12_18) R->L }
% 80.95/10.83 fresh14(fresh6(fresh44(fresh33(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 105 R->L }
% 80.95/10.83 fresh14(fresh6(fresh44(fresh33(q_9(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 93 (n_s3_type12_18) R->L }
% 80.95/10.83 fresh14(fresh6(fresh44(fresh34(p_10(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by lemma 104 }
% 80.95/10.83 fresh14(fresh6(fresh44(fresh34(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.83 = { by axiom 44 (n_s3_type12_18) }
% 80.95/10.84 fresh14(fresh6(fresh44(q_8(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.84 = { by axiom 91 (n_s3_type12_13) }
% 80.95/10.84 fresh14(fresh6(fresh43(p_7(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.84 = { by lemma 107 }
% 80.95/10.84 fresh14(fresh6(fresh43(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.84 = { by axiom 41 (n_s3_type12_13) }
% 80.95/10.84 fresh14(fresh6(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.84 = { by axiom 58 (n_s3_type12_9) }
% 80.95/10.84 fresh14(q_4(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.84 = { by axiom 98 (n_s3_type12_5) }
% 80.95/10.84 fresh13(p_3(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a)
% 80.95/10.84 = { by lemma 111 }
% 80.95/10.84 fresh13(true, true, a, a, a, a, a, a, a)
% 80.95/10.84 = { by axiom 55 (n_s3_type12_5) }
% 80.95/10.84 true
% 80.95/10.84
% 80.95/10.84 Goal 1 (n_s3_goal_1): tuple(p_0(a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a)) = tuple(true, true).
% 80.95/10.84 Proof:
% 80.95/10.84 tuple(p_0(a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 22 (n_s3_type11_2) R->L }
% 80.95/10.84 tuple(fresh78(true, true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 113 R->L }
% 80.95/10.84 tuple(fresh78(q_2(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 82 (n_s3_type11_2) }
% 80.95/10.84 tuple(fresh77(q_1(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 52 (n_s3_type12_3) R->L }
% 80.95/10.84 tuple(fresh77(fresh18(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 57 (n_s3_type12_7) R->L }
% 80.95/10.84 tuple(fresh77(fresh18(fresh9(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 110 R->L }
% 80.95/10.84 tuple(fresh77(fresh18(fresh9(p_4(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 99 (n_s3_type12_7) R->L }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(q_5(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 38 (n_s3_type12_11) R->L }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(fresh48(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 43 (n_s3_type12_15) R->L }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(fresh48(fresh39(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 106 R->L }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(fresh48(fresh39(p_8(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 92 (n_s3_type12_15) R->L }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(fresh48(fresh40(q_9(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 105 }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(fresh48(fresh40(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 42 (n_s3_type12_15) }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(fresh48(q_7(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 90 (n_s3_type12_11) }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(fresh47(p_6(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 108 }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(fresh47(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 39 (n_s3_type12_11) }
% 80.95/10.84 tuple(fresh77(fresh18(fresh10(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 56 (n_s3_type12_7) }
% 80.95/10.84 tuple(fresh77(fresh18(q_3(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 97 (n_s3_type12_3) }
% 80.95/10.84 tuple(fresh77(fresh17(p_2(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 112 }
% 80.95/10.84 tuple(fresh77(fresh17(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 53 (n_s3_type12_3) }
% 80.95/10.84 tuple(fresh77(true, true, a, a, a, a, a, a, a), q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 23 (n_s3_type11_2) }
% 80.95/10.84 tuple(true, q_0(a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 36 (n_s3_type12_1) R->L }
% 80.95/10.84 tuple(true, fresh52(true, true, a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 113 R->L }
% 80.95/10.84 tuple(true, fresh52(q_2(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 89 (n_s3_type12_1) }
% 80.95/10.84 tuple(true, fresh51(p_1(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 28 (n_s3_type11_3) R->L }
% 80.95/10.84 tuple(true, fresh51(fresh66(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 111 R->L }
% 80.95/10.84 tuple(true, fresh51(fresh66(p_3(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 85 (n_s3_type11_3) }
% 80.95/10.84 tuple(true, fresh51(fresh65(p_2(a, a, a, a, a, a, a), true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a))
% 80.95/10.84 = { by lemma 112 }
% 80.95/10.84 tuple(true, fresh51(fresh65(true, true, a, a, a, a, a, a, a), true, a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 29 (n_s3_type11_3) }
% 80.95/10.84 tuple(true, fresh51(true, true, a, a, a, a, a, a, a))
% 80.95/10.84 = { by axiom 37 (n_s3_type12_1) }
% 80.95/10.84 tuple(true, true)
% 80.95/10.84 % SZS output end Proof
% 80.95/10.84
% 80.95/10.84 RESULT: Unsatisfiable (the axioms are contradictory).
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