TSTP Solution File: SWW597_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW597_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 20:59:23 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW597_2 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 20:17:35 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(tptp_fun_K_7_type, type, (
% 0.21/0.45 tptp_fun_K_7: ( color * $int * $int * array_color ) > $int)).
% 0.21/0.45 tff(tb2t1_type, type, (
% 0.21/0.45 tb2t1: uni > array_color)).
% 0.21/0.45 tff(mk_array_type, type, (
% 0.21/0.45 mk_array: ( ty * $int * uni ) > uni)).
% 0.21/0.45 tff(t2tb3_type, type, (
% 0.21/0.45 t2tb3: map_int_color > uni)).
% 0.21/0.45 tff(tptp_fun_A2_10_type, type, (
% 0.21/0.45 tptp_fun_A2_10: map_int_color)).
% 0.21/0.45 tff(tptp_fun_A_9_type, type, (
% 0.21/0.45 tptp_fun_A_9: $int)).
% 0.21/0.45 tff(color1_type, type, (
% 0.21/0.45 color1: ty)).
% 0.21/0.45 tff(tptp_fun_B_11_type, type, (
% 0.21/0.45 tptp_fun_B_11: $int)).
% 0.21/0.45 tff(tptp_fun_I1_14_type, type, (
% 0.21/0.45 tptp_fun_I1_14: $int)).
% 0.21/0.45 tff(white_type, type, (
% 0.21/0.45 white: color)).
% 0.21/0.45 tff(tb2t2_type, type, (
% 0.21/0.45 tb2t2: uni > color)).
% 0.21/0.45 tff(get1_type, type, (
% 0.21/0.45 get1: ( ty * uni * $int ) > uni)).
% 0.21/0.45 tff(t2tb1_type, type, (
% 0.21/0.45 t2tb1: array_color > uni)).
% 0.21/0.45 tff(monochrome_type, type, (
% 0.21/0.45 monochrome: ( array_color * $int * $int * color ) > $o)).
% 0.21/0.45 tff(tptp_fun_I_12_type, type, (
% 0.21/0.45 tptp_fun_I_12: $int)).
% 0.21/0.45 tff(permut_all_type, type, (
% 0.21/0.45 permut_all: ( ty * uni * uni ) > $o)).
% 0.21/0.45 tff(tptp_fun_A1_8_type, type, (
% 0.21/0.45 tptp_fun_A1_8: map_int_color)).
% 0.21/0.45 tff(red_type, type, (
% 0.21/0.45 red: color)).
% 0.21/0.45 tff(tptp_fun_R_13_type, type, (
% 0.21/0.45 tptp_fun_R_13: $int)).
% 0.21/0.45 tff(blue_type, type, (
% 0.21/0.45 blue: color)).
% 0.21/0.45 tff(get_type, type, (
% 0.21/0.45 get: ( ty * ty * uni * uni ) > uni)).
% 0.21/0.45 tff(t2tb_type, type, (
% 0.21/0.45 t2tb: $int > uni)).
% 0.21/0.45 tff(int_type, type, (
% 0.21/0.45 int: ty)).
% 0.21/0.45 tff(elts_type, type, (
% 0.21/0.45 elts: ( ty * uni ) > uni)).
% 0.21/0.45 tff(sort_type, type, (
% 0.21/0.45 sort: ( ty * uni ) > $o)).
% 0.21/0.45 tff(map_type, type, (
% 0.21/0.45 map: ( ty * ty ) > ty)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 (^[A: array_color, I: $int, J: $int, C: color] : refl((~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))))) <=> (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))))) <=> ![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (^[A: array_color, I: $int, J: $int, C: color] : rewrite((~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))))) <=> (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 (![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))))) <=> ![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.45 tff(5,plain,
% 0.21/0.45 (![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))))) <=> ![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 (^[A: array_color, I: $int, J: $int, C: color] : trans(monotonicity(rewrite(((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) <=> ((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))), trans(monotonicity(rewrite((~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C))) <=> (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))), ((monochrome(A, I, J, C) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C)))) <=> (monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))), rewrite((monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))) <=> (monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))), ((monochrome(A, I, J, C) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C)))) <=> (monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))), ((((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C))))) <=> (((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) & (monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))))), rewrite((((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) & (monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))))) <=> (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))), ((((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C))))) <=> (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (![A: array_color, I: $int, J: $int, C: color] : (((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C))))) <=> ![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (^[A: array_color, I: $int, J: $int, C: color] : rewrite((((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($greatereq($sum(tptp_fun_K_7(C, J, I, A), $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C))))) <=> (((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (![A: array_color, I: $int, J: $int, C: color] : (((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($greatereq($sum(tptp_fun_K_7(C, J, I, A), $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C))))) <=> ![A: array_color, I: $int, J: $int, C: color] : (((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 (^[A: array_color, I: $int, J: $int, C: color] : rewrite((monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) <=> (monochrome(A, I, J, C) <=> ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 (![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) <=> ![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (^[A: array_color, I: $int, J: $int, C: color] : rewrite((monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq(I, K) & (~$lesseq(J, K)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) <=> (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq(I, K) & (~$lesseq(J, K)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) <=> ![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq(I, K) & (~$lesseq(J, K)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) <=> ![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq(I, K) & (~$lesseq(J, K)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (^[A: array_color, I: $int, J: $int, C: color] : rewrite((monochrome(A, I, J, C) <=> ![K: $int] : (($lesseq(I, K) & $less(K, J)) => (tb2t2(get1(color1, t2tb1(A), K)) = C))) <=> (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq(I, K) & (~$lesseq(J, K)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(16,plain,
% 0.21/0.46 (![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : (($lesseq(I, K) & $less(K, J)) => (tb2t2(get1(color1, t2tb1(A), K)) = C))) <=> ![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq(I, K) & (~$lesseq(J, K)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.46 tff(17,axiom,(![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : (($lesseq(I, K) & $less(K, J)) => (tb2t2(get1(color1, t2tb1(A), K)) = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','monochrome_def')).
% 0.21/0.46 tff(18,plain,
% 0.21/0.46 (![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq(I, K) & (~$lesseq(J, K)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq(I, K) & (~$lesseq(J, K)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 (![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 (![A: array_color, I: $int, J: $int, C: color] : (monochrome(A, I, J, C) <=> ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.21/0.46 tff(22,plain,(
% 0.21/0.46 ![A: array_color, I: $int, J: $int, C: color] : (((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($greatereq($sum(tptp_fun_K_7(C, J, I, A), $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[21])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 (![A: array_color, I: $int, J: $int, C: color] : (((~monochrome(A, I, J, C)) | ![K: $int] : ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | (tb2t2(get1(color1, t2tb1(A), K)) = C))) & (monochrome(A, I, J, C) | (~((~($lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) & (~$lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0)))) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I1!14)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))) <=> ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I1!14)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 ((~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | $lesseq($sum(I1!14, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, B!11)), 0))))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))) <=> (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I1!14)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | $lesseq($sum(I1!14, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, B!11)), 0))))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))) <=> ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I1!14)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 (((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | $lesseq($sum(I1!14, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, B!11)), 0))))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))) <=> ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I1!14)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[28, 26])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | $lesseq($sum(I1!14, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, B!11)), 0))))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I1!14)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I1!14)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I1!14)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))) | (monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (($greatereq(A!9, 0) & ((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & $greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)) & $greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))) <=> ($greatereq(A!9, 0) & (~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)) & $greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & ($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0))) & ($greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))) <=> ((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & $greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)) & $greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(37,plain,
% 0.21/0.48 ((~(~($greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))))) <=> ($greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 ((~($greatereq(B!11, 0) & $greatereq($sum(I!12, $product(-1, B!11)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $lesseq($sum(R!13, $product(-1, A!9)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))) <=> (~($greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 ((~(~($greatereq(B!11, 0) & $greatereq($sum(I!12, $product(-1, B!11)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $lesseq($sum(R!13, $product(-1, A!9)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))))) <=> (~(~($greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.48 tff(40,plain,
% 0.21/0.48 ((~(~($greatereq(B!11, 0) & $greatereq($sum(I!12, $product(-1, B!11)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $lesseq($sum(R!13, $product(-1, A!9)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))))) <=> ($greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[39, 37])).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 ((~(~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0))))) <=> ($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(42,plain,
% 0.21/0.48 ((~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$greatereq($sum(I!12, $product(-1, A!9)), 0)))) <=> (~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(43,plain,
% 0.21/0.48 ((~(~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$greatereq($sum(I!12, $product(-1, A!9)), 0))))) <=> (~(~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[42])).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 ((~(~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$greatereq($sum(I!12, $product(-1, A!9)), 0))))) <=> ($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[43, 41])).
% 0.21/0.48 tff(45,plain,
% 0.21/0.48 ((~(~(tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white))) <=> (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(46,plain,
% 0.21/0.48 ((~((~($sum(I1!14, $product(-1, I!12)) = 1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) <=> (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(47,plain,
% 0.21/0.48 (((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I1!14, $product(-1, I!12)) = 1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (~(~(tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white))) & (~(~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$greatereq($sum(I!12, $product(-1, A!9)), 0))))) & (~(~($greatereq(B!11, 0) & $greatereq($sum(I!12, $product(-1, B!11)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $lesseq($sum(R!13, $product(-1, A!9)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))))) <=> ((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & ($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0))) & ($greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[46, 45, 44, 40])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 (((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I1!14, $product(-1, I!12)) = 1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (~(~(tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white))) & (~(~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$greatereq($sum(I!12, $product(-1, A!9)), 0))))) & (~(~($greatereq(B!11, 0) & $greatereq($sum(I!12, $product(-1, B!11)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $lesseq($sum(R!13, $product(-1, A!9)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))))) <=> ((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & $greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)) & $greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[47, 36])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 ((~(~$greatereq(A!9, 0))) <=> $greatereq(A!9, 0)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (((~(~$greatereq(A!9, 0))) & ((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I1!14, $product(-1, I!12)) = 1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (~(~(tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white))) & (~(~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$greatereq($sum(I!12, $product(-1, A!9)), 0))))) & (~(~($greatereq(B!11, 0) & $greatereq($sum(I!12, $product(-1, B!11)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $lesseq($sum(R!13, $product(-1, A!9)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))))))) <=> ($greatereq(A!9, 0) & ((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & $greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)) & $greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[49, 48])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (((~(~$greatereq(A!9, 0))) & ((~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I1!14, $product(-1, I!12)) = 1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (~(~(tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white))) & (~(~($greatereq(A!9, 0) & $greatereq(I!12, 0) & (~$greatereq($sum(I!12, $product(-1, A!9)), 0))))) & (~(~($greatereq(B!11, 0) & $greatereq($sum(I!12, $product(-1, B!11)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $lesseq($sum(R!13, $product(-1, A!9)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))))))) <=> ($greatereq(A!9, 0) & (~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)) & $greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[50, 35])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 ((~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ($greatereq($sum(I, $product(-1, R)), 0) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(B, 0) & $greatereq($sum(I, $product(-1, B)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))) <=> (~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ($greatereq($sum(I, $product(-1, R)), 0) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(B, 0) & $greatereq($sum(I, $product(-1, B)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 ((~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : (![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq($sum(R, $product(-1, I)), 0) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~($greatereq(B, 0) & $lesseq($sum(B, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))) <=> (~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ($greatereq($sum(I, $product(-1, R)), 0) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(B, 0) & $greatereq($sum(I, $product(-1, B)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 ((~![A: $int, A1: map_int_color] : ((~$lesseq(0, A)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ((~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq(R, I) | ![I1: $int] : ((~(I1 = $sum(1, I))) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, B) & $lesseq(B, I) & $lesseq(I, R) & $lesseq(R, A) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))) <=> (~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : (![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq($sum(R, $product(-1, I)), 0) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~($greatereq(B, 0) & $lesseq($sum(B, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 ((~![A: $int, A1: map_int_color] : ((~$lesseq(0, A)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ((~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq(R, I) | ![I1: $int] : ((~(I1 = $sum(1, I))) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, B) & $lesseq(B, I) & $lesseq(I, R) & $lesseq(R, A) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))) <=> (~![A: $int, A1: map_int_color] : ((~$lesseq(0, A)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ((~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq(R, I) | ![I1: $int] : ((~(I1 = $sum(1, I))) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, B) & $lesseq(B, I) & $lesseq(I, R) & $lesseq(R, A) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 ((~![A: $int, A1: map_int_color] : ($lesseq(0, A) => ![R: $int, I: $int, B: $int, A2: map_int_color] : (((((((($lesseq(0, B) & $lesseq(B, I)) & $lesseq(I, R)) & $lesseq(R, A)) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue)) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white)) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red)) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))) => ($less(I, R) => ((($lesseq(0, A) & $lesseq(0, I)) & $less(I, A)) => ((tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white) => ![I1: $int] : ((I1 = $sum(I, 1)) => monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)))))))) <=> (~![A: $int, A1: map_int_color] : ((~$lesseq(0, A)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ((~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq(R, I) | ![I1: $int] : ((~(I1 = $sum(1, I))) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, B) & $lesseq(B, I) & $lesseq(I, R) & $lesseq(R, A) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(57,axiom,(~![A: $int, A1: map_int_color] : ($lesseq(0, A) => ![R: $int, I: $int, B: $int, A2: map_int_color] : (((((((($lesseq(0, B) & $lesseq(B, I)) & $lesseq(I, R)) & $lesseq(R, A)) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue)) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white)) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red)) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))) => ($less(I, R) => ((($lesseq(0, A) & $lesseq(0, I)) & $less(I, A)) => ((tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white) => ![I1: $int] : ((I1 = $sum(I, 1)) => monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_dutch_flag')).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_color] : ((~$lesseq(0, A)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ((~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq(R, I) | ![I1: $int] : ((~(I1 = $sum(1, I))) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, B) & $lesseq(B, I) & $lesseq(I, R) & $lesseq(R, A) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_color] : ((~$lesseq(0, A)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ((~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq(R, I) | ![I1: $int] : ((~(I1 = $sum(1, I))) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, B) & $lesseq(B, I) & $lesseq(I, R) & $lesseq(R, A) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_color] : ((~$lesseq(0, A)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ((~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq(R, I) | ![I1: $int] : ((~(I1 = $sum(1, I))) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, B) & $lesseq(B, I) & $lesseq(I, R) & $lesseq(R, A) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_color] : ((~$lesseq(0, A)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ((~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq(R, I) | ![I1: $int] : ((~(I1 = $sum(1, I))) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~($lesseq(0, A) & $lesseq(0, I) & (~$lesseq(A, I)))) | (~($lesseq(0, B) & $lesseq(B, I) & $lesseq(I, R) & $lesseq(R, A) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : (![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | $lesseq($sum(R, $product(-1, I)), 0) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$lesseq($sum(A, $product(-1, I)), 0)))) | (~($greatereq(B, 0) & $lesseq($sum(B, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ($greatereq($sum(I, $product(-1, R)), 0) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(B, 0) & $greatereq($sum(I, $product(-1, B)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[62, 53])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ($greatereq($sum(I, $product(-1, R)), 0) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(B, 0) & $greatereq($sum(I, $product(-1, B)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[63, 52])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 (~![A: $int, A1: map_int_color] : ((~$greatereq(A, 0)) | ![R: $int, I: $int, B: $int, A2: map_int_color] : ($greatereq($sum(I, $product(-1, R)), 0) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I1, white)) | (~(tb2t2(get(color1, int, t2tb3(A2), t2tb(I))) = white)) | (~($greatereq(A, 0) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, A)), 0)))) | (~($greatereq(B, 0) & $greatereq($sum(I, $product(-1, B)), 0) & $lesseq($sum(I, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, A)), 0) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), 0, B, blue) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), B, I, white) & monochrome(tb2t1(mk_array(color1, A, t2tb3(A2))), R, A, red) & permut_all(color1, mk_array(color1, A, t2tb3(A1)), mk_array(color1, A, t2tb3(A2)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[64, 52])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 ($greatereq(A!9, 0) & (~$greatereq($sum(I!12, $product(-1, R!13)), 0)) & (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))) & (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white) & $greatereq(I!12, 0) & (~$lesseq($sum(A!9, $product(-1, I!12)), 0)) & $greatereq(B!11, 0) & $lesseq($sum(B!11, $product(-1, I!12)), 0) & $lesseq($sum(I!12, $product(-1, R!13)), 0) & $greatereq($sum(A!9, $product(-1, R!13)), 0) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), 0, B!11, blue) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) & monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), R!13, A!9, red) & permut_all(color1, mk_array(color1, A!9, t2tb3(A1!8)), mk_array(color1, A!9, t2tb3(A2!10)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[65, 51])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 (~((~($sum(I!12, $product(-1, I1!14)) = -1)) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white))),
% 0.21/0.50 inference(and_elim,[status(thm)],[66])).
% 0.21/0.50 tff(68,plain,
% 0.21/0.50 (~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white)),
% 0.21/0.50 inference(or_elim,[status(thm)],[67])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 ((~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))) | monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 ((~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I1!14, white) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))) | (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (~($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[70, 34])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 (($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))) | (~$lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (~$lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12))) = white),
% 0.21/0.50 inference(and_elim,[status(thm)],[66])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (^[X: map_int_color] : refl(sort(map(int, color1), t2tb3(X)) <=> sort(map(int, color1), t2tb3(X)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (![X: map_int_color] : sort(map(int, color1), t2tb3(X)) <=> ![X: map_int_color] : sort(map(int, color1), t2tb3(X))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (![X: map_int_color] : sort(map(int, color1), t2tb3(X)) <=> ![X: map_int_color] : sort(map(int, color1), t2tb3(X))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(78,axiom,(![X: map_int_color] : sort(map(int, color1), t2tb3(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort3')).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 (![X: map_int_color] : sort(map(int, color1), t2tb3(X))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.50 tff(80,plain,(
% 0.21/0.50 ![X: map_int_color] : sort(map(int, color1), t2tb3(X))),
% 0.21/0.50 inference(skolemize,[status(sab)],[79])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 (![X: map_int_color] : sort(map(int, color1), t2tb3(X))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 ((~![X: map_int_color] : sort(map(int, color1), t2tb3(X))) | sort(map(int, color1), t2tb3(A2!10))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (sort(map(int, color1), t2tb3(A2!10))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (^[A: ty, U: $int, U1: uni] : refl(((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 (^[A: ty, U: $int, U1: uni] : rewrite((sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1)) <=> ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (![A: ty, U: $int, U1: uni] : (sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1)) <=> ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.50 tff(89,axiom,(![A: ty, U: $int, U1: uni] : (sort(map(int, A), U1) => (elts(A, mk_array(A, U, U1)) = U1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','elts_def')).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.21/0.50 tff(92,plain,(
% 0.21/0.50 ![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.50 inference(skolemize,[status(sab)],[91])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 (![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 (((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, color1), t2tb3(A2!10))) | (elts(color1, mk_array(color1, A!9, t2tb3(A2!10))) = t2tb3(A2!10)))) <=> ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, color1), t2tb3(A2!10))) | (elts(color1, mk_array(color1, A!9, t2tb3(A2!10))) = t2tb3(A2!10)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | ((~sort(map(int, color1), t2tb3(A2!10))) | (elts(color1, mk_array(color1, A!9, t2tb3(A2!10))) = t2tb3(A2!10)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 ((~![A: ty, U: $int, U1: uni] : ((~sort(map(int, A), U1)) | (elts(A, mk_array(A, U, U1)) = U1))) | (~sort(map(int, color1), t2tb3(A2!10))) | (elts(color1, mk_array(color1, A!9, t2tb3(A2!10))) = t2tb3(A2!10))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 ((~sort(map(int, color1), t2tb3(A2!10))) | (elts(color1, mk_array(color1, A!9, t2tb3(A2!10))) = t2tb3(A2!10))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 (elts(color1, mk_array(color1, A!9, t2tb3(A2!10))) = t2tb3(A2!10)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[97, 83])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (t2tb3(A2!10) = elts(color1, mk_array(color1, A!9, t2tb3(A2!10)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[98])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 (get(color1, int, t2tb3(A2!10), t2tb(I!12)) = get(color1, int, elts(color1, mk_array(color1, A!9, t2tb3(A2!10))), t2tb(I!12))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[99])).
% 0.21/0.50 tff(101,plain,
% 0.21/0.50 (get(color1, int, elts(color1, mk_array(color1, A!9, t2tb3(A2!10))), t2tb(I!12)) = get(color1, int, t2tb3(A2!10), t2tb(I!12))),
% 0.21/0.50 inference(symmetry,[status(thm)],[100])).
% 0.21/0.50 tff(102,plain,
% 0.21/0.50 (^[A: ty, A1: uni, I: $int] : refl((get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(103,plain,
% 0.21/0.50 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I))) <=> ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(105,axiom,(![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','get_def')).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.50 tff(107,plain,(
% 0.21/0.50 ![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[106])).
% 0.21/0.50 tff(108,plain,
% 0.21/0.50 (![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.21/0.50 tff(109,plain,
% 0.21/0.50 ((~![A: ty, A1: uni, I: $int] : (get1(A, A1, I) = get(A, int, elts(A, A1), t2tb(I)))) | (get1(color1, mk_array(color1, A!9, t2tb3(A2!10)), I!12) = get(color1, int, elts(color1, mk_array(color1, A!9, t2tb3(A2!10))), t2tb(I!12)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (get1(color1, mk_array(color1, A!9, t2tb3(A2!10)), I!12) = get(color1, int, elts(color1, mk_array(color1, A!9, t2tb3(A2!10))), t2tb(I!12))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.51 tff(111,assumption,(I!12 = tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10))))), introduced(assumption)).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(113,plain,
% 0.21/0.51 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(114,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR1')).
% 0.21/0.51 tff(115,plain,
% 0.21/0.51 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.51 tff(116,plain,(
% 0.21/0.51 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.51 inference(skolemize,[status(sab)],[115])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))) = mk_array(color1, A!9, t2tb3(A2!10)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(119,plain,
% 0.21/0.51 (t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))) = mk_array(color1, A!9, t2tb3(A2!10))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 (mk_array(color1, A!9, t2tb3(A2!10)) = t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))))),
% 0.21/0.51 inference(symmetry,[status(thm)],[119])).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 (get1(color1, mk_array(color1, A!9, t2tb3(A2!10)), I!12) = get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[120, 111])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 (get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10))))) = get1(color1, mk_array(color1, A!9, t2tb3(A2!10)), I!12)),
% 0.21/0.51 inference(symmetry,[status(thm)],[121])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 (get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10))))) = get(color1, int, t2tb3(A2!10), t2tb(I!12))),
% 0.21/0.51 inference(transitivity,[status(thm)],[122, 110, 101])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = tb2t2(get(color1, int, t2tb3(A2!10), t2tb(I!12)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.51 tff(125,plain,
% 0.21/0.51 (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white),
% 0.21/0.51 inference(transitivity,[status(thm)],[124, 74])).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 (($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))) | (~(tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(127,plain,
% 0.21/0.51 (~(tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[126, 71])).
% 0.21/0.51 tff(128,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[127, 125])).
% 0.21/0.51 tff(129,plain,(~(I!12 = tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(130,plain,
% 0.21/0.51 (((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))) <=> ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(131,plain,
% 0.21/0.51 ((~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | $lesseq($sum(I!12, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, B!11)), 0))))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))) <=> (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(132,plain,
% 0.21/0.51 (((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | $lesseq($sum(I!12, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, B!11)), 0))))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))) <=> ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[131])).
% 0.21/0.51 tff(133,plain,
% 0.21/0.51 (((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | $lesseq($sum(I!12, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, B!11)), 0))))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))) <=> ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[132, 130])).
% 0.21/0.51 tff(134,plain,
% 0.21/0.51 ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | $lesseq($sum(I!12, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, B!11)), 0))))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(135,plain,
% 0.21/0.51 ((~![A: array_color, I: $int, J: $int, C: color] : (~((~((~monochrome(A, I, J, C)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(A), K)) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))) | (~(monochrome(A, I, J, C) | (~($lesseq($sum(J, $product(-1, tptp_fun_K_7(C, J, I, A))), 0) | (tb2t2(get1(color1, t2tb1(A), tptp_fun_K_7(C, J, I, A))) = C) | (~$lesseq($sum(I, $product(-1, tptp_fun_K_7(C, J, I, A))), 0))))))))) | (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.51 tff(136,plain,
% 0.21/0.51 (~((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[135, 25])).
% 0.21/0.51 tff(137,plain,
% 0.21/0.51 (((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~(monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white) | (~($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I!12, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))))))) | ((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(138,plain,
% 0.21/0.51 ((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.21/0.51 tff(139,plain,
% 0.21/0.51 (monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)),
% 0.21/0.51 inference(and_elim,[status(thm)],[66])).
% 0.21/0.51 tff(140,plain,
% 0.21/0.51 ((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | (~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(141,plain,
% 0.21/0.51 ((~((~monochrome(tb2t1(mk_array(color1, A!9, t2tb3(A2!10))), B!11, I!12, white)) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0)))) | ![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.51 tff(142,plain,
% 0.21/0.51 (![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[141, 138])).
% 0.21/0.51 tff(143,plain,
% 0.21/0.51 (($lesseq($sum(I1!14, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))) | $lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(144,plain,
% 0.21/0.51 ($lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[143, 71])).
% 0.21/0.51 tff(145,plain,
% 0.21/0.51 (((~![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))) | ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))) <=> ((~![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 (((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) <=> ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(147,plain,
% 0.21/0.52 ($greatereq($sum($product(-1, I!12), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10))))), 0) <=> $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(148,plain,
% 0.21/0.52 ($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, I!12)) = $sum($product(-1, I!12), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 ($greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, I!12)), 0) <=> $greatereq($sum($product(-1, I!12), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10))))), 0)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[148])).
% 0.21/0.52 tff(150,plain,
% 0.21/0.52 ($greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, I!12)), 0) <=> $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)),
% 0.21/0.52 inference(transitivity,[status(thm)],[149, 147])).
% 0.21/0.52 tff(151,plain,
% 0.21/0.52 ((~$greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, B!11)), 0)) <=> (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(152,plain,
% 0.21/0.52 (((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, B!11)), 0)) | $greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, I!12)), 0)) <=> ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[151, 150])).
% 0.21/0.52 tff(153,plain,
% 0.21/0.52 (((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, B!11)), 0)) | $greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, I!12)), 0)) <=> ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.52 inference(transitivity,[status(thm)],[152, 146])).
% 0.21/0.52 tff(154,plain,
% 0.21/0.52 (((~![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))) | ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, B!11)), 0)) | $greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, I!12)), 0))) <=> ((~![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))) | ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[153])).
% 0.21/0.52 tff(155,plain,
% 0.21/0.52 (((~![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))) | ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, B!11)), 0)) | $greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, I!12)), 0))) <=> ((~![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.52 inference(transitivity,[status(thm)],[154, 145])).
% 0.21/0.52 tff(156,plain,
% 0.21/0.52 ((~![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))) | ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, B!11)), 0)) | $greatereq($sum(tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), $product(-1, I!12)), 0))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(157,plain,
% 0.21/0.53 ((~![K: $int] : ((tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), K)) = white) | (~$greatereq($sum(K, $product(-1, B!11)), 0)) | $greatereq($sum(K, $product(-1, I!12)), 0))) | (tb2t2(get1(color1, t2tb1(tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))), tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))) = white) | (~$lesseq($sum(B!11, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | $lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.53 tff(158,plain,
% 0.21/0.53 ($lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[157, 127, 144, 142])).
% 0.21/0.53 tff(159,plain,
% 0.21/0.53 ((I!12 = tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10))))) | (~$lesseq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)) | (~$greatereq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.53 tff(160,plain,
% 0.21/0.53 ((I!12 = tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10))))) | (~$greatereq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.21/0.53 tff(161,plain,
% 0.21/0.53 (~$greatereq($sum(I!12, $product(-1, tptp_fun_K_7(white, I1!14, B!11, tb2t1(mk_array(color1, A!9, t2tb3(A2!10)))))), 0)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[160, 129])).
% 0.21/0.53 tff(162,plain,
% 0.21/0.53 ($sum(I!12, $product(-1, I1!14)) = -1),
% 0.21/0.53 inference(or_elim,[status(thm)],[67])).
% 0.21/0.53 tff(163,plain,
% 0.21/0.53 ((~($sum(I!12, $product(-1, I1!14)) = -1)) | $greatereq($sum(I!12, $product(-1, I1!14)), -1)),
% 0.21/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.53 tff(164,plain,
% 0.21/0.53 ($greatereq($sum(I!12, $product(-1, I1!14)), -1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.21/0.53 tff(165,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(theory_lemma,[status(thm)],[164, 161, 73])).
% 0.21/0.53 % SZS output end Proof
%------------------------------------------------------------------------------