TSTP Solution File: SWW589_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW589_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 20:59:22 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW589_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 19:58:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(tb2t2_type, type, (
% 0.20/0.47 tb2t2: uni > $int)).
% 0.20/0.47 tff(t2tb2_type, type, (
% 0.20/0.47 t2tb2: $int > uni)).
% 0.20/0.47 tff(tptp_fun_I_27_type, type, (
% 0.20/0.47 tptp_fun_I_27: $int)).
% 0.20/0.47 tff(tptp_fun_W2_24_type, type, (
% 0.20/0.47 tptp_fun_W2_24: $int)).
% 0.20/0.47 tff(get_type, type, (
% 0.20/0.47 get: ( ty * ty * uni * uni ) > uni)).
% 0.20/0.47 tff(tptp_fun_J_30_type, type, (
% 0.20/0.47 tptp_fun_J_30: $int)).
% 0.20/0.47 tff(t2tb5_type, type, (
% 0.20/0.47 t2tb5: map_int_int > uni)).
% 0.20/0.47 tff(tptp_fun_T1_29_type, type, (
% 0.20/0.47 tptp_fun_T1_29: map_int_int)).
% 0.20/0.47 tff(int_type, type, (
% 0.20/0.47 int: ty)).
% 0.20/0.47 tff(set_type, type, (
% 0.20/0.47 set: ( ty * ty * uni * uni * uni ) > uni)).
% 0.20/0.47 tff(tptp_fun_T_28_type, type, (
% 0.20/0.47 tptp_fun_T_28: map_int_int)).
% 0.20/0.47 tff(tb2t5_type, type, (
% 0.20/0.47 tb2t5: uni > map_int_int)).
% 0.20/0.47 tff(sort1_type, type, (
% 0.20/0.47 sort1: ( ty * uni ) > $o)).
% 0.20/0.47 tff(tptp_fun_W11_25_type, type, (
% 0.20/0.47 tptp_fun_W11_25: uni)).
% 0.20/0.47 tff(map_type, type, (
% 0.20/0.47 map: ( ty * ty ) > ty)).
% 0.20/0.47 tff(char_type, type, (
% 0.20/0.47 char: ty)).
% 0.20/0.47 tff(tptp_fun_W21_23_type, type, (
% 0.20/0.47 tptp_fun_W21_23: uni)).
% 0.20/0.47 tff(tptp_fun_W1_26_type, type, (
% 0.20/0.47 tptp_fun_W1_26: $int)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 ((($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & $greatereq($sum(W2!24, $product(-1, I!27)), 0)) & $greatereq(W2!24, 0) & $greatereq(W2!24, -1) & ($greatereq(W1!26, 0) & $greatereq(W2!24, 0)) & sort1(map(int, char), W21!23) & sort1(map(int, char), W11!25)) <=> ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & $greatereq($sum(W2!24, $product(-1, I!27)), 0) & $greatereq(W2!24, 0) & $greatereq(W1!26, 0) & sort1(map(int, char), W21!23) & sort1(map(int, char), W11!25))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 ((~(~sort1(map(int, char), W11!25))) <=> sort1(map(int, char), W11!25)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 ((~(~sort1(map(int, char), W21!23))) <=> sort1(map(int, char), W21!23)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 ((~(~($greatereq(W1!26, 0) & $greatereq(W2!24, 0)))) <=> ($greatereq(W1!26, 0) & $greatereq(W2!24, 0))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 ((~(~$greatereq(W2!24, -1))) <=> $greatereq(W2!24, -1)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 ((~(~$greatereq(W2!24, 0))) <=> $greatereq(W2!24, 0)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 ((($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0)))) & ($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1))) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & ($greatereq(I!27, 0) & $greatereq($sum(W2!24, $product(-1, I!27)), 0))) <=> ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & $greatereq($sum(W2!24, $product(-1, I!27)), 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 ((~(~($greatereq(I!27, 0) & $greatereq($sum(W2!24, $product(-1, I!27)), 0)))) <=> ($greatereq(I!27, 0) & $greatereq($sum(W2!24, $product(-1, I!27)), 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 ((~($greatereq(I!27, 0) & $lesseq($sum(I!27, $product(-1, W2!24)), 0))) <=> (~($greatereq(I!27, 0) & $greatereq($sum(W2!24, $product(-1, I!27)), 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 ((~(~($greatereq(I!27, 0) & $lesseq($sum(I!27, $product(-1, W2!24)), 0)))) <=> (~(~($greatereq(I!27, 0) & $greatereq($sum(W2!24, $product(-1, I!27)), 0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 ((~(~($greatereq(I!27, 0) & $lesseq($sum(I!27, $product(-1, W2!24)), 0)))) <=> ($greatereq(I!27, 0) & $greatereq($sum(W2!24, $product(-1, I!27)), 0))),
% 0.20/0.48 inference(transitivity,[status(thm)],[10, 8])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (^[J: $int] : rewrite(((~($greatereq(J, 0) & (~$lesseq($sum(I!27, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) <=> ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I!27, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) <=> ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 ((~(~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1))))) <=> ($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 ((~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$greatereq($sum(I!27, $product(-1, W2!24)), 1)))) <=> (~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 ((~(~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$greatereq($sum(I!27, $product(-1, W2!24)), 1))))) <=> (~(~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 ((~(~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$greatereq($sum(I!27, $product(-1, W2!24)), 1))))) <=> ($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 ((($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27))))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0)))) <=> ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 ((~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(J!30, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))))) = 0))) <=> (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 ((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27))))))))) <=> ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 ((~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24))))))) <=> (~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 ((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24)))))))) <=> (~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 ((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24)))))))) <=> ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24)))))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(J!30, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))))) = 0)))) <=> (($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27))))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[23, 19])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24)))))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(J!30, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))))) = 0)))) <=> ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[24, 18])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 ((((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24)))))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(J!30, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))))) = 0)))) & (~(~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$greatereq($sum(I!27, $product(-1, W2!24)), 1))))) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I!27, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & (~(~($greatereq(I!27, 0) & $lesseq($sum(I!27, $product(-1, W2!24)), 0))))) <=> (($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0)))) & ($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1))) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & ($greatereq(I!27, 0) & $greatereq($sum(W2!24, $product(-1, I!27)), 0)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[25, 17, 13, 11])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 ((((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24)))))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(J!30, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))))) = 0)))) & (~(~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$greatereq($sum(I!27, $product(-1, W2!24)), 1))))) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I!27, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & (~(~($greatereq(I!27, 0) & $lesseq($sum(I!27, $product(-1, W2!24)), 0))))) <=> ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & $greatereq($sum(W2!24, $product(-1, I!27)), 0))),
% 0.20/0.48 inference(transitivity,[status(thm)],[26, 7])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (((((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24)))))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(J!30, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))))) = 0)))) & (~(~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$greatereq($sum(I!27, $product(-1, W2!24)), 1))))) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I!27, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & (~(~($greatereq(I!27, 0) & $lesseq($sum(I!27, $product(-1, W2!24)), 0))))) & (~(~$greatereq(W2!24, 0))) & (~(~$greatereq(W2!24, -1))) & (~(~($greatereq(W1!26, 0) & $greatereq(W2!24, 0)))) & (~(~sort1(map(int, char), W21!23))) & (~(~sort1(map(int, char), W11!25)))) <=> (($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & $greatereq($sum(W2!24, $product(-1, I!27)), 0)) & $greatereq(W2!24, 0) & $greatereq(W2!24, -1) & ($greatereq(W1!26, 0) & $greatereq(W2!24, 0)) & sort1(map(int, char), W21!23) & sort1(map(int, char), W11!25))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[27, 6, 5, 4, 3, 2])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (((((~(~($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum($product(-1, I!27), W2!24)))))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(J!30, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))))) = 0)))) & (~(~($greatereq(W2!24, -1) & $greatereq(I!27, 0) & (~$greatereq($sum(I!27, $product(-1, W2!24)), 1))))) & ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I!27, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & (~(~($greatereq(I!27, 0) & $lesseq($sum(I!27, $product(-1, W2!24)), 0))))) & (~(~$greatereq(W2!24, 0))) & (~(~$greatereq(W2!24, -1))) & (~(~($greatereq(W1!26, 0) & $greatereq(W2!24, 0)))) & (~(~sort1(map(int, char), W21!23))) & (~(~sort1(map(int, char), W11!25)))) <=> ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & $greatereq($sum(W2!24, $product(-1, I!27)), 0) & $greatereq(W2!24, 0) & $greatereq(W1!26, 0) & sort1(map(int, char), W21!23) & sort1(map(int, char), W11!25))),
% 0.20/0.48 inference(transitivity,[status(thm)],[28, 1])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 ((~![W1: $int, W11: uni, W2: $int, W21: uni] : (![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum($product(-1, I), W2))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T1), t2tb2(J))))) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, W2)), 1)))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T), t2tb2(J))))) = 0))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0)))) | (~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)))) <=> (~![W1: $int, W11: uni, W2: $int, W21: uni] : (![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum($product(-1, I), W2))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T1), t2tb2(J))))) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, W2)), 1)))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T), t2tb2(J))))) = 0))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0)))) | (~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 ((~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0))) | ![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(tb2t2(get(int, int, t2tb5(T1), t2tb2(J))), $sum($product(-1, W2), J)) = 0))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(tb2t2(get(int, int, t2tb5(T), t2tb2(J))), $sum($product(-1, W2), J)) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$lesseq($sum(W2, $product(-1, I)), -1))))))) <=> (~![W1: $int, W11: uni, W2: $int, W21: uni] : (![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum($product(-1, I), W2))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T1), t2tb2(J))))) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, W2)), 1)))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T), t2tb2(J))))) = 0))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0)))) | (~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 ((~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($lesseq(-1, W2) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, $sum(-1, J))))) | (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(-1, W2) & $lesseq(0, I) & (~$lesseq(W2, $sum(-1, I))))) | (~![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, J)))) | (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(0, I) & $lesseq(I, W2)))) | (~$lesseq(0, W2)) | (~$lesseq(-1, W2)) | (~($lesseq(0, W1) & $lesseq(0, W2))))) <=> (~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0))) | ![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(tb2t2(get(int, int, t2tb5(T1), t2tb2(J))), $sum($product(-1, W2), J)) = 0))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(tb2t2(get(int, int, t2tb5(T), t2tb2(J))), $sum($product(-1, W2), J)) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$lesseq($sum(W2, $product(-1, I)), -1)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 ((~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($lesseq(-1, W2) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, $sum(-1, J))))) | (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(-1, W2) & $lesseq(0, I) & (~$lesseq(W2, $sum(-1, I))))) | (~![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, J)))) | (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(0, I) & $lesseq(I, W2)))) | (~$lesseq(0, W2)) | (~$lesseq(-1, W2)) | (~($lesseq(0, W1) & $lesseq(0, W2))))) <=> (~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($lesseq(-1, W2) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, $sum(-1, J))))) | (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(-1, W2) & $lesseq(0, I) & (~$lesseq(W2, $sum(-1, I))))) | (~![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, J)))) | (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(0, I) & $lesseq(I, W2)))) | (~$lesseq(0, W2)) | (~$lesseq(-1, W2)) | (~($lesseq(0, W1) & $lesseq(0, W2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 ((~![W1: $int, W11: uni, W2: $int, W21: uni] : (sort1(map(int, char), W11) => (sort1(map(int, char), W21) => (($lesseq(0, W1) & $lesseq(0, W2)) => ($lesseq(0, $sum(W2, 1)) => ($lesseq(0, $sum(W2, 1)) => ($lesseq(0, W2) => ![T: map_int_int, I: $int] : (($lesseq(0, I) & $lesseq(I, W2)) => (![J: $int] : (($lesseq(0, J) & $less(J, I)) => (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $difference(W2, J))) => ((($lesseq(0, $sum(W2, 1)) & $lesseq(0, I)) & $less(I, $sum(W2, 1))) => ![T1: map_int_int] : (($lesseq(0, $sum(W2, 1)) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($difference(W2, I)))))) => ![J: $int] : (($lesseq(0, J) & $less(J, $sum(I, 1))) => (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $difference(W2, J)))))))))))))) <=> (~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($lesseq(-1, W2) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, $sum(-1, J))))) | (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(-1, W2) & $lesseq(0, I) & (~$lesseq(W2, $sum(-1, I))))) | (~![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, J)))) | (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(0, I) & $lesseq(I, W2)))) | (~$lesseq(0, W2)) | (~$lesseq(-1, W2)) | (~($lesseq(0, W1) & $lesseq(0, W2)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(35,axiom,(~![W1: $int, W11: uni, W2: $int, W21: uni] : (sort1(map(int, char), W11) => (sort1(map(int, char), W21) => (($lesseq(0, W1) & $lesseq(0, W2)) => ($lesseq(0, $sum(W2, 1)) => ($lesseq(0, $sum(W2, 1)) => ($lesseq(0, W2) => ![T: map_int_int, I: $int] : (($lesseq(0, I) & $lesseq(I, W2)) => (![J: $int] : (($lesseq(0, J) & $less(J, I)) => (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $difference(W2, J))) => ((($lesseq(0, $sum(W2, 1)) & $lesseq(0, I)) & $less(I, $sum(W2, 1))) => ![T1: map_int_int] : (($lesseq(0, $sum(W2, 1)) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($difference(W2, I)))))) => ![J: $int] : (($lesseq(0, J) & $less(J, $sum(I, 1))) => (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $difference(W2, J)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_distance')).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($lesseq(-1, W2) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, $sum(-1, J))))) | (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(-1, W2) & $lesseq(0, I) & (~$lesseq(W2, $sum(-1, I))))) | (~![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, J)))) | (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(0, I) & $lesseq(I, W2)))) | (~$lesseq(0, W2)) | (~$lesseq(-1, W2)) | (~($lesseq(0, W1) & $lesseq(0, W2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($lesseq(-1, W2) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, $sum(-1, J))))) | (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(-1, W2) & $lesseq(0, I) & (~$lesseq(W2, $sum(-1, I))))) | (~![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, J)))) | (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(0, I) & $lesseq(I, W2)))) | (~$lesseq(0, W2)) | (~$lesseq(-1, W2)) | (~($lesseq(0, W1) & $lesseq(0, W2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 (~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($lesseq(-1, W2) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, $sum(-1, J))))) | (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(-1, W2) & $lesseq(0, I) & (~$lesseq(W2, $sum(-1, I))))) | (~![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, J)))) | (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(0, I) & $lesseq(I, W2)))) | (~$lesseq(0, W2)) | (~$lesseq(-1, W2)) | (~($lesseq(0, W1) & $lesseq(0, W2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 (~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($lesseq(-1, W2) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, $sum(-1, J))))) | (tb2t2(get(int, int, t2tb5(T1), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(-1, W2) & $lesseq(0, I) & (~$lesseq(W2, $sum(-1, I))))) | (~![J: $int] : ((~($lesseq(0, J) & (~$lesseq(I, J)))) | (tb2t2(get(int, int, t2tb5(T), t2tb2(J))) = $sum(W2, $product(-1, J))))) | (~($lesseq(0, I) & $lesseq(I, W2)))) | (~$lesseq(0, W2)) | (~$lesseq(-1, W2)) | (~($lesseq(0, W1) & $lesseq(0, W2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (~![W1: $int, W11: uni, W2: $int, W21: uni] : ((~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)) | ![T: map_int_int, I: $int] : ((~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0))) | ![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum(W2, $product(-1, I)))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(tb2t2(get(int, int, t2tb5(T1), t2tb2(J))), $sum($product(-1, W2), J)) = 0))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(tb2t2(get(int, int, t2tb5(T), t2tb2(J))), $sum($product(-1, W2), J)) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$lesseq($sum(W2, $product(-1, I)), -1))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (~![W1: $int, W11: uni, W2: $int, W21: uni] : (![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum($product(-1, I), W2))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T1), t2tb2(J))))) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, W2)), 1)))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T), t2tb2(J))))) = 0))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0)))) | (~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[40, 31])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (~![W1: $int, W11: uni, W2: $int, W21: uni] : (![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum($product(-1, I), W2))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T1), t2tb2(J))))) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, W2)), 1)))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T), t2tb2(J))))) = 0))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0)))) | (~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[41, 30])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (~![W1: $int, W11: uni, W2: $int, W21: uni] : (![T: map_int_int, I: $int] : (![T1: map_int_int] : ((~($greatereq(W2, -1) & (T1 = tb2t5(set(int, int, t2tb5(T), t2tb2(I), t2tb2($sum($product(-1, I), W2))))))) | ![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), -1)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T1), t2tb2(J))))) = 0))) | (~($greatereq(W2, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, W2)), 1)))) | (~![J: $int] : ((~($greatereq(J, 0) & (~$lesseq($sum(I, $product(-1, J)), 0)))) | ($sum(J, $sum($product(-1, W2), tb2t2(get(int, int, t2tb5(T), t2tb2(J))))) = 0))) | (~($greatereq(I, 0) & $lesseq($sum(I, $product(-1, W2)), 0)))) | (~$greatereq(W2, 0)) | (~$greatereq(W2, -1)) | (~($greatereq(W1, 0) & $greatereq(W2, 0))) | (~sort1(map(int, char), W21)) | (~sort1(map(int, char), W11)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[42, 30])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 ($greatereq(W2!24, -1) & (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) & (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))) & $greatereq(I!27, 0) & (~$lesseq($sum(W2!24, $product(-1, I!27)), -1)) & ![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) & $greatereq($sum(W2!24, $product(-1, I!27)), 0) & $greatereq(W2!24, 0) & $greatereq(W1!26, 0) & sort1(map(int, char), W21!23) & sort1(map(int, char), W11!25)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[43, 29])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (T1!29 = tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))),
% 0.20/0.49 inference(and_elim,[status(thm)],[44])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (t2tb5(T1!29) = t2tb5(tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 (t2tb5(tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) = t2tb5(T1!29)),
% 0.20/0.49 inference(symmetry,[status(thm)],[46])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (![J: uni] : (t2tb5(tb2t5(J)) = J) <=> ![J: uni] : (t2tb5(tb2t5(J)) = J)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (![J: uni] : (t2tb5(tb2t5(J)) = J) <=> ![J: uni] : (t2tb5(tb2t5(J)) = J)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(50,axiom,(![J: uni] : (t2tb5(tb2t5(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR5')).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (![J: uni] : (t2tb5(tb2t5(J)) = J)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.49 tff(52,plain,(
% 0.20/0.49 ![J: uni] : (t2tb5(tb2t5(J)) = J)),
% 0.20/0.49 inference(skolemize,[status(sab)],[51])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (![J: uni] : (t2tb5(tb2t5(J)) = J)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 ((~![J: uni] : (t2tb5(tb2t5(J)) = J)) | (t2tb5(tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) = set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (t2tb5(tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))))) = set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))) = t2tb5(tb2t5(set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27))))))),
% 0.20/0.49 inference(symmetry,[status(thm)],[55])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))) = t2tb5(T1!29)),
% 0.20/0.49 inference(transitivity,[status(thm)],[56, 47])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = get(int, int, t2tb5(T1!29), t2tb2(J!30))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (^[X: $int] : refl(sort1(int, t2tb2(X)) <=> sort1(int, t2tb2(X)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (![X: $int] : sort1(int, t2tb2(X)) <=> ![X: $int] : sort1(int, t2tb2(X))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (![X: $int] : sort1(int, t2tb2(X)) <=> ![X: $int] : sort1(int, t2tb2(X))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(62,axiom,(![X: $int] : sort1(int, t2tb2(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort8')).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (![X: $int] : sort1(int, t2tb2(X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.49 tff(64,plain,(
% 0.20/0.49 ![X: $int] : sort1(int, t2tb2(X))),
% 0.20/0.49 inference(skolemize,[status(sab)],[63])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (![X: $int] : sort1(int, t2tb2(X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 ((~![X: $int] : sort1(int, t2tb2(X))) | sort1(int, t2tb2(J!30))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (sort1(int, t2tb2(J!30))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 ((~![X: $int] : sort1(int, t2tb2(X))) | sort1(int, t2tb2(I!27))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (sort1(int, t2tb2(I!27))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : rewrite(((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : refl(((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : rewrite(((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[75, 73])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B1: uni] : rewrite(((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) <=> ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), (![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) <=> ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), ((sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> (sort1(A, A2) => ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), rewrite((sort1(A, A2) => ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), ((sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), ((sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> (sort1(A, A1) => ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))))), rewrite((sort1(A, A1) => ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))), ((sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.49 tff(80,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (sort1(A, A1) => (sort1(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','select_neq')).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.49 tff(83,plain,(
% 0.20/0.49 ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[82])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort1(A, A1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[84, 71])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb2(J!30))) | (~sort1(int, t2tb2(I!27))) | ![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb2(J!30))) | (~sort1(int, t2tb2(I!27))) | ![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort1(int, t2tb2(J!30))) | (~sort1(int, t2tb2(I!27))) | ![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort1(A, A2)) | (~sort1(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort1(int, t2tb2(J!30))) | (~sort1(int, t2tb2(I!27))) | ![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[88, 85, 69, 67])).
% 0.20/0.49 tff(90,assumption,(~(t2tb2(I!27) = t2tb2(J!30))), introduced(assumption)).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (((~![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))) | ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))) <=> ((~![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))) | (t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 ((~![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))) | ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 ((~![B1: uni] : ((t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), B1), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))))) | (t2tb2(I!27) = t2tb2(J!30)) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[93, 90, 89])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (t2tb5(T1!29) = set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[46, 55])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (get(int, int, t2tb5(T1!29), t2tb2(J!30)) = get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (get(int, int, t2tb5(T1!29), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))),
% 0.20/0.49 inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 (tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))) = tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 ((~(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))) = tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))))) | $lesseq($sum(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 ($lesseq($sum(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 (![J: uni] : (t2tb2(tb2t2(J)) = J) <=> ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 (![J: uni] : (t2tb2(tb2t2(J)) = J) <=> ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(103,axiom,(![J: uni] : (t2tb2(tb2t2(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR2')).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 (![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.50 tff(105,plain,(
% 0.20/0.50 ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(skolemize,[status(sab)],[104])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 (![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 ((~![J: uni] : (t2tb2(tb2t2(J)) = J)) | (t2tb2(tb2t2(t2tb2(J!30))) = t2tb2(J!30))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(108,plain,
% 0.20/0.50 (t2tb2(tb2t2(t2tb2(J!30))) = t2tb2(J!30)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.50 tff(109,plain,
% 0.20/0.50 (^[I: $int] : refl(($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0) <=> ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.50 tff(111,plain,
% 0.20/0.50 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t2(t2tb2(I)), $product(-1, I)) = $sum($product(-1, I), tb2t2(t2tb2(I)))), (($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t2(t2tb2(I))) = 0))), rewrite(($sum($product(-1, I), tb2t2(t2tb2(I))) = 0) <=> ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)), (($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(112,plain,
% 0.20/0.50 (![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.50 tff(113,plain,
% 0.20/0.50 (^[I: $int] : rewrite((tb2t2(t2tb2(I)) = I) <=> ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(114,plain,
% 0.20/0.50 (![I: $int] : (tb2t2(t2tb2(I)) = I) <=> ![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 (![I: $int] : (tb2t2(t2tb2(I)) = I) <=> ![I: $int] : (tb2t2(t2tb2(I)) = I)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(116,axiom,(![I: $int] : (tb2t2(t2tb2(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL2')).
% 0.20/0.50 tff(117,plain,
% 0.20/0.50 (![I: $int] : (tb2t2(t2tb2(I)) = I)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.50 tff(118,plain,
% 0.20/0.50 (![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[118, 112])).
% 0.20/0.50 tff(120,plain,(
% 0.20/0.50 ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.20/0.50 inference(skolemize,[status(sab)],[119])).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))) = 0)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 ($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 ((~($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))) = 0)) | $lesseq($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 ($lesseq($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 ((~($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))) = 0)) | $greatereq($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 ($greatereq($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.20/0.50 tff(128,assumption,(~$greatereq(tb2t2(t2tb2(J!30)), 0)), introduced(assumption)).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 (~((~($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1)))) | ($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0))),
% 0.20/0.50 inference(and_elim,[status(thm)],[44])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 ($greatereq(J!30, 0) & (~$lesseq($sum(I!27, $product(-1, J!30)), -1))),
% 0.20/0.50 inference(or_elim,[status(thm)],[129])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 ($greatereq(J!30, 0)),
% 0.20/0.50 inference(and_elim,[status(thm)],[130])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[131, 128, 125])).
% 0.20/0.50 tff(133,plain,($greatereq(tb2t2(t2tb2(J!30)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(134,assumption,(~$lesseq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0)), introduced(assumption)).
% 0.20/0.50 tff(135,assumption,(t2tb2(I!27) = t2tb2(J!30)), introduced(assumption)).
% 0.20/0.50 tff(136,plain,
% 0.20/0.50 ((~![X: $int] : sort1(int, t2tb2(X))) | sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 (sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[136, 65])).
% 0.20/0.50 tff(138,plain,
% 0.20/0.50 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : refl(((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : trans(monotonicity(rewrite(((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)) <=> ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> (sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))))), rewrite((sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.50 tff(143,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','select_eq')).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.20/0.50 tff(146,plain,(
% 0.20/0.50 ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[145])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (((get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30))) | (~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27)))))) <=> ((~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30))) | (~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30))) | (~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[150, 148])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30))) | (~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(int, t2tb2($sum(W2!24, $product(-1, I!27))))) | (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 ((get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))) | (~(t2tb2(I!27) = t2tb2(J!30)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[153, 147, 137])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[154, 135])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (t2tb2($sum(W2!24, $product(-1, I!27))) = get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30))),
% 0.20/0.50 inference(symmetry,[status(thm)],[155])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 (t2tb2($sum(W2!24, $product(-1, I!27))) = get(int, int, t2tb5(T1!29), t2tb2(J!30))),
% 0.20/0.50 inference(transitivity,[status(thm)],[156, 58])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 (tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))) = tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[157])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))) = tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))),
% 0.20/0.50 inference(symmetry,[status(thm)],[158])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 ((~(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))) = tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))) | $greatereq($sum(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 ($greatereq($sum(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 (((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 (($sum($sum(W2!24, $product(-1, I!27)), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))) = 0) <=> ($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 (((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum($sum(W2!24, $product(-1, I!27)), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 (((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum($sum(W2!24, $product(-1, I!27)), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0))),
% 0.20/0.50 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum($sum(W2!24, $product(-1, I!27)), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))) = 0)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 ($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[167, 121])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 ((~($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0)) | $lesseq($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 ($lesseq($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(I!27, $product(-1, tb2t2(t2tb2(I!27)))) = 0)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 ($sum(I!27, $product(-1, tb2t2(t2tb2(I!27)))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[171, 121])).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 ((~($sum(I!27, $product(-1, tb2t2(t2tb2(I!27)))) = 0)) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(I!27)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 ($lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(I!27)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.20/0.50 tff(175,plain,
% 0.20/0.50 (tb2t2(t2tb2(I!27)) = tb2t2(t2tb2(J!30))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[135])).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 ((~(tb2t2(t2tb2(I!27)) = tb2t2(t2tb2(J!30)))) | $lesseq($sum(tb2t2(t2tb2(I!27)), $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 ($lesseq($sum(tb2t2(t2tb2(I!27)), $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[177, 174, 170, 161, 134, 127])).
% 0.20/0.50 tff(179,plain,((~(t2tb2(I!27) = t2tb2(J!30))) | $lesseq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 (~(t2tb2(I!27) = t2tb2(J!30))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[179, 134])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[93, 180, 89])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 (get(int, int, t2tb5(T1!29), t2tb2(J!30)) = get(int, int, t2tb5(T!28), t2tb2(J!30))),
% 0.20/0.50 inference(transitivity,[status(thm)],[96, 181])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 (tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))) = tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[182])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 ((~(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))) = tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))))) | $greatereq($sum(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(185,plain,
% 0.20/0.50 ($greatereq($sum(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 (get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))) = get(int, int, t2tb5(T!28), t2tb2(J!30))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))) = tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[186])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 (tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))) = tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))),
% 0.20/0.50 inference(symmetry,[status(thm)],[187])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 ((~(tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))) = tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) | $greatereq($sum(tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 ($greatereq($sum(tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.20/0.50 tff(191,assumption,($lesseq($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))), 0)), introduced(assumption)).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[191, 190, 185, 134, 127])).
% 0.20/0.50 tff(193,plain,((~$lesseq($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))), 0)) | $lesseq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 (~$lesseq($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[193, 134])).
% 0.20/0.50 tff(195,plain,
% 0.20/0.50 ((~($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0)) | $lesseq($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (~($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (^[J: $int] : refl(((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0)) <=> ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0)) <=> ![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[197])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (^[J: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0))) <=> (~((~$greatereq(J, 0)) | $greatereq($sum(J, $product(-1, I!27)), 0)))), ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) <=> (~(~((~$greatereq(J, 0)) | $greatereq($sum(J, $product(-1, I!27)), 0)))))), rewrite((~(~((~$greatereq(J, 0)) | $greatereq($sum(J, $product(-1, I!27)), 0)))) <=> ((~$greatereq(J, 0)) | $greatereq($sum(J, $product(-1, I!27)), 0))), ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) <=> ((~$greatereq(J, 0)) | $greatereq($sum(J, $product(-1, I!27)), 0)))), (((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) <=> (((~$greatereq(J, 0)) | $greatereq($sum(J, $product(-1, I!27)), 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)))), rewrite((((~$greatereq(J, 0)) | $greatereq($sum(J, $product(-1, I!27)), 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) <=> ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))), (((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) <=> ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 (![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0)) <=> ![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[199])).
% 0.20/0.51 tff(201,plain,
% 0.20/0.51 (![J: $int] : ((~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, I!27)), 0)))) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0))),
% 0.20/0.51 inference(and_elim,[status(thm)],[44])).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 (![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.51 tff(203,plain,
% 0.20/0.51 (![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.20/0.51 tff(204,plain,
% 0.20/0.51 (((~![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))) | ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0))) <=> ((~![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))) | (~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 (((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)) <=> ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 ($greatereq($sum($product(-1, I!27), tb2t2(t2tb2(J!30))), 0) <=> $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(207,plain,
% 0.20/0.51 ($sum(tb2t2(t2tb2(J!30)), $product(-1, I!27)) = $sum($product(-1, I!27), tb2t2(t2tb2(J!30)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 ($greatereq($sum(tb2t2(t2tb2(J!30)), $product(-1, I!27)), 0) <=> $greatereq($sum($product(-1, I!27), tb2t2(t2tb2(J!30))), 0)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[207])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 ($greatereq($sum(tb2t2(t2tb2(J!30)), $product(-1, I!27)), 0) <=> $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.51 inference(transitivity,[status(thm)],[208, 206])).
% 0.20/0.51 tff(210,plain,
% 0.20/0.51 (($sum($product(-1, W2!24), $sum(tb2t2(t2tb2(J!30)), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0) <=> ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(211,plain,
% 0.20/0.51 ($sum(tb2t2(t2tb2(J!30)), $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = $sum($product(-1, W2!24), $sum(tb2t2(t2tb2(J!30)), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 (($sum(tb2t2(t2tb2(J!30)), $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0) <=> ($sum($product(-1, W2!24), $sum(tb2t2(t2tb2(J!30)), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[211])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 (($sum(tb2t2(t2tb2(J!30)), $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0) <=> ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0)),
% 0.20/0.51 inference(transitivity,[status(thm)],[212, 210])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 (((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(tb2t2(t2tb2(J!30)), $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0) | $greatereq($sum(tb2t2(t2tb2(J!30)), $product(-1, I!27)), 0)) <=> ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[213, 209])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 (((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(tb2t2(t2tb2(J!30)), $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0) | $greatereq($sum(tb2t2(t2tb2(J!30)), $product(-1, I!27)), 0)) <=> ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0))),
% 0.20/0.51 inference(transitivity,[status(thm)],[214, 205])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (((~![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))) | ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(tb2t2(t2tb2(J!30)), $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0) | $greatereq($sum(tb2t2(t2tb2(J!30)), $product(-1, I!27)), 0))) <=> ((~![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))) | ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (((~![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))) | ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(tb2t2(t2tb2(J!30)), $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0) | $greatereq($sum(tb2t2(t2tb2(J!30)), $product(-1, I!27)), 0))) <=> ((~![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))) | (~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0))),
% 0.20/0.51 inference(transitivity,[status(thm)],[216, 204])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 ((~![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))) | ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(tb2t2(t2tb2(J!30)), $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) = 0) | $greatereq($sum(tb2t2(t2tb2(J!30)), $product(-1, I!27)), 0))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 ((~![J: $int] : ((~$greatereq(J, 0)) | ($sum(J, $sum($product(-1, W2!24), tb2t2(get(int, int, t2tb5(T!28), t2tb2(J))))) = 0) | $greatereq($sum(J, $product(-1, I!27)), 0))) | (~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 ((~$greatereq(tb2t2(t2tb2(J!30)), 0)) | ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[219, 203])).
% 0.20/0.51 tff(221,plain,
% 0.20/0.51 ($lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[220, 196, 133])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 ($lesseq($sum(I!27, $product(-1, J!30)), 0) | (~$lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)) | (~$greatereq($sum(J!30, $product(-1, tb2t2(t2tb2(J!30)))), 0))),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 ($lesseq($sum(I!27, $product(-1, J!30)), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[222, 221, 127])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 (~$lesseq($sum(I!27, $product(-1, J!30)), -1)),
% 0.20/0.51 inference(and_elim,[status(thm)],[130])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 (I!27 = tb2t2(t2tb2(J!30))),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[224, 223, 127, 125])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 ((~($sum(I!27, $product(-1, tb2t2(t2tb2(I!27)))) = 0)) | $greatereq($sum(I!27, $product(-1, tb2t2(t2tb2(I!27)))), 0)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 ($greatereq($sum(I!27, $product(-1, tb2t2(t2tb2(I!27)))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[226, 172])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (I!27 = tb2t2(t2tb2(I!27))),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[227, 174])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 (tb2t2(t2tb2(I!27)) = I!27),
% 0.20/0.51 inference(symmetry,[status(thm)],[228])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 (tb2t2(t2tb2(I!27)) = tb2t2(t2tb2(J!30))),
% 0.20/0.51 inference(transitivity,[status(thm)],[229, 225])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 (t2tb2(tb2t2(t2tb2(I!27))) = t2tb2(tb2t2(t2tb2(J!30)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[230])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 ((~![J: uni] : (t2tb2(tb2t2(J)) = J)) | (t2tb2(tb2t2(t2tb2(I!27))) = t2tb2(I!27))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(233,plain,
% 0.20/0.51 (t2tb2(tb2t2(t2tb2(I!27))) = t2tb2(I!27)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[232, 106])).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 (t2tb2(I!27) = t2tb2(tb2t2(t2tb2(I!27)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[233])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 (t2tb2(I!27) = t2tb2(J!30)),
% 0.20/0.51 inference(transitivity,[status(thm)],[234, 231, 108])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[180, 235])).
% 0.20/0.51 tff(237,plain,($lesseq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (~($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0)),
% 0.20/0.51 inference(or_elim,[status(thm)],[129])).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 (($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))) = 0) | (~$lesseq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0)) | (~$greatereq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0))),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 ((~$lesseq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0)) | (~$greatereq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.20/0.51 tff(241,plain,
% 0.20/0.51 (~$greatereq($sum(W2!24, $sum($product(-1, J!30), $product(-1, tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[240, 237])).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 ((~(tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))) = tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))) | $lesseq($sum(tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))), 0)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(243,plain,
% 0.20/0.51 ($lesseq($sum(tb2t2(get(int, int, t2tb5(T!28), t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30))))))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[242, 188])).
% 0.20/0.51 tff(244,assumption,($lesseq($sum(I!27, $product(-1, J!30)), 0)), introduced(assumption)).
% 0.20/0.51 tff(245,plain,
% 0.20/0.51 (I!27 = tb2t2(t2tb2(J!30))),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[224, 244, 127, 125])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (tb2t2(t2tb2(I!27)) = tb2t2(t2tb2(J!30))),
% 0.20/0.51 inference(transitivity,[status(thm)],[229, 245])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 (t2tb2(tb2t2(t2tb2(I!27))) = t2tb2(tb2t2(t2tb2(J!30)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[246])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (t2tb2(I!27) = t2tb2(J!30)),
% 0.20/0.51 inference(transitivity,[status(thm)],[234, 247, 108])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[90, 248])).
% 0.20/0.51 tff(250,plain,((~$lesseq($sum(I!27, $product(-1, J!30)), 0)) | (t2tb2(I!27) = t2tb2(J!30))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 (~$lesseq($sum(I!27, $product(-1, J!30)), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[250, 90])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 ($lesseq($sum(I!27, $product(-1, J!30)), 0) | (~$lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[222, 127])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 (~$lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 (($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0) | $lesseq($sum(I!27, $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[220, 133])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 ($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 ((~($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))) = 0)) | $greatereq($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))), 0)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 ($greatereq($sum(W2!24, $sum($product(-1, tb2t2(t2tb2(J!30))), $product(-1, tb2t2(get(int, int, t2tb5(T!28), t2tb2(tb2t2(t2tb2(J!30)))))))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[256, 255])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[125, 257, 243, 241, 100])).
% 0.20/0.51 tff(259,plain,(t2tb2(I!27) = t2tb2(J!30)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30)) = t2tb2($sum(W2!24, $product(-1, I!27)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[154, 259])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (t2tb2($sum(W2!24, $product(-1, I!27))) = get(int, int, set(int, int, t2tb5(T!28), t2tb2(I!27), t2tb2($sum(W2!24, $product(-1, I!27)))), t2tb2(J!30))),
% 0.20/0.51 inference(symmetry,[status(thm)],[260])).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 (t2tb2($sum(W2!24, $product(-1, I!27))) = get(int, int, t2tb5(T1!29), t2tb2(J!30))),
% 0.20/0.51 inference(transitivity,[status(thm)],[261, 58])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))) = tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[262])).
% 0.20/0.51 tff(264,plain,
% 0.20/0.51 (tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))) = tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))),
% 0.20/0.52 inference(symmetry,[status(thm)],[263])).
% 0.20/0.52 tff(265,plain,
% 0.20/0.52 ((~(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))) = tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))) | $lesseq($sum(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))), 0)),
% 0.20/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.52 tff(266,plain,
% 0.20/0.52 ($lesseq($sum(tb2t2(get(int, int, t2tb5(T1!29), t2tb2(J!30))), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27)))))), 0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.20/0.52 tff(267,plain,
% 0.20/0.52 (tb2t2(t2tb2(I!27)) = tb2t2(t2tb2(J!30))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[259])).
% 0.20/0.52 tff(268,plain,
% 0.20/0.52 ((~(tb2t2(t2tb2(I!27)) = tb2t2(t2tb2(J!30)))) | $greatereq($sum(tb2t2(t2tb2(I!27)), $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 ($greatereq($sum(tb2t2(t2tb2(I!27)), $product(-1, tb2t2(t2tb2(J!30)))), 0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 ((~($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))) = 0)) | $greatereq($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))), 0)),
% 0.20/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 ($greatereq($sum(W2!24, $sum($product(-1, I!27), $product(-1, tb2t2(t2tb2($sum(W2!24, $product(-1, I!27))))))), 0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[270, 168])).
% 0.20/0.52 tff(272,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(theory_lemma,[status(thm)],[241, 271, 269, 227, 125, 266])).
% 0.20/0.52 % SZS output end Proof
%------------------------------------------------------------------------------