TSTP Solution File: SWW641_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW641_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:32 EDT 2022
% Result : Theorem 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWW641_2 : TPTP v8.1.0. Released v6.1.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 20:33:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 tff(infix_eqeq1_type, type, (
% 0.18/0.50 infix_eqeq1: ( string2 * string2 ) > $o)).
% 0.18/0.50 tff(app2_type, type, (
% 0.18/0.50 app2: ( string2 * string2 ) > string2)).
% 0.18/0.50 tff(string3_type, type, (
% 0.18/0.50 string3: rope1 > string2)).
% 0.18/0.50 tff(tptp_fun_R_4_type, type, (
% 0.18/0.50 tptp_fun_R_4: rope1)).
% 0.18/0.50 tff(tb2t2_type, type, (
% 0.18/0.50 tb2t2: uni > rope1)).
% 0.18/0.50 tff(get_type, type, (
% 0.18/0.50 get: ( ty * ty * uni * uni ) > uni)).
% 0.18/0.50 tff(t2tb_type, type, (
% 0.18/0.50 t2tb: $int > uni)).
% 0.18/0.50 tff(tptp_fun_I_5_type, type, (
% 0.18/0.50 tptp_fun_I_5: $int)).
% 0.18/0.50 tff(t2tb3_type, type, (
% 0.18/0.50 t2tb3: map_int_rope > uni)).
% 0.18/0.50 tff(tptp_fun_Q1_6_type, type, (
% 0.18/0.50 tptp_fun_Q1_6: map_int_rope)).
% 0.18/0.50 tff(int_type, type, (
% 0.18/0.50 int: ty)).
% 0.18/0.50 tff(rope_type, type, (
% 0.18/0.50 rope: ty)).
% 0.18/0.50 tff(string_of_array1_type, type, (
% 0.18/0.50 string_of_array1: ( array_rope * $int * $int ) > string2)).
% 0.18/0.50 tff(max3_type, type, (
% 0.18/0.50 max3: $int)).
% 0.18/0.50 tff(tb2t1_type, type, (
% 0.18/0.50 tb2t1: uni > array_rope)).
% 0.18/0.50 tff(mk_array1_type, type, (
% 0.18/0.50 mk_array1: ( ty * $int * uni ) > uni)).
% 0.18/0.50 tff(tptp_fun_Q_7_type, type, (
% 0.18/0.50 tptp_fun_Q_7: $int)).
% 0.18/0.50 tff(tptp_fun_Q2_9_type, type, (
% 0.18/0.50 tptp_fun_Q2_9: map_int_rope)).
% 0.18/0.50 tff(get2_type, type, (
% 0.18/0.50 get2: ( ty * uni * $int ) > uni)).
% 0.18/0.50 tff(t2tb1_type, type, (
% 0.18/0.50 t2tb1: array_rope > uni)).
% 0.18/0.50 tff(length5_type, type, (
% 0.18/0.50 length5: ( ty * uni ) > $int)).
% 0.18/0.50 tff(length3_type, type, (
% 0.18/0.50 length3: string2 > $int)).
% 0.18/0.50 tff(tb2t_type, type, (
% 0.18/0.50 tb2t: uni > $int)).
% 0.18/0.50 tff(match_rope1_type, type, (
% 0.18/0.50 match_rope1: ( ty * rope1 * uni * uni * uni ) > uni)).
% 0.18/0.50 tff(app_proj_31_type, type, (
% 0.18/0.50 app_proj_31: rope1 > $int)).
% 0.18/0.50 tff(str_proj_31_type, type, (
% 0.18/0.50 str_proj_31: rope1 > $int)).
% 0.18/0.50 tff(fib1_type, type, (
% 0.18/0.50 fib1: $int > $int)).
% 0.18/0.50 tff(inv1_type, type, (
% 0.18/0.50 inv1: rope1 > $o)).
% 0.18/0.50 tff(tptp_fun_Rqt_8_type, type, (
% 0.18/0.50 tptp_fun_Rqt_8: rope1)).
% 0.18/0.50 tff(tb2t3_type, type, (
% 0.18/0.50 tb2t3: uni > map_int_rope)).
% 0.18/0.50 tff(set_type, type, (
% 0.18/0.50 set: ( ty * ty * uni * uni * uni ) > uni)).
% 0.18/0.50 tff(t2tb2_type, type, (
% 0.18/0.50 t2tb2: rope1 > uni)).
% 0.18/0.50 tff(elts_type, type, (
% 0.18/0.50 elts: ( ty * uni ) > uni)).
% 0.18/0.50 tff(sort1_type, type, (
% 0.18/0.50 sort1: ( ty * uni ) > $o)).
% 0.18/0.50 tff(map_type, type, (
% 0.18/0.50 map: ( ty * ty ) > ty)).
% 0.18/0.50 tff(1,plain,
% 0.18/0.50 (((inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4)) & ((~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & $greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))) & ($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))) & ($greatereq(Q!7, 0) & $greatereq(I!5, 2) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & ($sum(max3, $product(-1, Q!7)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)))))), 0)))) <=> (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4) & (~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & $greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))) & $greatereq(Q!7, 0) & $greatereq(I!5, 2) & ($sum(max3, $product(-1, Q!7)) = -1) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)))))), 0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(2,plain,
% 0.18/0.50 (($greatereq(Q!7, 0) & $greatereq(I!5, 2) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & ($sum(Q!7, $product(-1, max3)) = 1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0))) <=> ($greatereq(Q!7, 0) & $greatereq(I!5, 2) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & ($sum(max3, $product(-1, Q!7)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)))))), 0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(3,plain,
% 0.18/0.50 ((~(~($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))))) <=> ($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(4,plain,
% 0.18/0.50 (((~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & ($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))) & (inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))) <=> ((~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & $greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(5,plain,
% 0.18/0.50 ((~(~(inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))))) <=> (inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(6,plain,
% 0.18/0.50 ((~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) <=> (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(7,plain,
% 0.18/0.50 ((~$greatereq($sum(tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))), $product(-1, fib1($sum(1, I!5)))), 0)) <=> (~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(8,plain,
% 0.18/0.50 (((~$greatereq($sum(tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))), $product(-1, fib1($sum(1, I!5)))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & (~(~($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))))) & (~(~(inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))))) <=> ((~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & ($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))) & (inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[7, 6, 3, 5])).
% 0.18/0.50 tff(9,plain,
% 0.18/0.50 (((~$greatereq($sum(tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))), $product(-1, fib1($sum(1, I!5)))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & (~(~($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))))) & (~(~(inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))))) <=> ((~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & $greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[8, 4])).
% 0.18/0.50 tff(10,plain,
% 0.18/0.50 ((~(~(inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4)))) <=> (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(11,plain,
% 0.18/0.50 (((~(~(inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4)))) & ((~$greatereq($sum(tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))), $product(-1, fib1($sum(1, I!5)))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & (~(~($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))))) & (~(~(inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))))) & (~(~($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))))) & ($greatereq(Q!7, 0) & $greatereq(I!5, 2) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & ($sum(Q!7, $product(-1, max3)) = 1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0)))) <=> ((inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4)) & ((~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & $greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))) & ($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))) & ($greatereq(Q!7, 0) & $greatereq(I!5, 2) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & ($sum(max3, $product(-1, Q!7)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)))))), 0))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[10, 9, 3, 2])).
% 0.18/0.51 tff(12,plain,
% 0.18/0.51 (((~(~(inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4)))) & ((~$greatereq($sum(tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))), $product(-1, fib1($sum(1, I!5)))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & (~(~($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))))) & (~(~(inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))))) & (~(~($greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0))))) & ($greatereq(Q!7, 0) & $greatereq(I!5, 2) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & ($sum(Q!7, $product(-1, max3)) = 1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0)))) <=> (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4) & (~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & $greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))) & $greatereq(Q!7, 0) & $greatereq(I!5, 2) & ($sum(max3, $product(-1, Q!7)) = -1) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)))))), 0)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[11, 1])).
% 0.18/0.51 tff(13,plain,
% 0.18/0.51 ((~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ($greatereq($sum(tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))), $product(-1, fib1($sum(1, I)))), 0) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R)))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Q)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0)))))) <=> (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ($greatereq($sum(tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))), $product(-1, fib1($sum(1, I)))), 0) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R)))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Q)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(14,plain,
% 0.18/0.51 ((~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | (~($greatereq(I, 0) & (~$lesseq($sum(Q, $product(-1, I)), 0)))) | ![Rqt: rope1] : (![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq($sum(fib1($sum(1, I)), $product(-1, tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(Q, $product(-1, I)), 0))))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$lesseq($sum(Q, $product(-1, I)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)))), $product(-1, tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))), 0)))))) <=> (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ($greatereq($sum(tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))), $product(-1, fib1($sum(1, I)))), 0) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R)))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Q)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(15,plain,
% 0.18/0.51 ((~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))))) <=> (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | (~($greatereq(I, 0) & (~$lesseq($sum(Q, $product(-1, I)), 0)))) | ![Rqt: rope1] : (![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq($sum(fib1($sum(1, I)), $product(-1, tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(Q, $product(-1, I)), 0))))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$lesseq($sum(Q, $product(-1, I)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)))), $product(-1, tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))), 0))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(16,plain,
% 0.18/0.51 ((~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))))) <=> (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))))))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(17,plain,
% 0.18/0.51 ((~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((((((($lesseq(0, Q) & $lesseq(2, I)) & $less(I, Q)) & (Q = $sum(max3, 1))) & inv1(R)) & ![J: $int] : (($lesseq(2, J) & $lesseq(J, max3)) => inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))))) & $less($sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(max3, 1))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))), fib1($sum(max3, 1)))) => (($lesseq(0, I) & $less(I, Q)) => ((inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R)) => ![Rqt: rope1] : ((inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R)))) => ($less(tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))), fib1($sum(I, 1))) => (($lesseq(0, I) & $less(I, Q)) => ![Q2: map_int_rope] : (($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))) => (infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(I, 1), $sum(max3, 1)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(I, 1), $sum(max3, 1))) => infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(max3, 1)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(max3, 1)), string3(R)))))))))))) <=> (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))))))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(18,axiom,(~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((((((($lesseq(0, Q) & $lesseq(2, I)) & $less(I, Q)) & (Q = $sum(max3, 1))) & inv1(R)) & ![J: $int] : (($lesseq(2, J) & $lesseq(J, max3)) => inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))))) & $less($sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(max3, 1))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))), fib1($sum(max3, 1)))) => (($lesseq(0, I) & $less(I, Q)) => ((inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R)) => ![Rqt: rope1] : ((inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R)))) => ($less(tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))), fib1($sum(I, 1))) => (($lesseq(0, I) & $less(I, Q)) => ![Q2: map_int_rope] : (($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))) => (infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(I, 1), $sum(max3, 1)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(I, 1), $sum(max3, 1))) => infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(max3, 1)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(max3, 1)), string3(R)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_insert')).
% 0.18/0.51 tff(19,plain,
% 0.18/0.51 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.51 tff(20,plain,
% 0.18/0.51 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.18/0.51 tff(21,plain,
% 0.18/0.51 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.18/0.51 tff(22,plain,
% 0.18/0.51 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.18/0.51 tff(23,plain,
% 0.18/0.51 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ((~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq(fib1($sum(1, I)), tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt))))) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($lesseq(0, Q) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($lesseq(0, I) & (~$lesseq(Q, I))))) | (~($lesseq(0, I) & (~$lesseq(Q, I)))) | (~($lesseq(0, Q) & $lesseq(2, I) & (~$lesseq(Q, I)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.18/0.51 tff(24,plain,
% 0.18/0.51 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | (~($greatereq(I, 0) & (~$lesseq($sum(Q, $product(-1, I)), 0)))) | ![Rqt: rope1] : (![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R))))) | $lesseq($sum(fib1($sum(1, I)), $product(-1, tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))))), 0) | (~($greatereq(I, 0) & (~$lesseq($sum(Q, $product(-1, I)), 0))))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$lesseq($sum(Q, $product(-1, I)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)))), $product(-1, tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))), 0)))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.18/0.51 tff(25,plain,
% 0.18/0.51 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ($greatereq($sum(tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))), $product(-1, fib1($sum(1, I)))), 0) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R)))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Q)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0)))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.18/0.52 tff(26,plain,
% 0.18/0.52 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ($greatereq($sum(tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))), $product(-1, fib1($sum(1, I)))), 0) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R)))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Q)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0)))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.18/0.52 tff(27,plain,
% 0.18/0.52 (~![Q: $int, Q1: map_int_rope, I: $int, R: rope1] : ((~(inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))) & inv1(R))) | ![Rqt: rope1] : ($greatereq($sum(tb2t(match_rope1(int, Rqt, t2tb(0), t2tb(str_proj_31(Rqt)), t2tb(app_proj_31(Rqt)))), $product(-1, fib1($sum(1, I)))), 0) | ![Q2: map_int_rope] : ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), $sum(1, I), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), $sum(1, I), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))), I, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3)), string3(R))) | (~($greatereq(Q, 0) & (Q2 = tb2t3(set(rope, int, t2tb3(Q1), t2tb(I), t2tb2(Rqt))))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~(inv1(Rqt) & infix_eqeq1(string3(Rqt), app2(string3(tb2t2(get(rope, int, t2tb3(Q1), t2tb(I)))), string3(R)))))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Q)), 0)))) | (~($greatereq(Q, 0) & $greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Q)), 0)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_array1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))), I, $sum(1, max3))), $product(-1, fib1($sum(1, max3))))), 0)))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[26, 13])).
% 0.18/0.52 tff(28,plain,
% 0.18/0.52 (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) & inv1(R!4) & (~$lesseq($sum(fib1($sum(1, I!5)), $product(-1, tb2t(match_rope1(int, Rqt!8, t2tb(0), t2tb(str_proj_31(Rqt!8)), t2tb(app_proj_31(Rqt!8)))))), 0)) & (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))) & $greatereq(I!5, 0) & (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)) & inv1(Rqt!8) & infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))) & $greatereq(Q!7, 0) & $greatereq(I!5, 2) & ($sum(max3, $product(-1, Q!7)) = -1) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)))))), 0))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[27, 12])).
% 0.18/0.52 tff(29,plain,
% 0.18/0.52 ($sum(max3, $product(-1, Q!7)) = -1),
% 0.18/0.52 inference(and_elim,[status(thm)],[28])).
% 0.18/0.52 tff(30,plain,
% 0.18/0.52 ((~($sum(max3, $product(-1, Q!7)) = -1)) | $lesseq($sum(max3, $product(-1, Q!7)), -1)),
% 0.18/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.52 tff(31,plain,
% 0.18/0.52 ($lesseq($sum(max3, $product(-1, Q!7)), -1)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.18/0.52 tff(32,plain,
% 0.18/0.52 (^[A: ty, U: $int, U1: uni] : refl(($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0) <=> ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(33,plain,
% 0.18/0.52 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)),
% 0.18/0.52 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.52 tff(34,plain,
% 0.18/0.52 (^[A: ty, U: $int, U1: uni] : trans(monotonicity(rewrite($sum(length5(A, mk_array1(A, U, U1)), $product(-1, U)) = $sum($product(-1, U), length5(A, mk_array1(A, U, U1)))), (($sum(length5(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ($sum($product(-1, U), length5(A, mk_array1(A, U, U1))) = 0))), rewrite(($sum($product(-1, U), length5(A, mk_array1(A, U, U1))) = 0) <=> ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)), (($sum(length5(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(35,plain,
% 0.18/0.52 (![A: ty, U: $int, U1: uni] : ($sum(length5(A, mk_array1(A, U, U1)), $product(-1, U)) = 0) <=> ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)),
% 0.18/0.52 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.52 tff(36,plain,
% 0.18/0.52 (^[A: ty, U: $int, U1: uni] : rewrite((length5(A, mk_array1(A, U, U1)) = U) <=> ($sum(length5(A, mk_array1(A, U, U1)), $product(-1, U)) = 0))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(37,plain,
% 0.18/0.52 (![A: ty, U: $int, U1: uni] : (length5(A, mk_array1(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : ($sum(length5(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.18/0.52 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.52 tff(38,plain,
% 0.18/0.52 (![A: ty, U: $int, U1: uni] : (length5(A, mk_array1(A, U, U1)) = U) <=> ![A: ty, U: $int, U1: uni] : (length5(A, mk_array1(A, U, U1)) = U)),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(39,axiom,(![A: ty, U: $int, U1: uni] : (length5(A, mk_array1(A, U, U1)) = U)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','length_def2')).
% 0.18/0.52 tff(40,plain,
% 0.18/0.52 (![A: ty, U: $int, U1: uni] : (length5(A, mk_array1(A, U, U1)) = U)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.52 tff(41,plain,
% 0.18/0.52 (![A: ty, U: $int, U1: uni] : ($sum(length5(A, mk_array1(A, U, U1)), $product(-1, U)) = 0)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.18/0.52 tff(42,plain,
% 0.18/0.52 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.18/0.52 tff(43,plain,(
% 0.18/0.52 ![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)),
% 0.18/0.52 inference(skolemize,[status(sab)],[42])).
% 0.18/0.52 tff(44,plain,
% 0.18/0.52 (![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.18/0.52 tff(45,plain,
% 0.18/0.52 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)) | ($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))) = 0)),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(46,plain,
% 0.18/0.52 ($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))) = 0),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.18/0.52 tff(47,plain,
% 0.18/0.52 ((~($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))) = 0)) | $lesseq($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))), 0)),
% 0.18/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.52 tff(48,plain,
% 0.18/0.52 ($lesseq($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))), 0)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.18/0.52 tff(49,plain,
% 0.18/0.52 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(50,plain,
% 0.18/0.52 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(51,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR1')).
% 0.18/0.52 tff(52,plain,
% 0.18/0.52 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.52 tff(53,plain,(
% 0.18/0.52 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.18/0.52 inference(skolemize,[status(sab)],[52])).
% 0.18/0.52 tff(54,plain,
% 0.18/0.52 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.18/0.52 tff(55,plain,
% 0.18/0.52 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))) = mk_array1(rope, Q!7, t2tb3(Q1!6)))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(56,plain,
% 0.18/0.52 (t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))) = mk_array1(rope, Q!7, t2tb3(Q1!6))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.18/0.52 tff(57,plain,
% 0.18/0.52 (length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))) = length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6)))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[56])).
% 0.18/0.52 tff(58,plain,
% 0.18/0.52 (length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))))),
% 0.18/0.52 inference(symmetry,[status(thm)],[57])).
% 0.18/0.52 tff(59,plain,
% 0.18/0.52 ((~(length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))) | $lesseq($sum(length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)),
% 0.18/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.52 tff(60,plain,
% 0.18/0.52 ($lesseq($sum(length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.52 tff(61,assumption,(~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)), introduced(assumption)).
% 0.18/0.52 tff(62,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(theory_lemma,[status(thm)],[61, 60, 48, 31])).
% 0.18/0.52 tff(63,plain,($lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.52 tff(64,assumption,($lesseq($sum(max3, $product(-1, I!5)), -1)), introduced(assumption)).
% 0.18/0.52 tff(65,plain,
% 0.18/0.52 ((~($sum(max3, $product(-1, Q!7)) = -1)) | $greatereq($sum(max3, $product(-1, Q!7)), -1)),
% 0.18/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.52 tff(66,plain,
% 0.18/0.52 ($greatereq($sum(max3, $product(-1, Q!7)), -1)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[65, 29])).
% 0.18/0.52 tff(67,plain,
% 0.18/0.52 (~$greatereq($sum(I!5, $product(-1, Q!7)), 0)),
% 0.18/0.52 inference(and_elim,[status(thm)],[28])).
% 0.18/0.52 tff(68,assumption,(~$greatereq($sum(max3, $product(-1, I!5)), 0)), introduced(assumption)).
% 0.18/0.52 tff(69,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(theory_lemma,[status(thm)],[68, 67, 66])).
% 0.18/0.52 tff(70,plain,($greatereq($sum(max3, $product(-1, I!5)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.52 tff(71,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(theory_lemma,[status(thm)],[70, 64])).
% 0.18/0.52 tff(72,plain,(~$lesseq($sum(max3, $product(-1, I!5)), -1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.52 tff(73,plain,
% 0.18/0.52 ($greatereq(I!5, 0)),
% 0.18/0.52 inference(and_elim,[status(thm)],[28])).
% 0.18/0.52 tff(74,plain,
% 0.18/0.52 (^[Q: array_rope, L: $int, U: $int] : refl(($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) <=> ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(75,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) <=> ![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[74])).
% 0.18/0.52 tff(76,plain,
% 0.18/0.52 (^[Q: array_rope, L: $int, U: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)) <=> (~($greatereq($sum(L, $product(-1, U)), 0) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))))), ((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) <=> (~(~($greatereq($sum(L, $product(-1, U)), 0) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))))))), rewrite((~(~($greatereq($sum(L, $product(-1, U)), 0) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))))) <=> ($greatereq($sum(L, $product(-1, U)), 0) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))), ((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) <=> ($greatereq($sum(L, $product(-1, U)), 0) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))))), (((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> (($greatereq($sum(L, $product(-1, U)), 0) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))))), rewrite((($greatereq($sum(L, $product(-1, U)), 0) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))), (((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(77,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.52 tff(78,plain,
% 0.18/0.52 (^[Q: array_rope, L: $int, U: $int] : rewrite(((~($greatereq(L, 0) & (~$lesseq($sum(U, $product(-1, L)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(79,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((~($greatereq(L, 0) & (~$lesseq($sum(U, $product(-1, L)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ![Q: array_rope, L: $int, U: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.52 tff(80,plain,
% 0.18/0.52 (^[Q: array_rope, L: $int, U: $int] : rewrite(((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ((~($greatereq(L, 0) & (~$lesseq($sum(U, $product(-1, L)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(81,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ![Q: array_rope, L: $int, U: $int] : ((~($greatereq(L, 0) & (~$lesseq($sum(U, $product(-1, L)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.52 tff(82,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ![Q: array_rope, L: $int, U: $int] : ((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(83,plain,
% 0.18/0.52 (^[Q: array_rope, L: $int, U: $int] : trans(monotonicity(trans(monotonicity(rewrite(($lesseq(0, L) & $less(L, U)) <=> ($lesseq(0, L) & (~$lesseq(U, L)))), ((($lesseq(0, L) & $less(L, U)) & $lesseq(U, length5(rope, t2tb1(Q)))) <=> (($lesseq(0, L) & (~$lesseq(U, L))) & $lesseq(U, length5(rope, t2tb1(Q)))))), rewrite((($lesseq(0, L) & (~$lesseq(U, L))) & $lesseq(U, length5(rope, t2tb1(Q)))) <=> ($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))), ((($lesseq(0, L) & $less(L, U)) & $lesseq(U, length5(rope, t2tb1(Q)))) <=> ($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q)))))), rewrite(infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(L, 1), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) <=> infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))), (((($lesseq(0, L) & $less(L, U)) & $lesseq(U, length5(rope, t2tb1(Q)))) => infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(L, 1), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> (($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q)))) => infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))))), rewrite((($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q)))) => infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))), (((($lesseq(0, L) & $less(L, U)) & $lesseq(U, length5(rope, t2tb1(Q)))) => infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(L, 1), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(84,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((($lesseq(0, L) & $less(L, U)) & $lesseq(U, length5(rope, t2tb1(Q)))) => infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(L, 1), U), string3(tb2t2(get2(rope, t2tb1(Q), L)))))) <=> ![Q: array_rope, L: $int, U: $int] : ((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.52 tff(85,axiom,(![Q: array_rope, L: $int, U: $int] : ((($lesseq(0, L) & $less(L, U)) & $lesseq(U, length5(rope, t2tb1(Q)))) => infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(L, 1), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','string_of_array_concat_left')).
% 0.18/0.52 tff(86,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.52 tff(87,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((~($lesseq(0, L) & (~$lesseq(U, L)) & $lesseq(U, length5(rope, t2tb1(Q))))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.18/0.52 tff(88,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((~($greatereq(L, 0) & (~$lesseq($sum(U, $product(-1, L)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[87, 81])).
% 0.18/0.52 tff(89,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[88, 79])).
% 0.18/0.52 tff(90,plain,(
% 0.18/0.52 ![Q: array_rope, L: $int, U: $int] : ((~($greatereq(L, 0) & (~$greatereq($sum(L, $product(-1, U)), 0)) & $lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0))) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))))),
% 0.18/0.52 inference(skolemize,[status(sab)],[89])).
% 0.18/0.52 tff(91,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[90, 77])).
% 0.18/0.52 tff(92,plain,
% 0.18/0.52 (![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[91, 75])).
% 0.18/0.52 tff(93,plain,
% 0.18/0.52 (((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))))) <=> ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(94,plain,
% 0.18/0.52 (($lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1))) <=> ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(95,plain,
% 0.18/0.52 ((~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)) <=> (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(96,plain,
% 0.18/0.52 ($greatereq($sum(-1, $sum($product(-1, max3), I!5)), 0) <=> $lesseq($sum(max3, $product(-1, I!5)), -1)),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(97,plain,
% 0.18/0.52 ($sum(I!5, $sum(-1, $product(-1, max3))) = $sum(-1, $sum($product(-1, max3), I!5))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(98,plain,
% 0.18/0.52 ($sum($product(-1, 1), $product(-1, max3)) = $sum(-1, $product(-1, max3))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(99,plain,
% 0.18/0.53 ($product(-1, $sum(1, max3)) = $sum($product(-1, 1), $product(-1, max3))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(100,plain,
% 0.18/0.53 ($product(-1, $sum(1, max3)) = $sum(-1, $product(-1, max3))),
% 0.18/0.53 inference(transitivity,[status(thm)],[99, 98])).
% 0.18/0.53 tff(101,plain,
% 0.18/0.53 ($sum(I!5, $product(-1, $sum(1, max3))) = $sum(I!5, $sum(-1, $product(-1, max3)))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[100])).
% 0.18/0.53 tff(102,plain,
% 0.18/0.53 ($sum(I!5, $product(-1, $sum(1, max3))) = $sum(-1, $sum($product(-1, max3), I!5))),
% 0.18/0.53 inference(transitivity,[status(thm)],[101, 97])).
% 0.18/0.53 tff(103,plain,
% 0.18/0.53 ($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) <=> $greatereq($sum(-1, $sum($product(-1, max3), I!5)), 0)),
% 0.18/0.53 inference(monotonicity,[status(thm)],[102])).
% 0.18/0.53 tff(104,plain,
% 0.18/0.53 ($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) <=> $lesseq($sum(max3, $product(-1, I!5)), -1)),
% 0.18/0.53 inference(transitivity,[status(thm)],[103, 96])).
% 0.18/0.53 tff(105,plain,
% 0.18/0.53 (($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0))) <=> ($lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[104, 95])).
% 0.18/0.53 tff(106,plain,
% 0.18/0.53 (($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0))) <=> ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))))),
% 0.18/0.53 inference(transitivity,[status(thm)],[105, 94])).
% 0.18/0.53 tff(107,plain,
% 0.18/0.53 (((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)))) <=> ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[106])).
% 0.18/0.53 tff(108,plain,
% 0.18/0.53 (((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)))) <=> ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))))),
% 0.18/0.53 inference(transitivity,[status(thm)],[107, 93])).
% 0.18/0.53 tff(109,plain,
% 0.18/0.53 ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(110,plain,
% 0.18/0.53 ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.18/0.53 tff(111,plain,
% 0.18/0.53 ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[110, 92, 73])).
% 0.18/0.53 tff(112,plain,
% 0.18/0.53 (infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[111, 72, 63])).
% 0.18/0.53 tff(113,plain,
% 0.18/0.53 (^[S1: string2, S2: string2] : refl(((~infix_eqeq1(S1, S2)) | (S1 = S2)) <=> ((~infix_eqeq1(S1, S2)) | (S1 = S2)))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(114,plain,
% 0.18/0.53 (![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2)) <=> ![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[113])).
% 0.18/0.53 tff(115,plain,
% 0.18/0.53 (![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2)) <=> ![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(116,plain,
% 0.18/0.53 (^[S1: string2, S2: string2] : rewrite((infix_eqeq1(S1, S2) => (S1 = S2)) <=> ((~infix_eqeq1(S1, S2)) | (S1 = S2)))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(117,plain,
% 0.18/0.53 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) => (S1 = S2)) <=> ![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[116])).
% 0.18/0.53 tff(118,axiom,(![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) => (S1 = S2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','extensionality')).
% 0.18/0.53 tff(119,plain,
% 0.18/0.53 (![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.53 tff(120,plain,
% 0.18/0.53 (![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.18/0.53 tff(121,plain,(
% 0.18/0.53 ![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))),
% 0.18/0.53 inference(skolemize,[status(sab)],[120])).
% 0.18/0.53 tff(122,plain,
% 0.18/0.53 (![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.18/0.53 tff(123,plain,
% 0.18/0.53 (((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))))) <=> ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | (~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(124,plain,
% 0.18/0.53 ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(125,plain,
% 0.18/0.53 ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | (~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.53 tff(126,plain,
% 0.18/0.53 (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[125, 122, 112])).
% 0.18/0.53 tff(127,plain,
% 0.18/0.53 (app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3))),
% 0.18/0.53 inference(symmetry,[status(thm)],[126])).
% 0.18/0.53 tff(128,plain,
% 0.18/0.53 (^[X: map_int_rope] : refl(sort1(map(int, rope), t2tb3(X)) <=> sort1(map(int, rope), t2tb3(X)))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(129,plain,
% 0.18/0.53 (![X: map_int_rope] : sort1(map(int, rope), t2tb3(X)) <=> ![X: map_int_rope] : sort1(map(int, rope), t2tb3(X))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.53 tff(130,plain,
% 0.18/0.53 (![X: map_int_rope] : sort1(map(int, rope), t2tb3(X)) <=> ![X: map_int_rope] : sort1(map(int, rope), t2tb3(X))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(131,axiom,(![X: map_int_rope] : sort1(map(int, rope), t2tb3(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort3')).
% 0.18/0.53 tff(132,plain,
% 0.18/0.53 (![X: map_int_rope] : sort1(map(int, rope), t2tb3(X))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.53 tff(133,plain,(
% 0.18/0.53 ![X: map_int_rope] : sort1(map(int, rope), t2tb3(X))),
% 0.18/0.53 inference(skolemize,[status(sab)],[132])).
% 0.18/0.53 tff(134,plain,
% 0.18/0.53 (![X: map_int_rope] : sort1(map(int, rope), t2tb3(X))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.18/0.53 tff(135,plain,
% 0.18/0.53 ((~![X: map_int_rope] : sort1(map(int, rope), t2tb3(X))) | sort1(map(int, rope), t2tb3(Q1!6))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(136,plain,
% 0.18/0.53 (sort1(map(int, rope), t2tb3(Q1!6))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.18/0.53 tff(137,plain,
% 0.18/0.53 (^[A: ty, U: $int, U1: uni] : refl(((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(138,plain,
% 0.18/0.53 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[137])).
% 0.18/0.53 tff(139,plain,
% 0.18/0.53 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(140,plain,
% 0.18/0.53 (^[A: ty, U: $int, U1: uni] : rewrite((sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1)))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(141,plain,
% 0.18/0.53 (![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[140])).
% 0.18/0.53 tff(142,axiom,(![A: ty, U: $int, U1: uni] : (sort1(map(int, A), U1) => (elts(A, mk_array1(A, U, U1)) = U1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','elts_def1')).
% 0.18/0.53 tff(143,plain,
% 0.18/0.53 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.18/0.53 tff(144,plain,
% 0.18/0.53 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.18/0.53 tff(145,plain,(
% 0.18/0.53 ![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.18/0.53 inference(skolemize,[status(sab)],[144])).
% 0.18/0.53 tff(146,plain,
% 0.18/0.53 (![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.18/0.53 tff(147,plain,
% 0.18/0.53 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, rope), t2tb3(Q1!6))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = t2tb3(Q1!6)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, rope), t2tb3(Q1!6))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = t2tb3(Q1!6)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(148,plain,
% 0.18/0.53 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, rope), t2tb3(Q1!6))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = t2tb3(Q1!6)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(149,plain,
% 0.18/0.53 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, rope), t2tb3(Q1!6))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = t2tb3(Q1!6))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.18/0.53 tff(150,plain,
% 0.18/0.53 ((~sort1(map(int, rope), t2tb3(Q1!6))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = t2tb3(Q1!6))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[149, 146])).
% 0.18/0.53 tff(151,plain,
% 0.18/0.53 (elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = t2tb3(Q1!6)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[150, 136])).
% 0.18/0.53 tff(152,plain,
% 0.18/0.53 (get(rope, int, elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))), t2tb(I!5)) = get(rope, int, t2tb3(Q1!6), t2tb(I!5))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[151])).
% 0.18/0.53 tff(153,plain,
% 0.18/0.53 (^[A: ty, A1: uni, I: $int] : refl((get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(154,plain,
% 0.18/0.53 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[153])).
% 0.18/0.53 tff(155,plain,
% 0.18/0.53 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(156,axiom,(![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','get_def')).
% 0.18/0.53 tff(157,plain,
% 0.18/0.53 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.18/0.53 tff(158,plain,(
% 0.18/0.53 ![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.18/0.53 inference(skolemize,[status(sab)],[157])).
% 0.18/0.53 tff(159,plain,
% 0.18/0.53 (![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.18/0.53 tff(160,plain,
% 0.18/0.53 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(rope, mk_array1(rope, Q!7, t2tb3(Q1!6)), I!5) = get(rope, int, elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))), t2tb(I!5)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(161,plain,
% 0.18/0.53 (get2(rope, mk_array1(rope, Q!7, t2tb3(Q1!6)), I!5) = get(rope, int, elts(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))), t2tb(I!5))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.18/0.53 tff(162,plain,
% 0.18/0.53 (get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5) = get2(rope, mk_array1(rope, Q!7, t2tb3(Q1!6)), I!5)),
% 0.18/0.54 inference(monotonicity,[status(thm)],[56])).
% 0.18/0.54 tff(163,plain,
% 0.18/0.54 (get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5) = get(rope, int, t2tb3(Q1!6), t2tb(I!5))),
% 0.18/0.54 inference(transitivity,[status(thm)],[162, 161, 152])).
% 0.18/0.54 tff(164,plain,
% 0.18/0.54 (tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)) = tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[163])).
% 0.18/0.54 tff(165,plain,
% 0.18/0.54 (string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))) = string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[164])).
% 0.18/0.54 tff(166,plain,
% 0.18/0.54 (string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))) = string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5)))),
% 0.18/0.54 inference(symmetry,[status(thm)],[165])).
% 0.18/0.54 tff(167,plain,
% 0.18/0.54 (app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6)))), I!5))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[166])).
% 0.18/0.54 tff(168,plain,
% 0.18/0.54 (app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3))),
% 0.18/0.54 inference(transitivity,[status(thm)],[167, 127])).
% 0.18/0.54 tff(169,plain,
% 0.18/0.54 (app2(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))), string3(R!4)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[168])).
% 0.18/0.54 tff(170,plain,
% 0.18/0.54 ((~(length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))) = length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))) | $greatereq($sum(length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)),
% 0.18/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.54 tff(171,plain,
% 0.18/0.54 ($greatereq($sum(length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[170, 58])).
% 0.18/0.54 tff(172,plain,
% 0.18/0.54 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))) = mk_array1(rope, Q!7, t2tb3(Q2!9)))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(173,plain,
% 0.18/0.54 (t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))) = mk_array1(rope, Q!7, t2tb3(Q2!9))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[172, 54])).
% 0.18/0.54 tff(174,plain,
% 0.18/0.54 (length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))) = length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9)))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[173])).
% 0.18/0.54 tff(175,plain,
% 0.18/0.54 (length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))) = length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))))),
% 0.18/0.54 inference(symmetry,[status(thm)],[174])).
% 0.18/0.54 tff(176,plain,
% 0.18/0.54 ((~(length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))) = length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))) | $lesseq($sum(length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0)),
% 0.18/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.54 tff(177,plain,
% 0.18/0.54 ($lesseq($sum(length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.18/0.54 tff(178,plain,
% 0.18/0.54 ((~![A: ty, U: $int, U1: uni] : ($sum(U, $product(-1, length5(A, mk_array1(A, U, U1)))) = 0)) | ($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))))) = 0)),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(179,plain,
% 0.18/0.54 ($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))))) = 0),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[178, 44])).
% 0.18/0.54 tff(180,plain,
% 0.18/0.54 ((~($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))))) = 0)) | $lesseq($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))))), 0)),
% 0.18/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.54 tff(181,plain,
% 0.18/0.54 ($lesseq($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))))), 0)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.18/0.54 tff(182,plain,
% 0.18/0.54 ((~($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))) = 0)) | $greatereq($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))), 0)),
% 0.18/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.54 tff(183,plain,
% 0.18/0.54 ($greatereq($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))), 0)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[182, 46])).
% 0.18/0.54 tff(184,plain,
% 0.18/0.54 ($lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1) | (~$lesseq($sum(length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0)) | (~$lesseq($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))))), 0)) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), -1)) | (~$greatereq($sum(length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))))))), 0)) | (~$greatereq($sum(Q!7, $product(-1, length5(rope, mk_array1(rope, Q!7, t2tb3(Q1!6))))), 0))),
% 0.18/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.54 tff(185,plain,
% 0.18/0.54 ($lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[184, 183, 181, 63, 177, 171])).
% 0.18/0.54 tff(186,plain,
% 0.18/0.54 (((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))))) <=> ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(187,plain,
% 0.18/0.54 (($lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1))) <=> ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(188,plain,
% 0.18/0.54 ((~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0)) <=> (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(189,plain,
% 0.18/0.54 (($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0))) <=> ($lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[104, 188])).
% 0.18/0.54 tff(190,plain,
% 0.18/0.54 (($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0))) <=> ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))))),
% 0.18/0.54 inference(transitivity,[status(thm)],[189, 187])).
% 0.18/0.54 tff(191,plain,
% 0.18/0.54 (((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0)))) <=> ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[190])).
% 0.18/0.54 tff(192,plain,
% 0.18/0.54 (((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0)))) <=> ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))))),
% 0.18/0.54 inference(transitivity,[status(thm)],[191, 186])).
% 0.18/0.54 tff(193,plain,
% 0.18/0.54 ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | ($greatereq($sum(I!5, $product(-1, $sum(1, max3))), 0) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))) | (~$greatereq(I!5, 0)) | (~$lesseq($sum($sum(1, max3), $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), 0)))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(194,plain,
% 0.18/0.54 ((~![Q: array_rope, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | infix_eqeq1(string_of_array1(Q, L, U), app2(string_of_array1(Q, $sum(1, L), U), string3(tb2t2(get2(rope, t2tb1(Q), L))))) | (~$greatereq(L, 0)) | (~$lesseq($sum(U, $product(-1, length5(rope, t2tb1(Q)))), 0)))) | (~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)) | (~$greatereq(I!5, 0)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.18/0.54 tff(195,plain,
% 0.18/0.54 ((~$lesseq($sum(max3, $product(-1, length5(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))))), -1)) | $lesseq($sum(max3, $product(-1, I!5)), -1) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[194, 92, 73])).
% 0.18/0.54 tff(196,plain,
% 0.18/0.54 (infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[195, 72, 185])).
% 0.18/0.54 tff(197,plain,
% 0.18/0.54 (((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))))) <=> ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | (~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(198,plain,
% 0.18/0.54 ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(199,plain,
% 0.18/0.54 ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | (~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.18/0.54 tff(200,plain,
% 0.18/0.54 (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[199, 122, 196])).
% 0.18/0.54 tff(201,plain,
% 0.18/0.54 (app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3))),
% 0.18/0.54 inference(symmetry,[status(thm)],[200])).
% 0.18/0.54 tff(202,plain,
% 0.18/0.54 (![I: rope1] : (tb2t2(t2tb2(I)) = I) <=> ![I: rope1] : (tb2t2(t2tb2(I)) = I)),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(203,plain,
% 0.18/0.54 (![I: rope1] : (tb2t2(t2tb2(I)) = I) <=> ![I: rope1] : (tb2t2(t2tb2(I)) = I)),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(204,axiom,(![I: rope1] : (tb2t2(t2tb2(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL2')).
% 0.18/0.54 tff(205,plain,
% 0.18/0.54 (![I: rope1] : (tb2t2(t2tb2(I)) = I)),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.18/0.54 tff(206,plain,(
% 0.18/0.54 ![I: rope1] : (tb2t2(t2tb2(I)) = I)),
% 0.18/0.54 inference(skolemize,[status(sab)],[205])).
% 0.18/0.54 tff(207,plain,
% 0.18/0.54 (![I: rope1] : (tb2t2(t2tb2(I)) = I)),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.18/0.55 tff(208,plain,
% 0.18/0.55 ((~![I: rope1] : (tb2t2(t2tb2(I)) = I)) | (tb2t2(t2tb2(Rqt!8)) = Rqt!8)),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(209,plain,
% 0.18/0.55 (tb2t2(t2tb2(Rqt!8)) = Rqt!8),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.18/0.55 tff(210,plain,
% 0.18/0.55 (^[X: rope1] : refl(sort1(rope, t2tb2(X)) <=> sort1(rope, t2tb2(X)))),
% 0.18/0.55 inference(bind,[status(th)],[])).
% 0.18/0.55 tff(211,plain,
% 0.18/0.55 (![X: rope1] : sort1(rope, t2tb2(X)) <=> ![X: rope1] : sort1(rope, t2tb2(X))),
% 0.18/0.55 inference(quant_intro,[status(thm)],[210])).
% 0.18/0.55 tff(212,plain,
% 0.18/0.55 (![X: rope1] : sort1(rope, t2tb2(X)) <=> ![X: rope1] : sort1(rope, t2tb2(X))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(213,axiom,(![X: rope1] : sort1(rope, t2tb2(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.18/0.55 tff(214,plain,
% 0.18/0.55 (![X: rope1] : sort1(rope, t2tb2(X))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.18/0.55 tff(215,plain,(
% 0.18/0.55 ![X: rope1] : sort1(rope, t2tb2(X))),
% 0.18/0.55 inference(skolemize,[status(sab)],[214])).
% 0.18/0.55 tff(216,plain,
% 0.18/0.55 (![X: rope1] : sort1(rope, t2tb2(X))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.18/0.55 tff(217,plain,
% 0.18/0.55 ((~![X: rope1] : sort1(rope, t2tb2(X))) | sort1(rope, t2tb2(Rqt!8))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(218,plain,
% 0.18/0.55 (sort1(rope, t2tb2(Rqt!8))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.18/0.55 tff(219,plain,
% 0.18/0.55 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : refl(((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))))),
% 0.18/0.55 inference(bind,[status(th)],[])).
% 0.18/0.55 tff(220,plain,
% 0.18/0.55 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.18/0.55 inference(quant_intro,[status(thm)],[219])).
% 0.18/0.55 tff(221,plain,
% 0.18/0.55 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(222,plain,
% 0.18/0.55 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : trans(monotonicity(rewrite(((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)) <=> ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> (sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))))), rewrite((sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))))),
% 0.18/0.55 inference(bind,[status(th)],[])).
% 0.18/0.55 tff(223,plain,
% 0.18/0.55 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.18/0.55 inference(quant_intro,[status(thm)],[222])).
% 0.18/0.55 tff(224,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','select_eq')).
% 0.18/0.55 tff(225,plain,
% 0.18/0.55 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.18/0.55 tff(226,plain,
% 0.18/0.55 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.18/0.55 tff(227,plain,(
% 0.18/0.55 ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.18/0.55 inference(skolemize,[status(sab)],[226])).
% 0.18/0.55 tff(228,plain,
% 0.18/0.55 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.18/0.55 tff(229,plain,
% 0.18/0.55 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(rope, t2tb2(Rqt!8))) | (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(rope, t2tb2(Rqt!8))) | (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(230,plain,
% 0.18/0.55 (((get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)) | $false | (~sort1(rope, t2tb2(Rqt!8)))) <=> ((~sort1(rope, t2tb2(Rqt!8))) | (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(231,plain,
% 0.18/0.55 ((~$true) <=> $false),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(232,plain,
% 0.18/0.55 ((t2tb(I!5) = t2tb(I!5)) <=> $true),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(233,plain,
% 0.18/0.55 ((~(t2tb(I!5) = t2tb(I!5))) <=> (~$true)),
% 0.18/0.55 inference(monotonicity,[status(thm)],[232])).
% 0.18/0.55 tff(234,plain,
% 0.18/0.55 ((~(t2tb(I!5) = t2tb(I!5))) <=> $false),
% 0.18/0.55 inference(transitivity,[status(thm)],[233, 231])).
% 0.18/0.55 tff(235,plain,
% 0.18/0.55 (((get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)) | (~(t2tb(I!5) = t2tb(I!5))) | (~sort1(rope, t2tb2(Rqt!8)))) <=> ((get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)) | $false | (~sort1(rope, t2tb2(Rqt!8))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[234])).
% 0.18/0.55 tff(236,plain,
% 0.18/0.55 (((get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)) | (~(t2tb(I!5) = t2tb(I!5))) | (~sort1(rope, t2tb2(Rqt!8)))) <=> ((~sort1(rope, t2tb2(Rqt!8))) | (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)))),
% 0.18/0.55 inference(transitivity,[status(thm)],[235, 230])).
% 0.18/0.55 tff(237,plain,
% 0.18/0.55 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)) | (~(t2tb(I!5) = t2tb(I!5))) | (~sort1(rope, t2tb2(Rqt!8))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(rope, t2tb2(Rqt!8))) | (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[236])).
% 0.18/0.55 tff(238,plain,
% 0.18/0.55 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)) | (~(t2tb(I!5) = t2tb(I!5))) | (~sort1(rope, t2tb2(Rqt!8))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(rope, t2tb2(Rqt!8))) | (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)))),
% 0.18/0.55 inference(transitivity,[status(thm)],[237, 229])).
% 0.18/0.55 tff(239,plain,
% 0.18/0.55 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)) | (~(t2tb(I!5) = t2tb(I!5))) | (~sort1(rope, t2tb2(Rqt!8))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(240,plain,
% 0.18/0.55 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(rope, t2tb2(Rqt!8))) | (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.18/0.55 tff(241,plain,
% 0.18/0.55 (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = t2tb2(Rqt!8)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[240, 228, 218])).
% 0.18/0.55 tff(242,plain,
% 0.18/0.55 (![J: uni] : (t2tb3(tb2t3(J)) = J) <=> ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(243,plain,
% 0.18/0.55 (![J: uni] : (t2tb3(tb2t3(J)) = J) <=> ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(244,axiom,(![J: uni] : (t2tb3(tb2t3(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR3')).
% 0.18/0.55 tff(245,plain,
% 0.18/0.55 (![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.18/0.55 tff(246,plain,(
% 0.18/0.55 ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 0.18/0.55 inference(skolemize,[status(sab)],[245])).
% 0.18/0.55 tff(247,plain,
% 0.18/0.55 (![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.18/0.55 tff(248,plain,
% 0.18/0.55 ((~![J: uni] : (t2tb3(tb2t3(J)) = J)) | (t2tb3(tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))) = set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(249,plain,
% 0.18/0.55 (t2tb3(tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))) = set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.18/0.55 tff(250,plain,
% 0.18/0.55 (~((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) | (~($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))))))),
% 0.18/0.55 inference(and_elim,[status(thm)],[28])).
% 0.18/0.55 tff(251,plain,
% 0.18/0.55 ($greatereq(Q!7, 0) & (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8))))),
% 0.18/0.55 inference(or_elim,[status(thm)],[250])).
% 0.18/0.55 tff(252,plain,
% 0.18/0.55 (Q2!9 = tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))),
% 0.18/0.55 inference(and_elim,[status(thm)],[251])).
% 0.18/0.55 tff(253,plain,
% 0.18/0.55 (t2tb3(Q2!9) = t2tb3(tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[252])).
% 0.18/0.55 tff(254,plain,
% 0.18/0.55 (t2tb3(Q2!9) = set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8))),
% 0.18/0.55 inference(transitivity,[status(thm)],[253, 249])).
% 0.18/0.55 tff(255,plain,
% 0.18/0.55 (sort1(map(int, rope), t2tb3(Q2!9)) <=> sort1(map(int, rope), set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[254])).
% 0.18/0.55 tff(256,plain,
% 0.18/0.55 (sort1(map(int, rope), set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8))) <=> sort1(map(int, rope), t2tb3(Q2!9))),
% 0.18/0.55 inference(symmetry,[status(thm)],[255])).
% 0.18/0.55 tff(257,plain,
% 0.18/0.55 (^[A: ty, B: ty, X: uni, X1: uni, X2: uni] : refl(sort1(map(A, B), set(B, A, X, X1, X2)) <=> sort1(map(A, B), set(B, A, X, X1, X2)))),
% 0.18/0.55 inference(bind,[status(th)],[])).
% 0.18/0.55 tff(258,plain,
% 0.18/0.55 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.18/0.55 inference(quant_intro,[status(thm)],[257])).
% 0.18/0.55 tff(259,plain,
% 0.18/0.55 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(260,axiom,(![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','set_sort2')).
% 0.18/0.55 tff(261,plain,
% 0.18/0.55 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.18/0.55 tff(262,plain,(
% 0.18/0.55 ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.18/0.55 inference(skolemize,[status(sab)],[261])).
% 0.18/0.55 tff(263,plain,
% 0.18/0.55 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[262, 258])).
% 0.18/0.55 tff(264,plain,
% 0.18/0.55 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))) | sort1(map(int, rope), set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(265,plain,
% 0.18/0.55 (sort1(map(int, rope), set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.18/0.55 tff(266,plain,
% 0.18/0.55 (sort1(map(int, rope), t2tb3(Q2!9))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[265, 256])).
% 0.18/0.55 tff(267,plain,
% 0.18/0.55 (((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, rope), t2tb3(Q2!9))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))) = t2tb3(Q2!9)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, rope), t2tb3(Q2!9))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))) = t2tb3(Q2!9)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(268,plain,
% 0.18/0.55 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | ((~sort1(map(int, rope), t2tb3(Q2!9))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))) = t2tb3(Q2!9)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(269,plain,
% 0.18/0.55 ((~![A: ty, U: $int, U1: uni] : ((~sort1(map(int, A), U1)) | (elts(A, mk_array1(A, U, U1)) = U1))) | (~sort1(map(int, rope), t2tb3(Q2!9))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))) = t2tb3(Q2!9))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.18/0.55 tff(270,plain,
% 0.18/0.55 ((~sort1(map(int, rope), t2tb3(Q2!9))) | (elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))) = t2tb3(Q2!9))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[269, 146])).
% 0.18/0.55 tff(271,plain,
% 0.18/0.55 (elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))) = t2tb3(Q2!9)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[270, 266])).
% 0.18/0.55 tff(272,plain,
% 0.18/0.55 (t2tb3(Q2!9) = elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9)))),
% 0.18/0.55 inference(symmetry,[status(thm)],[271])).
% 0.18/0.55 tff(273,plain,
% 0.18/0.55 (t2tb3(tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)))) = t2tb3(Q2!9)),
% 0.18/0.55 inference(symmetry,[status(thm)],[253])).
% 0.18/0.55 tff(274,plain,
% 0.18/0.55 (set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)) = t2tb3(tb2t3(set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[249])).
% 0.18/0.55 tff(275,plain,
% 0.18/0.55 (set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)) = elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9)))),
% 0.18/0.55 inference(transitivity,[status(thm)],[274, 273, 272])).
% 0.18/0.55 tff(276,plain,
% 0.18/0.55 (get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5)) = get(rope, int, elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))), t2tb(I!5))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[275])).
% 0.18/0.55 tff(277,plain,
% 0.18/0.55 (get(rope, int, elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))), t2tb(I!5)) = get(rope, int, set(rope, int, t2tb3(Q1!6), t2tb(I!5), t2tb2(Rqt!8)), t2tb(I!5))),
% 0.18/0.55 inference(symmetry,[status(thm)],[276])).
% 0.18/0.55 tff(278,plain,
% 0.18/0.55 ((~![A: ty, A1: uni, I: $int] : (get2(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get2(rope, mk_array1(rope, Q!7, t2tb3(Q2!9)), I!5) = get(rope, int, elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))), t2tb(I!5)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(279,plain,
% 0.18/0.55 (get2(rope, mk_array1(rope, Q!7, t2tb3(Q2!9)), I!5) = get(rope, int, elts(rope, mk_array1(rope, Q!7, t2tb3(Q2!9))), t2tb(I!5))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[278, 159])).
% 0.18/0.55 tff(280,plain,
% 0.18/0.55 (mk_array1(rope, Q!7, t2tb3(Q2!9)) = t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))))),
% 0.18/0.55 inference(symmetry,[status(thm)],[173])).
% 0.18/0.55 tff(281,plain,
% 0.18/0.55 (get2(rope, mk_array1(rope, Q!7, t2tb3(Q2!9)), I!5) = get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)),
% 0.18/0.55 inference(monotonicity,[status(thm)],[280])).
% 0.18/0.55 tff(282,plain,
% 0.18/0.55 (get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5) = get2(rope, mk_array1(rope, Q!7, t2tb3(Q2!9)), I!5)),
% 0.18/0.55 inference(symmetry,[status(thm)],[281])).
% 0.18/0.55 tff(283,plain,
% 0.18/0.55 (get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5) = t2tb2(Rqt!8)),
% 0.18/0.55 inference(transitivity,[status(thm)],[282, 279, 277, 241])).
% 0.18/0.55 tff(284,plain,
% 0.18/0.55 (tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)) = tb2t2(t2tb2(Rqt!8))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[283])).
% 0.18/0.55 tff(285,plain,
% 0.18/0.55 (tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)) = Rqt!8),
% 0.18/0.55 inference(transitivity,[status(thm)],[284, 209])).
% 0.18/0.55 tff(286,plain,
% 0.18/0.55 (string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))) = string3(Rqt!8)),
% 0.18/0.55 inference(monotonicity,[status(thm)],[285])).
% 0.18/0.55 tff(287,plain,
% 0.18/0.55 (string3(Rqt!8) = string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))),
% 0.18/0.55 inference(symmetry,[status(thm)],[286])).
% 0.18/0.55 tff(288,plain,
% 0.18/0.55 (infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))),
% 0.18/0.55 inference(and_elim,[status(thm)],[28])).
% 0.18/0.55 tff(289,plain,
% 0.18/0.55 (((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | ((~infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))) | (string3(Rqt!8) = app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))) <=> ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | (~infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))) | (string3(Rqt!8) = app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(290,plain,
% 0.18/0.55 ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | ((~infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))) | (string3(Rqt!8) = app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(291,plain,
% 0.18/0.55 ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | (~infix_eqeq1(string3(Rqt!8), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))) | (string3(Rqt!8) = app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.18/0.55 tff(292,plain,
% 0.18/0.55 (string3(Rqt!8) = app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[291, 122, 288])).
% 0.18/0.55 tff(293,plain,
% 0.18/0.55 (app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)) = string3(Rqt!8)),
% 0.18/0.55 inference(symmetry,[status(thm)],[292])).
% 0.18/0.55 tff(294,plain,
% 0.18/0.55 (app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4)) = string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5)))),
% 0.18/0.55 inference(transitivity,[status(thm)],[293, 287])).
% 0.18/0.55 tff(295,plain,
% 0.18/0.55 (infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))),
% 0.18/0.55 inference(or_elim,[status(thm)],[250])).
% 0.18/0.55 tff(296,plain,
% 0.18/0.55 (((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3))))) <=> ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | (~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3))))),
% 0.18/0.56 inference(rewrite,[status(thm)],[])).
% 0.18/0.56 tff(297,plain,
% 0.18/0.56 ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(298,plain,
% 0.18/0.56 ((~![S1: string2, S2: string2] : ((~infix_eqeq1(S1, S2)) | (S1 = S2))) | (~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))) | (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.18/0.56 tff(299,plain,
% 0.18/0.56 (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[298, 122, 295])).
% 0.18/0.56 tff(300,plain,
% 0.18/0.56 (string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3))),
% 0.18/0.56 inference(symmetry,[status(thm)],[299])).
% 0.18/0.56 tff(301,plain,
% 0.18/0.56 (app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))) = app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get2(rope, t2tb1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9)))), I!5))))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[300, 294])).
% 0.18/0.56 tff(302,plain,
% 0.18/0.56 (app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))) = string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3))),
% 0.18/0.56 inference(transitivity,[status(thm)],[301, 201])).
% 0.18/0.56 tff(303,plain,
% 0.18/0.56 (infix_eqeq1(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))), app2(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))), string3(R!4))) <=> infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4)))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[302, 169])).
% 0.18/0.56 tff(304,plain,
% 0.18/0.56 (infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4))) <=> infix_eqeq1(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))), app2(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))), string3(R!4)))),
% 0.18/0.56 inference(symmetry,[status(thm)],[303])).
% 0.18/0.56 tff(305,plain,
% 0.18/0.56 ((~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4)))) <=> (~infix_eqeq1(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))), app2(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))), string3(R!4))))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[304])).
% 0.18/0.56 tff(306,plain,
% 0.18/0.56 (~infix_eqeq1(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q2!9))), I!5, $sum(1, max3)), app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), I!5, $sum(1, max3)), string3(R!4)))),
% 0.18/0.56 inference(or_elim,[status(thm)],[250])).
% 0.18/0.56 tff(307,plain,
% 0.18/0.56 (~infix_eqeq1(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))), app2(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))), string3(R!4)))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.18/0.56 tff(308,plain,
% 0.18/0.56 (^[S1: string2, S2: string2, S3: string2] : refl(infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3)) <=> infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3)))),
% 0.18/0.56 inference(bind,[status(th)],[])).
% 0.18/0.56 tff(309,plain,
% 0.18/0.56 (![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3)) <=> ![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3))),
% 0.18/0.56 inference(quant_intro,[status(thm)],[308])).
% 0.18/0.56 tff(310,plain,
% 0.18/0.56 (![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3)) <=> ![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3))),
% 0.18/0.56 inference(rewrite,[status(thm)],[])).
% 0.18/0.56 tff(311,axiom,(![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','app_assoc')).
% 0.18/0.57 tff(312,plain,
% 0.18/0.57 (![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3))),
% 0.18/0.57 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.18/0.57 tff(313,plain,(
% 0.18/0.57 ![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3))),
% 0.18/0.57 inference(skolemize,[status(sab)],[312])).
% 0.18/0.57 tff(314,plain,
% 0.18/0.57 (![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3))),
% 0.18/0.57 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.18/0.57 tff(315,plain,
% 0.18/0.57 ((~![S1: string2, S2: string2, S3: string2] : infix_eqeq1(app2(S1, app2(S2, S3)), app2(app2(S1, S2), S3))) | infix_eqeq1(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))), app2(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))), string3(R!4)))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(316,plain,
% 0.18/0.57 (infix_eqeq1(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), app2(string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5)))), string3(R!4))), app2(app2(string_of_array1(tb2t1(mk_array1(rope, Q!7, t2tb3(Q1!6))), $sum(1, I!5), $sum(1, max3)), string3(tb2t2(get(rope, int, t2tb3(Q1!6), t2tb(I!5))))), string3(R!4)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.18/0.57 tff(317,plain,
% 0.18/0.57 ($false),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[316, 307])).
% 0.18/0.57 % SZS output end Proof
%------------------------------------------------------------------------------